1,0,0,78,0.153000," ","int(arccsc(a*x^5)/x,x)","\int \frac{\mathrm{arccsc}\left(a \,x^{5}\right)}{x}\, dx"," ",0,"int(arccsc(a*x^5)/x,x)","F"
2,1,43,38,0.055000," ","int(x^3*arccsc(x^(1/2)),x)","\frac{x^{4} \mathrm{arccsc}\left(\sqrt{x}\right)}{4}+\frac{\left(x -1\right) \left(5 x^{3}+6 x^{2}+8 x +16\right)}{140 \sqrt{\frac{x -1}{x}}\, \sqrt{x}}"," ",0,"1/4*x^4*arccsc(x^(1/2))+1/140*(x-1)*(5*x^3+6*x^2+8*x+16)/((x-1)/x)^(1/2)/x^(1/2)","A"
3,1,38,31,0.052000," ","int(x^2*arccsc(x^(1/2)),x)","\frac{x^{3} \mathrm{arccsc}\left(\sqrt{x}\right)}{3}+\frac{\left(x -1\right) \left(3 x^{2}+4 x +8\right)}{45 \sqrt{\frac{x -1}{x}}\, \sqrt{x}}"," ",0,"1/3*x^3*arccsc(x^(1/2))+1/45*(x-1)*(3*x^2+4*x+8)/((x-1)/x)^(1/2)/x^(1/2)","A"
4,1,31,24,0.050000," ","int(x*arccsc(x^(1/2)),x)","\frac{x^{2} \mathrm{arccsc}\left(\sqrt{x}\right)}{2}+\frac{\left(x -1\right) \left(x +2\right)}{6 \sqrt{\frac{x -1}{x}}\, \sqrt{x}}"," ",0,"1/2*x^2*arccsc(x^(1/2))+1/6*(x-1)*(x+2)/((x-1)/x)^(1/2)/x^(1/2)","A"
5,1,24,12,0.050000," ","int(arccsc(x^(1/2)),x)","x \,\mathrm{arccsc}\left(\sqrt{x}\right)+\frac{x -1}{\sqrt{\frac{x -1}{x}}\, \sqrt{x}}"," ",0,"x*arccsc(x^(1/2))+1/((x-1)/x)^(1/2)/x^(1/2)*(x-1)","A"
6,1,105,62,0.114000," ","int(arccsc(x^(1/2))/x,x)","i \mathrm{arccsc}\left(\sqrt{x}\right)^{2}-2 \,\mathrm{arccsc}\left(\sqrt{x}\right) \ln \left(1+\frac{i}{\sqrt{x}}+\sqrt{1-\frac{1}{x}}\right)-2 \,\mathrm{arccsc}\left(\sqrt{x}\right) \ln \left(1-\frac{i}{\sqrt{x}}-\sqrt{1-\frac{1}{x}}\right)+2 i \polylog \left(2, -\frac{i}{\sqrt{x}}-\sqrt{1-\frac{1}{x}}\right)+2 i \polylog \left(2, \frac{i}{\sqrt{x}}+\sqrt{1-\frac{1}{x}}\right)"," ",0,"I*arccsc(x^(1/2))^2-2*arccsc(x^(1/2))*ln(1+I/x^(1/2)+(1-1/x)^(1/2))-2*arccsc(x^(1/2))*ln(1-I/x^(1/2)-(1-1/x)^(1/2))+2*I*polylog(2,-I/x^(1/2)-(1-1/x)^(1/2))+2*I*polylog(2,I/x^(1/2)+(1-1/x)^(1/2))","A"
7,1,46,28,0.052000," ","int(arccsc(x^(1/2))/x^2,x)","-\frac{\mathrm{arccsc}\left(\sqrt{x}\right)}{x}+\frac{\sqrt{x -1}\, \left(\arctan \left(\frac{1}{\sqrt{x -1}}\right) x -\sqrt{x -1}\right)}{2 \sqrt{\frac{x -1}{x}}\, x^{\frac{3}{2}}}"," ",0,"-arccsc(x^(1/2))/x+1/2*(x-1)^(1/2)*(arctan(1/(x-1)^(1/2))*x-(x-1)^(1/2))/((x-1)/x)^(1/2)/x^(3/2)","A"
8,1,57,38,0.051000," ","int(arccsc(x^(1/2))/x^3,x)","-\frac{\mathrm{arccsc}\left(\sqrt{x}\right)}{2 x^{2}}+\frac{\sqrt{x -1}\, \left(3 \arctan \left(\frac{1}{\sqrt{x -1}}\right) x^{2}-3 x \sqrt{x -1}-2 \sqrt{x -1}\right)}{16 \sqrt{\frac{x -1}{x}}\, x^{\frac{5}{2}}}"," ",0,"-1/2*arccsc(x^(1/2))/x^2+1/16*(x-1)^(1/2)*(3*arctan(1/(x-1)^(1/2))*x^2-3*x*(x-1)^(1/2)-2*(x-1)^(1/2))/((x-1)/x)^(1/2)/x^(5/2)","A"
9,1,66,46,0.060000," ","int(x^2*arccsc(a/x),x)","-a^{3} \left(-\frac{x^{3} \mathrm{arccsc}\left(\frac{a}{x}\right)}{3 a^{3}}-\frac{\left(-1+\frac{a^{2}}{x^{2}}\right) \left(\frac{2 a^{2}}{x^{2}}+1\right) x^{4}}{9 \sqrt{\frac{\left(-1+\frac{a^{2}}{x^{2}}\right) x^{2}}{a^{2}}}\, a^{4}}\right)"," ",0,"-a^3*(-1/3/a^3*x^3*arccsc(a/x)-1/9*(-1+a^2/x^2)*(2*a^2/x^2+1)/((-1+a^2/x^2)*x^2/a^2)^(1/2)/a^4*x^4)","A"
10,1,93,39,0.060000," ","int(x*arccsc(a/x),x)","\frac{x^{2} \mathrm{arccsc}\left(\frac{a}{x}\right)}{2}-\frac{a \sqrt{-1+\frac{a^{2}}{x^{2}}}\, x \arctan \left(\frac{1}{\sqrt{-1+\frac{a^{2}}{x^{2}}}}\right)}{4 \sqrt{\frac{\left(-1+\frac{a^{2}}{x^{2}}\right) x^{2}}{a^{2}}}}+\frac{\left(-1+\frac{a^{2}}{x^{2}}\right) x^{3}}{4 a \sqrt{\frac{\left(-1+\frac{a^{2}}{x^{2}}\right) x^{2}}{a^{2}}}}"," ",0,"1/2*x^2*arccsc(a/x)-1/4*a*(-1+a^2/x^2)^(1/2)/((-1+a^2/x^2)*x^2/a^2)^(1/2)*x*arctan(1/(-1+a^2/x^2)^(1/2))+1/4/a*(-1+a^2/x^2)/((-1+a^2/x^2)*x^2/a^2)^(1/2)*x^3","B"
11,1,52,23,0.060000," ","int(arccsc(a/x),x)","-a \left(-\frac{\mathrm{arccsc}\left(\frac{a}{x}\right) x}{a}-\frac{x^{2} \left(-1+\frac{a^{2}}{x^{2}}\right)}{\sqrt{\frac{\left(-1+\frac{a^{2}}{x^{2}}\right) x^{2}}{a^{2}}}\, a^{2}}\right)"," ",0,"-a*(-arccsc(a/x)/a*x-1/((-1+a^2/x^2)*x^2/a^2)^(1/2)/a^2*x^2*(-1+a^2/x^2))","B"
12,1,125,73,0.116000," ","int(arccsc(a/x)/x,x)","-\frac{i \mathrm{arccsc}\left(\frac{a}{x}\right)^{2}}{2}+\mathrm{arccsc}\left(\frac{a}{x}\right) \ln \left(1+\frac{i x}{a}+\sqrt{1-\frac{x^{2}}{a^{2}}}\right)+\mathrm{arccsc}\left(\frac{a}{x}\right) \ln \left(1-\frac{i x}{a}-\sqrt{1-\frac{x^{2}}{a^{2}}}\right)-i \polylog \left(2, -\frac{i x}{a}-\sqrt{1-\frac{x^{2}}{a^{2}}}\right)-i \polylog \left(2, \frac{i x}{a}+\sqrt{1-\frac{x^{2}}{a^{2}}}\right)"," ",0,"-1/2*I*arccsc(a/x)^2+arccsc(a/x)*ln(1+I*x/a+(1-x^2/a^2)^(1/2))+arccsc(a/x)*ln(1-I/a*x-(1-x^2/a^2)^(1/2))-I*polylog(2,-I/a*x-(1-x^2/a^2)^(1/2))-I*polylog(2,I*x/a+(1-x^2/a^2)^(1/2))","A"
13,1,42,30,0.048000," ","int(arccsc(a/x)/x^2,x)","-\frac{\mathrm{arccsc}\left(\frac{a}{x}\right)}{x}-\frac{\ln \left(\frac{a}{x}+\frac{a \sqrt{1-\frac{x^{2}}{a^{2}}}}{x}\right)}{a}"," ",0,"-arccsc(a/x)/x-1/a*ln(a/x+1/x*a*(1-x^2/a^2)^(1/2))","A"
14,1,54,32,0.059000," ","int(arccsc(a/x)/x^3,x)","-\frac{\frac{a^{2} \mathrm{arccsc}\left(\frac{a}{x}\right)}{2 x^{2}}+\frac{x \left(-1+\frac{a^{2}}{x^{2}}\right)}{2 \sqrt{\frac{\left(-1+\frac{a^{2}}{x^{2}}\right) x^{2}}{a^{2}}}\, a}}{a^{2}}"," ",0,"-1/a^2*(1/2*a^2/x^2*arccsc(a/x)+1/2/((-1+a^2/x^2)*x^2/a^2)^(1/2)/a*x*(-1+a^2/x^2))","A"
15,1,98,50,0.060000," ","int(arccsc(a/x)/x^4,x)","-\frac{\mathrm{arccsc}\left(\frac{a}{x}\right)}{3 x^{3}}-\frac{-1+\frac{a^{2}}{x^{2}}}{6 a^{3} \sqrt{\frac{\left(-1+\frac{a^{2}}{x^{2}}\right) x^{2}}{a^{2}}}}-\frac{\sqrt{-1+\frac{a^{2}}{x^{2}}}\, x \ln \left(\frac{a}{x}+\sqrt{-1+\frac{a^{2}}{x^{2}}}\right)}{6 a^{4} \sqrt{\frac{\left(-1+\frac{a^{2}}{x^{2}}\right) x^{2}}{a^{2}}}}"," ",0,"-1/3*arccsc(a/x)/x^3-1/6/a^3*(-1+a^2/x^2)/((-1+a^2/x^2)*x^2/a^2)^(1/2)-1/6/a^4*(-1+a^2/x^2)^(1/2)/((-1+a^2/x^2)*x^2/a^2)^(1/2)*x*ln(a/x+(-1+a^2/x^2)^(1/2))","A"
16,1,166,95,0.121000," ","int(arccsc(a*x^n)/x,x)","\frac{i \mathrm{arccsc}\left(a \,x^{n}\right)^{2}}{2 n}-\frac{\mathrm{arccsc}\left(a \,x^{n}\right) \ln \left(1+\frac{i x^{-n}}{a}+\sqrt{1-\frac{x^{-2 n}}{a^{2}}}\right)}{n}-\frac{\mathrm{arccsc}\left(a \,x^{n}\right) \ln \left(1-\frac{i x^{-n}}{a}-\sqrt{1-\frac{x^{-2 n}}{a^{2}}}\right)}{n}+\frac{i \polylog \left(2, -\frac{i x^{-n}}{a}-\sqrt{1-\frac{x^{-2 n}}{a^{2}}}\right)}{n}+\frac{i \polylog \left(2, \frac{i x^{-n}}{a}+\sqrt{1-\frac{x^{-2 n}}{a^{2}}}\right)}{n}"," ",0,"1/2*I*arccsc(a*x^n)^2/n-1/n*arccsc(a*x^n)*ln(1+I/a/(x^n)+(1-1/a^2/(x^n)^2)^(1/2))-1/n*arccsc(a*x^n)*ln(1-I/a/(x^n)-(1-1/a^2/(x^n)^2)^(1/2))+I/n*polylog(2,-I/a/(x^n)-(1-1/a^2/(x^n)^2)^(1/2))+I/n*polylog(2,I/a/(x^n)+(1-1/a^2/(x^n)^2)^(1/2))","A"
17,1,507,173,0.066000," ","int(x^4*arccsc(b*x+a),x)","-\frac{77 \left(-1+\left(b x +a \right)^{2}\right) a^{3}}{60 b^{5} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}-\frac{71 \left(-1+\left(b x +a \right)^{2}\right) a}{120 b^{5} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}+\frac{3 \sqrt{-1+\left(b x +a \right)^{2}}\, \ln \left(b x +a +\sqrt{-1+\left(b x +a \right)^{2}}\right)}{40 b^{5} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}-\frac{11 \left(-1+\left(b x +a \right)^{2}\right) x^{2} a}{60 b^{3} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}+\frac{29 \left(-1+\left(b x +a \right)^{2}\right) x \,a^{2}}{60 b^{4} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}+\frac{\left(-1+\left(b x +a \right)^{2}\right) x^{3}}{20 b^{2} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}+\frac{\sqrt{-1+\left(b x +a \right)^{2}}\, a^{5} \arctan \left(\frac{1}{\sqrt{-1+\left(b x +a \right)^{2}}}\right)}{5 b^{5} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}+\frac{\sqrt{-1+\left(b x +a \right)^{2}}\, a^{4} \ln \left(b x +a +\sqrt{-1+\left(b x +a \right)^{2}}\right)}{b^{5} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}+\frac{3 \left(-1+\left(b x +a \right)^{2}\right) x}{40 b^{4} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}+\frac{\sqrt{-1+\left(b x +a \right)^{2}}\, a^{2} \ln \left(b x +a +\sqrt{-1+\left(b x +a \right)^{2}}\right)}{b^{5} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}+\frac{x^{5} \mathrm{arccsc}\left(b x +a \right)}{5}"," ",0,"-77/60/b^5*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^3-71/120/b^5*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a+3/40/b^5*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*ln(b*x+a+(-1+(b*x+a)^2)^(1/2))-11/60/b^3*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*x^2*a+29/60/b^4*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*x*a^2+1/20/b^2*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*x^3+1/5/b^5*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^5*arctan(1/(-1+(b*x+a)^2)^(1/2))+1/b^5*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^4*ln(b*x+a+(-1+(b*x+a)^2)^(1/2))+3/40/b^4*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*x+1/b^5*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^2*ln(b*x+a+(-1+(b*x+a)^2)^(1/2))+1/5*x^5*arccsc(b*x+a)","B"
18,1,360,135,0.060000," ","int(x^3*arccsc(b*x+a),x)","\frac{x^{4} \mathrm{arccsc}\left(b x +a \right)}{4}+\frac{\left(-1+\left(b x +a \right)^{2}\right) x^{2}}{12 b^{2} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}-\frac{\sqrt{-1+\left(b x +a \right)^{2}}\, a^{4} \arctan \left(\frac{1}{\sqrt{-1+\left(b x +a \right)^{2}}}\right)}{4 b^{4} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}-\frac{\left(-1+\left(b x +a \right)^{2}\right) x a}{3 b^{3} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}-\frac{\sqrt{-1+\left(b x +a \right)^{2}}\, a^{3} \ln \left(b x +a +\sqrt{-1+\left(b x +a \right)^{2}}\right)}{b^{4} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}+\frac{13 \left(-1+\left(b x +a \right)^{2}\right) a^{2}}{12 b^{4} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}-\frac{\sqrt{-1+\left(b x +a \right)^{2}}\, a \ln \left(b x +a +\sqrt{-1+\left(b x +a \right)^{2}}\right)}{2 b^{4} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}+\frac{-1+\left(b x +a \right)^{2}}{6 b^{4} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}"," ",0,"1/4*x^4*arccsc(b*x+a)+1/12/b^2*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*x^2-1/4/b^4*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^4*arctan(1/(-1+(b*x+a)^2)^(1/2))-1/3/b^3*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*x*a-1/b^4*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^3*ln(b*x+a+(-1+(b*x+a)^2)^(1/2))+13/12/b^4*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^2-1/2/b^4*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a*ln(b*x+a+(-1+(b*x+a)^2)^(1/2))+1/6/b^4*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)","B"
19,1,272,100,0.061000," ","int(x^2*arccsc(b*x+a),x)","\frac{x^{3} \mathrm{arccsc}\left(b x +a \right)}{3}+\frac{\sqrt{-1+\left(b x +a \right)^{2}}\, a^{3} \arctan \left(\frac{1}{\sqrt{-1+\left(b x +a \right)^{2}}}\right)}{3 b^{3} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}+\frac{\left(-1+\left(b x +a \right)^{2}\right) x}{6 b^{2} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}+\frac{\sqrt{-1+\left(b x +a \right)^{2}}\, a^{2} \ln \left(b x +a +\sqrt{-1+\left(b x +a \right)^{2}}\right)}{b^{3} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}-\frac{5 \left(-1+\left(b x +a \right)^{2}\right) a}{6 b^{3} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}+\frac{\sqrt{-1+\left(b x +a \right)^{2}}\, \ln \left(b x +a +\sqrt{-1+\left(b x +a \right)^{2}}\right)}{6 b^{3} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}"," ",0,"1/3*x^3*arccsc(b*x+a)+1/3/b^3*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^3*arctan(1/(-1+(b*x+a)^2)^(1/2))+1/6/b^2*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*x+1/b^3*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^2*ln(b*x+a+(-1+(b*x+a)^2)^(1/2))-5/6/b^3*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a+1/6/b^3*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*ln(b*x+a+(-1+(b*x+a)^2)^(1/2))","B"
20,1,127,69,0.057000," ","int(x*arccsc(b*x+a),x)","\frac{x^{2} \mathrm{arccsc}\left(b x +a \right)}{2}-\frac{a^{2} \mathrm{arccsc}\left(b x +a \right)}{2 b^{2}}-\frac{\sqrt{-1+\left(b x +a \right)^{2}}\, a \ln \left(b x +a +\sqrt{-1+\left(b x +a \right)^{2}}\right)}{b^{2} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}+\frac{-1+\left(b x +a \right)^{2}}{2 b^{2} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}"," ",0,"1/2*x^2*arccsc(b*x+a)-1/2*a^2*arccsc(b*x+a)/b^2-1/b^2/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*(-1+(b*x+a)^2)^(1/2)*a*ln(b*x+a+(-1+(b*x+a)^2)^(1/2))+1/2/b^2/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*(-1+(b*x+a)^2)","A"
21,1,50,34,0.052000," ","int(arccsc(b*x+a),x)","x \,\mathrm{arccsc}\left(b x +a \right)+\frac{\mathrm{arccsc}\left(b x +a \right) a}{b}+\frac{\ln \left(b x +a +\left(b x +a \right) \sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b}"," ",0,"x*arccsc(b*x+a)+1/b*arccsc(b*x+a)*a+1/b*ln(b*x+a+(b*x+a)*(1-1/(b*x+a)^2)^(1/2))","A"
22,1,607,269,1.133000," ","int(arccsc(b*x+a)/x,x)","\frac{\mathrm{arccsc}\left(b x +a \right) \ln \left(\frac{-a \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)+\sqrt{a^{2}-1}+i}{i+\sqrt{a^{2}-1}}\right) a^{2}}{a^{2}-1}+\frac{\mathrm{arccsc}\left(b x +a \right) \ln \left(\frac{a \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)+\sqrt{a^{2}-1}-i}{-i+\sqrt{a^{2}-1}}\right) a^{2}}{a^{2}-1}-\frac{\mathrm{arccsc}\left(b x +a \right) \ln \left(\frac{-a \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)+\sqrt{a^{2}-1}+i}{i+\sqrt{a^{2}-1}}\right)}{a^{2}-1}-\frac{\mathrm{arccsc}\left(b x +a \right) \ln \left(\frac{a \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)+\sqrt{a^{2}-1}-i}{-i+\sqrt{a^{2}-1}}\right)}{a^{2}-1}-\frac{i \dilog \left(\frac{-a \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)+\sqrt{a^{2}-1}+i}{i+\sqrt{a^{2}-1}}\right) a^{2}}{a^{2}-1}-\frac{i \dilog \left(\frac{a \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)+\sqrt{a^{2}-1}-i}{-i+\sqrt{a^{2}-1}}\right) a^{2}}{a^{2}-1}+\frac{i \dilog \left(\frac{-a \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)+\sqrt{a^{2}-1}+i}{i+\sqrt{a^{2}-1}}\right)}{a^{2}-1}+\frac{i \dilog \left(\frac{a \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)+\sqrt{a^{2}-1}-i}{-i+\sqrt{a^{2}-1}}\right)}{a^{2}-1}-i \dilog \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)+i \dilog \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)-\mathrm{arccsc}\left(b x +a \right) \ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)"," ",0,"arccsc(b*x+a)/(a^2-1)*ln((-a*(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+(a^2-1)^(1/2)+I)/(I+(a^2-1)^(1/2)))*a^2+arccsc(b*x+a)/(a^2-1)*ln((a*(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+(a^2-1)^(1/2)-I)/(-I+(a^2-1)^(1/2)))*a^2-arccsc(b*x+a)/(a^2-1)*ln((-a*(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+(a^2-1)^(1/2)+I)/(I+(a^2-1)^(1/2)))-arccsc(b*x+a)/(a^2-1)*ln((a*(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+(a^2-1)^(1/2)-I)/(-I+(a^2-1)^(1/2)))-I/(a^2-1)*dilog((-a*(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+(a^2-1)^(1/2)+I)/(I+(a^2-1)^(1/2)))*a^2-I/(a^2-1)*dilog((a*(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+(a^2-1)^(1/2)-I)/(-I+(a^2-1)^(1/2)))*a^2+I/(a^2-1)*dilog((-a*(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+(a^2-1)^(1/2)+I)/(I+(a^2-1)^(1/2)))+I/(a^2-1)*dilog((a*(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+(a^2-1)^(1/2)-I)/(-I+(a^2-1)^(1/2)))-I*dilog(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+I*dilog(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))-arccsc(b*x+a)*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))","B"
23,1,154,63,0.063000," ","int(arccsc(b*x+a)/x^2,x)","-\frac{\mathrm{arccsc}\left(b x +a \right)}{x}-\frac{b \sqrt{-1+\left(b x +a \right)^{2}}\, \arctan \left(\frac{1}{\sqrt{-1+\left(b x +a \right)^{2}}}\right)}{\sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a}+\frac{b \sqrt{-1+\left(b x +a \right)^{2}}\, \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{-1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)-2}{b x}\right)}{\sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a \sqrt{a^{2}-1}}"," ",0,"-arccsc(b*x+a)/x-b*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a*arctan(1/(-1+(b*x+a)^2)^(1/2))+b*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a/(a^2-1)^(1/2)*ln(2*((a^2-1)^(1/2)*(-1+(b*x+a)^2)^(1/2)+a*(b*x+a)-1)/b/x)","B"
24,1,453,109,0.068000," ","int(arccsc(b*x+a)/x^3,x)","-\frac{\mathrm{arccsc}\left(b x +a \right)}{2 x^{2}}+\frac{b^{2} \sqrt{-1+\left(b x +a \right)^{2}}\, \arctan \left(\frac{1}{\sqrt{-1+\left(b x +a \right)^{2}}}\right)}{2 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)}-\frac{b^{2} \sqrt{-1+\left(b x +a \right)^{2}}\, a^{2} \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{-1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)-2}{b x}\right)}{\sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{\frac{5}{2}}}-\frac{b^{2} \sqrt{-1+\left(b x +a \right)^{2}}\, \arctan \left(\frac{1}{\sqrt{-1+\left(b x +a \right)^{2}}}\right)}{2 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a^{2} \left(a^{2}-1\right)}+\frac{b \left(-1+\left(b x +a \right)^{2}\right)}{2 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a \left(a^{2}-1\right) x}+\frac{3 b^{2} \sqrt{-1+\left(b x +a \right)^{2}}\, \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{-1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)-2}{b x}\right)}{2 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{\frac{5}{2}}}-\frac{b^{2} \sqrt{-1+\left(b x +a \right)^{2}}\, \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{-1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)-2}{b x}\right)}{2 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a^{2} \left(a^{2}-1\right)^{\frac{5}{2}}}"," ",0,"-1/2*arccsc(b*x+a)/x^2+1/2*b^2*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/(a^2-1)*arctan(1/(-1+(b*x+a)^2)^(1/2))-b^2*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^2/(a^2-1)^(5/2)*ln(2*((a^2-1)^(1/2)*(-1+(b*x+a)^2)^(1/2)+a*(b*x+a)-1)/b/x)-1/2*b^2*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a^2/(a^2-1)*arctan(1/(-1+(b*x+a)^2)^(1/2))+1/2*b*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a/(a^2-1)/x+3/2*b^2*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/(a^2-1)^(5/2)*ln(2*((a^2-1)^(1/2)*(-1+(b*x+a)^2)^(1/2)+a*(b*x+a)-1)/b/x)-1/2*b^2*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a^2/(a^2-1)^(5/2)*ln(2*((a^2-1)^(1/2)*(-1+(b*x+a)^2)^(1/2)+a*(b*x+a)-1)/b/x)","B"
25,1,759,160,0.073000," ","int(arccsc(b*x+a)/x^4,x)","-\frac{\mathrm{arccsc}\left(b x +a \right)}{3 x^{3}}-\frac{b^{3} \sqrt{-1+\left(b x +a \right)^{2}}\, a \arctan \left(\frac{1}{\sqrt{-1+\left(b x +a \right)^{2}}}\right)}{3 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{2}}+\frac{b^{3} \sqrt{-1+\left(b x +a \right)^{2}}\, a^{3} \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{-1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)-2}{b x}\right)}{\sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{\frac{7}{2}}}+\frac{2 b^{3} \sqrt{-1+\left(b x +a \right)^{2}}\, \arctan \left(\frac{1}{\sqrt{-1+\left(b x +a \right)^{2}}}\right)}{3 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a \left(a^{2}-1\right)^{2}}-\frac{5 b^{2} \left(-1+\left(b x +a \right)^{2}\right)}{6 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{2} x}-\frac{11 b^{3} \sqrt{-1+\left(b x +a \right)^{2}}\, a \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{-1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)-2}{b x}\right)}{6 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{\frac{7}{2}}}+\frac{b \left(-1+\left(b x +a \right)^{2}\right) a}{6 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{2} x^{2}}-\frac{b^{3} \sqrt{-1+\left(b x +a \right)^{2}}\, \arctan \left(\frac{1}{\sqrt{-1+\left(b x +a \right)^{2}}}\right)}{3 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a^{3} \left(a^{2}-1\right)^{2}}+\frac{b^{2} \left(-1+\left(b x +a \right)^{2}\right)}{3 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a^{2} \left(a^{2}-1\right)^{2} x}+\frac{7 b^{3} \sqrt{-1+\left(b x +a \right)^{2}}\, \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{-1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)-2}{b x}\right)}{6 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a \left(a^{2}-1\right)^{\frac{7}{2}}}-\frac{b \left(-1+\left(b x +a \right)^{2}\right)}{6 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a \left(a^{2}-1\right)^{2} x^{2}}-\frac{b^{3} \sqrt{-1+\left(b x +a \right)^{2}}\, \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{-1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)-2}{b x}\right)}{3 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a^{3} \left(a^{2}-1\right)^{\frac{7}{2}}}"," ",0,"-1/3*arccsc(b*x+a)/x^3-1/3*b^3*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a/(a^2-1)^2*arctan(1/(-1+(b*x+a)^2)^(1/2))+b^3*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^3/(a^2-1)^(7/2)*ln(2*((a^2-1)^(1/2)*(-1+(b*x+a)^2)^(1/2)+a*(b*x+a)-1)/b/x)+2/3*b^3*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a/(a^2-1)^2*arctan(1/(-1+(b*x+a)^2)^(1/2))-5/6*b^2*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/(a^2-1)^2/x-11/6*b^3*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a/(a^2-1)^(7/2)*ln(2*((a^2-1)^(1/2)*(-1+(b*x+a)^2)^(1/2)+a*(b*x+a)-1)/b/x)+1/6*b*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a/(a^2-1)^2/x^2-1/3*b^3*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a^3/(a^2-1)^2*arctan(1/(-1+(b*x+a)^2)^(1/2))+1/3*b^2*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a^2/(a^2-1)^2/x+7/6*b^3*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a/(a^2-1)^(7/2)*ln(2*((a^2-1)^(1/2)*(-1+(b*x+a)^2)^(1/2)+a*(b*x+a)-1)/b/x)-1/6*b*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a/(a^2-1)^2/x^2-1/3*b^3*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a^3/(a^2-1)^(7/2)*ln(2*((a^2-1)^(1/2)*(-1+(b*x+a)^2)^(1/2)+a*(b*x+a)-1)/b/x)","B"
26,1,1172,215,0.074000," ","int(arccsc(b*x+a)/x^5,x)","-\frac{\mathrm{arccsc}\left(b x +a \right)}{4 x^{4}}+\frac{b^{4} \sqrt{-1+\left(b x +a \right)^{2}}\, a^{2} \arctan \left(\frac{1}{\sqrt{-1+\left(b x +a \right)^{2}}}\right)}{4 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{3}}-\frac{b^{4} \sqrt{-1+\left(b x +a \right)^{2}}\, a^{4} \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{-1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)-2}{b x}\right)}{\sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{\frac{9}{2}}}-\frac{3 b^{4} \sqrt{-1+\left(b x +a \right)^{2}}\, \arctan \left(\frac{1}{\sqrt{-1+\left(b x +a \right)^{2}}}\right)}{4 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{3}}+\frac{13 b^{3} \left(-1+\left(b x +a \right)^{2}\right) a}{12 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{3} x}+\frac{2 b^{4} \sqrt{-1+\left(b x +a \right)^{2}}\, a^{2} \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{-1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)-2}{b x}\right)}{\sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{\frac{9}{2}}}-\frac{b^{2} \left(-1+\left(b x +a \right)^{2}\right) a^{2}}{3 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{3} x^{2}}+\frac{3 b^{4} \sqrt{-1+\left(b x +a \right)^{2}}\, \arctan \left(\frac{1}{\sqrt{-1+\left(b x +a \right)^{2}}}\right)}{4 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a^{2} \left(a^{2}-1\right)^{3}}-\frac{17 b^{3} \left(-1+\left(b x +a \right)^{2}\right)}{24 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a \left(a^{2}-1\right)^{3} x}+\frac{b \left(-1+\left(b x +a \right)^{2}\right) a^{3}}{12 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{3} x^{3}}-\frac{15 b^{4} \sqrt{-1+\left(b x +a \right)^{2}}\, \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{-1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)-2}{b x}\right)}{8 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{\frac{9}{2}}}+\frac{11 b^{2} \left(-1+\left(b x +a \right)^{2}\right)}{24 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{3} x^{2}}-\frac{b^{4} \sqrt{-1+\left(b x +a \right)^{2}}\, \arctan \left(\frac{1}{\sqrt{-1+\left(b x +a \right)^{2}}}\right)}{4 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a^{4} \left(a^{2}-1\right)^{3}}+\frac{b^{3} \left(-1+\left(b x +a \right)^{2}\right)}{4 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a^{3} \left(a^{2}-1\right)^{3} x}-\frac{b \left(-1+\left(b x +a \right)^{2}\right) a}{6 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}-1\right)^{3} x^{3}}+\frac{9 b^{4} \sqrt{-1+\left(b x +a \right)^{2}}\, \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{-1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)-2}{b x}\right)}{8 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a^{2} \left(a^{2}-1\right)^{\frac{9}{2}}}-\frac{b^{2} \left(-1+\left(b x +a \right)^{2}\right)}{8 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a^{2} \left(a^{2}-1\right)^{3} x^{2}}+\frac{b \left(-1+\left(b x +a \right)^{2}\right)}{12 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a \left(a^{2}-1\right)^{3} x^{3}}-\frac{b^{4} \sqrt{-1+\left(b x +a \right)^{2}}\, \ln \left(\frac{2 \sqrt{a^{2}-1}\, \sqrt{-1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)-2}{b x}\right)}{4 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a^{4} \left(a^{2}-1\right)^{\frac{9}{2}}}"," ",0,"-1/4*arccsc(b*x+a)/x^4+1/4*b^4*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^2/(a^2-1)^3*arctan(1/(-1+(b*x+a)^2)^(1/2))-b^4*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^4/(a^2-1)^(9/2)*ln(2*((a^2-1)^(1/2)*(-1+(b*x+a)^2)^(1/2)+a*(b*x+a)-1)/b/x)-3/4*b^4*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/(a^2-1)^3*arctan(1/(-1+(b*x+a)^2)^(1/2))+13/12*b^3*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a/(a^2-1)^3/x+2*b^4*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^2/(a^2-1)^(9/2)*ln(2*((a^2-1)^(1/2)*(-1+(b*x+a)^2)^(1/2)+a*(b*x+a)-1)/b/x)-1/3*b^2*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^2/(a^2-1)^3/x^2+3/4*b^4*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a^2/(a^2-1)^3*arctan(1/(-1+(b*x+a)^2)^(1/2))-17/24*b^3*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a/(a^2-1)^3/x+1/12*b*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^3/(a^2-1)^3/x^3-15/8*b^4*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/(a^2-1)^(9/2)*ln(2*((a^2-1)^(1/2)*(-1+(b*x+a)^2)^(1/2)+a*(b*x+a)-1)/b/x)+11/24*b^2*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/(a^2-1)^3/x^2-1/4*b^4*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a^4/(a^2-1)^3*arctan(1/(-1+(b*x+a)^2)^(1/2))+1/4*b^3*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a^3/(a^2-1)^3/x-1/6*b*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a/(a^2-1)^3/x^3+9/8*b^4*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a^2/(a^2-1)^(9/2)*ln(2*((a^2-1)^(1/2)*(-1+(b*x+a)^2)^(1/2)+a*(b*x+a)-1)/b/x)-1/8*b^2*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a^2/(a^2-1)^3/x^2+1/12*b*(-1+(b*x+a)^2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a/(a^2-1)^3/x^3-1/4*b^4*(-1+(b*x+a)^2)^(1/2)/((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a^4/(a^2-1)^(9/2)*ln(2*((a^2-1)^(1/2)*(-1+(b*x+a)^2)^(1/2)+a*(b*x+a)-1)/b/x)","B"
27,1,769,414,6.967000," ","int(x^3*arccsc(b*x+a)^2,x)","-\frac{5 a x}{6 b^{3}}-\frac{a^{4} \mathrm{arccsc}\left(b x +a \right)^{2}}{4 b^{4}}+\frac{3 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \mathrm{arccsc}\left(b x +a \right) x \,a^{2}}{2 b^{3}}-\frac{\ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{3 b^{4}}+\frac{2 \ln \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{3 b^{4}}-\frac{\ln \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}-1\right)}{3 b^{4}}-\frac{11 a^{2}}{12 b^{4}}+\frac{x^{2}}{12 b^{2}}+\frac{x^{4} \mathrm{arccsc}\left(b x +a \right)^{2}}{4}+\frac{13 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \mathrm{arccsc}\left(b x +a \right) a^{3}}{6 b^{4}}+\frac{\sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \mathrm{arccsc}\left(b x +a \right) a}{3 b^{4}}+\frac{\sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \mathrm{arccsc}\left(b x +a \right) x^{3}}{6 b}+\frac{\sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \mathrm{arccsc}\left(b x +a \right) x}{3 b^{3}}+\frac{2 a^{3} \mathrm{arccsc}\left(b x +a \right) \ln \left(1-\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{4}}-\frac{2 a^{3} \mathrm{arccsc}\left(b x +a \right) \ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{4}}-\frac{3 i \mathrm{arccsc}\left(b x +a \right) a^{2}}{b^{4}}+\frac{a \,\mathrm{arccsc}\left(b x +a \right) \ln \left(1-\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{4}}-\frac{a \,\mathrm{arccsc}\left(b x +a \right) \ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{4}}-\frac{i a \polylog \left(2, \frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{4}}+\frac{2 i a^{3} \polylog \left(2, -\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{4}}+\frac{i a \polylog \left(2, -\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{4}}-\frac{2 i a^{3} \polylog \left(2, \frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{4}}+\frac{6 a^{2} \ln \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{4}}-\frac{3 a^{2} \ln \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}-1\right)}{b^{4}}-\frac{i \mathrm{arccsc}\left(b x +a \right)}{3 b^{4}}-\frac{3 a^{2} \ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{4}}-\frac{\sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \mathrm{arccsc}\left(b x +a \right) x^{2} a}{2 b^{2}}"," ",0,"-5/6*a*x/b^3-1/4*a^4*arccsc(b*x+a)^2/b^4-I*a*polylog(2,I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))/b^4+2*I*a^3*polylog(2,-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))/b^4+I*a*polylog(2,-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))/b^4-2*I*a^3*polylog(2,I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))/b^4+3/2/b^3*((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)*arccsc(b*x+a)*x*a^2-11/12/b^4*a^2+1/12/b^2*x^2-1/3/b^4*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+2/3/b^4*ln(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))-1/3/b^4*ln(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2)-1)+6/b^4*a^2*ln(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))-3/b^4*a^2*ln(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2)-1)-1/3*I/b^4*arccsc(b*x+a)-3/b^4*a^2*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+1/4*x^4*arccsc(b*x+a)^2+2/b^4*a^3*arccsc(b*x+a)*ln(1-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))-2/b^4*a^3*arccsc(b*x+a)*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+13/6/b^4*((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)*arccsc(b*x+a)*a^3+1/3/b^4*((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)*arccsc(b*x+a)*a+1/6/b*((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)*arccsc(b*x+a)*x^3+1/3/b^3*((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)*arccsc(b*x+a)*x-3*I/b^4*arccsc(b*x+a)*a^2+1/b^4*a*arccsc(b*x+a)*ln(1-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))-1/b^4*a*arccsc(b*x+a)*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))-1/2/b^2*((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)*arccsc(b*x+a)*x^2*a","A"
28,1,545,322,1.755000," ","int(x^2*arccsc(b*x+a)^2,x)","-\frac{4 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \mathrm{arccsc}\left(b x +a \right) x a}{3 b^{2}}+\frac{i \polylog \left(2, \frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{3 b^{3}}-\frac{2 a^{2} \mathrm{arccsc}\left(b x +a \right) \ln \left(1-\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}+\frac{2 a^{2} \mathrm{arccsc}\left(b x +a \right) \ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}+\frac{x^{3} \mathrm{arccsc}\left(b x +a \right)^{2}}{3}-\frac{5 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \mathrm{arccsc}\left(b x +a \right) a^{2}}{3 b^{3}}+\frac{\sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \mathrm{arccsc}\left(b x +a \right) x^{2}}{3 b}+\frac{2 i a \,\mathrm{arccsc}\left(b x +a \right)}{b^{3}}+\frac{2 i a^{2} \polylog \left(2, \frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}+\frac{2 a \ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}-\frac{4 \ln \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right) a}{b^{3}}+\frac{2 a \ln \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}-1\right)}{b^{3}}+\frac{\mathrm{arccsc}\left(b x +a \right) \ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{3 b^{3}}-\frac{\mathrm{arccsc}\left(b x +a \right) \ln \left(1-\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{3 b^{3}}+\frac{a^{3} \mathrm{arccsc}\left(b x +a \right)^{2}}{3 b^{3}}+\frac{a}{3 b^{3}}+\frac{x}{3 b^{2}}-\frac{i \polylog \left(2, -\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{3 b^{3}}-\frac{2 i a^{2} \polylog \left(2, -\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}"," ",0,"-4/3/b^2*((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)*arccsc(b*x+a)*x*a+2*I*a^2*polylog(2,I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))/b^3-2/b^3*a^2*arccsc(b*x+a)*ln(1-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))+2/b^3*a^2*arccsc(b*x+a)*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+1/3*x^3*arccsc(b*x+a)^2-5/3/b^3*((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)*arccsc(b*x+a)*a^2+1/3/b*((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)*arccsc(b*x+a)*x^2+1/3*I*polylog(2,I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))/b^3+2*I/b^3*a*arccsc(b*x+a)+2/b^3*a*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))-4/b^3*ln(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))*a+2/b^3*a*ln(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2)-1)+1/3/b^3*arccsc(b*x+a)*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))-1/3/b^3*arccsc(b*x+a)*ln(1-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))+1/3*a^3*arccsc(b*x+a)^2/b^3+1/3/b^3*a+1/3*x/b^2-1/3*I*polylog(2,-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))/b^3-2*I*a^2*polylog(2,-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))/b^3","A"
29,1,250,173,0.342000," ","int(x*arccsc(b*x+a)^2,x)","-\frac{a^{2} \mathrm{arccsc}\left(b x +a \right)^{2}}{2 b^{2}}+\frac{2 a \,\mathrm{arccsc}\left(b x +a \right) \ln \left(1-\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{2}}-\frac{2 a \,\mathrm{arccsc}\left(b x +a \right) \ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{2}}+\frac{2 i a \dilog \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{2}}-\frac{2 i a \dilog \left(1-\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{2}}+\frac{x^{2} \mathrm{arccsc}\left(b x +a \right)^{2}}{2}+\frac{\sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \mathrm{arccsc}\left(b x +a \right) x}{b}+\frac{\sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \mathrm{arccsc}\left(b x +a \right) a}{b^{2}}-\frac{\ln \left(\frac{1}{b x +a}\right)}{b^{2}}"," ",0,"-1/2*a^2*arccsc(b*x+a)^2/b^2+2/b^2*a*arccsc(b*x+a)*ln(1-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))-2/b^2*a*arccsc(b*x+a)*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+2*I/b^2*a*dilog(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))-2*I/b^2*a*dilog(1-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))+1/2*x^2*arccsc(b*x+a)^2+1/b*((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)*arccsc(b*x+a)*x+1/b^2*((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)*arccsc(b*x+a)*a-1/b^2*ln(1/(b*x+a))","A"
30,1,167,120,0.241000," ","int(arccsc(b*x+a)^2,x)","x \mathrm{arccsc}\left(b x +a \right)^{2}+\frac{\mathrm{arccsc}\left(b x +a \right)^{2} a}{b}-\frac{2 \,\mathrm{arccsc}\left(b x +a \right) \ln \left(1-\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b}+\frac{2 \,\mathrm{arccsc}\left(b x +a \right) \ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b}-\frac{2 i \dilog \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b}+\frac{2 i \dilog \left(1-\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b}"," ",0,"x*arccsc(b*x+a)^2+1/b*arccsc(b*x+a)^2*a-2/b*arccsc(b*x+a)*ln(1-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))+2/b*arccsc(b*x+a)*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))-2*I/b*dilog(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+2*I/b*dilog(1-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))","A"
31,0,0,415,1.915000," ","int(arccsc(b*x+a)^2/x,x)","\int \frac{\mathrm{arccsc}\left(b x +a \right)^{2}}{x}\, dx"," ",0,"int(arccsc(b*x+a)^2/x,x)","F"
32,1,297,280,1.381000," ","int(arccsc(b*x+a)^2/x^2,x)","-\frac{b \mathrm{arccsc}\left(b x +a \right)^{2}}{a}-\frac{\mathrm{arccsc}\left(b x +a \right)^{2}}{x}-\frac{2 b \,\mathrm{arccsc}\left(b x +a \right) \ln \left(\frac{-a \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)+\sqrt{a^{2}-1}+i}{i+\sqrt{a^{2}-1}}\right)}{a \sqrt{a^{2}-1}}+\frac{2 b \,\mathrm{arccsc}\left(b x +a \right) \ln \left(\frac{a \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)+\sqrt{a^{2}-1}-i}{-i+\sqrt{a^{2}-1}}\right)}{a \sqrt{a^{2}-1}}-\frac{2 i b \dilog \left(\frac{a \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)+\sqrt{a^{2}-1}-i}{-i+\sqrt{a^{2}-1}}\right)}{a \sqrt{a^{2}-1}}+\frac{2 i b \dilog \left(\frac{-a \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)+\sqrt{a^{2}-1}+i}{i+\sqrt{a^{2}-1}}\right)}{a \sqrt{a^{2}-1}}"," ",0,"-b*arccsc(b*x+a)^2/a-arccsc(b*x+a)^2/x-2*b/a*arccsc(b*x+a)/(a^2-1)^(1/2)*ln((-a*(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+(a^2-1)^(1/2)+I)/(I+(a^2-1)^(1/2)))+2*b/a*arccsc(b*x+a)/(a^2-1)^(1/2)*ln((a*(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+(a^2-1)^(1/2)-I)/(-I+(a^2-1)^(1/2)))-2*I*b/a/(a^2-1)^(1/2)*dilog((a*(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+(a^2-1)^(1/2)-I)/(-I+(a^2-1)^(1/2)))+2*I*b/a/(a^2-1)^(1/2)*dilog((-a*(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+(a^2-1)^(1/2)+I)/(I+(a^2-1)^(1/2)))","A"
33,1,809,594,2.720000," ","int(x^2*arccsc(b*x+a)^3,x)","-\frac{6 i a \polylog \left(2, \frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}-\frac{i \mathrm{arccsc}\left(b x +a \right) \polylog \left(2, -\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}-\frac{2 \mathrm{arccsc}\left(b x +a \right)^{2} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, x a}{b^{2}}+\frac{i \mathrm{arccsc}\left(b x +a \right) \polylog \left(2, \frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}-\frac{6 i a \polylog \left(2, -\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}-\frac{\mathrm{arccsc}\left(b x +a \right)^{2} \ln \left(1-\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{2 b^{3}}+\frac{\mathrm{arccsc}\left(b x +a \right)^{2} \ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{2 b^{3}}+\frac{6 a^{2} \polylog \left(3, -\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}-\frac{6 a^{2} \polylog \left(3, \frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}+\frac{\mathrm{arccsc}\left(b x +a \right) x}{b^{2}}+\frac{\mathrm{arccsc}\left(b x +a \right) a}{b^{3}}-\frac{5 \mathrm{arccsc}\left(b x +a \right)^{2} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, a^{2}}{2 b^{3}}+\frac{\mathrm{arccsc}\left(b x +a \right)^{2} \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, x^{2}}{2 b}+\frac{a^{3} \mathrm{arccsc}\left(b x +a \right)^{3}}{3 b^{3}}-\frac{3 i a \mathrm{arccsc}\left(b x +a \right)^{2}}{b^{3}}+\frac{6 a \,\mathrm{arccsc}\left(b x +a \right) \ln \left(1-\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}+\frac{6 a \,\mathrm{arccsc}\left(b x +a \right) \ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}-\frac{3 a^{2} \mathrm{arccsc}\left(b x +a \right)^{2} \ln \left(1-\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}+\frac{3 a^{2} \mathrm{arccsc}\left(b x +a \right)^{2} \ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}+\frac{6 i a^{2} \mathrm{arccsc}\left(b x +a \right) \polylog \left(2, \frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}-\frac{6 i a^{2} \mathrm{arccsc}\left(b x +a \right) \polylog \left(2, -\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}+\frac{2 \arctanh \left(\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}+\frac{\polylog \left(3, -\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}-\frac{\polylog \left(3, \frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{3}}+\frac{x^{3} \mathrm{arccsc}\left(b x +a \right)^{3}}{3}"," ",0,"-2/b^2*arccsc(b*x+a)^2*((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)*x*a-3*I*a*arccsc(b*x+a)^2/b^3-1/2/b^3*arccsc(b*x+a)^2*ln(1-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))+1/2/b^3*arccsc(b*x+a)^2*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+1/b^2*arccsc(b*x+a)*x+1/b^3*arccsc(b*x+a)*a+6*I*a^2*arccsc(b*x+a)*polylog(2,I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))/b^3-6*I*a^2*arccsc(b*x+a)*polylog(2,-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))/b^3+6/b^3*a*arccsc(b*x+a)*ln(1-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))+6/b^3*a*arccsc(b*x+a)*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))-3/b^3*a^2*arccsc(b*x+a)^2*ln(1-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))+3/b^3*a^2*arccsc(b*x+a)^2*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))-5/2/b^3*arccsc(b*x+a)^2*((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)*a^2+1/2/b*arccsc(b*x+a)^2*((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)*x^2-6*I/b^3*a*polylog(2,I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))-I*arccsc(b*x+a)*polylog(2,-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))/b^3+I*arccsc(b*x+a)*polylog(2,I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))/b^3+1/3*a^3*arccsc(b*x+a)^3/b^3+2/b^3*arctanh(I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+polylog(3,-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))/b^3-polylog(3,I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))/b^3+1/3*x^3*arccsc(b*x+a)^3+6*a^2*polylog(3,-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))/b^3-6*a^2*polylog(3,I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))/b^3-6*I/b^3*a*polylog(2,-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))","A"
34,1,481,336,1.618000," ","int(x*arccsc(b*x+a)^3,x)","\frac{x^{2} \mathrm{arccsc}\left(b x +a \right)^{3}}{2}+\frac{3 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \mathrm{arccsc}\left(b x +a \right)^{2} x}{2 b}-\frac{a^{2} \mathrm{arccsc}\left(b x +a \right)^{3}}{2 b^{2}}+\frac{3 \sqrt{\frac{-1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \mathrm{arccsc}\left(b x +a \right)^{2} a}{2 b^{2}}+\frac{3 i \mathrm{arccsc}\left(b x +a \right)^{2}}{2 b^{2}}-\frac{3 a \mathrm{arccsc}\left(b x +a \right)^{2} \ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{2}}+\frac{3 a \mathrm{arccsc}\left(b x +a \right)^{2} \ln \left(1-\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{2}}-\frac{6 i a \,\mathrm{arccsc}\left(b x +a \right) \polylog \left(2, \frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{2}}+\frac{6 a \polylog \left(3, \frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{2}}-\frac{3 \,\mathrm{arccsc}\left(b x +a \right) \ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{2}}+\frac{6 i a \,\mathrm{arccsc}\left(b x +a \right) \polylog \left(2, -\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{2}}-\frac{6 a \polylog \left(3, -\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{2}}-\frac{3 \,\mathrm{arccsc}\left(b x +a \right) \ln \left(1-\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{2}}+\frac{3 i \polylog \left(2, \frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{2}}+\frac{3 i \polylog \left(2, -\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b^{2}}"," ",0,"1/2*x^2*arccsc(b*x+a)^3+3/2/b*((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)*arccsc(b*x+a)^2*x-1/2*a^2*arccsc(b*x+a)^3/b^2+3/2/b^2*((-1+(b*x+a)^2)/(b*x+a)^2)^(1/2)*arccsc(b*x+a)^2*a+3/2*I*arccsc(b*x+a)^2/b^2-3/b^2*a*arccsc(b*x+a)^2*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+3/b^2*a*arccsc(b*x+a)^2*ln(1-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))-6*I*a*arccsc(b*x+a)*polylog(2,I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))/b^2+6*a*polylog(3,I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))/b^2-3/b^2*arccsc(b*x+a)*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+6*I*a*arccsc(b*x+a)*polylog(2,-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))/b^2-6*a*polylog(3,-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))/b^2-3/b^2*arccsc(b*x+a)*ln(1-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))+3*I/b^2*polylog(2,I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+3*I/b^2*polylog(2,-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))","A"
35,1,247,198,0.632000," ","int(arccsc(b*x+a)^3,x)","x \mathrm{arccsc}\left(b x +a \right)^{3}+\frac{\mathrm{arccsc}\left(b x +a \right)^{3} a}{b}-\frac{3 \mathrm{arccsc}\left(b x +a \right)^{2} \ln \left(1-\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b}+\frac{3 \mathrm{arccsc}\left(b x +a \right)^{2} \ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b}+\frac{6 i \mathrm{arccsc}\left(b x +a \right) \polylog \left(2, \frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b}-\frac{6 i \mathrm{arccsc}\left(b x +a \right) \polylog \left(2, -\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b}+\frac{6 \polylog \left(3, -\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b}-\frac{6 \polylog \left(3, \frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{b}"," ",0,"x*arccsc(b*x+a)^3+1/b*arccsc(b*x+a)^3*a-3/b*arccsc(b*x+a)^2*ln(1-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))+3/b*arccsc(b*x+a)^2*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+6*I*arccsc(b*x+a)*polylog(2,I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))/b-6*I*arccsc(b*x+a)*polylog(2,-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))/b+6*polylog(3,-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))/b-6*polylog(3,I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))/b","A"
36,0,0,564,2.084000," ","int(arccsc(b*x+a)^3/x,x)","\int \frac{\mathrm{arccsc}\left(b x +a \right)^{3}}{x}\, dx"," ",0,"int(arccsc(b*x+a)^3/x,x)","F"
37,0,0,416,2.473000," ","int(arccsc(b*x+a)^3/x^2,x)","\int \frac{\mathrm{arccsc}\left(b x +a \right)^{3}}{x^{2}}\, dx"," ",0,"int(arccsc(b*x+a)^3/x^2,x)","F"
38,1,65,42,0.109000," ","int(x^3*arccsc(b*x^4+a),x)","\frac{\mathrm{arccsc}\left(b \,x^{4}+a \right) x^{4}}{4}+\frac{\mathrm{arccsc}\left(b \,x^{4}+a \right) a}{4 b}+\frac{\ln \left(b \,x^{4}+a +\left(b \,x^{4}+a \right) \sqrt{1-\frac{1}{\left(b \,x^{4}+a \right)^{2}}}\right)}{4 b}"," ",0,"1/4*arccsc(b*x^4+a)*x^4+1/4/b*arccsc(b*x^4+a)*a+1/4/b*ln(b*x^4+a+(b*x^4+a)*(1-1/(b*x^4+a)^2)^(1/2))","A"
39,0,0,46,0.085000," ","int(x^(n-1)*arccsc(a+b*x^n),x)","\int x^{n -1} \mathrm{arccsc}\left(a +b \,x^{n}\right)\, dx"," ",0,"int(x^(n-1)*arccsc(a+b*x^n),x)","F"
40,1,199,113,0.121000," ","int(arccsc(c*exp(b*x+a)),x)","\frac{i \mathrm{arccsc}\left(c \,{\mathrm e}^{b x +a}\right)^{2}}{2 b}-\frac{\mathrm{arccsc}\left(c \,{\mathrm e}^{b x +a}\right) \ln \left(1+\frac{i {\mathrm e}^{-b x -a}}{c}+\sqrt{1-\frac{{\mathrm e}^{-2 b x -2 a}}{c^{2}}}\right)}{b}-\frac{\mathrm{arccsc}\left(c \,{\mathrm e}^{b x +a}\right) \ln \left(1-\frac{i {\mathrm e}^{-b x -a}}{c}-\sqrt{1-\frac{{\mathrm e}^{-2 b x -2 a}}{c^{2}}}\right)}{b}+\frac{i \polylog \left(2, -\frac{i {\mathrm e}^{-b x -a}}{c}-\sqrt{1-\frac{{\mathrm e}^{-2 b x -2 a}}{c^{2}}}\right)}{b}+\frac{i \polylog \left(2, \frac{i {\mathrm e}^{-b x -a}}{c}+\sqrt{1-\frac{{\mathrm e}^{-2 b x -2 a}}{c^{2}}}\right)}{b}"," ",0,"1/2*I*arccsc(c*exp(b*x+a))^2/b-1/b*arccsc(c*exp(b*x+a))*ln(1+I/c/exp(b*x+a)+(1-1/c^2/exp(b*x+a)^2)^(1/2))-1/b*arccsc(c*exp(b*x+a))*ln(1-I/c/exp(b*x+a)-(1-1/c^2/exp(b*x+a)^2)^(1/2))+I/b*polylog(2,-I/c/exp(b*x+a)-(1-1/c^2/exp(b*x+a)^2)^(1/2))+I/b*polylog(2,I/c/exp(b*x+a)+(1-1/c^2/exp(b*x+a)^2)^(1/2))","A"
41,0,0,101,0.056000," ","int(exp(arccsc(a*x))*x^2,x)","\int {\mathrm e}^{\mathrm{arccsc}\left(a x \right)} x^{2}\, dx"," ",0,"int(exp(arccsc(a*x))*x^2,x)","F"
42,0,0,101,0.056000," ","int(exp(arccsc(a*x))*x,x)","\int {\mathrm e}^{\mathrm{arccsc}\left(a x \right)} x\, dx"," ",0,"int(exp(arccsc(a*x))*x,x)","F"
43,0,0,101,0.053000," ","int(exp(arccsc(a*x)),x)","\int {\mathrm e}^{\mathrm{arccsc}\left(a x \right)}\, dx"," ",0,"int(exp(arccsc(a*x)),x)","F"
44,0,0,50,0.056000," ","int(exp(arccsc(a*x))/x,x)","\int \frac{{\mathrm e}^{\mathrm{arccsc}\left(a x \right)}}{x}\, dx"," ",0,"int(exp(arccsc(a*x))/x,x)","F"
45,0,0,31,0.055000," ","int(exp(arccsc(a*x))/x^2,x)","\int \frac{{\mathrm e}^{\mathrm{arccsc}\left(a x \right)}}{x^{2}}\, dx"," ",0,"int(exp(arccsc(a*x))/x^2,x)","F"
46,0,0,35,0.056000," ","int(exp(arccsc(a*x))/x^3,x)","\int \frac{{\mathrm e}^{\mathrm{arccsc}\left(a x \right)}}{x^{3}}\, dx"," ",0,"int(exp(arccsc(a*x))/x^3,x)","F"
47,0,0,70,0.055000," ","int(exp(arccsc(a*x))/x^4,x)","\int \frac{{\mathrm e}^{\mathrm{arccsc}\left(a x \right)}}{x^{4}}\, dx"," ",0,"int(exp(arccsc(a*x))/x^4,x)","F"
48,0,0,69,0.053000," ","int(exp(arccsc(a*x))/x^5,x)","\int \frac{{\mathrm e}^{\mathrm{arccsc}\left(a x \right)}}{x^{5}}\, dx"," ",0,"int(exp(arccsc(a*x))/x^5,x)","F"
49,1,158,91,0.358000," ","int(arccsc(b*x+a)/(a*d/b+d*x),x)","\frac{i \mathrm{arccsc}\left(b x +a \right)^{2}}{2 d}-\frac{\mathrm{arccsc}\left(b x +a \right) \ln \left(1+\frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{d}+\frac{i \polylog \left(2, -\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{d}-\frac{\mathrm{arccsc}\left(b x +a \right) \ln \left(1-\frac{i}{b x +a}-\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{d}+\frac{i \polylog \left(2, \frac{i}{b x +a}+\sqrt{1-\frac{1}{\left(b x +a \right)^{2}}}\right)}{d}"," ",0,"1/2*I*arccsc(b*x+a)^2/d-1/d*arccsc(b*x+a)*ln(1+I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))+I/d*polylog(2,-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))-1/d*arccsc(b*x+a)*ln(1-I/(b*x+a)-(1-1/(b*x+a)^2)^(1/2))+I/d*polylog(2,I/(b*x+a)+(1-1/(b*x+a)^2)^(1/2))","A"