1,1,177,96,0.054000," ","int(x^6*(a+b*arccsc(c*x)),x)","\frac{x^{7} a}{7}+\frac{b \,x^{7} \mathrm{arccsc}\left(c x \right)}{7}+\frac{b \,x^{6}}{42 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,x^{4}}{168 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{5 b \,x^{2}}{336 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{5 b}{112 c^{7} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{5 b \sqrt{c^{2} x^{2}-1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{112 c^{8} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/7*x^7*a+1/7*b*x^7*arccsc(c*x)+1/42/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^6+1/168/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^4+5/336/c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2-5/112/c^7*b/((c^2*x^2-1)/c^2/x^2)^(1/2)+5/112/c^8*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*ln(c*x+(c^2*x^2-1)^(1/2))","A"
2,1,83,75,0.051000," ","int(x^5*(a+b*arccsc(c*x)),x)","\frac{\frac{c^{6} x^{6} a}{6}+b \left(\frac{c^{6} x^{6} \mathrm{arccsc}\left(c x \right)}{6}+\frac{\left(c^{2} x^{2}-1\right) \left(3 c^{4} x^{4}+4 c^{2} x^{2}+8\right)}{90 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c x}\right)}{c^{6}}"," ",0,"1/c^6*(1/6*c^6*x^6*a+b*(1/6*c^6*x^6*arccsc(c*x)+1/90*(c^2*x^2-1)*(3*c^4*x^4+4*c^2*x^2+8)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c/x))","A"
3,1,150,75,0.050000," ","int(x^4*(a+b*arccsc(c*x)),x)","\frac{a \,x^{5}}{5}+\frac{x^{5} b \,\mathrm{arccsc}\left(c x \right)}{5}+\frac{b \,x^{4}}{20 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,x^{2}}{40 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{3 b}{40 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{3 b \sqrt{c^{2} x^{2}-1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{40 c^{6} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/5*a*x^5+1/5*x^5*b*arccsc(c*x)+1/20/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^4+1/40/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2-3/40/c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)+3/40/c^6*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*ln(c*x+(c^2*x^2-1)^(1/2))","A"
4,1,74,54,0.049000," ","int(x^3*(a+b*arccsc(c*x)),x)","\frac{\frac{a \,c^{4} x^{4}}{4}+b \left(\frac{c^{4} x^{4} \mathrm{arccsc}\left(c x \right)}{4}+\frac{\left(c^{2} x^{2}-1\right) \left(c^{2} x^{2}+2\right)}{12 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c x}\right)}{c^{4}}"," ",0,"1/c^4*(1/4*a*c^4*x^4+b*(1/4*c^4*x^4*arccsc(c*x)+1/12*(c^2*x^2-1)*(c^2*x^2+2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c/x))","A"
5,1,123,54,0.051000," ","int(x^2*(a+b*arccsc(c*x)),x)","\frac{x^{3} a}{3}+\frac{x^{3} b \,\mathrm{arccsc}\left(c x \right)}{3}+\frac{b \,x^{2}}{6 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b}{6 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \sqrt{c^{2} x^{2}-1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{6 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/3*x^3*a+1/3*x^3*b*arccsc(c*x)+1/6/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2-1/6/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)+1/6/c^4*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*ln(c*x+(c^2*x^2-1)^(1/2))","B"
6,1,65,33,0.049000," ","int(x*(a+b*arccsc(c*x)),x)","\frac{\frac{c^{2} x^{2} a}{2}+b \left(\frac{c^{2} x^{2} \mathrm{arccsc}\left(c x \right)}{2}+\frac{c^{2} x^{2}-1}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c x}\right)}{c^{2}}"," ",0,"1/c^2*(1/2*c^2*x^2*a+b*(1/2*c^2*x^2*arccsc(c*x)+1/2/((c^2*x^2-1)/c^2/x^2)^(1/2)/c/x*(c^2*x^2-1)))","A"
7,1,37,29,0.048000," ","int(a+b*arccsc(c*x),x)","a x +b x \,\mathrm{arccsc}\left(c x \right)+\frac{b \ln \left(c x +c x \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c}"," ",0,"a*x+b*x*arccsc(c*x)+b/c*ln(c*x+c*x*(1-1/c^2/x^2)^(1/2))","A"
8,1,140,86,0.184000," ","int((a+b*arccsc(c*x))/x,x)","a \ln \left(c x \right)+\frac{i b \mathrm{arccsc}\left(c x \right)^{2}}{2}-b \,\mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-b \,\mathrm{arccsc}\left(c x \right) \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+i b \polylog \left(2, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+i b \polylog \left(2, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)"," ",0,"a*ln(c*x)+1/2*I*b*arccsc(c*x)^2-b*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))-b*arccsc(c*x)*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))+I*b*polylog(2,-I/c/x-(1-1/c^2/x^2)^(1/2))+I*b*polylog(2,I/c/x+(1-1/c^2/x^2)^(1/2))","A"
9,1,63,32,0.049000," ","int((a+b*arccsc(c*x))/x^2,x)","c \left(-\frac{a}{c x}+b \left(-\frac{\mathrm{arccsc}\left(c x \right)}{c x}-\frac{c^{2} x^{2}-1}{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{2} x^{2}}\right)\right)"," ",0,"c*(-a/c/x+b*(-1/c/x*arccsc(c*x)-1/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^2/x^2*(c^2*x^2-1)))","A"
10,1,118,46,0.050000," ","int((a+b*arccsc(c*x))/x^3,x)","-\frac{a}{2 x^{2}}-\frac{b \,\mathrm{arccsc}\left(c x \right)}{2 x^{2}}+\frac{c b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{c b}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{b}{4 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}"," ",0,"-1/2*a/x^2-1/2*b/x^2*arccsc(c*x)+1/4*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*arctan(1/(c^2*x^2-1)^(1/2))-1/4*c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x+1/4/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^3","B"
11,1,75,53,0.049000," ","int((a+b*arccsc(c*x))/x^4,x)","c^{3} \left(-\frac{a}{3 c^{3} x^{3}}+b \left(-\frac{\mathrm{arccsc}\left(c x \right)}{3 c^{3} x^{3}}-\frac{\left(c^{2} x^{2}-1\right) \left(2 c^{2} x^{2}+1\right)}{9 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{4} x^{4}}\right)\right)"," ",0,"c^3*(-1/3*a/c^3/x^3+b*(-1/3/c^3/x^3*arccsc(c*x)-1/9*(c^2*x^2-1)*(2*c^2*x^2+1)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^4/x^4))","A"
12,1,147,67,0.049000," ","int((a+b*arccsc(c*x))/x^5,x)","-\frac{a}{4 x^{4}}-\frac{b \,\mathrm{arccsc}\left(c x \right)}{4 x^{4}}+\frac{3 c^{3} b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{32 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{3 c^{3} b}{32 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{c b}{32 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}+\frac{b}{16 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{5}}"," ",0,"-1/4*a/x^4-1/4*b/x^4*arccsc(c*x)+3/32*c^3*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*arctan(1/(c^2*x^2-1)^(1/2))-3/32*c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x+1/32*c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^3+1/16/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^5","B"
13,1,83,71,0.049000," ","int((a+b*arccsc(c*x))/x^6,x)","c^{5} \left(-\frac{a}{5 c^{5} x^{5}}+b \left(-\frac{\mathrm{arccsc}\left(c x \right)}{5 c^{5} x^{5}}-\frac{\left(c^{2} x^{2}-1\right) \left(8 c^{4} x^{4}+4 c^{2} x^{2}+3\right)}{75 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{6} x^{6}}\right)\right)"," ",0,"c^5*(-1/5*a/c^5/x^5+b*(-1/5/c^5/x^5*arccsc(c*x)-1/75*(c^2*x^2-1)*(8*c^4*x^4+4*c^2*x^2+3)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^6/x^6))","A"
14,1,174,88,0.052000," ","int((a+b*arccsc(c*x))/x^7,x)","-\frac{a}{6 x^{6}}-\frac{b \,\mathrm{arccsc}\left(c x \right)}{6 x^{6}}+\frac{5 c^{5} b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{96 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{5 c^{5} b}{96 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{5 c^{3} b}{288 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}+\frac{c b}{144 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{5}}+\frac{b}{36 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{7}}"," ",0,"-1/6*a/x^6-1/6*b/x^6*arccsc(c*x)+5/96*c^5*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*arctan(1/(c^2*x^2-1)^(1/2))-5/96*c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x+5/288*c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^3+1/144*c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^5+1/36/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^7","A"
15,1,208,93,0.281000," ","int(x^3*(a+b*arccsc(c*x))^2,x)","\frac{a^{2} x^{4}}{4}+\frac{b^{2} \mathrm{arccsc}\left(c x \right)^{2} x^{4}}{4}+\frac{b^{2} \mathrm{arccsc}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}{6 c}+\frac{b^{2} x^{2}}{12 c^{2}}+\frac{b^{2} \mathrm{arccsc}\left(c x \right) x \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{3 c^{3}}-\frac{b^{2} \ln \left(\frac{1}{c x}\right)}{3 c^{4}}+\frac{a b \,x^{4} \mathrm{arccsc}\left(c x \right)}{2}+\frac{a b \,x^{3}}{6 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{a b x}{6 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{a b}{3 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/4*a^2*x^4+1/4*b^2*arccsc(c*x)^2*x^4+1/6/c*b^2*arccsc(c*x)*((c^2*x^2-1)/c^2/x^2)^(1/2)*x^3+1/12*b^2*x^2/c^2+1/3/c^3*b^2*arccsc(c*x)*x*((c^2*x^2-1)/c^2/x^2)^(1/2)-1/3/c^4*b^2*ln(1/c/x)+1/2*a*b*x^4*arccsc(c*x)+1/6/c*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^3+1/6/c^3*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x-1/3/c^5*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x","B"
16,1,327,159,1.255000," ","int(x^2*(a+b*arccsc(c*x))^2,x)","\frac{x^{3} a^{2}}{3}+\frac{b^{2} x^{3} \mathrm{arccsc}\left(c x \right)^{2}}{3}+\frac{b^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \mathrm{arccsc}\left(c x \right) x^{2}}{3 c}+\frac{b^{2} x}{3 c^{2}}+\frac{b^{2} \mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{3 c^{3}}-\frac{i b^{2} \polylog \left(2, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{3 c^{3}}-\frac{b^{2} \mathrm{arccsc}\left(c x \right) \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{3 c^{3}}+\frac{i b^{2} \polylog \left(2, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{3 c^{3}}+\frac{2 x^{3} a b \,\mathrm{arccsc}\left(c x \right)}{3}+\frac{a b \,x^{2}}{3 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{a b}{3 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{a b \sqrt{c^{2} x^{2}-1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{3 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/3*x^3*a^2+1/3*b^2*x^3*arccsc(c*x)^2+1/3/c*b^2*((c^2*x^2-1)/c^2/x^2)^(1/2)*arccsc(c*x)*x^2+1/3*b^2*x/c^2+1/3/c^3*b^2*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))-1/3*I*b^2*polylog(2,-I/c/x-(1-1/c^2/x^2)^(1/2))/c^3-1/3/c^3*b^2*arccsc(c*x)*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))+1/3*I*b^2*polylog(2,I/c/x+(1-1/c^2/x^2)^(1/2))/c^3+2/3*x^3*a*b*arccsc(c*x)+1/3/c*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2-1/3/c^3*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)+1/3/c^4*a*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*ln(c*x+(c^2*x^2-1)^(1/2))","B"
17,1,133,51,0.265000," ","int(x*(a+b*arccsc(c*x))^2,x)","\frac{a^{2} x^{2}}{2}+\frac{x^{2} b^{2} \mathrm{arccsc}\left(c x \right)^{2}}{2}+\frac{b^{2} \mathrm{arccsc}\left(c x \right) x \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{c}-\frac{b^{2} \ln \left(\frac{1}{c x}\right)}{c^{2}}+a b \,x^{2} \mathrm{arccsc}\left(c x \right)+\frac{a b x}{c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{a b}{c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/2*a^2*x^2+1/2*x^2*b^2*arccsc(c*x)^2+1/c*b^2*arccsc(c*x)*x*((c^2*x^2-1)/c^2/x^2)^(1/2)-1/c^2*b^2*ln(1/c/x)+a*b*x^2*arccsc(c*x)+1/c*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x-1/c^3*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x","B"
18,1,196,118,0.264000," ","int((a+b*arccsc(c*x))^2,x)","x \,b^{2} \mathrm{arccsc}\left(c x \right)^{2}+2 x a b \,\mathrm{arccsc}\left(c x \right)-\frac{2 b^{2} \mathrm{arccsc}\left(c x \right) \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c}+\frac{2 b^{2} \mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c}-\frac{2 i \dilog \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right) b^{2}}{c}+\frac{2 i \dilog \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right) b^{2}}{c}+a^{2} x +\frac{2 \ln \left(c x +c x \sqrt{1-\frac{1}{c^{2} x^{2}}}\right) a b}{c}"," ",0,"x*b^2*arccsc(c*x)^2+2*x*a*b*arccsc(c*x)-2/c*b^2*arccsc(c*x)*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))+2/c*b^2*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))-2*I/c*dilog(1+I/c/x+(1-1/c^2/x^2)^(1/2))*b^2+2*I/c*dilog(1-I/c/x-(1-1/c^2/x^2)^(1/2))*b^2+a^2*x+2/c*ln(c*x+c*x*(1-1/c^2/x^2)^(1/2))*a*b","A"
19,1,361,127,0.219000," ","int((a+b*arccsc(c*x))^2/x,x)","a^{2} \ln \left(c x \right)+\frac{i b^{2} \mathrm{arccsc}\left(c x \right)^{3}}{3}-b^{2} \mathrm{arccsc}\left(c x \right)^{2} \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+2 i b^{2} \mathrm{arccsc}\left(c x \right) \polylog \left(2, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-2 b^{2} \polylog \left(3, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-b^{2} \mathrm{arccsc}\left(c x \right)^{2} \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+2 i b^{2} \mathrm{arccsc}\left(c x \right) \polylog \left(2, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-2 b^{2} \polylog \left(3, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+i a b \mathrm{arccsc}\left(c x \right)^{2}-2 a b \,\mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-2 a b \,\mathrm{arccsc}\left(c x \right) \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+2 i a b \polylog \left(2, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+2 i a b \polylog \left(2, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)"," ",0,"a^2*ln(c*x)+1/3*I*b^2*arccsc(c*x)^3-b^2*arccsc(c*x)^2*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))+2*I*b^2*arccsc(c*x)*polylog(2,-I/c/x-(1-1/c^2/x^2)^(1/2))-2*b^2*polylog(3,-I/c/x-(1-1/c^2/x^2)^(1/2))-b^2*arccsc(c*x)^2*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))+2*I*b^2*arccsc(c*x)*polylog(2,I/c/x+(1-1/c^2/x^2)^(1/2))-2*b^2*polylog(3,I/c/x+(1-1/c^2/x^2)^(1/2))+I*a*b*arccsc(c*x)^2-2*a*b*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))-2*a*b*arccsc(c*x)*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))+2*I*a*b*polylog(2,-I/c/x-(1-1/c^2/x^2)^(1/2))+2*I*a*b*polylog(2,I/c/x+(1-1/c^2/x^2)^(1/2))","B"
20,1,118,48,0.179000," ","int((a+b*arccsc(c*x))^2/x^2,x)","c \left(-\frac{a^{2}}{c x}+b^{2} \left(-\frac{\mathrm{arccsc}\left(c x \right)^{2}}{c x}+\frac{2}{c x}-2 \,\mathrm{arccsc}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\right)+2 a b \left(-\frac{\mathrm{arccsc}\left(c x \right)}{c x}-\frac{c^{2} x^{2}-1}{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{2} x^{2}}\right)\right)"," ",0,"c*(-a^2/c/x+b^2*(-1/c/x*arccsc(c*x)^2+2/c/x-2*arccsc(c*x)*((c^2*x^2-1)/c^2/x^2)^(1/2))+2*a*b*(-1/c/x*arccsc(c*x)-1/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^2/x^2*(c^2*x^2-1)))","B"
21,1,191,76,0.148000," ","int((a+b*arccsc(c*x))^2/x^3,x)","-\frac{a^{2}}{2 x^{2}}+\frac{b^{2} c^{2} \mathrm{arccsc}\left(c x \right)^{2}}{4}-\frac{b^{2} \mathrm{arccsc}\left(c x \right)^{2}}{2 x^{2}}-\frac{c \,b^{2} \mathrm{arccsc}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{2 x}+\frac{b^{2}}{4 x^{2}}-\frac{a b \,\mathrm{arccsc}\left(c x \right)}{x^{2}}+\frac{c a b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{c a b}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{a b}{2 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}"," ",0,"-1/2*a^2/x^2+1/4*b^2*c^2*arccsc(c*x)^2-1/2*b^2*arccsc(c*x)^2/x^2-1/2*c*b^2*arccsc(c*x)/x*((c^2*x^2-1)/c^2/x^2)^(1/2)+1/4*b^2/x^2-a*b/x^2*arccsc(c*x)+1/2*c*a*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*arctan(1/(c^2*x^2-1)^(1/2))-1/2*c*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x+1/2/c*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^3","B"
22,1,154,88,0.566000," ","int((a+b*arccsc(c*x))^2/x^4,x)","c^{3} \left(-\frac{a^{2}}{3 c^{3} x^{3}}+b^{2} \left(-\frac{\mathrm{arccsc}\left(c x \right)^{2}}{3 c^{3} x^{3}}-\frac{2 \,\mathrm{arccsc}\left(c x \right) \left(2 c^{2} x^{2}+1\right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{9 c^{2} x^{2}}+\frac{2}{27 c^{3} x^{3}}+\frac{4}{9 c x}\right)+2 a b \left(-\frac{\mathrm{arccsc}\left(c x \right)}{3 c^{3} x^{3}}-\frac{\left(c^{2} x^{2}-1\right) \left(2 c^{2} x^{2}+1\right)}{9 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{4} x^{4}}\right)\right)"," ",0,"c^3*(-1/3*a^2/c^3/x^3+b^2*(-1/3/c^3/x^3*arccsc(c*x)^2-2/9*arccsc(c*x)*(2*c^2*x^2+1)/c^2/x^2*((c^2*x^2-1)/c^2/x^2)^(1/2)+2/27/c^3/x^3+4/9/c/x)+2*a*b*(-1/3/c^3/x^3*arccsc(c*x)-1/9*(c^2*x^2-1)*(2*c^2*x^2+1)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^4/x^4))","A"
23,1,265,116,0.464000," ","int((a+b*arccsc(c*x))^2/x^5,x)","-\frac{a^{2}}{4 x^{4}}-\frac{b^{2} \mathrm{arccsc}\left(c x \right)^{2}}{4 x^{4}}+\frac{3 b^{2} c^{4} \mathrm{arccsc}\left(c x \right)^{2}}{32}-\frac{3 c^{3} b^{2} \mathrm{arccsc}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{16 x}-\frac{c \,b^{2} \mathrm{arccsc}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{8 x^{3}}+\frac{b^{2}}{32 x^{4}}+\frac{3 b^{2} c^{2}}{32 x^{2}}-\frac{a b \,\mathrm{arccsc}\left(c x \right)}{2 x^{4}}+\frac{3 c^{3} a b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{3 c^{3} a b}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{c a b}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}+\frac{a b}{8 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{5}}"," ",0,"-1/4*a^2/x^4-1/4*b^2/x^4*arccsc(c*x)^2+3/32*b^2*c^4*arccsc(c*x)^2-3/16*c^3*b^2*arccsc(c*x)/x*((c^2*x^2-1)/c^2/x^2)^(1/2)-1/8*c*b^2*arccsc(c*x)/x^3*((c^2*x^2-1)/c^2/x^2)^(1/2)+1/32*b^2/x^4+3/32*b^2*c^2/x^2-1/2*a*b/x^4*arccsc(c*x)+3/16*c^3*a*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*arctan(1/(c^2*x^2-1)^(1/2))-3/16*c^3*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x+1/16*c*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^3+1/8/c*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^5","B"
24,1,510,213,1.064000," ","int(x^3*(a+b*arccsc(c*x))^3,x)","\frac{x^{4} a^{3}}{4}+\frac{b^{3} \mathrm{arccsc}\left(c x \right)^{3} x^{4}}{4}+\frac{b^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \mathrm{arccsc}\left(c x \right)^{2} x^{3}}{4 c}+\frac{b^{3} \mathrm{arccsc}\left(c x \right)^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}{2 c^{3}}+\frac{i b^{3} \mathrm{arccsc}\left(c x \right)^{2}}{2 c^{4}}+\frac{b^{3} \mathrm{arccsc}\left(c x \right) x^{2}}{4 c^{2}}+\frac{b^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}{4 c^{3}}+\frac{i b^{3} \polylog \left(2, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{4}}-\frac{b^{3} \mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{4}}-\frac{b^{3} \mathrm{arccsc}\left(c x \right) \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{4}}+\frac{i b^{3} \polylog \left(2, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{4}}-\frac{i b^{3}}{4 c^{4}}+\frac{3 a^{2} b \,x^{4} \mathrm{arccsc}\left(c x \right)}{4}+\frac{a^{2} b \,x^{3}}{4 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{a^{2} b x}{4 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{a^{2} b}{2 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{3 a \,b^{2} \mathrm{arccsc}\left(c x \right)^{2} x^{4}}{4}+\frac{a \,b^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \mathrm{arccsc}\left(c x \right) x^{3}}{2 c}+\frac{x^{2} a \,b^{2}}{4 c^{2}}+\frac{a \,b^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \mathrm{arccsc}\left(c x \right) x}{c^{3}}-\frac{a \,b^{2} \ln \left(\frac{1}{c x}\right)}{c^{4}}"," ",0,"1/4*x^4*a^3+1/4*b^3*arccsc(c*x)^3*x^4+1/4/c*b^3*((c^2*x^2-1)/c^2/x^2)^(1/2)*arccsc(c*x)^2*x^3+1/2/c^3*b^3*arccsc(c*x)^2*((c^2*x^2-1)/c^2/x^2)^(1/2)*x+1/2*I/c^4*b^3*arccsc(c*x)^2+1/4/c^2*b^3*arccsc(c*x)*x^2+1/4/c^3*b^3*((c^2*x^2-1)/c^2/x^2)^(1/2)*x+I/c^4*b^3*polylog(2,I/c/x+(1-1/c^2/x^2)^(1/2))-1/c^4*b^3*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))-1/c^4*b^3*arccsc(c*x)*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))+I/c^4*b^3*polylog(2,-I/c/x-(1-1/c^2/x^2)^(1/2))-1/4*I/c^4*b^3+3/4*a^2*b*x^4*arccsc(c*x)+1/4/c*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^3+1/4/c^3*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x-1/2/c^5*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x+3/4*a*b^2*arccsc(c*x)^2*x^4+1/2/c*a*b^2*((c^2*x^2-1)/c^2/x^2)^(1/2)*arccsc(c*x)*x^3+1/4/c^2*x^2*a*b^2+1/c^3*a*b^2*((c^2*x^2-1)/c^2/x^2)^(1/2)*arccsc(c*x)*x-1/c^4*a*b^2*ln(1/c/x)","B"
25,1,648,270,1.547000," ","int(x^2*(a+b*arccsc(c*x))^3,x)","\frac{a^{3} x^{3}}{3}+\frac{x^{3} b^{3} \mathrm{arccsc}\left(c x \right)^{3}}{3}+\frac{b^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \mathrm{arccsc}\left(c x \right)^{2} x^{2}}{2 c}+\frac{b^{3} \mathrm{arccsc}\left(c x \right) x}{c^{2}}-\frac{b^{3} \mathrm{arccsc}\left(c x \right)^{2} \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{2 c^{3}}+\frac{i b^{3} \mathrm{arccsc}\left(c x \right) \polylog \left(2, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{3}}-\frac{b^{3} \polylog \left(3, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{3}}+\frac{b^{3} \mathrm{arccsc}\left(c x \right)^{2} \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{2 c^{3}}-\frac{i a \,b^{2} \polylog \left(2, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{3}}+\frac{b^{3} \polylog \left(3, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{3}}+\frac{2 b^{3} \arctanh \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{3}}+b^{2} x^{3} a \mathrm{arccsc}\left(c x \right)^{2}+\frac{a \,b^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \mathrm{arccsc}\left(c x \right) x^{2}}{c}-\frac{i b^{3} \mathrm{arccsc}\left(c x \right) \polylog \left(2, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{3}}+\frac{i a \,b^{2} \polylog \left(2, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{3}}-\frac{a \,b^{2} \mathrm{arccsc}\left(c x \right) \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{3}}+\frac{a \,b^{2} \mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{3}}+\frac{a \,b^{2} x}{c^{2}}+x^{3} a^{2} b \,\mathrm{arccsc}\left(c x \right)+\frac{a^{2} b \,x^{2}}{2 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{a^{2} b}{2 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{a^{2} b \sqrt{c^{2} x^{2}-1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{2 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/3*a^3*x^3+1/3*x^3*b^3*arccsc(c*x)^3+1/2/c*b^3*((c^2*x^2-1)/c^2/x^2)^(1/2)*arccsc(c*x)^2*x^2+1/c^2*b^3*arccsc(c*x)*x-1/2/c^3*b^3*arccsc(c*x)^2*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))+I/c^3*b^3*arccsc(c*x)*polylog(2,I/c/x+(1-1/c^2/x^2)^(1/2))-b^3*polylog(3,I/c/x+(1-1/c^2/x^2)^(1/2))/c^3+1/2/c^3*b^3*arccsc(c*x)^2*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))+I/c^3*a*b^2*polylog(2,I/c/x+(1-1/c^2/x^2)^(1/2))+b^3*polylog(3,-I/c/x-(1-1/c^2/x^2)^(1/2))/c^3+2/c^3*b^3*arctanh(I/c/x+(1-1/c^2/x^2)^(1/2))+b^2*x^3*a*arccsc(c*x)^2+1/c*a*b^2*((c^2*x^2-1)/c^2/x^2)^(1/2)*arccsc(c*x)*x^2-I/c^3*b^3*arccsc(c*x)*polylog(2,-I/c/x-(1-1/c^2/x^2)^(1/2))-I/c^3*a*b^2*polylog(2,-I/c/x-(1-1/c^2/x^2)^(1/2))-1/c^3*a*b^2*arccsc(c*x)*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))+1/c^3*a*b^2*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))+a*b^2*x/c^2+x^3*a^2*b*arccsc(c*x)+1/2/c*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2-1/2/c^3*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)+1/2/c^4*a^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*ln(c*x+(c^2*x^2-1)^(1/2))","B"
26,1,349,142,0.875000," ","int(x*(a+b*arccsc(c*x))^3,x)","\frac{x^{2} a^{3}}{2}+\frac{x^{2} b^{3} \mathrm{arccsc}\left(c x \right)^{3}}{2}+\frac{3 b^{3} \mathrm{arccsc}\left(c x \right)^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}{2 c}+\frac{3 i b^{3} \mathrm{arccsc}\left(c x \right)^{2}}{2 c^{2}}-\frac{3 b^{3} \mathrm{arccsc}\left(c x \right) \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{2}}-\frac{3 b^{3} \mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{2}}+\frac{3 i b^{3} \polylog \left(2, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{2}}+\frac{3 i b^{3} \polylog \left(2, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{2}}+\frac{3 x^{2} a \,b^{2} \mathrm{arccsc}\left(c x \right)^{2}}{2}+\frac{3 a \,b^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \mathrm{arccsc}\left(c x \right) x}{c}-\frac{3 a \,b^{2} \ln \left(\frac{1}{c x}\right)}{c^{2}}+\frac{3 a^{2} b \,x^{2} \mathrm{arccsc}\left(c x \right)}{2}+\frac{3 a^{2} b x}{2 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{3 a^{2} b}{2 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/2*x^2*a^3+1/2*x^2*b^3*arccsc(c*x)^3+3/2/c*b^3*arccsc(c*x)^2*((c^2*x^2-1)/c^2/x^2)^(1/2)*x+3/2*I/c^2*b^3*arccsc(c*x)^2-3/c^2*b^3*arccsc(c*x)*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))-3/c^2*b^3*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))+3*I/c^2*b^3*polylog(2,-I/c/x-(1-1/c^2/x^2)^(1/2))+3*I/c^2*b^3*polylog(2,I/c/x+(1-1/c^2/x^2)^(1/2))+3/2*x^2*a*b^2*arccsc(c*x)^2+3/c*a*b^2*((c^2*x^2-1)/c^2/x^2)^(1/2)*arccsc(c*x)*x-3/c^2*a*b^2*ln(1/c/x)+3/2*a^2*b*x^2*arccsc(c*x)+3/2/c*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x-3/2/c^3*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x","B"
27,1,437,202,0.763000," ","int((a+b*arccsc(c*x))^3,x)","x \,b^{3} \mathrm{arccsc}\left(c x \right)^{3}+3 x a \,b^{2} \mathrm{arccsc}\left(c x \right)^{2}+\frac{3 b^{3} \mathrm{arccsc}\left(c x \right)^{2} \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c}-\frac{3 b^{3} \mathrm{arccsc}\left(c x \right)^{2} \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c}-\frac{6 i \polylog \left(2, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right) \mathrm{arccsc}\left(c x \right) b^{3}}{c}+\frac{6 i b^{3} \mathrm{arccsc}\left(c x \right) \polylog \left(2, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c}+3 x \,a^{2} b \,\mathrm{arccsc}\left(c x \right)+\frac{6 i \dilog \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right) a \,b^{2}}{c}-\frac{6 i \dilog \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right) a \,b^{2}}{c}+\frac{6 a \,b^{2} \mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c}-\frac{6 a \,b^{2} \mathrm{arccsc}\left(c x \right) \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c}+x \,a^{3}+\frac{6 b^{3} \polylog \left(3, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c}-\frac{6 b^{3} \polylog \left(3, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c}+\frac{3 \ln \left(c x +c x \sqrt{1-\frac{1}{c^{2} x^{2}}}\right) a^{2} b}{c}"," ",0,"x*b^3*arccsc(c*x)^3+3*x*a*b^2*arccsc(c*x)^2+3/c*b^3*arccsc(c*x)^2*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))-3/c*b^3*arccsc(c*x)^2*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))-6*I/c*polylog(2,-I/c/x-(1-1/c^2/x^2)^(1/2))*arccsc(c*x)*b^3+6*I/c*b^3*arccsc(c*x)*polylog(2,I/c/x+(1-1/c^2/x^2)^(1/2))+3*x*a^2*b*arccsc(c*x)+6*I/c*dilog(1-I/c/x-(1-1/c^2/x^2)^(1/2))*a*b^2-6*I/c*dilog(1+I/c/x+(1-1/c^2/x^2)^(1/2))*a*b^2+6/c*a*b^2*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))-6/c*a*b^2*arccsc(c*x)*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))+x*a^3+6*b^3*polylog(3,-I/c/x-(1-1/c^2/x^2)^(1/2))/c-6*b^3*polylog(3,I/c/x+(1-1/c^2/x^2)^(1/2))/c+3/c*ln(c*x+c*x*(1-1/c^2/x^2)^(1/2))*a^2*b","B"
28,1,666,169,0.265000," ","int((a+b*arccsc(c*x))^3/x,x)","a^{3} \ln \left(c x \right)+3 i a^{2} b \polylog \left(2, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-b^{3} \mathrm{arccsc}\left(c x \right)^{3} \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+6 i a \,b^{2} \mathrm{arccsc}\left(c x \right) \polylog \left(2, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-6 b^{3} \mathrm{arccsc}\left(c x \right) \polylog \left(3, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+3 i b^{3} \mathrm{arccsc}\left(c x \right)^{2} \polylog \left(2, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-b^{3} \mathrm{arccsc}\left(c x \right)^{3} \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+3 i b^{3} \mathrm{arccsc}\left(c x \right)^{2} \polylog \left(2, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-6 b^{3} \mathrm{arccsc}\left(c x \right) \polylog \left(3, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+6 i a \,b^{2} \mathrm{arccsc}\left(c x \right) \polylog \left(2, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+\frac{i b^{3} \mathrm{arccsc}\left(c x \right)^{4}}{4}-3 a \,b^{2} \mathrm{arccsc}\left(c x \right)^{2} \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+i a \,b^{2} \mathrm{arccsc}\left(c x \right)^{3}-3 a \,b^{2} \mathrm{arccsc}\left(c x \right)^{2} \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-6 i b^{3} \polylog \left(4, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-6 a \,b^{2} \polylog \left(3, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-6 a \,b^{2} \polylog \left(3, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-6 i b^{3} \polylog \left(4, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-3 a^{2} b \,\mathrm{arccsc}\left(c x \right) \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-3 a^{2} b \,\mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+\frac{3 i a^{2} b \mathrm{arccsc}\left(c x \right)^{2}}{2}+3 i a^{2} b \polylog \left(2, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)"," ",0,"a^3*ln(c*x)-6*I*b^3*polylog(4,-I/c/x-(1-1/c^2/x^2)^(1/2))-b^3*arccsc(c*x)^3*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))+1/4*I*b^3*arccsc(c*x)^4-6*b^3*arccsc(c*x)*polylog(3,-I/c/x-(1-1/c^2/x^2)^(1/2))+I*a*b^2*arccsc(c*x)^3-b^3*arccsc(c*x)^3*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))+3*I*b^3*arccsc(c*x)^2*polylog(2,-I/c/x-(1-1/c^2/x^2)^(1/2))-6*b^3*arccsc(c*x)*polylog(3,I/c/x+(1-1/c^2/x^2)^(1/2))+6*I*a*b^2*arccsc(c*x)*polylog(2,-I/c/x-(1-1/c^2/x^2)^(1/2))+3*I*a^2*b*polylog(2,-I/c/x-(1-1/c^2/x^2)^(1/2))-3*a*b^2*arccsc(c*x)^2*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))+3/2*I*a^2*b*arccsc(c*x)^2-3*a*b^2*arccsc(c*x)^2*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))-6*I*b^3*polylog(4,I/c/x+(1-1/c^2/x^2)^(1/2))-6*a*b^2*polylog(3,-I/c/x-(1-1/c^2/x^2)^(1/2))-6*a*b^2*polylog(3,I/c/x+(1-1/c^2/x^2)^(1/2))+3*I*b^3*arccsc(c*x)^2*polylog(2,I/c/x+(1-1/c^2/x^2)^(1/2))-3*a^2*b*arccsc(c*x)*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))-3*a^2*b*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))+3*I*a^2*b*polylog(2,I/c/x+(1-1/c^2/x^2)^(1/2))+6*I*a*b^2*arccsc(c*x)*polylog(2,I/c/x+(1-1/c^2/x^2)^(1/2))","B"
29,1,199,76,0.219000," ","int((a+b*arccsc(c*x))^3/x^2,x)","c \left(-\frac{a^{3}}{c x}+b^{3} \left(-\frac{\mathrm{arccsc}\left(c x \right)^{3}}{c x}-3 \mathrm{arccsc}\left(c x \right)^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}+6 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}+\frac{6 \,\mathrm{arccsc}\left(c x \right)}{c x}\right)+3 a \,b^{2} \left(-\frac{\mathrm{arccsc}\left(c x \right)^{2}}{c x}+\frac{2}{c x}-2 \,\mathrm{arccsc}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\right)+3 a^{2} b \left(-\frac{\mathrm{arccsc}\left(c x \right)}{c x}-\frac{c^{2} x^{2}-1}{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{2} x^{2}}\right)\right)"," ",0,"c*(-a^3/c/x+b^3*(-1/c/x*arccsc(c*x)^3-3*arccsc(c*x)^2*((c^2*x^2-1)/c^2/x^2)^(1/2)+6*((c^2*x^2-1)/c^2/x^2)^(1/2)+6/c/x*arccsc(c*x))+3*a*b^2*(-1/c/x*arccsc(c*x)^2+2/c/x-2*arccsc(c*x)*((c^2*x^2-1)/c^2/x^2)^(1/2))+3*a^2*b*(-1/c/x*arccsc(c*x)-1/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^2/x^2*(c^2*x^2-1)))","B"
30,1,315,109,0.383000," ","int((a+b*arccsc(c*x))^3/x^3,x)","-\frac{a^{3}}{2 x^{2}}+\frac{c^{2} b^{3} \mathrm{arccsc}\left(c x \right)^{3}}{4}-\frac{b^{3} \mathrm{arccsc}\left(c x \right)^{3}}{2 x^{2}}-\frac{3 c \,b^{3} \mathrm{arccsc}\left(c x \right)^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{4 x}-\frac{3 b^{3} c^{2} \mathrm{arccsc}\left(c x \right)}{8}+\frac{3 b^{3} \mathrm{arccsc}\left(c x \right)}{4 x^{2}}+\frac{3 c \,b^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{8 x}+\frac{3 c^{2} a \,b^{2} \mathrm{arccsc}\left(c x \right)^{2}}{4}-\frac{3 a \,b^{2} \mathrm{arccsc}\left(c x \right)^{2}}{2 x^{2}}-\frac{3 c a \,b^{2} \mathrm{arccsc}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{2 x}+\frac{3 a \,b^{2}}{4 x^{2}}-\frac{3 a^{2} b \,\mathrm{arccsc}\left(c x \right)}{2 x^{2}}+\frac{3 c \,a^{2} b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{3 c \,a^{2} b}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{3 a^{2} b}{4 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}"," ",0,"-1/2*a^3/x^2+1/4*c^2*b^3*arccsc(c*x)^3-1/2*b^3*arccsc(c*x)^3/x^2-3/4*c*b^3*arccsc(c*x)^2/x*((c^2*x^2-1)/c^2/x^2)^(1/2)-3/8*b^3*c^2*arccsc(c*x)+3/4*b^3/x^2*arccsc(c*x)+3/8*c*b^3*((c^2*x^2-1)/c^2/x^2)^(1/2)/x+3/4*c^2*a*b^2*arccsc(c*x)^2-3/2*a*b^2*arccsc(c*x)^2/x^2-3/2*c*a*b^2*arccsc(c*x)/x*((c^2*x^2-1)/c^2/x^2)^(1/2)+3/4*a*b^2/x^2-3/2*a^2*b/x^2*arccsc(c*x)+3/4*c*a^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*arctan(1/(c^2*x^2-1)^(1/2))-3/4*c*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x+3/4/c*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^3","B"
31,1,299,148,0.594000," ","int((a+b*arccsc(c*x))^3/x^4,x)","c^{3} \left(-\frac{a^{3}}{3 c^{3} x^{3}}+b^{3} \left(-\frac{\mathrm{arccsc}\left(c x \right)^{3}}{3 c^{3} x^{3}}-\frac{\mathrm{arccsc}\left(c x \right)^{2} \left(2 c^{2} x^{2}+1\right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{3 c^{2} x^{2}}+\frac{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{3}+\frac{4 \,\mathrm{arccsc}\left(c x \right)}{3 c x}+\frac{2 \,\mathrm{arccsc}\left(c x \right)}{9 c^{3} x^{3}}+\frac{2 \left(2 c^{2} x^{2}+1\right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{27 c^{2} x^{2}}\right)+3 a \,b^{2} \left(-\frac{\mathrm{arccsc}\left(c x \right)^{2}}{3 c^{3} x^{3}}-\frac{2 \,\mathrm{arccsc}\left(c x \right) \left(2 c^{2} x^{2}+1\right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{9 c^{2} x^{2}}+\frac{2}{27 c^{3} x^{3}}+\frac{4}{9 c x}\right)+3 a^{2} b \left(-\frac{\mathrm{arccsc}\left(c x \right)}{3 c^{3} x^{3}}-\frac{\left(c^{2} x^{2}-1\right) \left(2 c^{2} x^{2}+1\right)}{9 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{4} x^{4}}\right)\right)"," ",0,"c^3*(-1/3*a^3/c^3/x^3+b^3*(-1/3/c^3/x^3*arccsc(c*x)^3-1/3*arccsc(c*x)^2*(2*c^2*x^2+1)/c^2/x^2*((c^2*x^2-1)/c^2/x^2)^(1/2)+4/3*((c^2*x^2-1)/c^2/x^2)^(1/2)+4/3/c/x*arccsc(c*x)+2/9/c^3/x^3*arccsc(c*x)+2/27*(2*c^2*x^2+1)/c^2/x^2*((c^2*x^2-1)/c^2/x^2)^(1/2))+3*a*b^2*(-1/3/c^3/x^3*arccsc(c*x)^2-2/9*arccsc(c*x)*(2*c^2*x^2+1)/c^2/x^2*((c^2*x^2-1)/c^2/x^2)^(1/2)+2/27/c^3/x^3+4/9/c/x)+3*a^2*b*(-1/3/c^3/x^3*arccsc(c*x)-1/9*(c^2*x^2-1)*(2*c^2*x^2+1)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^4/x^4))","B"
32,1,472,182,0.757000," ","int((a+b*arccsc(c*x))^3/x^5,x)","-\frac{a^{3}}{4 x^{4}}-\frac{b^{3} \mathrm{arccsc}\left(c x \right)^{3}}{4 x^{4}}+\frac{3 c^{4} b^{3} \mathrm{arccsc}\left(c x \right)^{3}}{32}-\frac{9 c^{3} b^{3} \mathrm{arccsc}\left(c x \right)^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{32 x}-\frac{3 c \,b^{3} \mathrm{arccsc}\left(c x \right)^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{16 x^{3}}+\frac{3 b^{3} \mathrm{arccsc}\left(c x \right)}{32 x^{4}}+\frac{45 c^{3} b^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{256 x}+\frac{3 c \,b^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{128 x^{3}}-\frac{45 b^{3} c^{4} \mathrm{arccsc}\left(c x \right)}{256}+\frac{9 c^{2} b^{3} \mathrm{arccsc}\left(c x \right)}{32 x^{2}}-\frac{3 a \,b^{2} \mathrm{arccsc}\left(c x \right)^{2}}{4 x^{4}}+\frac{9 c^{4} a \,b^{2} \mathrm{arccsc}\left(c x \right)^{2}}{32}-\frac{9 c^{3} a \,b^{2} \mathrm{arccsc}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{16 x}-\frac{3 c a \,b^{2} \mathrm{arccsc}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{8 x^{3}}+\frac{3 a \,b^{2}}{32 x^{4}}+\frac{9 c^{2} a \,b^{2}}{32 x^{2}}-\frac{3 a^{2} b \,\mathrm{arccsc}\left(c x \right)}{4 x^{4}}+\frac{9 c^{3} a^{2} b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{32 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{9 c^{3} a^{2} b}{32 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{3 c \,a^{2} b}{32 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}+\frac{3 a^{2} b}{16 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{5}}"," ",0,"-1/4*a^3/x^4-1/4*b^3/x^4*arccsc(c*x)^3+3/32*c^4*b^3*arccsc(c*x)^3-9/32*c^3*b^3*arccsc(c*x)^2/x*((c^2*x^2-1)/c^2/x^2)^(1/2)-3/16*c*b^3*arccsc(c*x)^2/x^3*((c^2*x^2-1)/c^2/x^2)^(1/2)+3/32*b^3/x^4*arccsc(c*x)+45/256*c^3*b^3*((c^2*x^2-1)/c^2/x^2)^(1/2)/x+3/128*c*b^3/x^3*((c^2*x^2-1)/c^2/x^2)^(1/2)-45/256*b^3*c^4*arccsc(c*x)+9/32*c^2*b^3/x^2*arccsc(c*x)-3/4*a*b^2/x^4*arccsc(c*x)^2+9/32*c^4*a*b^2*arccsc(c*x)^2-9/16*c^3*a*b^2*arccsc(c*x)/x*((c^2*x^2-1)/c^2/x^2)^(1/2)-3/8*c*a*b^2*arccsc(c*x)/x^3*((c^2*x^2-1)/c^2/x^2)^(1/2)+3/32*a*b^2/x^4+9/32*c^2*a*b^2/x^2-3/4*a^2*b/x^4*arccsc(c*x)+9/32*c^3*a^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*arctan(1/(c^2*x^2-1)^(1/2))-9/32*c^3*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x+3/32*c*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^3+3/16/c*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^5","B"
33,0,0,14,2.294000," ","int(x/(a+b*arccsc(c*x)),x)","\int \frac{x}{a +b \,\mathrm{arccsc}\left(c x \right)}\, dx"," ",0,"int(x/(a+b*arccsc(c*x)),x)","F"
34,0,0,12,0.901000," ","int(1/(a+b*arccsc(c*x)),x)","\int \frac{1}{a +b \,\mathrm{arccsc}\left(c x \right)}\, dx"," ",0,"int(1/(a+b*arccsc(c*x)),x)","F"
35,0,0,16,1.046000," ","int(1/x/(a+b*arccsc(c*x)),x)","\int \frac{1}{x \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}\, dx"," ",0,"int(1/x/(a+b*arccsc(c*x)),x)","F"
36,1,48,47,0.178000," ","int(1/x^2/(a+b*arccsc(c*x)),x)","c \left(-\frac{\Si \left(\frac{a}{b}+\mathrm{arccsc}\left(c x \right)\right) \sin \left(\frac{a}{b}\right)}{b}-\frac{\Ci \left(\frac{a}{b}+\mathrm{arccsc}\left(c x \right)\right) \cos \left(\frac{a}{b}\right)}{b}\right)"," ",0,"c*(-Si(a/b+arccsc(c*x))*sin(a/b)/b-Ci(a/b+arccsc(c*x))*cos(a/b)/b)","A"
37,1,58,59,0.098000," ","int(1/x^3/(a+b*arccsc(c*x)),x)","c^{2} \left(-\frac{\Si \left(\frac{2 a}{b}+2 \,\mathrm{arccsc}\left(c x \right)\right) \cos \left(\frac{2 a}{b}\right)}{2 b}+\frac{\Ci \left(\frac{2 a}{b}+2 \,\mathrm{arccsc}\left(c x \right)\right) \sin \left(\frac{2 a}{b}\right)}{2 b}\right)"," ",0,"c^2*(-1/2*Si(2*a/b+2*arccsc(c*x))*cos(2*a/b)/b+1/2*Ci(2*a/b+2*arccsc(c*x))*sin(2*a/b)/b)","A"
38,1,102,109,0.099000," ","int(1/x^4/(a+b*arccsc(c*x)),x)","c^{3} \left(-\frac{\Si \left(\frac{a}{b}+\mathrm{arccsc}\left(c x \right)\right) \sin \left(\frac{a}{b}\right)}{4 b}-\frac{\Ci \left(\frac{a}{b}+\mathrm{arccsc}\left(c x \right)\right) \cos \left(\frac{a}{b}\right)}{4 b}+\frac{\Si \left(\frac{3 a}{b}+3 \,\mathrm{arccsc}\left(c x \right)\right) \sin \left(\frac{3 a}{b}\right)}{4 b}+\frac{\Ci \left(\frac{3 a}{b}+3 \,\mathrm{arccsc}\left(c x \right)\right) \cos \left(\frac{3 a}{b}\right)}{4 b}\right)"," ",0,"c^3*(-1/4*Si(a/b+arccsc(c*x))*sin(a/b)/b-1/4*Ci(a/b+arccsc(c*x))*cos(a/b)/b+1/4*Si(3*a/b+3*arccsc(c*x))*sin(3*a/b)/b+1/4*Ci(3*a/b+3*arccsc(c*x))*cos(3*a/b)/b)","A"
39,0,0,18,4.296000," ","int((d*x)^m*(a+b*arccsc(c*x))^3,x)","\int \left(d x \right)^{m} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)^{3}\, dx"," ",0,"int((d*x)^m*(a+b*arccsc(c*x))^3,x)","F"
40,0,0,18,3.973000," ","int((d*x)^m*(a+b*arccsc(c*x))^2,x)","\int \left(d x \right)^{m} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)^{2}\, dx"," ",0,"int((d*x)^m*(a+b*arccsc(c*x))^2,x)","F"
41,0,0,62,3.873000," ","int((d*x)^m*(a+b*arccsc(c*x)),x)","\int \left(d x \right)^{m} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)\, dx"," ",0,"int((d*x)^m*(a+b*arccsc(c*x)),x)","F"
42,0,0,18,2.826000," ","int((d*x)^m/(a+b*arccsc(c*x)),x)","\int \frac{\left(d x \right)^{m}}{a +b \,\mathrm{arccsc}\left(c x \right)}\, dx"," ",0,"int((d*x)^m/(a+b*arccsc(c*x)),x)","F"
43,0,0,18,2.918000," ","int((d*x)^m/(a+b*arccsc(c*x))^2,x)","\int \frac{\left(d x \right)^{m}}{\left(a +b \,\mathrm{arccsc}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((d*x)^m/(a+b*arccsc(c*x))^2,x)","F"
44,1,485,147,0.056000," ","int((e*x+d)^3*(a+b*arccsc(c*x)),x)","\frac{a \,e^{3} x^{4}}{4}+a \,e^{2} x^{3} d +\frac{3 a e \,x^{2} d^{2}}{2}+a x \,d^{3}+\frac{a \,d^{4}}{4 e}+\frac{b \,e^{3} \mathrm{arccsc}\left(c x \right) x^{4}}{4}+b \,e^{2} \mathrm{arccsc}\left(c x \right) x^{3} d +\frac{3 b e \,\mathrm{arccsc}\left(c x \right) x^{2} d^{2}}{2}+b \,\mathrm{arccsc}\left(c x \right) x \,d^{3}+\frac{b \,d^{4} \mathrm{arccsc}\left(c x \right)}{4 e}-\frac{b \sqrt{c^{2} x^{2}-1}\, d^{4} \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 c e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{b \sqrt{c^{2} x^{2}-1}\, d^{3} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{b \,e^{3} x^{3}}{12 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,e^{3} x}{12 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,e^{2} d \,x^{2}}{2 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,e^{2} d}{2 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{3 b e x \,d^{2}}{2 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{3 b e \,d^{2}}{2 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{b \,e^{2} \sqrt{c^{2} x^{2}-1}\, d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{2 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{b \,e^{3}}{6 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/4*a*e^3*x^4+a*e^2*x^3*d+3/2*a*e*x^2*d^2+a*x*d^3+1/4*a/e*d^4+1/4*b*e^3*arccsc(c*x)*x^4+b*e^2*arccsc(c*x)*x^3*d+3/2*b*e*arccsc(c*x)*x^2*d^2+b*arccsc(c*x)*x*d^3+1/4*b*d^4*arccsc(c*x)/e-1/4/c*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d^4*arctan(1/(c^2*x^2-1)^(1/2))+1/c^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d^3*ln(c*x+(c^2*x^2-1)^(1/2))+1/12/c*b*e^3/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^3+1/12/c^3*b*e^3/((c^2*x^2-1)/c^2/x^2)^(1/2)*x+1/2/c*b*e^2/((c^2*x^2-1)/c^2/x^2)^(1/2)*d*x^2-1/2/c^3*b*e^2/((c^2*x^2-1)/c^2/x^2)^(1/2)*d+3/2/c*b*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x*d^2-3/2/c^3*b*e/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d^2+1/2/c^4*b*e^2*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d*ln(c*x+(c^2*x^2-1)^(1/2))-1/6/c^5*b*e^3/((c^2*x^2-1)/c^2/x^2)^(1/2)/x","B"
45,1,361,109,0.054000," ","int((e*x+d)^2*(a+b*arccsc(c*x)),x)","\frac{a \,e^{2} x^{3}}{3}+a e d \,x^{2}+a x \,d^{2}+\frac{a \,d^{3}}{3 e}+\frac{b \,e^{2} \mathrm{arccsc}\left(c x \right) x^{3}}{3}+b e \,\mathrm{arccsc}\left(c x \right) x^{2} d +b \,\mathrm{arccsc}\left(c x \right) x \,d^{2}+\frac{b \,d^{3} \mathrm{arccsc}\left(c x \right)}{3 e}-\frac{b \sqrt{c^{2} x^{2}-1}\, d^{3} \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{3 c e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{b \sqrt{c^{2} x^{2}-1}\, d^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{b \,e^{2} x^{2}}{6 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,e^{2}}{6 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b e x d}{c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b e d}{c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{b \,e^{2} \sqrt{c^{2} x^{2}-1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{6 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/3*a*e^2*x^3+a*e*d*x^2+a*x*d^2+1/3*a/e*d^3+1/3*b*e^2*arccsc(c*x)*x^3+b*e*arccsc(c*x)*x^2*d+b*arccsc(c*x)*x*d^2+1/3*b*d^3*arccsc(c*x)/e-1/3/c*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d^3*arctan(1/(c^2*x^2-1)^(1/2))+1/c^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d^2*ln(c*x+(c^2*x^2-1)^(1/2))+1/6/c*b*e^2/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2-1/6/c^3*b*e^2/((c^2*x^2-1)/c^2/x^2)^(1/2)+1/c*b*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x*d-1/c^3*b*e/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d+1/6/c^4*b*e^2*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*ln(c*x+(c^2*x^2-1)^(1/2))","B"
46,1,140,73,0.053000," ","int((e*x+d)*(a+b*arccsc(c*x)),x)","\frac{a \,x^{2} e}{2}+a d x +\frac{b \,\mathrm{arccsc}\left(c x \right) x^{2} e}{2}+b \,\mathrm{arccsc}\left(c x \right) x d +\frac{b \sqrt{c^{2} x^{2}-1}\, d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{b x e}{2 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b e}{2 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/2*a*x^2*e+a*d*x+1/2*b*arccsc(c*x)*x^2*e+b*arccsc(c*x)*x*d+1/c^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*(c^2*x^2-1)^(1/2)*d*ln(c*x+(c^2*x^2-1)^(1/2))+1/2/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x*e-1/2/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e","A"
47,1,37,29,0.045000," ","int(a+b*arccsc(c*x),x)","a x +b x \,\mathrm{arccsc}\left(c x \right)+\frac{b \ln \left(c x +c x \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c}"," ",0,"a*x+b*x*arccsc(c*x)+b/c*ln(c*x+c*x*(1-1/c^2/x^2)^(1/2))","A"
48,1,869,316,1.114000," ","int((a+b*arccsc(c*x))/(e*x+d),x)","\frac{a \ln \left(c e x +d c \right)}{e}-\frac{b e \,\mathrm{arccsc}\left(c x \right) \ln \left(\frac{-d c \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-i e +\sqrt{c^{2} d^{2}-e^{2}}}{-i e +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{c^{2} d^{2}-e^{2}}-\frac{b e \,\mathrm{arccsc}\left(c x \right) \ln \left(\frac{d c \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+i e +\sqrt{c^{2} d^{2}-e^{2}}}{i e +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{c^{2} b \,d^{2} \mathrm{arccsc}\left(c x \right) \ln \left(\frac{-d c \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-i e +\sqrt{c^{2} d^{2}-e^{2}}}{-i e +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}+\frac{c^{2} b \,d^{2} \mathrm{arccsc}\left(c x \right) \ln \left(\frac{d c \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+i e +\sqrt{c^{2} d^{2}-e^{2}}}{i e +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{i c^{2} b \,d^{2} \dilog \left(\frac{-d c \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-i e +\sqrt{c^{2} d^{2}-e^{2}}}{-i e +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{i c^{2} b \,d^{2} \dilog \left(\frac{d c \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+i e +\sqrt{c^{2} d^{2}-e^{2}}}{i e +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{i b \dilog \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e}+\frac{i b e \dilog \left(\frac{-d c \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-i e +\sqrt{c^{2} d^{2}-e^{2}}}{-i e +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{i b e \dilog \left(\frac{d c \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+i e +\sqrt{c^{2} d^{2}-e^{2}}}{i e +\sqrt{c^{2} d^{2}-e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{i b \dilog \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e}-\frac{b \,\mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e}"," ",0,"a*ln(c*e*x+c*d)/e-b*e*arccsc(c*x)/(c^2*d^2-e^2)*ln((-d*c*(I/c/x+(1-1/c^2/x^2)^(1/2))-I*e+(c^2*d^2-e^2)^(1/2))/(-I*e+(c^2*d^2-e^2)^(1/2)))-b*e*arccsc(c*x)/(c^2*d^2-e^2)*ln((d*c*(I/c/x+(1-1/c^2/x^2)^(1/2))+I*e+(c^2*d^2-e^2)^(1/2))/(I*e+(c^2*d^2-e^2)^(1/2)))+c^2*b*d^2/e*arccsc(c*x)/(c^2*d^2-e^2)*ln((-d*c*(I/c/x+(1-1/c^2/x^2)^(1/2))-I*e+(c^2*d^2-e^2)^(1/2))/(-I*e+(c^2*d^2-e^2)^(1/2)))+c^2*b*d^2/e*arccsc(c*x)/(c^2*d^2-e^2)*ln((d*c*(I/c/x+(1-1/c^2/x^2)^(1/2))+I*e+(c^2*d^2-e^2)^(1/2))/(I*e+(c^2*d^2-e^2)^(1/2)))-I*c^2*b*d^2/e/(c^2*d^2-e^2)*dilog((-d*c*(I/c/x+(1-1/c^2/x^2)^(1/2))-I*e+(c^2*d^2-e^2)^(1/2))/(-I*e+(c^2*d^2-e^2)^(1/2)))-I*c^2*b*d^2/e/(c^2*d^2-e^2)*dilog((d*c*(I/c/x+(1-1/c^2/x^2)^(1/2))+I*e+(c^2*d^2-e^2)^(1/2))/(I*e+(c^2*d^2-e^2)^(1/2)))-I*b*dilog(I/c/x+(1-1/c^2/x^2)^(1/2))/e+I*b*e/(c^2*d^2-e^2)*dilog((-d*c*(I/c/x+(1-1/c^2/x^2)^(1/2))-I*e+(c^2*d^2-e^2)^(1/2))/(-I*e+(c^2*d^2-e^2)^(1/2)))+I*b*e/(c^2*d^2-e^2)*dilog((d*c*(I/c/x+(1-1/c^2/x^2)^(1/2))+I*e+(c^2*d^2-e^2)^(1/2))/(I*e+(c^2*d^2-e^2)^(1/2)))+I*b/e*dilog(1+I/c/x+(1-1/c^2/x^2)^(1/2))-b/e*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))","B"
49,1,214,98,0.063000," ","int((a+b*arccsc(c*x))/(e*x+d)^2,x)","-\frac{c a}{\left(c e x +d c \right) e}-\frac{c b \,\mathrm{arccsc}\left(c x \right)}{\left(c e x +d c \right) e}+\frac{b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{c e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d}-\frac{b \sqrt{c^{2} x^{2}-1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e -2 c^{2} d x -2 e}{c e x +d c}\right)}{c e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}"," ",0,"-c*a/(c*e*x+c*d)/e-c*b/(c*e*x+c*d)/e*arccsc(c*x)+1/c*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d*arctan(1/(c^2*x^2-1)^(1/2))-1/c*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/((c^2*d^2-e^2)/e^2)^(1/2)*ln(2*((c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e-c^2*d*x-e)/(c*e*x+c*d))","B"
50,1,1007,159,0.067000," ","int((a+b*arccsc(c*x))/(e*x+d)^3,x)","-\frac{c^{2} a}{2 \left(c e x +d c \right)^{2} e}-\frac{c^{2} b \,\mathrm{arccsc}\left(c x \right)}{2 \left(c e x +d c \right)^{2} e}+\frac{c^{2} b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}+\frac{c^{2} b \sqrt{c^{2} x^{2}-1}\, d \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{2 e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}-\frac{c^{2} b \sqrt{c^{2} x^{2}-1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e -2 c^{2} d x -2 e}{c e x +d c}\right)}{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}-\frac{c^{2} b \sqrt{c^{2} x^{2}-1}\, d \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e -2 c^{2} d x -2 e}{c e x +d c}\right)}{e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}-\frac{c^{2} b e x}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}+\frac{b e}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}-\frac{b \,e^{2} \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d^{2} \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}-\frac{b e \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}+\frac{b \,e^{2} \sqrt{c^{2} x^{2}-1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e -2 c^{2} d x -2 e}{c e x +d c}\right)}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}+\frac{b e \sqrt{c^{2} x^{2}-1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e -2 c^{2} d x -2 e}{c e x +d c}\right)}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}"," ",0,"-1/2*c^2*a/(c*e*x+c*d)^2/e-1/2*c^2*b/(c*e*x+c*d)^2/e*arccsc(c*x)+1/2*c^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/(c^2*d^2-e^2)/(c*e*x+c*d)*arctan(1/(c^2*x^2-1)^(1/2))+1/2*c^2*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d/(c^2*d^2-e^2)/(c*e*x+c*d)*arctan(1/(c^2*x^2-1)^(1/2))-c^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/((c^2*d^2-e^2)/e^2)^(1/2)/(c^2*d^2-e^2)/(c*e*x+c*d)*ln(2*((c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e-c^2*d*x-e)/(c*e*x+c*d))-c^2*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d/((c^2*d^2-e^2)/e^2)^(1/2)/(c^2*d^2-e^2)/(c*e*x+c*d)*ln(2*((c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e-c^2*d*x-e)/(c*e*x+c*d))-1/2*c^2*b*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d/(c^2*d^2-e^2)/(c*e*x+c*d)+1/2*b*e/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/(c^2*d^2-e^2)/(c*e*x+c*d)-1/2*b*e^2*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/d^2/(c^2*d^2-e^2)/(c*e*x+c*d)*arctan(1/(c^2*x^2-1)^(1/2))-1/2*b*e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/(c^2*d^2-e^2)/(c*e*x+c*d)*arctan(1/(c^2*x^2-1)^(1/2))+1/2*b*e^2*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/d^2/((c^2*d^2-e^2)/e^2)^(1/2)/(c^2*d^2-e^2)/(c*e*x+c*d)*ln(2*((c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e-c^2*d*x-e)/(c*e*x+c*d))+1/2*b*e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/((c^2*d^2-e^2)/e^2)^(1/2)/(c^2*d^2-e^2)/(c*e*x+c*d)*ln(2*((c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e-c^2*d*x-e)/(c*e*x+c*d))","B"
51,1,1222,445,0.086000," ","int(x^2*(a+b*arccsc(c*x))*(e*x+d)^(1/2),x)","\frac{2 a \left(\frac{\left(e x +d \right)^{\frac{7}{2}}}{7}-\frac{2 \left(e x +d \right)^{\frac{5}{2}} d}{5}+\frac{\left(e x +d \right)^{\frac{3}{2}} d^{2}}{3}\right)+2 b \left(\frac{\mathrm{arccsc}\left(c x \right) \left(e x +d \right)^{\frac{7}{2}}}{7}-\frac{2 \,\mathrm{arccsc}\left(c x \right) \left(e x +d \right)^{\frac{5}{2}} d}{5}+\frac{\mathrm{arccsc}\left(c x \right) \left(e x +d \right)^{\frac{3}{2}} d^{2}}{3}+\frac{\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{7}{2}} c^{3}}{35}-\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{5}{2}} c^{3} d}{15}+\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{2}}{21}+\frac{8 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{3} d^{3}}{105}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{3} d^{3}}{21}-\frac{16 d^{3} \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) c^{3}}{105}-\frac{2 \sqrt{\frac{c}{d c -e}}\, \sqrt{e x +d}\, c^{3} d^{3}}{105}-\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{2} d^{2} e}{21}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{2} d^{2} e}{21}-\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{3}{2}} c \,e^{2}}{35}+\frac{16 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d \,e^{2}}{105}-\frac{6 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d \,e^{2}}{35}+\frac{2 \sqrt{\frac{c}{d c -e}}\, \sqrt{e x +d}\, c d \,e^{2}}{105}+\frac{6 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e^{3}}{35}-\frac{6 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e^{3}}{35}}{c^{4} \sqrt{\frac{c}{d c -e}}\, x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e^{3}}"," ",0,"2/e^3*(a*(1/7*(e*x+d)^(7/2)-2/5*(e*x+d)^(5/2)*d+1/3*(e*x+d)^(3/2)*d^2)+b*(1/7*arccsc(c*x)*(e*x+d)^(7/2)-2/5*arccsc(c*x)*(e*x+d)^(5/2)*d+1/3*arccsc(c*x)*(e*x+d)^(3/2)*d^2+2/105/c^4*(3*(c/(c*d-e))^(1/2)*(e*x+d)^(7/2)*c^3-7*(c/(c*d-e))^(1/2)*(e*x+d)^(5/2)*c^3*d+5*(c/(c*d-e))^(1/2)*(e*x+d)^(3/2)*c^3*d^2+4*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^3*d^3+5*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^3*d^3-8*d^3*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*c^3-(c/(c*d-e))^(1/2)*(e*x+d)^(1/2)*c^3*d^3-5*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^2*d^2*e+5*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^2*d^2*e-3*(c/(c*d-e))^(1/2)*(e*x+d)^(3/2)*c*e^2+8*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d*e^2-9*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d*e^2+(c/(c*d-e))^(1/2)*(e*x+d)^(1/2)*c*d*e^2+9*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e^3-9*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e^3)/(c/(c*d-e))^(1/2)/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","B"
52,1,836,363,0.075000," ","int(x*(a+b*arccsc(c*x))*(e*x+d)^(1/2),x)","\frac{2 a \left(\frac{\left(e x +d \right)^{\frac{5}{2}}}{5}-\frac{\left(e x +d \right)^{\frac{3}{2}} d}{3}\right)+2 b \left(\frac{\mathrm{arccsc}\left(c x \right) \left(e x +d \right)^{\frac{5}{2}}}{5}-\frac{\mathrm{arccsc}\left(c x \right) \left(e x +d \right)^{\frac{3}{2}} d}{3}+\frac{\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{5}{2}} c^{2}}{15}-\frac{4 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{3}{2}} c^{2} d}{15}-\frac{2 d^{2} \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{2}}{15}-\frac{4 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{2} d^{2}}{15}+\frac{4 d^{2} \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) c^{2}}{15}+\frac{2 \sqrt{\frac{c}{d c -e}}\, \sqrt{e x +d}\, c^{2} d^{2}}{15}+\frac{4 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d e}{15}-\frac{4 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d e}{15}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e^{2}}{15}-\frac{2 \sqrt{\frac{c}{d c -e}}\, \sqrt{e x +d}\, e^{2}}{15}}{c^{3} \sqrt{\frac{c}{d c -e}}\, x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e^{2}}"," ",0,"2/e^2*(a*(1/5*(e*x+d)^(5/2)-1/3*(e*x+d)^(3/2)*d)+b*(1/5*arccsc(c*x)*(e*x+d)^(5/2)-1/3*arccsc(c*x)*(e*x+d)^(3/2)*d+2/15/c^3*((c/(c*d-e))^(1/2)*(e*x+d)^(5/2)*c^2-2*(c/(c*d-e))^(1/2)*(e*x+d)^(3/2)*c^2*d-d^2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^2-2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^2*d^2+2*d^2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*c^2+(c/(c*d-e))^(1/2)*(e*x+d)^(1/2)*c^2*d^2+2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d*e-2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d*e+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e^2-(c/(c*d-e))^(1/2)*(e*x+d)^(1/2)*e^2)/(c/(c*d-e))^(1/2)/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","B"
53,1,388,284,0.073000," ","int((a+b*arccsc(c*x))*(e*x+d)^(1/2),x)","\frac{\frac{2 \left(e x +d \right)^{\frac{3}{2}} a}{3}+2 b \left(\frac{\left(e x +d \right)^{\frac{3}{2}} \mathrm{arccsc}\left(c x \right)}{3}+\frac{2 \left(2 d \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c -\EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d -d \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) c +\EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e -\EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e \right) \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}}{3 c^{2} \sqrt{\frac{c}{d c -e}}\, x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e}"," ",0,"2/e*(1/3*(e*x+d)^(3/2)*a+b*(1/3*(e*x+d)^(3/2)*arccsc(c*x)+2/3/c^2*(2*d*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c-EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d-d*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*c+EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e-EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)/(c/(c*d-e))^(1/2)/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","A"
54,0,0,21,8.853000," ","int((a+b*arccsc(c*x))*(e*x+d)^(1/2)/x,x)","\int \frac{\left(a +b \,\mathrm{arccsc}\left(c x \right)\right) \sqrt{e x +d}}{x}\, dx"," ",0,"int((a+b*arccsc(c*x))*(e*x+d)^(1/2)/x,x)","F"
55,0,0,21,10.087000," ","int((a+b*arccsc(c*x))*(e*x+d)^(1/2)/x^2,x)","\int \frac{\left(a +b \,\mathrm{arccsc}\left(c x \right)\right) \sqrt{e x +d}}{x^{2}}\, dx"," ",0,"int((a+b*arccsc(c*x))*(e*x+d)^(1/2)/x^2,x)","F"
56,1,810,335,0.073000," ","int((e*x+d)^(3/2)*(a+b*arccsc(c*x)),x)","\frac{\frac{2 \left(e x +d \right)^{\frac{5}{2}} a}{5}+2 b \left(\frac{\mathrm{arccsc}\left(c x \right) \left(e x +d \right)^{\frac{5}{2}}}{5}+\frac{\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{5}{2}} c^{2}}{15}-\frac{4 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{3}{2}} c^{2} d}{15}+\frac{6 d^{2} \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{2}}{5}-\frac{14 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{2} d^{2}}{15}-\frac{2 d^{2} \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) c^{2}}{5}+\frac{2 \sqrt{\frac{c}{d c -e}}\, \sqrt{e x +d}\, c^{2} d^{2}}{15}+\frac{14 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d e}{15}-\frac{14 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d e}{15}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e^{2}}{15}-\frac{2 \sqrt{\frac{c}{d c -e}}\, \sqrt{e x +d}\, e^{2}}{15}}{c^{3} \sqrt{\frac{c}{d c -e}}\, x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e}"," ",0,"2/e*(1/5*(e*x+d)^(5/2)*a+b*(1/5*arccsc(c*x)*(e*x+d)^(5/2)+2/15/c^3*((c/(c*d-e))^(1/2)*(e*x+d)^(5/2)*c^2-2*(c/(c*d-e))^(1/2)*(e*x+d)^(3/2)*c^2*d+9*d^2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^2-7*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^2*d^2-3*d^2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*c^2+(c/(c*d-e))^(1/2)*(e*x+d)^(1/2)*c^2*d^2+7*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d*e-7*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d*e+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e^2-(c/(c*d-e))^(1/2)*(e*x+d)^(1/2)*e^2)/(c/(c*d-e))^(1/2)/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","B"
57,1,1248,645,0.083000," ","int(x^3*(a+b*arccsc(c*x))/(e*x+d)^(1/2),x)","\frac{2 a \left(\frac{\left(e x +d \right)^{\frac{7}{2}}}{7}-\frac{3 \left(e x +d \right)^{\frac{5}{2}} d}{5}+\left(e x +d \right)^{\frac{3}{2}} d^{2}-d^{3} \sqrt{e x +d}\right)+2 b \left(\frac{\mathrm{arccsc}\left(c x \right) \left(e x +d \right)^{\frac{7}{2}}}{7}-\frac{3 \,\mathrm{arccsc}\left(c x \right) \left(e x +d \right)^{\frac{5}{2}} d}{5}+\mathrm{arccsc}\left(c x \right) \left(e x +d \right)^{\frac{3}{2}} d^{2}-\mathrm{arccsc}\left(c x \right) d^{3} \sqrt{e x +d}+\frac{\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{7}{2}} c^{3}}{35}-\frac{4 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{5}{2}} c^{3} d}{15}+\frac{38 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{2}}{105}-\frac{16 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{3} d^{3}}{35}-\frac{32 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{3} d^{3}}{105}+\frac{32 d^{3} \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) c^{3}}{35}-\frac{16 \sqrt{\frac{c}{d c -e}}\, \sqrt{e x +d}\, c^{3} d^{3}}{105}+\frac{32 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{2} d^{2} e}{105}-\frac{32 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{2} d^{2} e}{105}-\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{3}{2}} c \,e^{2}}{35}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d \,e^{2}}{105}-\frac{6 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d \,e^{2}}{35}+\frac{16 \sqrt{\frac{c}{d c -e}}\, \sqrt{e x +d}\, c d \,e^{2}}{105}+\frac{6 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e^{3}}{35}-\frac{6 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e^{3}}{35}}{c^{4} \sqrt{\frac{c}{d c -e}}\, x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e^{4}}"," ",0,"2/e^4*(a*(1/7*(e*x+d)^(7/2)-3/5*(e*x+d)^(5/2)*d+(e*x+d)^(3/2)*d^2-d^3*(e*x+d)^(1/2))+b*(1/7*arccsc(c*x)*(e*x+d)^(7/2)-3/5*arccsc(c*x)*(e*x+d)^(5/2)*d+arccsc(c*x)*(e*x+d)^(3/2)*d^2-arccsc(c*x)*d^3*(e*x+d)^(1/2)+2/105/c^4*(3*(c/(c*d-e))^(1/2)*(e*x+d)^(7/2)*c^3-14*(c/(c*d-e))^(1/2)*(e*x+d)^(5/2)*c^3*d+19*(c/(c*d-e))^(1/2)*(e*x+d)^(3/2)*c^3*d^2-24*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^3*d^3-16*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^3*d^3+48*d^3*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*c^3-8*(c/(c*d-e))^(1/2)*(e*x+d)^(1/2)*c^3*d^3+16*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^2*d^2*e-16*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^2*d^2*e-3*(c/(c*d-e))^(1/2)*(e*x+d)^(3/2)*c*e^2+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d*e^2-9*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d*e^2+8*(c/(c*d-e))^(1/2)*(e*x+d)^(1/2)*c*d*e^2+9*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e^3-9*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e^3)/(c/(c*d-e))^(1/2)/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","A"
58,1,862,478,0.076000," ","int(x^2*(a+b*arccsc(c*x))/(e*x+d)^(1/2),x)","\frac{2 a \left(\frac{\left(e x +d \right)^{\frac{5}{2}}}{5}-\frac{2 \left(e x +d \right)^{\frac{3}{2}} d}{3}+d^{2} \sqrt{e x +d}\right)+2 b \left(\frac{\mathrm{arccsc}\left(c x \right) \left(e x +d \right)^{\frac{5}{2}}}{5}-\frac{2 \,\mathrm{arccsc}\left(c x \right) \left(e x +d \right)^{\frac{3}{2}} d}{3}+\mathrm{arccsc}\left(c x \right) d^{2} \sqrt{e x +d}+\frac{\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{5}{2}} c^{2}}{15}+\frac{8 d^{2} \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{2}}{15}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{2} d^{2}}{5}-\frac{16 d^{2} \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) c^{2}}{15}-\frac{4 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{3}{2}} c^{2} d}{15}-\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d e}{5}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d e}{5}+\frac{2 \sqrt{\frac{c}{d c -e}}\, \sqrt{e x +d}\, c^{2} d^{2}}{15}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e^{2}}{15}-\frac{2 \sqrt{\frac{c}{d c -e}}\, \sqrt{e x +d}\, e^{2}}{15}}{c^{3} \sqrt{\frac{c}{d c -e}}\, x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e^{3}}"," ",0,"2/e^3*(a*(1/5*(e*x+d)^(5/2)-2/3*(e*x+d)^(3/2)*d+d^2*(e*x+d)^(1/2))+b*(1/5*arccsc(c*x)*(e*x+d)^(5/2)-2/3*arccsc(c*x)*(e*x+d)^(3/2)*d+arccsc(c*x)*d^2*(e*x+d)^(1/2)+2/15/c^3*((c/(c*d-e))^(1/2)*(e*x+d)^(5/2)*c^2+4*d^2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^2+3*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^2*d^2-8*d^2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*c^2-2*(c/(c*d-e))^(1/2)*(e*x+d)^(3/2)*c^2*d-3*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d*e+3*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d*e+(c/(c*d-e))^(1/2)*(e*x+d)^(1/2)*c^2*d^2+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e^2-(c/(c*d-e))^(1/2)*(e*x+d)^(1/2)*e^2)/(c/(c*d-e))^(1/2)/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","A"
59,1,412,311,0.073000," ","int(x*(a+b*arccsc(c*x))/(e*x+d)^(1/2),x)","\frac{2 a \left(\frac{\left(e x +d \right)^{\frac{3}{2}}}{3}-d \sqrt{e x +d}\right)+2 b \left(\frac{\left(e x +d \right)^{\frac{3}{2}} \mathrm{arccsc}\left(c x \right)}{3}-\mathrm{arccsc}\left(c x \right) d \sqrt{e x +d}-\frac{2 \left(d \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c +\EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d -2 d \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) c -\EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e +\EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e \right) \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}}{3 c^{2} \sqrt{\frac{c}{d c -e}}\, x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e^{2}}"," ",0,"2/e^2*(a*(1/3*(e*x+d)^(3/2)-d*(e*x+d)^(1/2))+b*(1/3*(e*x+d)^(3/2)*arccsc(c*x)-arccsc(c*x)*d*(e*x+d)^(1/2)-2/3/c^2*(d*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c+EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d-2*d*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*c-EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e+EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)/(c/(c*d-e))^(1/2)/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","A"
60,1,254,196,0.069000," ","int((a+b*arccsc(c*x))/(e*x+d)^(1/2),x)","\frac{2 a \sqrt{e x +d}+2 b \left(\sqrt{e x +d}\, \mathrm{arccsc}\left(c x \right)+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \left(\EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right)-\EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right)\right)}{c \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}\, x \sqrt{\frac{c}{d c -e}}}\right)}{e}"," ",0,"2/e*(a*(e*x+d)^(1/2)+b*((e*x+d)^(1/2)*arccsc(c*x)+2/c*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*(EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))-EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2)))/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)/x/(c/(c*d-e))^(1/2)))","A"
61,0,0,21,4.565000," ","int((a+b*arccsc(c*x))/x/(e*x+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x \sqrt{e x +d}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x/(e*x+d)^(1/2),x)","F"
62,0,0,21,7.832000," ","int((a+b*arccsc(c*x))/x^2/(e*x+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x^{2} \sqrt{e x +d}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x^2/(e*x+d)^(1/2),x)","F"
63,1,890,501,0.082000," ","int(x^3*(a+b*arccsc(c*x))/(e*x+d)^(3/2),x)","\frac{2 a \left(\frac{\left(e x +d \right)^{\frac{5}{2}}}{5}-\left(e x +d \right)^{\frac{3}{2}} d +3 d^{2} \sqrt{e x +d}+\frac{d^{3}}{\sqrt{e x +d}}\right)+2 b \left(\frac{\mathrm{arccsc}\left(c x \right) \left(e x +d \right)^{\frac{5}{2}}}{5}-\mathrm{arccsc}\left(c x \right) \left(e x +d \right)^{\frac{3}{2}} d +3 \,\mathrm{arccsc}\left(c x \right) d^{2} \sqrt{e x +d}+\frac{\mathrm{arccsc}\left(c x \right) d^{3}}{\sqrt{e x +d}}+\frac{\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{5}{2}} c^{2}}{15}-\frac{4 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{3}{2}} c^{2} d}{15}+\frac{16 d^{2} \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{2}}{5}+\frac{16 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{2} d^{2}}{15}-\frac{32 d^{2} \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) c^{2}}{5}+\frac{2 \sqrt{\frac{c}{d c -e}}\, \sqrt{e x +d}\, c^{2} d^{2}}{15}-\frac{16 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d e}{15}+\frac{16 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d e}{15}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e^{2}}{15}-\frac{2 \sqrt{\frac{c}{d c -e}}\, \sqrt{e x +d}\, e^{2}}{15}}{c^{3} \sqrt{\frac{c}{d c -e}}\, x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e^{4}}"," ",0,"2/e^4*(a*(1/5*(e*x+d)^(5/2)-(e*x+d)^(3/2)*d+3*d^2*(e*x+d)^(1/2)+d^3/(e*x+d)^(1/2))+b*(1/5*arccsc(c*x)*(e*x+d)^(5/2)-arccsc(c*x)*(e*x+d)^(3/2)*d+3*arccsc(c*x)*d^2*(e*x+d)^(1/2)+arccsc(c*x)*d^3/(e*x+d)^(1/2)+2/15/c^3*((c/(c*d-e))^(1/2)*(e*x+d)^(5/2)*c^2-2*(c/(c*d-e))^(1/2)*(e*x+d)^(3/2)*c^2*d+24*d^2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^2+8*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^2*d^2-48*d^2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*c^2+(c/(c*d-e))^(1/2)*(e*x+d)^(1/2)*c^2*d^2-8*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d*e+8*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d*e+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e^2-(c/(c*d-e))^(1/2)*(e*x+d)^(1/2)*e^2)/(c/(c*d-e))^(1/2)/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","A"
64,1,441,334,0.076000," ","int(x^2*(a+b*arccsc(c*x))/(e*x+d)^(3/2),x)","\frac{2 a \left(\frac{\left(e x +d \right)^{\frac{3}{2}}}{3}-2 d \sqrt{e x +d}-\frac{d^{2}}{\sqrt{e x +d}}\right)+2 b \left(\frac{\left(e x +d \right)^{\frac{3}{2}} \mathrm{arccsc}\left(c x \right)}{3}-2 \,\mathrm{arccsc}\left(c x \right) d \sqrt{e x +d}-\frac{\mathrm{arccsc}\left(c x \right) d^{2}}{\sqrt{e x +d}}-\frac{2 \left(4 d \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c +\EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d -8 d \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) c -\EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e +\EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e \right) \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}}{3 c^{2} \sqrt{\frac{c}{d c -e}}\, x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e^{3}}"," ",0,"2/e^3*(a*(1/3*(e*x+d)^(3/2)-2*d*(e*x+d)^(1/2)-d^2/(e*x+d)^(1/2))+b*(1/3*(e*x+d)^(3/2)*arccsc(c*x)-2*arccsc(c*x)*d*(e*x+d)^(1/2)-arccsc(c*x)*d^2/(e*x+d)^(1/2)-2/3/c^2*(4*d*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c+EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d-8*d*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*c-EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e+EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)/(c/(c*d-e))^(1/2)/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","A"
65,1,277,220,0.074000," ","int(x*(a+b*arccsc(c*x))/(e*x+d)^(3/2),x)","\frac{2 a \left(\sqrt{e x +d}+\frac{d}{\sqrt{e x +d}}\right)+2 b \left(\sqrt{e x +d}\, \mathrm{arccsc}\left(c x \right)+\frac{\mathrm{arccsc}\left(c x \right) d}{\sqrt{e x +d}}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \left(\EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right)-2 \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right)\right)}{c \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}\, x \sqrt{\frac{c}{d c -e}}}\right)}{e^{2}}"," ",0,"2/e^2*(a*((e*x+d)^(1/2)+d/(e*x+d)^(1/2))+b*((e*x+d)^(1/2)*arccsc(c*x)+arccsc(c*x)*d/(e*x+d)^(1/2)+2/c*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*(EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))-2*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2)))/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)/x/(c/(c*d-e))^(1/2)))","A"
66,1,217,110,0.063000," ","int((a+b*arccsc(c*x))/(e*x+d)^(3/2),x)","\frac{-\frac{2 a}{\sqrt{e x +d}}+2 b \left(-\frac{\mathrm{arccsc}\left(c x \right)}{\sqrt{e x +d}}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right)}{c \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}\, x d \sqrt{\frac{c}{d c -e}}}\right)}{e}"," ",0,"2/e*(-1/(e*x+d)^(1/2)*a+b*(-1/(e*x+d)^(1/2)*arccsc(c*x)+2/c/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)/x/d/(c/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))))","A"
67,0,0,21,7.378000," ","int((a+b*arccsc(c*x))/x/(e*x+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x \left(e x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x/(e*x+d)^(3/2),x)","F"
68,-2,0,21,180.000000," ","int((a+b*arccsc(c*x))/x^2/(e*x+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x^{2} \left(e x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x^2/(e*x+d)^(3/2),x)","F"
69,1,1077,548,0.086000," ","int(x^3*(a+b*arccsc(c*x))/(e*x+d)^(5/2),x)","\frac{2 a \left(\frac{\left(e x +d \right)^{\frac{3}{2}}}{3}-3 d \sqrt{e x +d}+\frac{d^{3}}{3 \left(e x +d \right)^{\frac{3}{2}}}-\frac{3 d^{2}}{\sqrt{e x +d}}\right)+2 b \left(\frac{\left(e x +d \right)^{\frac{3}{2}} \mathrm{arccsc}\left(c x \right)}{3}-3 \,\mathrm{arccsc}\left(c x \right) d \sqrt{e x +d}+\frac{\mathrm{arccsc}\left(c x \right) d^{3}}{3 \left(e x +d \right)^{\frac{3}{2}}}-\frac{3 \,\mathrm{arccsc}\left(c x \right) d^{2}}{\sqrt{e x +d}}+\frac{\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{2} c^{3} d^{2}}{3}-\frac{16 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c^{3} d^{3}}{3}+\frac{32 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) \sqrt{e x +d}\, c^{3} d^{3}}{3}-\frac{4 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right) c^{3} d^{3}}{3}+\frac{2 \sqrt{\frac{c}{d c -e}}\, c^{3} d^{4}}{3}+\frac{14 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c d \,e^{2}}{3}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c d \,e^{2}}{3}-\frac{32 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) \sqrt{e x +d}\, c d \,e^{2}}{3}-\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, e^{3}}{3}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, e^{3}}{3}-\frac{2 \sqrt{\frac{c}{d c -e}}\, c \,d^{2} e^{2}}{3}}{c^{2} \left(d c -e \right) \sqrt{\frac{c}{d c -e}}\, \sqrt{e x +d}\, \left(d c +e \right) x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e^{4}}"," ",0,"2/e^4*(a*(1/3*(e*x+d)^(3/2)-3*d*(e*x+d)^(1/2)+1/3*d^3/(e*x+d)^(3/2)-3*d^2/(e*x+d)^(1/2))+b*(1/3*(e*x+d)^(3/2)*arccsc(c*x)-3*arccsc(c*x)*d*(e*x+d)^(1/2)+1/3*arccsc(c*x)*d^3/(e*x+d)^(3/2)-3*arccsc(c*x)*d^2/(e*x+d)^(1/2)+2/3/c^2*((c/(c*d-e))^(1/2)*(e*x+d)^2*c^3*d^2-8*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c^3*d^3+16*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*(e*x+d)^(1/2)*c^3*d^3-2*(c/(c*d-e))^(1/2)*(e*x+d)*c^3*d^3+(c/(c*d-e))^(1/2)*c^3*d^4+7*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c*d*e^2+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c*d*e^2-16*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*(e*x+d)^(1/2)*c*d*e^2-(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*e^3+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*e^3-(c/(c*d-e))^(1/2)*c*d^2*e^2)/(c*d-e)/(c/(c*d-e))^(1/2)/(e*x+d)^(1/2)/(c*d+e)/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","A"
70,1,1040,401,0.080000," ","int(x^2*(a+b*arccsc(c*x))/(e*x+d)^(5/2),x)","\frac{2 a \left(\sqrt{e x +d}-\frac{d^{2}}{3 \left(e x +d \right)^{\frac{3}{2}}}+\frac{2 d}{\sqrt{e x +d}}\right)+2 b \left(\sqrt{e x +d}\, \mathrm{arccsc}\left(c x \right)-\frac{\mathrm{arccsc}\left(c x \right) d^{2}}{3 \left(e x +d \right)^{\frac{3}{2}}}+\frac{2 \,\mathrm{arccsc}\left(c x \right) d}{\sqrt{e x +d}}+\frac{\frac{8 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c^{2} d^{2}}{3}-\frac{16 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) \sqrt{e x +d}\, c^{2} d^{2}}{3}-\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c^{2} d^{2}}{3}-\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{2} c^{2} d}{3}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c d e}{3}-\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c d e}{3}+\frac{4 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right) c^{2} d^{2}}{3}-2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, e^{2}+\frac{16 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) \sqrt{e x +d}\, e^{2}}{3}-\frac{2 \sqrt{\frac{c}{d c -e}}\, c^{2} d^{3}}{3}+\frac{2 \sqrt{\frac{c}{d c -e}}\, d \,e^{2}}{3}}{c \left(d c -e \right) \sqrt{\frac{c}{d c -e}}\, \sqrt{e x +d}\, \left(d c +e \right) x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e^{3}}"," ",0,"2/e^3*(a*((e*x+d)^(1/2)-1/3*d^2/(e*x+d)^(3/2)+2*d/(e*x+d)^(1/2))+b*((e*x+d)^(1/2)*arccsc(c*x)-1/3*arccsc(c*x)*d^2/(e*x+d)^(3/2)+2*arccsc(c*x)*d/(e*x+d)^(1/2)+2/3/c*(4*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c^2*d^2-8*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*(e*x+d)^(1/2)*c^2*d^2-(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c^2*d^2-(c/(c*d-e))^(1/2)*(e*x+d)^2*c^2*d+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c*d*e-(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c*d*e+2*(c/(c*d-e))^(1/2)*(e*x+d)*c^2*d^2-3*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*e^2+8*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*(e*x+d)^(1/2)*e^2-(c/(c*d-e))^(1/2)*c^2*d^3+(c/(c*d-e))^(1/2)*d*e^2)/(c*d-e)/(c/(c*d-e))^(1/2)/(e*x+d)^(1/2)/(c*d+e)/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","B"
71,1,913,284,0.079000," ","int(x*(a+b*arccsc(c*x))/(e*x+d)^(5/2),x)","\frac{2 a \left(\frac{d}{3 \left(e x +d \right)^{\frac{3}{2}}}-\frac{1}{\sqrt{e x +d}}\right)+2 b \left(\frac{\mathrm{arccsc}\left(c x \right) d}{3 \left(e x +d \right)^{\frac{3}{2}}}-\frac{\mathrm{arccsc}\left(c x \right)}{\sqrt{e x +d}}+\frac{\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{2} c^{2} d}{3}+\frac{4 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) \sqrt{e x +d}\, c^{2} d^{2}}{3}-\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c^{2} d^{2}}{3}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c^{2} d^{2}}{3}-\frac{4 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right) c^{2} d^{2}}{3}-\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c d e}{3}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c d e}{3}+\frac{2 \sqrt{\frac{c}{d c -e}}\, c^{2} d^{3}}{3}-\frac{4 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) \sqrt{e x +d}\, e^{2}}{3}-\frac{2 \sqrt{\frac{c}{d c -e}}\, d \,e^{2}}{3}}{c \left(d c -e \right) \sqrt{e x +d}\, \left(d c +e \right) \sqrt{\frac{c}{d c -e}}\, d x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e^{2}}"," ",0,"2/e^2*(a*(1/3*d/(e*x+d)^(3/2)-1/(e*x+d)^(1/2))+b*(1/3*arccsc(c*x)*d/(e*x+d)^(3/2)-1/(e*x+d)^(1/2)*arccsc(c*x)+2/3/c*((c/(c*d-e))^(1/2)*(e*x+d)^2*c^2*d+2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*(e*x+d)^(1/2)*c^2*d^2-(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c^2*d^2+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c^2*d^2-2*(c/(c*d-e))^(1/2)*(e*x+d)*c^2*d^2-(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c*d*e+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c*d*e+(c/(c*d-e))^(1/2)*c^2*d^3-2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*(e*x+d)^(1/2)*e^2-(c/(c*d-e))^(1/2)*d*e^2)/(c*d-e)/(e*x+d)^(1/2)/(c*d+e)/(c/(c*d-e))^(1/2)/d/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","B"
72,1,886,270,0.079000," ","int((a+b*arccsc(c*x))/(e*x+d)^(5/2),x)","\frac{-\frac{2 a}{3 \left(e x +d \right)^{\frac{3}{2}}}+2 b \left(-\frac{\mathrm{arccsc}\left(c x \right)}{3 \left(e x +d \right)^{\frac{3}{2}}}-\frac{2 \left(\sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{2} c^{2} d -\sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) \sqrt{e x +d}\, c^{2} d^{2}-\sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c^{2} d^{2}+\sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c^{2} d^{2}-2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right) c^{2} d^{2}-\sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c d e +\sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c d e +\sqrt{\frac{c}{d c -e}}\, c^{2} d^{3}+\sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) \sqrt{e x +d}\, e^{2}-\sqrt{\frac{c}{d c -e}}\, d \,e^{2}\right)}{3 c \left(d c -e \right) \sqrt{e x +d}\, \left(d c +e \right) \sqrt{\frac{c}{d c -e}}\, d^{2} x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e}"," ",0,"2/e*(-1/3*a/(e*x+d)^(3/2)+b*(-1/3/(e*x+d)^(3/2)*arccsc(c*x)-2/3/c*((c/(c*d-e))^(1/2)*(e*x+d)^2*c^2*d-(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*(e*x+d)^(1/2)*c^2*d^2-(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c^2*d^2+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c^2*d^2-2*(c/(c*d-e))^(1/2)*(e*x+d)*c^2*d^2-(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c*d*e+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c*d*e+(c/(c*d-e))^(1/2)*c^2*d^3+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*(e*x+d)^(1/2)*e^2-(c/(c*d-e))^(1/2)*d*e^2)/(c*d-e)/(e*x+d)^(1/2)/(c*d+e)/(c/(c*d-e))^(1/2)/d^2/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","B"
73,-2,0,21,180.000000," ","int((a+b*arccsc(c*x))/x/(e*x+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x \left(e x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x/(e*x+d)^(5/2),x)","F"
74,-2,0,21,180.000000," ","int((a+b*arccsc(c*x))/x^2/(e*x+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x^{2} \left(e x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x^2/(e*x+d)^(5/2),x)","F"
75,1,1640,491,0.081000," ","int((a+b*arccsc(c*x))/(e*x+d)^(7/2),x)","\frac{-\frac{2 a}{5 \left(e x +d \right)^{\frac{5}{2}}}+2 b \left(-\frac{\mathrm{arccsc}\left(c x \right)}{5 \left(e x +d \right)^{\frac{5}{2}}}-\frac{2 \left(7 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{3} c^{4} d^{3}-6 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{4} d^{4}+7 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{4} d^{4}-3 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{4} d^{4}-13 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{2} c^{4} d^{4}-7 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{3} e +7 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{3} e -3 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{3} c^{2} d \,e^{2}+5 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right) c^{4} d^{5}+2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{2} d^{2} e^{2}-3 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{2} d^{2} e^{2}+6 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{2} d^{2} e^{2}+5 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{2} c^{2} d^{2} e^{2}+\sqrt{\frac{c}{d c -e}}\, c^{4} d^{6}+3 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \left(e x +d \right)^{\frac{3}{2}} c d \,e^{3}-3 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \left(e x +d \right)^{\frac{3}{2}} c d \,e^{3}-8 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right) c^{2} d^{3} e^{2}-3 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) \left(e x +d \right)^{\frac{3}{2}} e^{4}-2 \sqrt{\frac{c}{d c -e}}\, c^{2} d^{4} e^{2}+3 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right) d \,e^{4}+\sqrt{\frac{c}{d c -e}}\, d^{2} e^{4}\right)}{15 c \left(d c -e \right) \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{3}{2}} \left(d c +e \right) \left(c^{2} d^{2}-e^{2}\right) d^{3} x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e}"," ",0,"2/e*(-1/5*a/(e*x+d)^(5/2)+b*(-1/5/(e*x+d)^(5/2)*arccsc(c*x)-2/15/c*(7*(c/(c*d-e))^(1/2)*(e*x+d)^3*c^4*d^3-6*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(3/2)*c^4*d^4+7*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(3/2)*c^4*d^4-3*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*(e*x+d)^(3/2)*c^4*d^4-13*(c/(c*d-e))^(1/2)*(e*x+d)^2*c^4*d^4-7*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(3/2)*c^3*d^3*e+7*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(3/2)*c^3*d^3*e-3*(c/(c*d-e))^(1/2)*(e*x+d)^3*c^2*d*e^2+5*(c/(c*d-e))^(1/2)*(e*x+d)*c^4*d^5+2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(3/2)*c^2*d^2*e^2-3*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(3/2)*c^2*d^2*e^2+6*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*(e*x+d)^(3/2)*c^2*d^2*e^2+5*(c/(c*d-e))^(1/2)*(e*x+d)^2*c^2*d^2*e^2+(c/(c*d-e))^(1/2)*c^4*d^6+3*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(3/2)*c*d*e^3-3*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(3/2)*c*d*e^3-8*(c/(c*d-e))^(1/2)*(e*x+d)*c^2*d^3*e^2-3*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*(e*x+d)^(3/2)*e^4-2*(c/(c*d-e))^(1/2)*c^2*d^4*e^2+3*(c/(c*d-e))^(1/2)*(e*x+d)*d*e^4+(c/(c*d-e))^(1/2)*d^2*e^4)/(c*d-e)/(c/(c*d-e))^(1/2)/(e*x+d)^(3/2)/(c*d+e)/(c^2*d^2-e^2)/d^3/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","B"
76,1,338,178,0.056000," ","int(x^4*(e*x^2+d)*(a+b*arccsc(c*x)),x)","\frac{a e \,x^{7}}{7}+\frac{a \,x^{5} d}{5}+\frac{b \,\mathrm{arccsc}\left(c x \right) e \,x^{7}}{7}+\frac{b \,\mathrm{arccsc}\left(c x \right) x^{5} d}{5}+\frac{b \,x^{6} e}{42 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,x^{4} e}{168 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,x^{4} d}{20 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,x^{2} d}{40 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{5 b \,x^{2} e}{336 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{3 b d}{40 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{3 b \sqrt{c^{2} x^{2}-1}\, d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{40 c^{6} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{5 b e}{112 c^{7} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{5 b \sqrt{c^{2} x^{2}-1}\, e \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{112 c^{8} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/7*a*e*x^7+1/5*a*x^5*d+1/7*b*arccsc(c*x)*e*x^7+1/5*b*arccsc(c*x)*x^5*d+1/42/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^6*e+1/168/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^4*e+1/20/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^4*d+1/40/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2*d+5/336/c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2*e-3/40/c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*d+3/40/c^6*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*(c^2*x^2-1)^(1/2)*d*ln(c*x+(c^2*x^2-1)^(1/2))-5/112/c^7*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e+5/112/c^8*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e*ln(c*x+(c^2*x^2-1)^(1/2))","A"
77,1,282,139,0.055000," ","int(x^2*(e*x^2+d)*(a+b*arccsc(c*x)),x)","\frac{a e \,x^{5}}{5}+\frac{a d \,x^{3}}{3}+\frac{b \,\mathrm{arccsc}\left(c x \right) e \,x^{5}}{5}+\frac{b \,\mathrm{arccsc}\left(c x \right) d \,x^{3}}{3}+\frac{b \,x^{4} e}{20 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,x^{2} e}{40 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b d \,x^{2}}{6 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b d}{6 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \sqrt{c^{2} x^{2}-1}\, d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{6 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{3 b e}{40 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{3 b \sqrt{c^{2} x^{2}-1}\, e \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{40 c^{6} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/5*a*e*x^5+1/3*a*d*x^3+1/5*b*arccsc(c*x)*e*x^5+1/3*b*arccsc(c*x)*d*x^3+1/20/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^4*e+1/40/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2*e+1/6/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*d*x^2-1/6/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*d+1/6/c^4*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*(c^2*x^2-1)^(1/2)*d*ln(c*x+(c^2*x^2-1)^(1/2))-3/40/c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e+3/40/c^6*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e*ln(c*x+(c^2*x^2-1)^(1/2))","B"
78,1,194,95,0.055000," ","int((e*x^2+d)*(a+b*arccsc(c*x)),x)","\frac{a e \,x^{3}}{3}+a d x +\frac{b \,\mathrm{arccsc}\left(c x \right) x^{3} e}{3}+b \,\mathrm{arccsc}\left(c x \right) x d +\frac{b \sqrt{c^{2} x^{2}-1}\, d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{b e \,x^{2}}{6 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b e}{6 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \sqrt{c^{2} x^{2}-1}\, e \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{6 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/3*a*e*x^3+a*d*x+1/3*b*arccsc(c*x)*x^3*e+b*arccsc(c*x)*x*d+1/c^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*(c^2*x^2-1)^(1/2)*d*ln(c*x+(c^2*x^2-1)^(1/2))+1/6/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e*x^2-1/6/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e+1/6/c^4*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e*ln(c*x+(c^2*x^2-1)^(1/2))","B"
79,1,136,79,0.060000," ","int((e*x^2+d)*(a+b*arccsc(c*x))/x^2,x)","a e x -\frac{a d}{x}+b \,\mathrm{arccsc}\left(c x \right) e x -\frac{b \,\mathrm{arccsc}\left(c x \right) d}{x}-\frac{c b d}{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b d}{c \,x^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \sqrt{c^{2} x^{2}-1}\, e \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"a*e*x-a*d/x+b*arccsc(c*x)*e*x-b*arccsc(c*x)*d/x-c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*d+b/c/x^2/((c^2*x^2-1)/c^2/x^2)^(1/2)*d+b/c^2*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e*ln(c*x+(c^2*x^2-1)^(1/2))","A"
80,1,121,91,0.062000," ","int((e*x^2+d)*(a+b*arccsc(c*x))/x^4,x)","c^{3} \left(\frac{a \left(-\frac{d}{3 c \,x^{3}}-\frac{e}{c x}\right)}{c^{2}}+\frac{b \left(-\frac{\mathrm{arccsc}\left(c x \right) d}{3 c \,x^{3}}-\frac{\mathrm{arccsc}\left(c x \right) e}{c x}-\frac{\left(c^{2} x^{2}-1\right) \left(2 c^{4} d \,x^{2}+9 c^{2} e \,x^{2}+c^{2} d \right)}{9 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{4} x^{4}}\right)}{c^{2}}\right)"," ",0,"c^3*(a/c^2*(-1/3/c*d/x^3-e/c/x)+b/c^2*(-1/3*arccsc(c*x)/c*d/x^3-arccsc(c*x)*e/c/x-1/9*(c^2*x^2-1)*(2*c^4*d*x^2+9*c^2*e*x^2+c^2*d)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^4/x^4))","A"
81,1,140,130,0.062000," ","int((e*x^2+d)*(a+b*arccsc(c*x))/x^6,x)","c^{5} \left(\frac{a \left(-\frac{e}{3 c^{3} x^{3}}-\frac{d}{5 c^{3} x^{5}}\right)}{c^{2}}+\frac{b \left(-\frac{\mathrm{arccsc}\left(c x \right) e}{3 c^{3} x^{3}}-\frac{\mathrm{arccsc}\left(c x \right) d}{5 c^{3} x^{5}}-\frac{\left(c^{2} x^{2}-1\right) \left(24 x^{4} c^{6} d +50 c^{4} e \,x^{4}+12 c^{4} d \,x^{2}+25 c^{2} e \,x^{2}+9 c^{2} d \right)}{225 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{6} x^{6}}\right)}{c^{2}}\right)"," ",0,"c^5*(a/c^2*(-1/3*e/c^3/x^3-1/5/c^3*d/x^5)+b/c^2*(-1/3*arccsc(c*x)*e/c^3/x^3-1/5*arccsc(c*x)/c^3*d/x^5-1/225*(c^2*x^2-1)*(24*c^6*d*x^4+50*c^4*e*x^4+12*c^4*d*x^2+25*c^2*e*x^2+9*c^2*d)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^6/x^6))","A"
82,1,158,169,0.064000," ","int((e*x^2+d)*(a+b*arccsc(c*x))/x^8,x)","c^{7} \left(\frac{a \left(-\frac{d}{7 c^{5} x^{7}}-\frac{e}{5 c^{5} x^{5}}\right)}{c^{2}}+\frac{b \left(-\frac{\mathrm{arccsc}\left(c x \right) d}{7 c^{5} x^{7}}-\frac{\mathrm{arccsc}\left(c x \right) e}{5 c^{5} x^{5}}-\frac{\left(c^{2} x^{2}-1\right) \left(240 c^{8} d \,x^{6}+392 e \,c^{6} x^{6}+120 x^{4} c^{6} d +196 c^{4} e \,x^{4}+90 c^{4} d \,x^{2}+147 c^{2} e \,x^{2}+75 c^{2} d \right)}{3675 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{8} x^{8}}\right)}{c^{2}}\right)"," ",0,"c^7*(a/c^2*(-1/7/c^5*d/x^7-1/5*e/c^5/x^5)+b/c^2*(-1/7*arccsc(c*x)/c^5*d/x^7-1/5*arccsc(c*x)*e/c^5/x^5-1/3675*(c^2*x^2-1)*(240*c^8*d*x^6+392*c^6*e*x^6+120*c^6*d*x^4+196*c^4*e*x^4+90*c^4*d*x^2+147*c^2*e*x^2+75*c^2*d)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^8/x^8))","A"
83,1,152,168,0.053000," ","int(x^5*(e*x^2+d)*(a+b*arccsc(c*x)),x)","\frac{\frac{a \left(\frac{1}{8} e \,c^{8} x^{8}+\frac{1}{6} c^{8} d \,x^{6}\right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arccsc}\left(c x \right) e \,c^{8} x^{8}}{8}+\frac{\mathrm{arccsc}\left(c x \right) c^{8} x^{6} d}{6}+\frac{\left(c^{2} x^{2}-1\right) \left(45 e \,c^{6} x^{6}+84 x^{4} c^{6} d +54 c^{4} e \,x^{4}+112 c^{4} d \,x^{2}+72 c^{2} e \,x^{2}+224 c^{2} d +144 e \right)}{2520 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c x}\right)}{c^{2}}}{c^{6}}"," ",0,"1/c^6*(a/c^2*(1/8*e*c^8*x^8+1/6*c^8*d*x^6)+b/c^2*(1/8*arccsc(c*x)*e*c^8*x^8+1/6*arccsc(c*x)*c^8*x^6*d+1/2520*(c^2*x^2-1)*(45*c^6*e*x^6+84*c^6*d*x^4+54*c^4*e*x^4+112*c^4*d*x^2+72*c^2*e*x^2+224*c^2*d+144*e)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c/x))","A"
84,1,134,131,0.053000," ","int(x^3*(e*x^2+d)*(a+b*arccsc(c*x)),x)","\frac{\frac{a \left(\frac{1}{6} e \,c^{6} x^{6}+\frac{1}{4} x^{4} c^{6} d \right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arccsc}\left(c x \right) e \,c^{6} x^{6}}{6}+\frac{\mathrm{arccsc}\left(c x \right) c^{6} x^{4} d}{4}+\frac{\left(c^{2} x^{2}-1\right) \left(6 c^{4} e \,x^{4}+15 c^{4} d \,x^{2}+8 c^{2} e \,x^{2}+30 c^{2} d +16 e \right)}{180 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c x}\right)}{c^{2}}}{c^{4}}"," ",0,"1/c^4*(a/c^2*(1/6*e*c^6*x^6+1/4*x^4*c^6*d)+b/c^2*(1/6*arccsc(c*x)*e*c^6*x^6+1/4*arccsc(c*x)*c^6*x^4*d+1/180*(c^2*x^2-1)*(6*c^4*e*x^4+15*c^4*d*x^2+8*c^2*e*x^2+30*c^2*d+16*e)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c/x))","A"
85,1,115,118,0.053000," ","int(x*(e*x^2+d)*(a+b*arccsc(c*x)),x)","\frac{\frac{a \left(\frac{1}{4} c^{4} e \,x^{4}+\frac{1}{2} c^{4} d \,x^{2}\right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arccsc}\left(c x \right) e \,c^{4} x^{4}}{4}+\frac{\mathrm{arccsc}\left(c x \right) c^{4} d \,x^{2}}{2}+\frac{\left(c^{2} x^{2}-1\right) \left(c^{2} e \,x^{2}+6 c^{2} d +2 e \right)}{12 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c x}\right)}{c^{2}}}{c^{2}}"," ",0,"1/c^2*(a/c^2*(1/4*c^4*e*x^4+1/2*c^4*d*x^2)+b/c^2*(1/4*arccsc(c*x)*e*c^4*x^4+1/2*arccsc(c*x)*c^4*d*x^2+1/12*(c^2*x^2-1)*(c^2*e*x^2+6*c^2*d+2*e)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c/x))","A"
86,1,198,140,3.304000," ","int((e*x^2+d)*(a+b*arccsc(c*x))/x,x)","\frac{a \,x^{2} e}{2}+d a \ln \left(c x \right)+\frac{i b d \mathrm{arccsc}\left(c x \right)^{2}}{2}+\frac{b \,\mathrm{arccsc}\left(c x \right) x^{2} e}{2}+\frac{b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x e}{2 c}-\frac{i b e}{2 c^{2}}-b d \,\mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-b d \,\mathrm{arccsc}\left(c x \right) \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+i b d \polylog \left(2, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+i b d \polylog \left(2, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)"," ",0,"1/2*a*x^2*e+d*a*ln(c*x)+1/2*I*b*d*arccsc(c*x)^2+1/2*b*arccsc(c*x)*x^2*e+1/2*b/c*((c^2*x^2-1)/c^2/x^2)^(1/2)*x*e-1/2*I*b/c^2*e-b*d*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))-b*d*arccsc(c*x)*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))+I*b*d*polylog(2,-I/c/x-(1-1/c^2/x^2)^(1/2))+I*b*d*polylog(2,I/c/x+(1-1/c^2/x^2)^(1/2))","A"
87,1,185,151,0.776000," ","int((e*x^2+d)*(a+b*arccsc(c*x))/x^3,x)","a e \ln \left(c x \right)-\frac{d a}{2 x^{2}}+\frac{i b e \mathrm{arccsc}\left(c x \right)^{2}}{2}-b e \,\mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-b e \,\mathrm{arccsc}\left(c x \right) \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+i b e \polylog \left(2, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+i b e \polylog \left(2, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+\frac{c^{2} b d \,\mathrm{arccsc}\left(c x \right) \cos \left(2 \,\mathrm{arccsc}\left(c x \right)\right)}{4}-\frac{c^{2} b \sin \left(2 \,\mathrm{arccsc}\left(c x \right)\right) d}{8}"," ",0,"a*e*ln(c*x)-1/2*d*a/x^2+1/2*I*b*e*arccsc(c*x)^2-b*e*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))-b*e*arccsc(c*x)*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))+I*b*e*polylog(2,-I/c/x-(1-1/c^2/x^2)^(1/2))+I*b*e*polylog(2,I/c/x+(1-1/c^2/x^2)^(1/2))+1/4*c^2*b*d*arccsc(c*x)*cos(2*arccsc(c*x))-1/8*c^2*b*sin(2*arccsc(c*x))*d","A"
88,1,494,222,0.056000," ","int(x^2*(e*x^2+d)^2*(a+b*arccsc(c*x)),x)","\frac{a \,e^{2} x^{7}}{7}+\frac{2 a e d \,x^{5}}{5}+\frac{a \,x^{3} d^{2}}{3}+\frac{b \,\mathrm{arccsc}\left(c x \right) e^{2} x^{7}}{7}+\frac{2 b \,\mathrm{arccsc}\left(c x \right) e d \,x^{5}}{5}+\frac{b \,\mathrm{arccsc}\left(c x \right) x^{3} d^{2}}{3}+\frac{b \,x^{6} e^{2}}{42 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,x^{4} e^{2}}{168 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,x^{4} e d}{10 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,x^{2} e d}{20 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,d^{2} x^{2}}{6 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,d^{2}}{6 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \sqrt{c^{2} x^{2}-1}\, d^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{6 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{5 b \,x^{2} e^{2}}{336 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{3 b e d}{20 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{3 b \sqrt{c^{2} x^{2}-1}\, e d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{20 c^{6} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{5 b \,e^{2}}{112 c^{7} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{5 b \sqrt{c^{2} x^{2}-1}\, e^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{112 c^{8} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/7*a*e^2*x^7+2/5*a*e*d*x^5+1/3*a*x^3*d^2+1/7*b*arccsc(c*x)*e^2*x^7+2/5*b*arccsc(c*x)*e*d*x^5+1/3*b*arccsc(c*x)*x^3*d^2+1/42/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^6*e^2+1/168/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^4*e^2+1/10/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^4*e*d+1/20/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2*e*d+1/6/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*d^2*x^2-1/6/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*d^2+1/6/c^4*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d^2*ln(c*x+(c^2*x^2-1)^(1/2))+5/336/c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2*e^2-3/20/c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e*d+3/20/c^6*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e*d*ln(c*x+(c^2*x^2-1)^(1/2))-5/112/c^7*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e^2+5/112/c^8*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e^2*ln(c*x+(c^2*x^2-1)^(1/2))","B"
89,1,371,169,0.056000," ","int((e*x^2+d)^2*(a+b*arccsc(c*x)),x)","\frac{a \,e^{2} x^{5}}{5}+\frac{2 a \,x^{3} d e}{3}+a x \,d^{2}+\frac{b \,\mathrm{arccsc}\left(c x \right) e^{2} x^{5}}{5}+\frac{2 b \,\mathrm{arccsc}\left(c x \right) x^{3} d e}{3}+b \,\mathrm{arccsc}\left(c x \right) x \,d^{2}+\frac{b \sqrt{c^{2} x^{2}-1}\, d^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{b \,x^{4} e^{2}}{20 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,x^{2} e^{2}}{40 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b e d \,x^{2}}{3 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b e d}{3 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \sqrt{c^{2} x^{2}-1}\, e d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{3 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{3 b \,e^{2}}{40 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{3 b \sqrt{c^{2} x^{2}-1}\, e^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{40 c^{6} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/5*a*e^2*x^5+2/3*a*x^3*d*e+a*x*d^2+1/5*b*arccsc(c*x)*e^2*x^5+2/3*b*arccsc(c*x)*x^3*d*e+b*arccsc(c*x)*x*d^2+1/c^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d^2*ln(c*x+(c^2*x^2-1)^(1/2))+1/20/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^4*e^2+1/40/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2*e^2+1/3/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e*d*x^2-1/3/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e*d+1/3/c^4*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e*d*ln(c*x+(c^2*x^2-1)^(1/2))-3/40/c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e^2+3/40/c^6*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e^2*ln(c*x+(c^2*x^2-1)^(1/2))","B"
90,1,286,145,0.061000," ","int((e*x^2+d)^2*(a+b*arccsc(c*x))/x^2,x)","\frac{a \,e^{2} x^{3}}{3}+2 a e d x -\frac{a \,d^{2}}{x}+\frac{b \,\mathrm{arccsc}\left(c x \right) x^{3} e^{2}}{3}+2 b \,\mathrm{arccsc}\left(c x \right) e d x -\frac{b \,\mathrm{arccsc}\left(c x \right) d^{2}}{x}-\frac{c b \,d^{2}}{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,d^{2}}{c \,x^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{2 b \sqrt{c^{2} x^{2}-1}\, e d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{b \,e^{2} x^{2}}{6 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,e^{2}}{6 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,e^{2} \sqrt{c^{2} x^{2}-1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{6 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/3*a*e^2*x^3+2*a*e*d*x-a*d^2/x+1/3*b*arccsc(c*x)*x^3*e^2+2*b*arccsc(c*x)*e*d*x-b*arccsc(c*x)*d^2/x-c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*d^2+b/c/x^2/((c^2*x^2-1)/c^2/x^2)^(1/2)*d^2+2*b/c^2*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e*d*ln(c*x+(c^2*x^2-1)^(1/2))+1/6/c*b*e^2/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2-1/6/c^3*b*e^2/((c^2*x^2-1)/c^2/x^2)^(1/2)+1/6/c^4*b*e^2*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*ln(c*x+(c^2*x^2-1)^(1/2))","A"
91,1,254,139,0.067000," ","int((e*x^2+d)^2*(a+b*arccsc(c*x))/x^4,x)","a x \,e^{2}-\frac{a \,d^{2}}{3 x^{3}}-\frac{2 a e d}{x}+b \,\mathrm{arccsc}\left(c x \right) x \,e^{2}-\frac{b \,\mathrm{arccsc}\left(c x \right) d^{2}}{3 x^{3}}-\frac{2 b \,\mathrm{arccsc}\left(c x \right) e d}{x}-\frac{2 c^{3} b \,d^{2}}{9 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{c b \,d^{2}}{9 x^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{2 c b e d}{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{2 b e d}{c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{2}}+\frac{b \,d^{2}}{9 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{4}}+\frac{b \sqrt{c^{2} x^{2}-1}\, e^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"a*x*e^2-1/3*a*d^2/x^3-2*a*e*d/x+b*arccsc(c*x)*x*e^2-1/3*b*arccsc(c*x)*d^2/x^3-2*b*arccsc(c*x)*e*d/x-2/9*c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*d^2+1/9*c*b/x^2/((c^2*x^2-1)/c^2/x^2)^(1/2)*d^2-2*c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e*d+2/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^2*e*d+1/9/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^4*d^2+1/c^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e^2*ln(c*x+(c^2*x^2-1)^(1/2))","A"
92,1,191,161,0.064000," ","int((e*x^2+d)^2*(a+b*arccsc(c*x))/x^6,x)","c^{5} \left(\frac{a \left(-\frac{2 e d}{3 c \,x^{3}}-\frac{e^{2}}{c x}-\frac{d^{2}}{5 c \,x^{5}}\right)}{c^{4}}+\frac{b \left(-\frac{2 \,\mathrm{arccsc}\left(c x \right) e d}{3 c \,x^{3}}-\frac{\mathrm{arccsc}\left(c x \right) e^{2}}{c x}-\frac{\mathrm{arccsc}\left(c x \right) d^{2}}{5 c \,x^{5}}-\frac{\left(c^{2} x^{2}-1\right) \left(24 x^{4} c^{8} d^{2}+100 c^{6} e d \,x^{4}+12 x^{2} c^{6} d^{2}+225 c^{4} e^{2} x^{4}+50 c^{4} d e \,x^{2}+9 d^{2} c^{4}\right)}{225 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{6} x^{6}}\right)}{c^{4}}\right)"," ",0,"c^5*(a/c^4*(-2/3/c*e*d/x^3-e^2/c/x-1/5*d^2/c/x^5)+b/c^4*(-2/3*arccsc(c*x)/c*e*d/x^3-arccsc(c*x)*e^2/c/x-1/5*arccsc(c*x)*d^2/c/x^5-1/225*(c^2*x^2-1)*(24*c^8*d^2*x^4+100*c^6*d*e*x^4+12*c^6*d^2*x^2+225*c^4*e^2*x^4+50*c^4*d*e*x^2+9*c^4*d^2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^6/x^6))","A"
93,1,223,211,0.066000," ","int((e*x^2+d)^2*(a+b*arccsc(c*x))/x^8,x)","c^{7} \left(\frac{a \left(-\frac{d^{2}}{7 c^{3} x^{7}}-\frac{e^{2}}{3 c^{3} x^{3}}-\frac{2 e d}{5 c^{3} x^{5}}\right)}{c^{4}}+\frac{b \left(-\frac{\mathrm{arccsc}\left(c x \right) d^{2}}{7 c^{3} x^{7}}-\frac{\mathrm{arccsc}\left(c x \right) e^{2}}{3 c^{3} x^{3}}-\frac{2 \,\mathrm{arccsc}\left(c x \right) e d}{5 c^{3} x^{5}}-\frac{\left(c^{2} x^{2}-1\right) \left(720 c^{10} d^{2} x^{6}+2352 c^{8} e d \,x^{6}+360 x^{4} c^{8} d^{2}+2450 e^{2} c^{6} x^{6}+1176 c^{6} e d \,x^{4}+270 x^{2} c^{6} d^{2}+1225 c^{4} e^{2} x^{4}+882 c^{4} d e \,x^{2}+225 d^{2} c^{4}\right)}{11025 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{8} x^{8}}\right)}{c^{4}}\right)"," ",0,"c^7*(a/c^4*(-1/7*d^2/c^3/x^7-1/3*e^2/c^3/x^3-2/5/c^3*e*d/x^5)+b/c^4*(-1/7*arccsc(c*x)*d^2/c^3/x^7-1/3*arccsc(c*x)*e^2/c^3/x^3-2/5*arccsc(c*x)/c^3*e*d/x^5-1/11025*(c^2*x^2-1)*(720*c^10*d^2*x^6+2352*c^8*d*e*x^6+360*c^8*d^2*x^4+2450*c^6*e^2*x^6+1176*c^6*d*e*x^4+270*c^6*d^2*x^2+1225*c^4*e^2*x^4+882*c^4*d*e*x^2+225*c^4*d^2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^8/x^8))","A"
94,1,214,212,0.056000," ","int(x^3*(e*x^2+d)^2*(a+b*arccsc(c*x)),x)","\frac{\frac{a \left(\frac{1}{8} e^{2} c^{8} x^{8}+\frac{1}{3} c^{8} e d \,x^{6}+\frac{1}{4} x^{4} c^{8} d^{2}\right)}{c^{4}}+\frac{b \left(\frac{\mathrm{arccsc}\left(c x \right) e^{2} c^{8} x^{8}}{8}+\frac{\mathrm{arccsc}\left(c x \right) c^{8} e d \,x^{6}}{3}+\frac{\mathrm{arccsc}\left(c x \right) c^{8} x^{4} d^{2}}{4}+\frac{\left(c^{2} x^{2}-1\right) \left(45 e^{2} c^{6} x^{6}+168 c^{6} e d \,x^{4}+210 x^{2} c^{6} d^{2}+54 c^{4} e^{2} x^{4}+224 c^{4} d e \,x^{2}+420 d^{2} c^{4}+72 c^{2} e^{2} x^{2}+448 c^{2} e d +144 e^{2}\right)}{2520 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c x}\right)}{c^{4}}}{c^{4}}"," ",0,"1/c^4*(a/c^4*(1/8*e^2*c^8*x^8+1/3*c^8*e*d*x^6+1/4*x^4*c^8*d^2)+b/c^4*(1/8*arccsc(c*x)*e^2*c^8*x^8+1/3*arccsc(c*x)*c^8*e*d*x^6+1/4*arccsc(c*x)*c^8*x^4*d^2+1/2520*(c^2*x^2-1)*(45*c^6*e^2*x^6+168*c^6*d*e*x^4+210*c^6*d^2*x^2+54*c^4*e^2*x^4+224*c^4*d*e*x^2+420*c^4*d^2+72*c^2*e^2*x^2+448*c^2*d*e+144*e^2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c/x))","A"
95,1,182,169,0.056000," ","int(x*(e*x^2+d)^2*(a+b*arccsc(c*x)),x)","\frac{\frac{a \left(\frac{1}{6} e^{2} c^{6} x^{6}+\frac{1}{2} c^{6} e d \,x^{4}+\frac{1}{2} x^{2} c^{6} d^{2}\right)}{c^{4}}+\frac{b \left(\frac{\mathrm{arccsc}\left(c x \right) e^{2} c^{6} x^{6}}{6}+\frac{\mathrm{arccsc}\left(c x \right) c^{6} x^{4} d e}{2}+\frac{\mathrm{arccsc}\left(c x \right) c^{6} x^{2} d^{2}}{2}+\frac{\left(c^{2} x^{2}-1\right) \left(3 c^{4} e^{2} x^{4}+15 c^{4} d e \,x^{2}+45 d^{2} c^{4}+4 c^{2} e^{2} x^{2}+30 c^{2} e d +8 e^{2}\right)}{90 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c x}\right)}{c^{4}}}{c^{2}}"," ",0,"1/c^2*(a/c^4*(1/6*e^2*c^6*x^6+1/2*c^6*e*d*x^4+1/2*x^2*c^6*d^2)+b/c^4*(1/6*arccsc(c*x)*e^2*c^6*x^6+1/2*arccsc(c*x)*c^6*x^4*d*e+1/2*arccsc(c*x)*c^6*x^2*d^2+1/90*(c^2*x^2-1)*(3*c^4*e^2*x^4+15*c^4*d*e*x^2+45*c^4*d^2+4*c^2*e^2*x^2+30*c^2*d*e+8*e^2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c/x))","A"
96,1,301,198,6.183000," ","int((e*x^2+d)^2*(a+b*arccsc(c*x))/x,x)","\frac{a \,e^{2} x^{4}}{4}+a e d \,x^{2}+a \,d^{2} \ln \left(c x \right)+\frac{i b \,d^{2} \mathrm{arccsc}\left(c x \right)^{2}}{2}+\frac{b \,\mathrm{arccsc}\left(c x \right) e^{2} x^{4}}{4}+b \,\mathrm{arccsc}\left(c x \right) x^{2} d e +\frac{b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3} e^{2}}{12 c}+\frac{b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d e}{c}-\frac{i b d e}{c^{2}}+\frac{b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \,e^{2}}{6 c^{3}}-\frac{i b \,e^{2}}{6 c^{4}}-b \,d^{2} \mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-b \,d^{2} \mathrm{arccsc}\left(c x \right) \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+i b \,d^{2} \polylog \left(2, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+i b \,d^{2} \polylog \left(2, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)"," ",0,"1/4*a*e^2*x^4+a*e*d*x^2+a*d^2*ln(c*x)+1/2*I*b*d^2*arccsc(c*x)^2+1/4*b*arccsc(c*x)*e^2*x^4+b*arccsc(c*x)*x^2*d*e+1/12*b/c*((c^2*x^2-1)/c^2/x^2)^(1/2)*x^3*e^2+b/c*((c^2*x^2-1)/c^2/x^2)^(1/2)*x*d*e-I*b/c^2*d*e+1/6*b/c^3*((c^2*x^2-1)/c^2/x^2)^(1/2)*x*e^2-1/6*I*b/c^4*e^2-b*d^2*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))-b*d^2*arccsc(c*x)*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))+I*b*d^2*polylog(2,-I/c/x-(1-1/c^2/x^2)^(1/2))+I*b*d^2*polylog(2,I/c/x+(1-1/c^2/x^2)^(1/2))","A"
97,1,276,201,4.297000," ","int((e*x^2+d)^2*(a+b*arccsc(c*x))/x^3,x)","\frac{a \,x^{2} e^{2}}{2}+2 a e d \ln \left(c x \right)-\frac{a \,d^{2}}{2 x^{2}}+i b d e \mathrm{arccsc}\left(c x \right)^{2}-\frac{c b \,d^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{4 x}+\frac{b \,c^{2} d^{2} \mathrm{arccsc}\left(c x \right)}{4}-\frac{b \,\mathrm{arccsc}\left(c x \right) d^{2}}{2 x^{2}}+\frac{b \,\mathrm{arccsc}\left(c x \right) x^{2} e^{2}}{2}+\frac{b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \,e^{2}}{2 c}-\frac{i b \,e^{2}}{2 c^{2}}-2 b e d \,\mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)-2 b e d \,\mathrm{arccsc}\left(c x \right) \ln \left(1-\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+2 i b e d \polylog \left(2, -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+2 i b e d \polylog \left(2, \frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)"," ",0,"1/2*a*x^2*e^2+2*a*e*d*ln(c*x)-1/2*a*d^2/x^2+I*b*d*e*arccsc(c*x)^2-1/4*c*b*d^2/x*((c^2*x^2-1)/c^2/x^2)^(1/2)+1/4*b*c^2*d^2*arccsc(c*x)-1/2*b*arccsc(c*x)*d^2/x^2+1/2*b*arccsc(c*x)*x^2*e^2+1/2/c*b*((c^2*x^2-1)/c^2/x^2)^(1/2)*x*e^2-1/2*I/c^2*b*e^2-2*b*e*d*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))-2*b*e*d*arccsc(c*x)*ln(1-I/c/x-(1-1/c^2/x^2)^(1/2))+2*I*b*e*d*polylog(2,-I/c/x-(1-1/c^2/x^2)^(1/2))+2*I*b*e*d*polylog(2,I/c/x+(1-1/c^2/x^2)^(1/2))","A"
98,1,407,551,4.272000," ","int(x^2*(a+b*arccsc(c*x))/(e*x^2+d),x)","\frac{a x}{e}-\frac{a d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{e \sqrt{d e}}+\frac{b \,\mathrm{arccsc}\left(c x \right) x}{e}+\frac{b \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c e}-\frac{b \ln \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}-1\right)}{c e}+\frac{c b d \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d +4 \textit{\_R1}^{2} e -c^{2} d \right) \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e \right)}\right)}{8 e^{2}}-\frac{c b d \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d -c^{2} d -4 e \right) \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e \right)}\right)}{8 e^{2}}"," ",0,"a*x/e-a*d/e/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+b*arccsc(c*x)/e*x+1/c*b/e*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))-1/c*b/e*ln(I/c/x+(1-1/c^2/x^2)^(1/2)-1)+1/8*c*b/e^2*d*sum((_R1^2*c^2*d+4*_R1^2*e-c^2*d)/_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-1/8*c*b/e^2*d*sum((_R1^2*c^2*d-c^2*d-4*e)/_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))","C"
99,1,401,552,1.124000," ","int(x*(a+b*arccsc(c*x))/(e*x^2+d),x)","\frac{a \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 e}-\frac{b \,\mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e}+\frac{i b \dilog \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e}-\frac{i b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d -c^{2} d -4 e \right) \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right)}{4 e}-\frac{i b \dilog \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e}-\frac{i c^{2} b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2}-1\right) \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right) d}{4 e}"," ",0,"1/2*a/e*ln(c^2*e*x^2+c^2*d)-b/e*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))+I*b/e*dilog(1+I/c/x+(1-1/c^2/x^2)^(1/2))-1/4*I*b*sum((_R1^2*c^2*d-c^2*d-4*e)/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))/e-I*b*dilog(I/c/x+(1-1/c^2/x^2)^(1/2))/e-1/4*I*c^2*b*sum((_R1^2-1)/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))*d/e","C"
100,1,272,517,2.036000," ","int((a+b*arccsc(c*x))/(e*x^2+d),x)","\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}-\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e \right)}\right)}{2}-\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\textit{\_R1} \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right)}{2}"," ",0,"a/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-1/2*c*b*sum(1/_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-1/2*c*b*sum(_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))","C"
101,1,2875,496,1.073000," ","int((a+b*arccsc(c*x))/x/(e*x^2+d),x)","\text{output too large to display}"," ",0,"1/2*b*c^2*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/(c^2*d+e)-1/4*I*b*c^2*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/(c^2*d+e)-1/2*I*b*c^2*arccsc(c*x)^2/(c^2*d+e)+5/2*b*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)*e/d/(c^2*d+e)+I*b/c^4*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*e^2/d^3+I*b/c^2*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d^2*e-2*b/c^2*e*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d^2-2*b/c^4*e^2*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d^3-b/c^2*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d^2*(e*(c^2*d+e))^(1/2)+I*b/c^2*arccsc(c*x)^2/d^2*(e*(c^2*d+e))^(1/2)+3/2*b*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-I*b*(e*(c^2*d+e))^(1/2)/d/(c^2*d+e)*arccsc(c*x)^2-5/4*I*b*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*e/d/(c^2*d+e)-5/2*I*b*arccsc(c*x)^2*e/d/(c^2*d+e)-3/4*I*b*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d/(c^2*d+e)*(e*(c^2*d+e))^(1/2)+2*I*b/c^4*arccsc(c*x)^2*e^2/d^3+1/2*I*b/d*sum((_R1^2*c^2*d-2*c^2*d-4*e)/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))+1/4*I*b*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d-1/2*b*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d+I*b*arccsc(c*x)^2/d-2*b/c^4*e*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d^3*(e*(c^2*d+e))^(1/2)+1/4*b*c^2*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/e/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-1/4*b*c^2*(e*(c^2*d+e))^(1/2)/e/(c^2*d+e)*arccsc(c*x)*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e))-4*I*b/c^2*e^2*arccsc(c*x)^2/d^2/(c^2*d+e)+I*b/c^4*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*e/d^3*(e*(c^2*d+e))^(1/2)+2*b/c^4*e^3*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d^3/(c^2*d+e)+4*b/c^2*e^2*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d^2/(c^2*d+e)-I*b/c^4*e^3*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d^3/(c^2*d+e)+2*I*b/c^4*arccsc(c*x)^2*e/d^3*(e*(c^2*d+e))^(1/2)-2*I*b/c^4*e^3*arccsc(c*x)^2/d^3/(c^2*d+e)-1/8*I*b*c^2*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/e/(c^2*d+e)*(e*(c^2*d+e))^(1/2)+1/8*I*b*c^2*(e*(c^2*d+e))^(1/2)/e/(c^2*d+e)*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e))-2*I*b/c^2*e^2*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d^2/(c^2*d+e)+1/2*I*b/c^2*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d^2*(e*(c^2*d+e))^(1/2)+2*I*b/c^2*arccsc(c*x)^2/d^2*e+1/4*I*b*(e*(c^2*d+e))^(1/2)/d/(c^2*d+e)*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e))-1/2*b*(e*(c^2*d+e))^(1/2)/d/(c^2*d+e)*arccsc(c*x)*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e))+3*b/c^2*e*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d^2/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-I*b/c^4*e^2*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d^3/(c^2*d+e)*(e*(c^2*d+e))^(1/2)+2*b/c^4*e^2*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d^3/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-2*I*b/c^4*e^2*arccsc(c*x)^2/d^3/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-3/2*I*b/c^2*e*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d^2/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-3*I*b/c^2*e*arccsc(c*x)^2/d^2/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-1/2*a/d*ln(c^2*e*x^2+c^2*d)+a/d*ln(c*x)","C"
102,1,332,558,3.983000," ","int((a+b*arccsc(c*x))/x^2/(e*x^2+d),x)","-\frac{a e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{d \sqrt{d e}}-\frac{a}{d x}-\frac{c b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{d}-\frac{b \,\mathrm{arccsc}\left(c x \right)}{d x}+\frac{c b e \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e \right)}\right)}{2 d}+\frac{c b e \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\textit{\_R1} \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right)}{2 d}"," ",0,"-a*e/d/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-a/d/x-c*b/d*((c^2*x^2-1)/c^2/x^2)^(1/2)-b*arccsc(c*x)/d/x+1/2*c*b*e/d*sum(1/_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))+1/2*c*b*e/d*sum(_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))","C"
103,1,729,671,1.828000," ","int(x^5*(a+b*arccsc(c*x))/(e*x^2+d)^2,x)","\frac{a \,x^{2}}{2 e^{2}}-\frac{a d \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{e^{3}}-\frac{c^{2} a \,d^{2}}{2 e^{3} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c^{2} b \,\mathrm{arccsc}\left(c x \right) x^{4}}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c^{2} b \,\mathrm{arccsc}\left(c x \right) d \,x^{2}}{e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{i b \,x^{2}}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{i b d}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{i b \sqrt{e \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 c^{2} d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}-2 c^{2} d -4 e}{4 \sqrt{c^{2} e d +e^{2}}}\right) d}{2 \left(c^{2} d +e \right) e^{3}}+\frac{2 b d \,\mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e^{3}}-\frac{2 i b d \dilog \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e^{3}}+\frac{i b d \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d -c^{2} d -4 e \right) \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right)}{2 e^{3}}+\frac{2 i b d \dilog \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e^{3}}+\frac{i c^{2} b \,d^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2}-1\right) \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right)}{2 e^{3}}"," ",0,"1/2*a*x^2/e^2-a/e^3*d*ln(c^2*e*x^2+c^2*d)-1/2*c^2*a/e^3*d^2/(c^2*e*x^2+c^2*d)+1/2*c^2*b/e/(c^2*e*x^2+c^2*d)*arccsc(c*x)*x^4+c^2*b/e^2/(c^2*e*x^2+c^2*d)*arccsc(c*x)*d*x^2+1/2*c*b/e/(c^2*e*x^2+c^2*d)*((c^2*x^2-1)/c^2/x^2)^(1/2)*x^3+1/2*c*b/e^2/(c^2*e*x^2+c^2*d)*((c^2*x^2-1)/c^2/x^2)^(1/2)*x*d-1/2*I*b/e/(c^2*e*x^2+c^2*d)*x^2-1/2*I*b/e^2/(c^2*e*x^2+c^2*d)*d+1/2*I*b*(e*(c^2*d+e))^(1/2)/(c^2*d+e)/e^3*arctanh(1/4*(2*c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2-2*c^2*d-4*e)/(c^2*d*e+e^2)^(1/2))*d+2*b/e^3*d*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))-2*I*b/e^3*d*dilog(1+I/c/x+(1-1/c^2/x^2)^(1/2))+1/2*I*b/e^3*d*sum((_R1^2*c^2*d-c^2*d-4*e)/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))+2*I*b/e^3*d*dilog(I/c/x+(1-1/c^2/x^2)^(1/2))+1/2*I*c^2*b/e^3*d^2*sum((_R1^2-1)/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))","C"
104,1,541,624,1.364000," ","int(x^3*(a+b*arccsc(c*x))/(e*x^2+d)^2,x)","\frac{c^{2} a d}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{a \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 e^{2}}-\frac{c^{2} b \,x^{2} \mathrm{arccsc}\left(c x \right)}{2 \left(c^{2} e \,x^{2}+c^{2} d \right) e}-\frac{i b \sqrt{e \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 c^{2} d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}-2 c^{2} d -4 e}{4 \sqrt{c^{2} e d +e^{2}}}\right)}{2 e^{2} \left(c^{2} d +e \right)}-\frac{b \,\mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e^{2}}+\frac{i b \dilog \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e^{2}}-\frac{i b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d -c^{2} d -4 e \right) \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right)}{4 e^{2}}-\frac{i b \dilog \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e^{2}}-\frac{i c^{2} b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2}-1\right) \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right) d}{4 e^{2}}"," ",0,"1/2*c^2*a/e^2*d/(c^2*e*x^2+c^2*d)+1/2*a/e^2*ln(c^2*e*x^2+c^2*d)-1/2*c^2*b*x^2*arccsc(c*x)/(c^2*e*x^2+c^2*d)/e-1/2*I*b*(e*(c^2*d+e))^(1/2)/e^2/(c^2*d+e)*arctanh(1/4*(2*c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2-2*c^2*d-4*e)/(c^2*d*e+e^2)^(1/2))-b/e^2*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))+I*b/e^2*dilog(1+I/c/x+(1-1/c^2/x^2)^(1/2))-1/4*I*b/e^2*sum((_R1^2*c^2*d-c^2*d-4*e)/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-I*b/e^2*dilog(I/c/x+(1-1/c^2/x^2)^(1/2))-1/4*I*c^2*b/e^2*sum((_R1^2-1)/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))*d","C"
105,1,354,112,0.081000," ","int(x*(a+b*arccsc(c*x))/(e*x^2+d)^2,x)","-\frac{c^{2} a}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{2} b \,\mathrm{arccsc}\left(c x \right)}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{2 c e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d}-\frac{b \sqrt{c^{2} x^{2}-1}\, \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right)}{4 c e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \sqrt{-\frac{c^{2} d +e}{e}}}-\frac{b \sqrt{c^{2} x^{2}-1}\, \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right)}{4 c e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \sqrt{-\frac{c^{2} d +e}{e}}}"," ",0,"-1/2*c^2*a/e/(c^2*e*x^2+c^2*d)-1/2*c^2*b/e/(c^2*e*x^2+c^2*d)*arccsc(c*x)+1/2/c*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d*arctan(1/(c^2*x^2-1)^(1/2))-1/4/c*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/(-(c^2*d+e)/e)^(1/2)*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))-1/4/c*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/(-(c^2*d+e)/e)^(1/2)*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))","B"
106,1,3036,569,2.613000," ","int((a+b*arccsc(c*x))/x/(e*x^2+d)^2,x)","\text{output too large to display}"," ",0,"-1/2*a/d^2*ln(c^2*e*x^2+c^2*d)+a/d^2*ln(c*x)+1/8*I*b*c^2*(e*(c^2*d+e))^(1/2)/d/e/(c^2*d+e)*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e))-3/2*I*b/c^2*e*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d^3/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-2*I*b/c^4*e^2*arccsc(c*x)^2/d^4/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-3*I*b/c^2*arccsc(c*x)^2/d^3/(c^2*d+e)*(e*(c^2*d+e))^(1/2)*e+3*b/c^2*e*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d^3/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-1/4*b*c^2*(e*(c^2*d+e))^(1/2)/d/e/(c^2*d+e)*arccsc(c*x)*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e))-1/8*I*b*c^2*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d/e/(c^2*d+e)*(e*(c^2*d+e))^(1/2)+1/2*a*c^2/d/(c^2*e*x^2+c^2*d)+2*b/c^4*e^3*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d^4/(c^2*d+e)-2*I*b/c^2*e^2*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d^3/(c^2*d+e)-I*b/c^4*e^3*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d^4/(c^2*d+e)-2*I*b/c^4*e^3*arccsc(c*x)^2/d^4/(c^2*d+e)-4*I*b/c^2*arccsc(c*x)^2/d^3/(c^2*d+e)*e^2+2*I*b/c^4*arccsc(c*x)^2*e/d^4*(e*(c^2*d+e))^(1/2)-1/2*b*c^2*x^2*arccsc(c*x)*e/(c^2*e*x^2+c^2*d)/d^2+1/4*I*b*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d^2-1/2*b*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d^2+I*b*arccsc(c*x)^2/d^2+1/2*I*b/d^2*sum((_R1^2*c^2*d-2*c^2*d-4*e)/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))+I*b/c^4*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*e/d^4*(e*(c^2*d+e))^(1/2)-2*b/c^4*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)*e/d^4*(e*(c^2*d+e))^(1/2)+4*b/c^2*e^2*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d^3/(c^2*d+e)+3/2*b*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d^2/(c^2*d+e)*(e*(c^2*d+e))^(1/2)+5/2*b*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d^2*e/(c^2*d+e)-1/2*b*(e*(c^2*d+e))^(1/2)/d^2/(c^2*d+e)*arccsc(c*x)*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e))+1/2*I*b/c^2*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d^3*(e*(c^2*d+e))^(1/2)-1/4*I*b*c^2*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d/(c^2*d+e)+2*I*b/c^2*arccsc(c*x)^2*e/d^3+2*I*b/c^4*arccsc(c*x)^2*e^2/d^4-1/2*I*b*c^2*arccsc(c*x)^2/d/(c^2*d+e)-5/4*I*b*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d^2*e/(c^2*d+e)-I*b*(e*(c^2*d+e))^(1/2)/d^2/(c^2*d+e)*arccsc(c*x)^2-3/4*I*b*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d^2/(c^2*d+e)*(e*(c^2*d+e))^(1/2)+1/4*I*b*(e*(c^2*d+e))^(1/2)/d^2/(c^2*d+e)*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e))-1/2*I*b*(e*(c^2*d+e))^(1/2)/d^2/(c^2*d+e)*arctanh(1/4*(2*c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2-2*c^2*d-4*e)/(c^2*d*e+e^2)^(1/2))-5/2*I*b*arccsc(c*x)^2/d^2/(c^2*d+e)*e-2*b/c^4*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)*e^2/d^4-b/c^2*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d^3*(e*(c^2*d+e))^(1/2)+I*b/c^2*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d^3*e+I*b/c^2*arccsc(c*x)^2/d^3*(e*(c^2*d+e))^(1/2)+1/2*b*c^2*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d/(c^2*d+e)+I*b/c^4*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*e^2/d^4-2*b/c^2*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)*e/d^3+2*b/c^4*e^2*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d^4/(c^2*d+e)*(e*(c^2*d+e))^(1/2)+1/4*b*c^2*ln(1-c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))*arccsc(c*x)/d/e/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-I*b/c^4*e^2*polylog(2,c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2/(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e))/d^4/(c^2*d+e)*(e*(c^2*d+e))^(1/2)","C"
107,1,1888,745,19.149000," ","int(x^4*(a+b*arccsc(c*x))/(e*x^2+d)^2,x)","\frac{a x}{e^{2}}+\frac{c^{2} a d x}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{3 a d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 e^{2} \sqrt{d e}}+\frac{c^{2} b \,x^{3} \mathrm{arccsc}\left(c x \right)}{e \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{3 c^{2} b x \,\mathrm{arccsc}\left(c x \right) d}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{b \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c \,e^{2}}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{2 c^{2} e^{2} d}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} e^{2} d^{2}}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{c^{4} e \,d^{2}}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{2 c^{2} e^{2} \left(c^{2} d +e \right) d}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{c^{2} e \left(c^{2} d +e \right) d}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} e \left(c^{2} d +e \right) d^{2}}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{c^{4} \left(c^{2} d +e \right) d^{2}}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{2 c^{2} e^{2} d}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} e^{2} d^{2}}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{c^{4} e \,d^{2}}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{2 c^{2} e^{2} \left(c^{2} d +e \right) d}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{c^{2} e \left(c^{2} d +e \right) d}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} e \left(c^{2} d +e \right) d^{2}}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{c^{4} \left(c^{2} d +e \right) d^{2}}-\frac{b \ln \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}-1\right)}{c \,e^{2}}-\frac{3 c b d \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d -c^{2} d -4 e \right) \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e \right)}\right)}{16 e^{3}}+\frac{3 c b d \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d +4 \textit{\_R1}^{2} e -c^{2} d \right) \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e \right)}\right)}{16 e^{3}}"," ",0,"a*x/e^2+1/2*c^2*a/e^2*d*x/(c^2*e*x^2+c^2*d)-3/2*a/e^2*d/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+c^2*b*x^3*arccsc(c*x)/e/(c^2*e*x^2+c^2*d)+3/2*c^2*b*x*arccsc(c*x)/e^2/(c^2*e*x^2+c^2*d)*d+1/c*b/e^2*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))+1/2/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e^2/d+1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e^2/d^2*(e*(c^2*d+e))^(1/2)+1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/d^2-1/2/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e^2/(c^2*d+e)/d*(e*(c^2*d+e))^(1/2)-1/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)/d-1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)/d^2*(e*(c^2*d+e))^(1/2)-1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^2+1/2/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e^2/d-1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e^2/d^2*(e*(c^2*d+e))^(1/2)+1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/d^2+1/2/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e^2/(c^2*d+e)/d*(e*(c^2*d+e))^(1/2)-1/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)/d+1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)/d^2*(e*(c^2*d+e))^(1/2)-1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^2-1/c*b/e^2*ln(I/c/x+(1-1/c^2/x^2)^(1/2)-1)-3/16*c*b/e^3*d*sum((_R1^2*c^2*d-c^2*d-4*e)/_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))+3/16*c*b/e^3*d*sum((_R1^2*c^2*d+4*_R1^2*e-c^2*d)/_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))","C"
108,1,1722,712,4.792000," ","int(x^2*(a+b*arccsc(c*x))/(e*x^2+d)^2,x)","-\frac{c^{2} a x}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 e \sqrt{d e}}-\frac{c^{2} b \,\mathrm{arccsc}\left(c x \right) x}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{2 c^{2} e \,d^{2}}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} e \,d^{3}}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{c^{4} d^{3}}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{2 c^{2} e \left(c^{2} d +e \right) d^{2}}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{c^{2} \left(c^{2} d +e \right) d^{2}}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} \left(c^{2} d +e \right) d^{3}}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) e}{c^{4} \left(c^{2} d +e \right) d^{3}}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{2 c^{2} e \,d^{2}}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} e \,d^{3}}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{c^{4} d^{3}}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{2 c^{2} e \left(c^{2} d +e \right) d^{2}}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{c^{2} \left(c^{2} d +e \right) d^{2}}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} \left(c^{2} d +e \right) d^{3}}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) e}{c^{4} \left(c^{2} d +e \right) d^{3}}-\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e \right)}\right)}{4 e}-\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\textit{\_R1} \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right)}{4 e}"," ",0,"-1/2*c^2*a/e*x/(c^2*e*x^2+c^2*d)+1/2*a/e/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-1/2*c^2*b*arccsc(c*x)/e*x/(c^2*e*x^2+c^2*d)-1/2/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/d^2-1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/d^3*(e*(c^2*d+e))^(1/2)-1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^3+1/2/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)/d^2*(e*(c^2*d+e))^(1/2)+1/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^2+1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^3*(e*(c^2*d+e))^(1/2)+1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))*e/(c^2*d+e)/d^3-1/2/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/d^2+1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/d^3*(e*(c^2*d+e))^(1/2)-1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^3-1/2/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)/d^2*(e*(c^2*d+e))^(1/2)+1/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^2-1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^3*(e*(c^2*d+e))^(1/2)+1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))*e/(c^2*d+e)/d^3-1/4*c*b/e*sum(1/_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-1/4*c*b/e*sum(_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))","C"
109,1,1716,706,5.046000," ","int((a+b*arccsc(c*x))/(e*x^2+d)^2,x)","\frac{c^{2} a x}{2 d \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 d \sqrt{d e}}+\frac{c^{2} b \,\mathrm{arccsc}\left(c x \right) x}{2 d \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e \right)}\right)}{4 d}-\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\textit{\_R1} \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right)}{4 d}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{2 c^{2} d^{3}}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} d^{4}}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) e}{c^{4} d^{4}}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{2 c^{2} \left(c^{2} d +e \right) d^{3}}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) e}{c^{2} \left(c^{2} d +e \right) d^{3}}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}\, e}{c^{4} d^{4} \left(c^{2} d +e \right)}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) e^{2}}{c^{4} d^{4} \left(c^{2} d +e \right)}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{2 c^{2} d^{3}}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} d^{4}}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) e}{c^{4} d^{4}}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{2 c^{2} \left(c^{2} d +e \right) d^{3}}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) e}{c^{2} \left(c^{2} d +e \right) d^{3}}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}\, e}{c^{4} d^{4} \left(c^{2} d +e \right)}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) e^{2}}{c^{4} d^{4} \left(c^{2} d +e \right)}"," ",0,"1/2*c^2*a*x/d/(c^2*e*x^2+c^2*d)+1/2*a/d/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+1/2*c^2*b*arccsc(c*x)*x/d/(c^2*e*x^2+c^2*d)-1/4*c*b/d*sum(1/_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-1/4*c*b/d*sum(_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))+1/2/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^3+1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4*(e*(c^2*d+e))^(1/2)+1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4*e-1/2/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^3*(e*(c^2*d+e))^(1/2)-1/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))*e/(c^2*d+e)/d^3-1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4/(c^2*d+e)*(e*(c^2*d+e))^(1/2)*e-1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4/(c^2*d+e)*e^2+1/2/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^3-1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4*(e*(c^2*d+e))^(1/2)+1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4*e+1/2/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^3*(e*(c^2*d+e))^(1/2)-1/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))*e/(c^2*d+e)/d^3+1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4/(c^2*d+e)*(e*(c^2*d+e))^(1/2)*e-1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4/(c^2*d+e)*e^2","C"
110,1,1784,748,19.918000," ","int((a+b*arccsc(c*x))/x^2/(e*x^2+d)^2,x)","-\frac{a e \,c^{2} x}{2 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{3 a e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 d^{2} \sqrt{d e}}-\frac{a}{d^{2} x}-\frac{b \,\mathrm{arccsc}\left(c x \right)}{d^{2} x}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) e^{2}}{c^{2} d^{4} \left(c^{2} d +e \right)}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, e^{3} \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{c^{4} d^{5} \left(c^{2} d +e \right)}+\frac{3 c b e \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e \right)}\right)}{4 d^{2}}+\frac{3 c b e \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\textit{\_R1} \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right)}{4 d^{2}}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, e \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} d^{5}}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) e^{2}}{c^{2} d^{4} \left(c^{2} d +e \right)}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, e^{3} \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{c^{4} d^{5} \left(c^{2} d +e \right)}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, e \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} d^{5}}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}\, e}{2 c^{2} d^{4} \left(c^{2} d +e \right)}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, e^{2} \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} d^{5} \left(c^{2} d +e \right)}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}\, e}{2 c^{2} d^{4} \left(c^{2} d +e \right)}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, e^{2} \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} d^{5} \left(c^{2} d +e \right)}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) e}{2 c^{2} d^{4}}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, e^{2} \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{c^{4} d^{5}}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) e}{2 c^{2} d^{4}}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, e^{2} \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{c^{4} d^{5}}-\frac{c b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{d^{2}}-\frac{b \,c^{2} x e \,\mathrm{arccsc}\left(c x \right)}{2 \left(c^{2} e \,x^{2}+c^{2} d \right) d^{2}}"," ",0,"-1/2*a/d^2*e*c^2*x/(c^2*e*x^2+c^2*d)-3/2*a/d^2*e/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-a/d^2/x-b*arccsc(c*x)/d^2/x+b/c^2*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4/(c^2*d+e)*e^2+b/c^4*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^3*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^5/(c^2*d+e)+3/4*c*b/d^2*e*sum(1/_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))+3/4*c*b/d^2*e*sum(_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-b/c^4*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^5*(e*(c^2*d+e))^(1/2)+b/c^2*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4/(c^2*d+e)*e^2+b/c^4*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^3*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^5/(c^2*d+e)+b/c^4*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^5*(e*(c^2*d+e))^(1/2)+1/2*b/c^2*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4/(c^2*d+e)*(e*(c^2*d+e))^(1/2)*e+b/c^4*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^5/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-1/2*b/c^2*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4/(c^2*d+e)*(e*(c^2*d+e))^(1/2)*e-b/c^4*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^5/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-1/2*b/c^2*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4*e-b/c^4*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^5-1/2*b/c^2*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4*e-b/c^4*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^5-c*b/d^2*((c^2*x^2-1)/c^2/x^2)^(1/2)-1/2*b*c^2*x*e*arccsc(c*x)/(c^2*e*x^2+c^2*d)/d^2","C"
111,1,1498,746,2.030000," ","int(x^5*(a+b*arccsc(c*x))/(e*x^2+d)^3,x)","\frac{a \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 e^{3}}-\frac{c^{4} a \,d^{2}}{4 e^{3} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}+\frac{c^{2} a d}{e^{3} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{3 c^{6} b \,\mathrm{arccsc}\left(c x \right) d \,x^{4}}{4 e \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{6} b \,\mathrm{arccsc}\left(c x \right) d^{2} x^{2}}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{c^{5} b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3} d}{8 e \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{c^{5} b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \,d^{2}}{8 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{i b \dilog \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e^{2} \left(c^{2} d +e \right)}-\frac{i c^{4} b \,x^{2} d}{4 e \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{i c^{2} b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2}-1\right) \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right) d}{4 e^{2} \left(c^{2} d +e \right)}-\frac{3 c^{4} b \,\mathrm{arccsc}\left(c x \right) x^{4}}{4 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{4} b \,\mathrm{arccsc}\left(c x \right) d \,x^{2}}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{i c^{4} b \,x^{4}}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{b \,\mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e^{2} \left(c^{2} d +e \right)}-\frac{5 i c^{2} b \sqrt{e \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 c^{2} d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}-2 c^{2} d -4 e}{4 \sqrt{c^{2} e d +e^{2}}}\right) d}{8 e^{3} \left(c^{2} d +e \right)^{2}}-\frac{i c^{2} b d \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d -c^{2} d -4 e \right) \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right)}{4 e^{3} \left(c^{2} d +e \right)}-\frac{i b \dilog \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e^{2} \left(c^{2} d +e \right)}-\frac{i b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d -c^{2} d -4 e \right) \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right)}{4 e^{2} \left(c^{2} d +e \right)}+\frac{i c^{2} b d \dilog \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e^{3} \left(c^{2} d +e \right)}-\frac{c^{2} b d \,\mathrm{arccsc}\left(c x \right) \ln \left(1+\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e^{3} \left(c^{2} d +e \right)}-\frac{i c^{4} b \,d^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2}-1\right) \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right)}{4 e^{3} \left(c^{2} d +e \right)}-\frac{i c^{4} b \,d^{2}}{8 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{3 i b \sqrt{e \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 c^{2} d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}-2 c^{2} d -4 e}{4 \sqrt{c^{2} e d +e^{2}}}\right)}{4 e^{2} \left(c^{2} d +e \right)^{2}}-\frac{i c^{2} b d \dilog \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{e^{3} \left(c^{2} d +e \right)}"," ",0,"1/2*a/e^3*ln(c^2*e*x^2+c^2*d)-1/4*c^4*a*d^2/e^3/(c^2*e*x^2+c^2*d)^2+c^2*a/e^3*d/(c^2*e*x^2+c^2*d)-3/4*c^6*b/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arccsc(c*x)*d*x^4-1/2*c^6*b/e^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arccsc(c*x)*d^2*x^2+1/8*c^5*b/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*((c^2*x^2-1)/c^2/x^2)^(1/2)*x^3*d+1/8*c^5*b/e^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*((c^2*x^2-1)/c^2/x^2)^(1/2)*x*d^2-1/4*I*c^2*b/e^3/(c^2*d+e)*d*sum((_R1^2*c^2*d-c^2*d-4*e)/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-1/4*I*c^4*b/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*x^2*d-1/4*I*c^2*b/e^2/(c^2*d+e)*sum((_R1^2-1)/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))*d-3/4*c^4*b/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arccsc(c*x)*x^4-1/2*c^4*b/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arccsc(c*x)*d*x^2-I*b/e^2/(c^2*d+e)*dilog(I/c/x+(1-1/c^2/x^2)^(1/2))-b/e^2/(c^2*d+e)*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))-1/8*I*c^4*b/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*x^4+I*b/e^2/(c^2*d+e)*dilog(1+I/c/x+(1-1/c^2/x^2)^(1/2))-1/4*I*b/e^2/(c^2*d+e)*sum((_R1^2*c^2*d-c^2*d-4*e)/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-1/8*I*c^4*b/e^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*d^2-3/4*I*b*(e*(c^2*d+e))^(1/2)/e^2/(c^2*d+e)^2*arctanh(1/4*(2*c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2-2*c^2*d-4*e)/(c^2*d*e+e^2)^(1/2))-c^2*b/e^3/(c^2*d+e)*d*arccsc(c*x)*ln(1+I/c/x+(1-1/c^2/x^2)^(1/2))+I*c^2*b/e^3/(c^2*d+e)*d*dilog(1+I/c/x+(1-1/c^2/x^2)^(1/2))-1/4*I*c^4*b/e^3/(c^2*d+e)*d^2*sum((_R1^2-1)/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-5/8*I*c^2*b*(e*(c^2*d+e))^(1/2)/e^3/(c^2*d+e)^2*arctanh(1/4*(2*c^2*d*(I/c/x+(1-1/c^2/x^2)^(1/2))^2-2*c^2*d-4*e)/(c^2*d*e+e^2)^(1/2))*d-I*c^2*b/e^3/(c^2*d+e)*d*dilog(I/c/x+(1-1/c^2/x^2)^(1/2))","C"
112,1,1870,135,0.087000," ","int(x^3*(a+b*arccsc(c*x))/(e*x^2+d)^3,x)","\frac{c^{4} a d}{4 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{2} a}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c^{4} b \,\mathrm{arccsc}\left(c x \right) d}{4 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{2} b \,\mathrm{arccsc}\left(c x \right)}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{3} b \sqrt{c^{2} x^{2}-1}\, x \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \left(c^{2} d +e \right) \left(c e x +\sqrt{-c^{2} e d}\right) \left(-c e x +\sqrt{-c^{2} e d}\right)}-\frac{c^{3} b \sqrt{c^{2} x^{2}-1}\, d \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \left(c^{2} d +e \right) \left(c e x +\sqrt{-c^{2} e d}\right) \left(-c e x +\sqrt{-c^{2} e d}\right)}+\frac{c^{3} b \sqrt{c^{2} x^{2}-1}\, x \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right)}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(c e x +\sqrt{-c^{2} e d}\right) \left(-c e x +\sqrt{-c^{2} e d}\right)}+\frac{c^{3} b \sqrt{c^{2} x^{2}-1}\, d \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right)}{16 e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(c e x +\sqrt{-c^{2} e d}\right) \left(-c e x +\sqrt{-c^{2} e d}\right)}+\frac{c^{3} b \sqrt{c^{2} x^{2}-1}\, x \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right)}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(c e x +\sqrt{-c^{2} e d}\right) \left(-c e x +\sqrt{-c^{2} e d}\right)}+\frac{c^{3} b \sqrt{c^{2} x^{2}-1}\, d \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right)}{16 e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(c e x +\sqrt{-c^{2} e d}\right) \left(-c e x +\sqrt{-c^{2} e d}\right)}-\frac{c b \sqrt{c^{2} x^{2}-1}\, e x \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d \left(c^{2} d +e \right) \left(c e x +\sqrt{-c^{2} e d}\right) \left(-c e x +\sqrt{-c^{2} e d}\right)}-\frac{c b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \left(c^{2} d +e \right) \left(c e x +\sqrt{-c^{2} e d}\right) \left(-c e x +\sqrt{-c^{2} e d}\right)}+\frac{c^{3} b x}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \left(c^{2} d +e \right) \left(c e x +\sqrt{-c^{2} e d}\right) \left(-c e x +\sqrt{-c^{2} e d}\right)}-\frac{c b}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \left(c^{2} d +e \right) \left(c e x +\sqrt{-c^{2} e d}\right) \left(-c e x +\sqrt{-c^{2} e d}\right)}+\frac{c b \sqrt{c^{2} x^{2}-1}\, e x \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right)}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(c e x +\sqrt{-c^{2} e d}\right) \left(-c e x +\sqrt{-c^{2} e d}\right)}+\frac{c b \sqrt{c^{2} x^{2}-1}\, \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right)}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(c e x +\sqrt{-c^{2} e d}\right) \left(-c e x +\sqrt{-c^{2} e d}\right)}+\frac{c b \sqrt{c^{2} x^{2}-1}\, e x \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right)}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(c e x +\sqrt{-c^{2} e d}\right) \left(-c e x +\sqrt{-c^{2} e d}\right)}+\frac{c b \sqrt{c^{2} x^{2}-1}\, \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right)}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(c e x +\sqrt{-c^{2} e d}\right) \left(-c e x +\sqrt{-c^{2} e d}\right)}"," ",0,"1/4*c^4*a/e^2*d/(c^2*e*x^2+c^2*d)^2-1/2*c^2*a/e^2/(c^2*e*x^2+c^2*d)+1/4*c^4*b*arccsc(c*x)/e^2*d/(c^2*e*x^2+c^2*d)^2-1/2*c^2*b*arccsc(c*x)/e^2/(c^2*e*x^2+c^2*d)-1/4*c^3*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/(c^2*d+e)/(c*e*x+(-c^2*e*d)^(1/2))/(-c*e*x+(-c^2*e*d)^(1/2))*arctan(1/(c^2*x^2-1)^(1/2))-1/4*c^3*b*(c^2*x^2-1)^(1/2)/e/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d/(c^2*d+e)/(c*e*x+(-c^2*e*d)^(1/2))/(-c*e*x+(-c^2*e*d)^(1/2))*arctan(1/(c^2*x^2-1)^(1/2))+1/16*c^3*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(c*e*x+(-c^2*e*d)^(1/2))/(-c*e*x+(-c^2*e*d)^(1/2))*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))+1/16*c^3*b*(c^2*x^2-1)^(1/2)/e/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(c*e*x+(-c^2*e*d)^(1/2))/(-c*e*x+(-c^2*e*d)^(1/2))*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))+1/16*c^3*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(c*e*x+(-c^2*e*d)^(1/2))/(-c*e*x+(-c^2*e*d)^(1/2))*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))+1/16*c^3*b*(c^2*x^2-1)^(1/2)/e/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(c*e*x+(-c^2*e*d)^(1/2))/(-c*e*x+(-c^2*e*d)^(1/2))*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))-1/4*c*b*(c^2*x^2-1)^(1/2)*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d/(c^2*d+e)/(c*e*x+(-c^2*e*d)^(1/2))/(-c*e*x+(-c^2*e*d)^(1/2))*arctan(1/(c^2*x^2-1)^(1/2))-1/4*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/(c^2*d+e)/(c*e*x+(-c^2*e*d)^(1/2))/(-c*e*x+(-c^2*e*d)^(1/2))*arctan(1/(c^2*x^2-1)^(1/2))+1/8*c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/(c^2*d+e)/(c*e*x+(-c^2*e*d)^(1/2))/(-c*e*x+(-c^2*e*d)^(1/2))-1/8*c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/(c^2*d+e)/(c*e*x+(-c^2*e*d)^(1/2))/(-c*e*x+(-c^2*e*d)^(1/2))+1/8*c*b*(c^2*x^2-1)^(1/2)*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(c*e*x+(-c^2*e*d)^(1/2))/(-c*e*x+(-c^2*e*d)^(1/2))*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))+1/8*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(c*e*x+(-c^2*e*d)^(1/2))/(-c*e*x+(-c^2*e*d)^(1/2))*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))+1/8*c*b*(c^2*x^2-1)^(1/2)*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(c*e*x+(-c^2*e*d)^(1/2))/(-c*e*x+(-c^2*e*d)^(1/2))*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))+1/8*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(c*e*x+(-c^2*e*d)^(1/2))/(-c*e*x+(-c^2*e*d)^(1/2))*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))","B"
113,1,1840,168,0.076000," ","int(x*(a+b*arccsc(c*x))/(e*x^2+d)^3,x)","-\frac{c^{4} a}{4 e \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{4} b \,\mathrm{arccsc}\left(c x \right)}{4 e \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{3} b \sqrt{c^{2} x^{2}-1}\, e x \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c^{3} b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{3 c^{3} b \sqrt{c^{2} x^{2}-1}\, e x \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right)}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{3 c^{3} b \sqrt{c^{2} x^{2}-1}\, \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right)}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{3 c^{3} b \sqrt{c^{2} x^{2}-1}\, e x \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right)}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{3 c^{3} b \sqrt{c^{2} x^{2}-1}\, \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right)}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c^{3} b x e}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{c b e}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c b \sqrt{c^{2} x^{2}-1}\, x \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right) e^{2}}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d^{2} \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right) e}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{c b \sqrt{c^{2} x^{2}-1}\, x \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right) e^{2}}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d^{2} \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{c b \sqrt{c^{2} x^{2}-1}\, \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right) e}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{c b \sqrt{c^{2} x^{2}-1}\, x \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right) e^{2}}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d^{2} \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{c b \sqrt{c^{2} x^{2}-1}\, \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right) e}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}"," ",0,"-1/4*c^4*a/e/(c^2*e*x^2+c^2*d)^2-1/4*c^4*b/e/(c^2*e*x^2+c^2*d)^2*arccsc(c*x)-1/4*c^3*b*(c^2*x^2-1)^(1/2)*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*arctan(1/(c^2*x^2-1)^(1/2))-1/4*c^3*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*arctan(1/(c^2*x^2-1)^(1/2))+3/16*c^3*b*(c^2*x^2-1)^(1/2)*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))+3/16*c^3*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))+3/16*c^3*b*(c^2*x^2-1)^(1/2)*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(c*e*x+(-c^2*e*d)^(1/2))/(-c*e*x+(-c^2*e*d)^(1/2))*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))+3/16*c^3*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(c*e*x+(-c^2*e*d)^(1/2))/(-c*e*x+(-c^2*e*d)^(1/2))*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))-1/8*c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*e+1/8*c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*e-1/4*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d^2/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*arctan(1/(c^2*x^2-1)^(1/2))*e^2-1/4*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*arctan(1/(c^2*x^2-1)^(1/2))*e+1/8*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d^2/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))*e^2+1/8*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))*e+1/8*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d^2/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(-(c^2*d+e)/e)^(1/2)/(c*e*x+(-c^2*e*d)^(1/2))*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))*e^2+1/8*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(-(c^2*d+e)/e)^(1/2)/(c*e*x+(-c^2*e*d)^(1/2))*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))*e","B"
114,1,5294,693,7.102000," ","int((a+b*arccsc(c*x))/x/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
115,1,3175,1012,5.009000," ","int(x^4*(a+b*arccsc(c*x))/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"-3/8*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e^2/(c^2*d+e)/d-1/8*c^5*b*x^4/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*((c^2*x^2-1)/c^2/x^2)^(1/2)-5/8*c^4*b*x^3/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arccsc(c*x)-3/16*c^3*b/e^2/(c^2*d+e)*d*sum(1/_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-3/16*c^3*b/e^2/(c^2*d+e)*d*sum(_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^3+7/4/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/d^2-3/8*c^6*b*x/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)/e^2*arccsc(c*x)*d^2-1/8*c^5*b*x^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)/e*((c^2*x^2-1)/c^2/x^2)^(1/2)*d-3/8*c^4*b*x/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)/e*arccsc(c*x)*d+1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)/d^3*(e*(c^2*d+e))^(1/2)-5/4/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/e/d^2*(e*(c^2*d+e))^(1/2)-3/4/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e^2/(c^2*d+e)/d^2*(e*(c^2*d+e))^(1/2)+3/4/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e^2/(c^2*d+e)/d^2*(e*(c^2*d+e))^(1/2)-5/8*c^6*b*x^3/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)/e*arccsc(c*x)*d-1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)/d^3*(e*(c^2*d+e))^(1/2)+5/4/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/e/d^2*(e*(c^2*d+e))^(1/2)+3/8*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e^2/(c^2*d+e)^2/d*(e*(c^2*d+e))^(1/2)-3/8*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e^2/(c^2*d+e)^2/d*(e*(c^2*d+e))^(1/2)-5/4/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)/d^2-1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/d^3*(e*(c^2*d+e))^(1/2)+1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/d^3*(e*(c^2*d+e))^(1/2)-1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^3+7/4/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/d^2-3/8*c^4*a/(c^2*e*x^2+c^2*d)^2/e^2*d*x+3/4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)^2/d-3/8*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e^2/(c^2*d+e)/d+3/4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)^2/d+3/8*a/e^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2*e/d^3-5/4/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)/d^2+1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2*e/d^3-5/8*c^4*a/(c^2*e*x^2+c^2*d)^2/e*x^3-3/16*c*b/e/(c^2*d+e)*sum(1/_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-3/16*c*b/e/(c^2*d+e)*sum(_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))","C"
116,1,2329,1018,7.794000," ","int(x^2*(a+b*arccsc(c*x))/(e*x^2+d)^3,x)","\frac{c^{5} b \,x^{4} e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right) d}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{8 \left(c^{2} d +e \right)^{2} e \,d^{2}}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{4 c^{2} \left(c^{2} d +e \right)^{2} d^{3}}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) e}{4 c^{2} \left(c^{2} d +e \right)^{2} d^{3}}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{8 \left(c^{2} d +e \right)^{2} e \,d^{2}}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{4 c^{2} \left(c^{2} d +e \right)^{2} d^{3}}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) e}{4 c^{2} \left(c^{2} d +e \right)^{2} d^{3}}+\frac{c^{5} b \,x^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{8 e \left(c^{2} d +e \right) d^{2}}-\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{4 c^{2} \left(c^{2} d +e \right) d^{3}}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{8 e \left(c^{2} d +e \right) d^{2}}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{4 c^{2} \left(c^{2} d +e \right) d^{3}}+\frac{c^{4} a \,x^{3}}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} d}-\frac{c^{4} a x}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} e}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 d e \sqrt{d e}}-\frac{c^{4} b x \,\mathrm{arccsc}\left(c x \right)}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{c^{6} b \,x^{3} \mathrm{arccsc}\left(c x \right)}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{6} b x \,\mathrm{arccsc}\left(c x \right) d}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right) e}+\frac{c^{4} b \,x^{3} e \,\mathrm{arccsc}\left(c x \right)}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right) d}-\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{4 c^{2} e \left(c^{2} d +e \right) d^{3}}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{4 c^{2} e \left(c^{2} d +e \right) d^{3}}+\frac{b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{4 \left(c^{2} d +e \right)^{2} d^{2}}-\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e \right)}\right)}{16 d \left(c^{2} d +e \right)}-\frac{c b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\textit{\_R1} \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right)}{16 d \left(c^{2} d +e \right)}-\frac{c^{3} b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e \right)}\right)}{16 e \left(c^{2} d +e \right)}-\frac{c^{3} b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(-2 c^{2} d -4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\textit{\_R1} \left(i \mathrm{arccsc}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{i}{c x}-\sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d -c^{2} d -2 e}\right)}{16 e \left(c^{2} d +e \right)}+\frac{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{i}{c x}+\sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{4 \left(c^{2} d +e \right)^{2} d^{2}}"," ",0,"1/8*c^5*b*x^4/(c^2*e*x^2+c^2*d)^2*e/(c^2*d+e)/d*((c^2*x^2-1)/c^2/x^2)^(1/2)+1/8*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/e/d^2*(e*(c^2*d+e))^(1/2)-1/8*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/e/d^2*(e*(c^2*d+e))^(1/2)-1/4/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/d^3*(e*(c^2*d+e))^(1/2)+1/4/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/d^3*(e*(c^2*d+e))^(1/2)+1/4/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2*e/d^3+1/4/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2*e/d^3+1/8*c^5*b*x^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*((c^2*x^2-1)/c^2/x^2)^(1/2)-1/16*c*b/d/(c^2*d+e)*sum(1/_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))+1/8*c^4*a/(c^2*e*x^2+c^2*d)^2/d*x^3-1/8*c^4*a/(c^2*e*x^2+c^2*d)^2/e*x+1/8*a/d/e/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-1/8*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)/d^2-1/8*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)/d^2-1/4/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^3-1/4/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^3-1/8*c^4*b*x/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arccsc(c*x)+1/8*c^6*b*x^3/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arccsc(c*x)-1/4/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)/d^3*(e*(c^2*d+e))^(1/2)+1/4/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)/d^3*(e*(c^2*d+e))^(1/2)-1/8*c^6*b*x/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)/e*arccsc(c*x)*d+1/8*c^4*b*x^3/(c^2*e*x^2+c^2*d)^2*e/(c^2*d+e)/d*arccsc(c*x)-1/16*c*b/d/(c^2*d+e)*sum(_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-1/16*c^3*b/e/(c^2*d+e)*sum(1/_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-1/16*c^3*b/e/(c^2*d+e)*sum(_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))+1/4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/d^2+1/4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/d^2","C"
117,1,3166,1002,10.036000," ","int((a+b*arccsc(c*x))/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"-5/8*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/d^3*(e*(c^2*d+e))^(1/2)-5/4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2*e/d^3+5/8*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/d^3*(e*(c^2*d+e))^(1/2)+5/8*c^6*b*x/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arccsc(c*x)-3/16*c*b/d^2/(c^2*d+e)*e*sum(1/_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-3/16*c*b/d^2/(c^2*d+e)*e*sum(_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-5/4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2*e/d^3+5/8*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^3+5/8*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^3-3/16*c^3*b/d/(c^2*d+e)*sum(1/_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))-3/16*c^3*b/d/(c^2*d+e)*sum(_R1/(_R1^2*c^2*d-c^2*d-2*e)*(I*arccsc(c*x)*ln((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-I/c/x-(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(-2*c^2*d-4*e)*_Z^2+c^2*d))+1/4*c^4*a*x/d/(c^2*e*x^2+c^2*d)^2+3/8*c^2*a/d^2*x/(c^2*e*x^2+c^2*d)+3/8*a/d^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+5/4/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-5/4/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4/(c^2*d+e)*(e*(c^2*d+e))^(1/2)+7/4/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4/(c^2*d+e)+1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^5/(c^2*d+e)-9/4/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4/(c^2*d+e)^2-1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^3*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^5/(c^2*d+e)^2+7/4/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4/(c^2*d+e)+1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^5/(c^2*d+e)-9/4/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4/(c^2*d+e)^2-1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^3*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^5/(c^2*d+e)^2+7/4/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4/(c^2*d+e)^2*(e*(c^2*d+e))^(1/2)+1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^5/(c^2*d+e)^2*(e*(c^2*d+e))^(1/2)+1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^5/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-7/4/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4/(c^2*d+e)^2*(e*(c^2*d+e))^(1/2)-1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctan(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^5/(c^2*d+e)^2*(e*(c^2*d+e))^(1/2)+3/8*c^6*b*x^3/(c^2*e*x^2+c^2*d)^2*e/(c^2*d+e)/d*arccsc(c*x)+3/8*c^4*b*x^3/(c^2*e*x^2+c^2*d)^2/d^2/(c^2*d+e)*arccsc(c*x)*e^2+5/8*c^4*b*x/(c^2*e*x^2+c^2*d)^2/d/(c^2*d+e)*arccsc(c*x)*e-1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e*arctanh(c*d*(I/c/x+(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^5/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-1/8*c^5*b*x^4/(c^2*e*x^2+c^2*d)^2/d^2/(c^2*d+e)*((c^2*x^2-1)/c^2/x^2)^(1/2)*e^2-1/8*c^5*b*x^2/(c^2*e*x^2+c^2*d)^2/d/(c^2*d+e)*((c^2*x^2-1)/c^2/x^2)^(1/2)*e","C"
118,0,0,343,7.372000," ","int(x^5*(a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x)","\int x^{5} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int(x^5*(a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x)","F"
119,0,0,246,6.635000," ","int(x^3*(a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x)","\int x^{3} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int(x^3*(a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x)","F"
120,0,0,159,5.056000," ","int(x*(a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x)","\int x \left(a +b \,\mathrm{arccsc}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int(x*(a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x)","F"
121,0,0,23,4.387000," ","int((a+b*arccsc(c*x))*(e*x^2+d)^(1/2)/x,x)","\int \frac{\left(a +b \,\mathrm{arccsc}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x}\, dx"," ",0,"int((a+b*arccsc(c*x))*(e*x^2+d)^(1/2)/x,x)","F"
122,0,0,23,1.296000," ","int((a+b*arccsc(c*x))*(e*x^2+d)^(1/2)/x^3,x)","\int \frac{\left(a +b \,\mathrm{arccsc}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x^{3}}\, dx"," ",0,"int((a+b*arccsc(c*x))*(e*x^2+d)^(1/2)/x^3,x)","F"
123,0,0,23,6.372000," ","int(x^2*(a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x)","\int x^{2} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int(x^2*(a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x)","F"
124,0,0,20,4.379000," ","int((a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x)","\int \left(a +b \,\mathrm{arccsc}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x)","F"
125,0,0,23,3.382000," ","int((a+b*arccsc(c*x))*(e*x^2+d)^(1/2)/x^2,x)","\int \frac{\left(a +b \,\mathrm{arccsc}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x^{2}}\, dx"," ",0,"int((a+b*arccsc(c*x))*(e*x^2+d)^(1/2)/x^2,x)","F"
126,0,0,286,6.424000," ","int((a+b*arccsc(c*x))*(e*x^2+d)^(1/2)/x^4,x)","\int \frac{\left(a +b \,\mathrm{arccsc}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x^{4}}\, dx"," ",0,"int((a+b*arccsc(c*x))*(e*x^2+d)^(1/2)/x^4,x)","F"
127,0,0,849,8.948000," ","int((a+b*arccsc(c*x))*(e*x^2+d)^(1/2)/x^6,x)","\int \frac{\left(a +b \,\mathrm{arccsc}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x^{6}}\, dx"," ",0,"int((a+b*arccsc(c*x))*(e*x^2+d)^(1/2)/x^6,x)","F"
128,0,0,318,6.428000," ","int(x^3*(e*x^2+d)^(3/2)*(a+b*arccsc(c*x)),x)","\int x^{3} \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)\, dx"," ",0,"int(x^3*(e*x^2+d)^(3/2)*(a+b*arccsc(c*x)),x)","F"
129,0,0,218,4.740000," ","int(x*(e*x^2+d)^(3/2)*(a+b*arccsc(c*x)),x)","\int x \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)\, dx"," ",0,"int(x*(e*x^2+d)^(3/2)*(a+b*arccsc(c*x)),x)","F"
130,0,0,23,3.975000," ","int((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{x}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x,x)","F"
131,0,0,23,1.069000," ","int((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x^3,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{x^{3}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x^3,x)","F"
132,0,0,23,5.865000," ","int(x^2*(e*x^2+d)^(3/2)*(a+b*arccsc(c*x)),x)","\int x^{2} \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)\, dx"," ",0,"int(x^2*(e*x^2+d)^(3/2)*(a+b*arccsc(c*x)),x)","F"
133,0,0,20,4.244000," ","int((e*x^2+d)^(3/2)*(a+b*arccsc(c*x)),x)","\int \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arccsc(c*x)),x)","F"
134,0,0,23,3.707000," ","int((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x^2,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{x^{2}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x^2,x)","F"
135,0,0,23,6.641000," ","int((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x^4,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{x^{4}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x^4,x)","F"
136,0,0,366,9.023000," ","int((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x^6,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{x^{6}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x^6,x)","F"
137,0,0,492,7.491000," ","int((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x^8,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{x^{8}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x^8,x)","F"
138,0,0,271,7.873000," ","int(x^5*(a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x^{5} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x^5*(a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x)","F"
139,0,0,187,7.302000," ","int(x^3*(a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x^3*(a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x)","F"
140,0,0,110,5.435000," ","int(x*(a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x*(a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x)","F"
141,0,0,23,4.178000," ","int((a+b*arccsc(c*x))/x/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x/(e*x^2+d)^(1/2),x)","F"
142,0,0,23,1.440000," ","int((a+b*arccsc(c*x))/x^3/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x^{3} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x^3/(e*x^2+d)^(1/2),x)","F"
143,0,0,23,7.451000," ","int(x^2*(a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x^{2} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x^2*(a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x)","F"
144,0,0,20,4.686000," ","int((a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x)","F"
145,0,0,221,4.445000," ","int((a+b*arccsc(c*x))/x^2/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x^{2} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x^2/(e*x^2+d)^(1/2),x)","F"
146,0,0,316,8.422000," ","int((a+b*arccsc(c*x))/x^4/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x^{4} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x^4/(e*x^2+d)^(1/2),x)","F"
147,0,0,212,7.404000," ","int(x^5*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{5} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^5*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x)","F"
148,0,0,132,6.681000," ","int(x^3*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x)","F"
149,0,0,69,4.786000," ","int(x*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x)","F"
150,0,0,23,3.842000," ","int((a+b*arccsc(c*x))/x/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x/(e*x^2+d)^(3/2),x)","F"
151,0,0,23,1.339000," ","int((a+b*arccsc(c*x))/x^3/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x^{3} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x^3/(e*x^2+d)^(3/2),x)","F"
152,0,0,23,6.200000," ","int(x^4*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{4} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^4*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x)","F"
153,0,0,23,6.918000," ","int(x^2*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{2} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x)","F"
154,0,0,97,4.350000," ","int((a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x)","F"
155,0,0,249,4.026000," ","int((a+b*arccsc(c*x))/x^2/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x^{2} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x^2/(e*x^2+d)^(3/2),x)","F"
156,0,0,205,7.342000," ","int(x^5*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{5} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^5*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x)","F"
157,0,0,139,6.727000," ","int(x^3*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^3*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x)","F"
158,0,0,117,4.939000," ","int(x*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x)","F"
159,0,0,23,3.726000," ","int((a+b*arccsc(c*x))/x/(e*x^2+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x \left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x/(e*x^2+d)^(5/2),x)","F"
160,0,0,23,1.347000," ","int((a+b*arccsc(c*x))/x^3/(e*x^2+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x^{3} \left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x^3/(e*x^2+d)^(5/2),x)","F"
161,0,0,23,8.811000," ","int(x^6*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{6} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^6*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x)","F"
162,0,0,23,6.298000," ","int(x^4*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{4} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^4*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x)","F"
163,0,0,242,6.914000," ","int(x^2*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{2} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^2*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x)","F"
164,0,0,258,4.315000," ","int((a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x)","F"
165,0,0,563,12.128000," ","int((f*x)^m*(e*x^2+d)^3*(a+b*arccsc(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right)^{3} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^3*(a+b*arccsc(c*x)),x)","F"
166,0,0,353,9.316000," ","int((f*x)^m*(e*x^2+d)^2*(a+b*arccsc(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right)^{2} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^2*(a+b*arccsc(c*x)),x)","F"
167,0,0,201,7.525000," ","int((f*x)^m*(e*x^2+d)*(a+b*arccsc(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right) \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)*(a+b*arccsc(c*x)),x)","F"
168,0,0,25,3.590000," ","int((f*x)^m*(a+b*arccsc(c*x))/(e*x^2+d),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{e \,x^{2}+d}\, dx"," ",0,"int((f*x)^m*(a+b*arccsc(c*x))/(e*x^2+d),x)","F"
169,0,0,25,6.050000," ","int((f*x)^m*(a+b*arccsc(c*x))/(e*x^2+d)^2,x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((f*x)^m*(a+b*arccsc(c*x))/(e*x^2+d)^2,x)","F"
170,0,0,25,4.785000," ","int((f*x)^m*(e*x^2+d)^(3/2)*(a+b*arccsc(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^(3/2)*(a+b*arccsc(c*x)),x)","F"
171,0,0,25,4.877000," ","int((f*x)^m*(a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x)","\int \left(f x \right)^{m} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int((f*x)^m*(a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x)","F"
172,0,0,25,6.561000," ","int((f*x)^m*(a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((f*x)^m*(a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x)","F"
173,0,0,25,6.271000," ","int((f*x)^m*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((f*x)^m*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x)","F"
174,0,0,341,13.067000," ","int(x^11*(a+b*arccsc(c*x))/(-c^4*x^4+1)^(1/2),x)","\int \frac{x^{11} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int(x^11*(a+b*arccsc(c*x))/(-c^4*x^4+1)^(1/2),x)","F"
175,0,0,228,9.292000," ","int(x^7*(a+b*arccsc(c*x))/(-c^4*x^4+1)^(1/2),x)","\int \frac{x^{7} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int(x^7*(a+b*arccsc(c*x))/(-c^4*x^4+1)^(1/2),x)","F"
176,0,0,106,6.284000," ","int(x^3*(a+b*arccsc(c*x))/(-c^4*x^4+1)^(1/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arccsc}\left(c x \right)\right)}{\sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int(x^3*(a+b*arccsc(c*x))/(-c^4*x^4+1)^(1/2),x)","F"
177,0,0,26,6.198000," ","int((a+b*arccsc(c*x))/x/(-c^4*x^4+1)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x \sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x/(-c^4*x^4+1)^(1/2),x)","F"
178,0,0,26,4.244000," ","int((a+b*arccsc(c*x))/x^5/(-c^4*x^4+1)^(1/2),x)","\int \frac{a +b \,\mathrm{arccsc}\left(c x \right)}{x^{5} \sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int((a+b*arccsc(c*x))/x^5/(-c^4*x^4+1)^(1/2),x)","F"