1,1,646,0,1.008527," ","integrate(x^6*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{2688} \, {\left(\frac{3 \, b x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{3 \, a x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}{c} + \frac{b x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}}{c^{2}} + \frac{21 \, b x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} \arcsin\left(\frac{1}{c x}\right)}{c^{3}} + \frac{21 \, a x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}{c^{3}} + \frac{9 \, b x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}}{c^{4}} + \frac{63 \, b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right)}{c^{5}} + \frac{63 \, a x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}{c^{5}} + \frac{45 \, b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c^{6}} + \frac{105 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right)}{c^{7}} + \frac{105 \, a x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c^{7}} + \frac{120 \, b \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{8}} - \frac{120 \, b \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{8}} + \frac{105 \, b \arcsin\left(\frac{1}{c x}\right)}{c^{9} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{105 \, a}{c^{9} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} - \frac{45 \, b}{c^{10} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{63 \, b \arcsin\left(\frac{1}{c x}\right)}{c^{11} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{63 \, a}{c^{11} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} - \frac{9 \, b}{c^{12} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{21 \, b \arcsin\left(\frac{1}{c x}\right)}{c^{13} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{21 \, a}{c^{13} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} - \frac{b}{c^{14} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}} + \frac{3 \, b \arcsin\left(\frac{1}{c x}\right)}{c^{15} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}} + \frac{3 \, a}{c^{15} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)} c"," ",0,"1/2688*(3*b*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7*arcsin(1/(c*x))/c + 3*a*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7/c + b*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6/c^2 + 21*b*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*arcsin(1/(c*x))/c^3 + 21*a*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5/c^3 + 9*b*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4/c^4 + 63*b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*arcsin(1/(c*x))/c^5 + 63*a*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3/c^5 + 45*b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c^6 + 105*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))/c^7 + 105*a*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c^7 + 120*b*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^8 - 120*b*log(1/(abs(c)*abs(x)))/c^8 + 105*b*arcsin(1/(c*x))/(c^9*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 105*a/(c^9*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) - 45*b/(c^10*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 63*b*arcsin(1/(c*x))/(c^11*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 63*a/(c^11*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) - 9*b/(c^12*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 21*b*arcsin(1/(c*x))/(c^13*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 21*a/(c^13*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) - b/(c^14*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6) + 3*b*arcsin(1/(c*x))/(c^15*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7) + 3*a/(c^15*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))*c","B",0
2,1,518,0,0.213374," ","integrate(x^5*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{5760} \, {\left(\frac{15 \, b x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{15 \, a x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}}{c} + \frac{6 \, b x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}{c^{2}} + \frac{90 \, b x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} \arcsin\left(\frac{1}{c x}\right)}{c^{3}} + \frac{90 \, a x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}}{c^{3}} + \frac{50 \, b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}{c^{4}} + \frac{225 \, b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{5}} + \frac{225 \, a x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c^{5}} + \frac{300 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c^{6}} + \frac{300 \, b \arcsin\left(\frac{1}{c x}\right)}{c^{7}} + \frac{300 \, a}{c^{7}} - \frac{300 \, b}{c^{8} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{225 \, b \arcsin\left(\frac{1}{c x}\right)}{c^{9} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{225 \, a}{c^{9} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} - \frac{50 \, b}{c^{10} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{90 \, b \arcsin\left(\frac{1}{c x}\right)}{c^{11} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{90 \, a}{c^{11} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} - \frac{6 \, b}{c^{12} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{15 \, b \arcsin\left(\frac{1}{c x}\right)}{c^{13} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}} + \frac{15 \, a}{c^{13} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}}\right)} c"," ",0,"1/5760*(15*b*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*arcsin(1/(c*x))/c + 15*a*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6/c + 6*b*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5/c^2 + 90*b*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*arcsin(1/(c*x))/c^3 + 90*a*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4/c^3 + 50*b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3/c^4 + 225*b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))/c^5 + 225*a*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c^5 + 300*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c^6 + 300*b*arcsin(1/(c*x))/c^7 + 300*a/c^7 - 300*b/(c^8*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 225*b*arcsin(1/(c*x))/(c^9*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 225*a/(c^9*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) - 50*b/(c^10*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 90*b*arcsin(1/(c*x))/(c^11*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 90*a/(c^11*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) - 6*b/(c^12*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 15*b*arcsin(1/(c*x))/(c^13*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6) + 15*a/(c^13*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6))*c","B",0
3,1,480,0,0.760958," ","integrate(x^4*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{320} \, {\left(\frac{2 \, b x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{2 \, a x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}{c} + \frac{b x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}}{c^{2}} + \frac{10 \, b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right)}{c^{3}} + \frac{10 \, a x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}{c^{3}} + \frac{8 \, b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c^{4}} + \frac{20 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right)}{c^{5}} + \frac{20 \, a x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c^{5}} + \frac{24 \, b \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{6}} - \frac{24 \, b \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{6}} + \frac{20 \, b \arcsin\left(\frac{1}{c x}\right)}{c^{7} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{20 \, a}{c^{7} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} - \frac{8 \, b}{c^{8} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{10 \, b \arcsin\left(\frac{1}{c x}\right)}{c^{9} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{10 \, a}{c^{9} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} - \frac{b}{c^{10} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{2 \, b \arcsin\left(\frac{1}{c x}\right)}{c^{11} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{2 \, a}{c^{11} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)} c"," ",0,"1/320*(2*b*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*arcsin(1/(c*x))/c + 2*a*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5/c + b*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4/c^2 + 10*b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*arcsin(1/(c*x))/c^3 + 10*a*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3/c^3 + 8*b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c^4 + 20*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))/c^5 + 20*a*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c^5 + 24*b*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^6 - 24*b*log(1/(abs(c)*abs(x)))/c^6 + 20*b*arcsin(1/(c*x))/(c^7*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 20*a/(c^7*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) - 8*b/(c^8*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 10*b*arcsin(1/(c*x))/(c^9*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 10*a/(c^9*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) - b/(c^10*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 2*b*arcsin(1/(c*x))/(c^11*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 2*a/(c^11*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))*c","B",0
4,1,352,0,0.165954," ","integrate(x^3*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{192} \, {\left(\frac{3 \, b x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{3 \, a x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}}{c} + \frac{2 \, b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}{c^{2}} + \frac{12 \, b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{3}} + \frac{12 \, a x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c^{3}} + \frac{18 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c^{4}} + \frac{18 \, b \arcsin\left(\frac{1}{c x}\right)}{c^{5}} + \frac{18 \, a}{c^{5}} - \frac{18 \, b}{c^{6} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{12 \, b \arcsin\left(\frac{1}{c x}\right)}{c^{7} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{12 \, a}{c^{7} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} - \frac{2 \, b}{c^{8} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3 \, b \arcsin\left(\frac{1}{c x}\right)}{c^{9} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{3 \, a}{c^{9} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}}\right)} c"," ",0,"1/192*(3*b*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*arcsin(1/(c*x))/c + 3*a*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4/c + 2*b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3/c^2 + 12*b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))/c^3 + 12*a*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c^3 + 18*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c^4 + 18*b*arcsin(1/(c*x))/c^5 + 18*a/c^5 - 18*b/(c^6*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 12*b*arcsin(1/(c*x))/(c^7*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 12*a/(c^7*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) - 2*b/(c^8*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3*b*arcsin(1/(c*x))/(c^9*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 3*a/(c^9*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4))*c","B",0
5,1,310,0,0.497844," ","integrate(x^2*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{24} \, {\left(\frac{b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{a x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}{c} + \frac{b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c^{2}} + \frac{3 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right)}{c^{3}} + \frac{3 \, a x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c^{3}} + \frac{4 \, b \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{4}} - \frac{4 \, b \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{4}} + \frac{3 \, b \arcsin\left(\frac{1}{c x}\right)}{c^{5} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3 \, a}{c^{5} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} - \frac{b}{c^{6} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{b \arcsin\left(\frac{1}{c x}\right)}{c^{7} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{a}{c^{7} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}\right)} c"," ",0,"1/24*(b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*arcsin(1/(c*x))/c + a*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3/c + b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c^2 + 3*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))/c^3 + 3*a*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c^3 + 4*b*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^4 - 4*b*log(1/(abs(c)*abs(x)))/c^4 + 3*b*arcsin(1/(c*x))/(c^5*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3*a/(c^5*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) - b/(c^6*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + b*arcsin(1/(c*x))/(c^7*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + a/(c^7*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3))*c","B",0
6,1,182,0,0.164045," ","integrate(x*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{8} \, {\left(\frac{b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{a x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c} + \frac{2 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c^{2}} + \frac{2 \, b \arcsin\left(\frac{1}{c x}\right)}{c^{3}} + \frac{2 \, a}{c^{3}} - \frac{2 \, b}{c^{4} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{b \arcsin\left(\frac{1}{c x}\right)}{c^{5} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{a}{c^{5} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}\right)} c"," ",0,"1/8*(b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))/c + a*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c + 2*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 + 2*b*arcsin(1/(c*x))/c^3 + 2*a/c^3 - 2*b/(c^4*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + b*arcsin(1/(c*x))/(c^5*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + a/(c^5*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2))*c","B",0
7,1,62,0,0.145730," ","integrate(a+b*arccsc(c*x),x, algorithm=""giac"")","\frac{1}{2} \, b c {\left(\frac{2 \, x \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right) - \log\left(-\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}}\right)} + a x"," ",0,"1/2*b*c*(2*x*arcsin(1/(c*x))/c + (log(sqrt(-1/(c^2*x^2) + 1) + 1) - log(-sqrt(-1/(c^2*x^2) + 1) + 1))/c^2) + a*x","B",0
8,-2,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Undef/Unsigned Inf encountered in limitLimit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
9,1,42,0,0.155751," ","integrate((a+b*arccsc(c*x))/x^2,x, algorithm=""giac"")","-{\left(b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{b \arcsin\left(\frac{1}{c x}\right)}{c x} + \frac{a}{c x}\right)} c"," ",0,"-(b*sqrt(-1/(c^2*x^2) + 1) + b*arcsin(1/(c*x))/(c*x) + a/(c*x))*c","A",0
10,1,66,0,0.149598," ","integrate((a+b*arccsc(c*x))/x^3,x, algorithm=""giac"")","-\frac{1}{4} \, {\left(2 \, b c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right) + 2 \, a c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + b c \arcsin\left(\frac{1}{c x}\right) + \frac{b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x}\right)} c"," ",0,"-1/4*(2*b*c*(1/(c^2*x^2) - 1)*arcsin(1/(c*x)) + 2*a*c*(1/(c^2*x^2) - 1) + b*c*arcsin(1/(c*x)) + b*sqrt(-1/(c^2*x^2) + 1)/x)*c","A",0
11,1,87,0,0.134819," ","integrate((a+b*arccsc(c*x))/x^4,x, algorithm=""giac"")","\frac{1}{9} \, {\left(b c^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 3 \, b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{3 \, b c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)}{x} - \frac{3 \, b c \arcsin\left(\frac{1}{c x}\right)}{x} - \frac{3 \, a}{c x^{3}}\right)} c"," ",0,"1/9*(b*c^2*(-1/(c^2*x^2) + 1)^(3/2) - 3*b*c^2*sqrt(-1/(c^2*x^2) + 1) - 3*b*c*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))/x - 3*b*c*arcsin(1/(c*x))/x - 3*a/(c*x^3))*c","A",0
12,1,117,0,0.153750," ","integrate((a+b*arccsc(c*x))/x^5,x, algorithm=""giac"")","-\frac{1}{32} \, {\left(8 \, b c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) + 16 \, b c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right) + 5 \, b c^{3} \arcsin\left(\frac{1}{c x}\right) - \frac{2 \, b c^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{x} + \frac{5 \, b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x} + \frac{8 \, a}{c x^{4}}\right)} c"," ",0,"-1/32*(8*b*c^3*(1/(c^2*x^2) - 1)^2*arcsin(1/(c*x)) + 16*b*c^3*(1/(c^2*x^2) - 1)*arcsin(1/(c*x)) + 5*b*c^3*arcsin(1/(c*x)) - 2*b*c^2*(-1/(c^2*x^2) + 1)^(3/2)/x + 5*b*c^2*sqrt(-1/(c^2*x^2) + 1)/x + 8*a/(c*x^4))*c","A",0
13,1,149,0,0.139419," ","integrate((a+b*arccsc(c*x))/x^6,x, algorithm=""giac"")","-\frac{1}{75} \, {\left(3 \, b c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 10 \, b c^{4} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + \frac{15 \, b c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)}{x} + 15 \, b c^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{30 \, b c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)}{x} + \frac{15 \, b c^{3} \arcsin\left(\frac{1}{c x}\right)}{x} + \frac{15 \, a}{c x^{5}}\right)} c"," ",0,"-1/75*(3*b*c^4*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1) - 10*b*c^4*(-1/(c^2*x^2) + 1)^(3/2) + 15*b*c^3*(1/(c^2*x^2) - 1)^2*arcsin(1/(c*x))/x + 15*b*c^4*sqrt(-1/(c^2*x^2) + 1) + 30*b*c^3*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))/x + 15*b*c^3*arcsin(1/(c*x))/x + 15*a/(c*x^5))*c","B",0
14,1,174,0,0.134774," ","integrate((a+b*arccsc(c*x))/x^7,x, algorithm=""giac"")","-\frac{1}{288} \, {\left(48 \, b c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right) + 144 \, b c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) + 144 \, b c^{5} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right) + 33 \, b c^{5} \arcsin\left(\frac{1}{c x}\right) + \frac{8 \, b c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x} - \frac{26 \, b c^{4} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{x} + \frac{33 \, b c^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x} + \frac{48 \, a}{c x^{6}}\right)} c"," ",0,"-1/288*(48*b*c^5*(1/(c^2*x^2) - 1)^3*arcsin(1/(c*x)) + 144*b*c^5*(1/(c^2*x^2) - 1)^2*arcsin(1/(c*x)) + 144*b*c^5*(1/(c^2*x^2) - 1)*arcsin(1/(c*x)) + 33*b*c^5*arcsin(1/(c*x)) + 8*b*c^4*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)/x - 26*b*c^4*(-1/(c^2*x^2) + 1)^(3/2)/x + 33*b*c^4*sqrt(-1/(c^2*x^2) + 1)/x + 48*a/(c*x^6))*c","B",0
15,1,811,0,0.391280," ","integrate(x^3*(a+b*arccsc(c*x))^2,x, algorithm=""giac"")","\frac{1}{192} \, {\left(\frac{3 \, b^{2} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} \arcsin\left(\frac{1}{c x}\right)^{2}}{c} + \frac{6 \, a b x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{3 \, a^{2} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}}{c} + \frac{4 \, b^{2} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right)}{c^{2}} + \frac{4 \, a b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}{c^{2}} + \frac{12 \, b^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)^{2}}{c^{3}} + \frac{24 \, a b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{3}} + \frac{12 \, a^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c^{3}} + \frac{4 \, b^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c^{3}} + \frac{36 \, b^{2} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right)}{c^{4}} + \frac{36 \, a b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c^{4}} + \frac{18 \, b^{2} \arcsin\left(\frac{1}{c x}\right)^{2}}{c^{5}} + \frac{36 \, a b \arcsin\left(\frac{1}{c x}\right)}{c^{5}} - \frac{128 \, b^{2} \log\left(2\right)}{c^{5}} + \frac{64 \, b^{2} \log\left(2 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 2\right)}{c^{5}} - \frac{64 \, b^{2} \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{5}} - \frac{64 \, b^{2} \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{5}} + \frac{18 \, a^{2}}{c^{5}} + \frac{8 \, b^{2}}{c^{5}} - \frac{36 \, b^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{6} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} - \frac{36 \, a b}{c^{6} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{12 \, b^{2} \arcsin\left(\frac{1}{c x}\right)^{2}}{c^{7} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{24 \, a b \arcsin\left(\frac{1}{c x}\right)}{c^{7} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{12 \, a^{2}}{c^{7} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{4 \, b^{2}}{c^{7} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} - \frac{4 \, b^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{8} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} - \frac{4 \, a b}{c^{8} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3 \, b^{2} \arcsin\left(\frac{1}{c x}\right)^{2}}{c^{9} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{6 \, a b \arcsin\left(\frac{1}{c x}\right)}{c^{9} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{3 \, a^{2}}{c^{9} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}}\right)} c"," ",0,"1/192*(3*b^2*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*arcsin(1/(c*x))^2/c + 6*a*b*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*arcsin(1/(c*x))/c + 3*a^2*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4/c + 4*b^2*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*arcsin(1/(c*x))/c^2 + 4*a*b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3/c^2 + 12*b^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))^2/c^3 + 24*a*b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))/c^3 + 12*a^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c^3 + 4*b^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c^3 + 36*b^2*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))/c^4 + 36*a*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c^4 + 18*b^2*arcsin(1/(c*x))^2/c^5 + 36*a*b*arcsin(1/(c*x))/c^5 - 128*b^2*log(2)/c^5 + 64*b^2*log(2*sqrt(-1/(c^2*x^2) + 1) + 2)/c^5 - 64*b^2*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^5 - 64*b^2*log(1/(abs(c)*abs(x)))/c^5 + 18*a^2/c^5 + 8*b^2/c^5 - 36*b^2*arcsin(1/(c*x))/(c^6*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) - 36*a*b/(c^6*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 12*b^2*arcsin(1/(c*x))^2/(c^7*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 24*a*b*arcsin(1/(c*x))/(c^7*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 12*a^2/(c^7*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 4*b^2/(c^7*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) - 4*b^2*arcsin(1/(c*x))/(c^8*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) - 4*a*b/(c^8*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3*b^2*arcsin(1/(c*x))^2/(c^9*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 6*a*b*arcsin(1/(c*x))/(c^9*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 3*a^2/(c^9*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4))*c","B",0
16,0,0,0,0.000000," ","integrate(x^2*(a+b*arccsc(c*x))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}^{2} x^{2}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)^2*x^2, x)","F",0
17,1,427,0,0.247877," ","integrate(x*(a+b*arccsc(c*x))^2,x, algorithm=""giac"")","\frac{1}{8} \, {\left(\frac{b^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)^{2}}{c} + \frac{2 \, a b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{a^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c} + \frac{4 \, b^{2} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right)}{c^{2}} + \frac{4 \, a b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c^{2}} + \frac{2 \, b^{2} \arcsin\left(\frac{1}{c x}\right)^{2}}{c^{3}} + \frac{4 \, a b \arcsin\left(\frac{1}{c x}\right)}{c^{3}} - \frac{16 \, b^{2} \log\left(2\right)}{c^{3}} + \frac{8 \, b^{2} \log\left(2 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 2\right)}{c^{3}} - \frac{8 \, b^{2} \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{3}} - \frac{8 \, b^{2} \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{3}} + \frac{2 \, a^{2}}{c^{3}} - \frac{4 \, b^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{4} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} - \frac{4 \, a b}{c^{4} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{b^{2} \arcsin\left(\frac{1}{c x}\right)^{2}}{c^{5} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{2 \, a b \arcsin\left(\frac{1}{c x}\right)}{c^{5} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{a^{2}}{c^{5} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}\right)} c"," ",0,"1/8*(b^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))^2/c + 2*a*b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))/c + a^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c + 4*b^2*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))/c^2 + 4*a*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 + 2*b^2*arcsin(1/(c*x))^2/c^3 + 4*a*b*arcsin(1/(c*x))/c^3 - 16*b^2*log(2)/c^3 + 8*b^2*log(2*sqrt(-1/(c^2*x^2) + 1) + 2)/c^3 - 8*b^2*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^3 - 8*b^2*log(1/(abs(c)*abs(x)))/c^3 + 2*a^2/c^3 - 4*b^2*arcsin(1/(c*x))/(c^4*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) - 4*a*b/(c^4*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + b^2*arcsin(1/(c*x))^2/(c^5*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 2*a*b*arcsin(1/(c*x))/(c^5*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + a^2/(c^5*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2))*c","B",0
18,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)^2, x)","F",0
19,-2,0,0,0.000000," ","integrate((a+b*arccsc(c*x))^2/x,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]ln of unsigned or minus infinity Error: Bad Argument Value","F(-2)",0
20,1,104,0,0.155329," ","integrate((a+b*arccsc(c*x))^2/x^2,x, algorithm=""giac"")","-{\left(2 \, b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arcsin\left(\frac{1}{c x}\right) + 2 \, a b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{b^{2} \arcsin\left(\frac{1}{c x}\right)^{2}}{c x} + \frac{2 \, a b \arcsin\left(\frac{1}{c x}\right)}{c x} + \frac{a^{2}}{c x} - \frac{2 \, b^{2}}{c x}\right)} c"," ",0,"-(2*b^2*sqrt(-1/(c^2*x^2) + 1)*arcsin(1/(c*x)) + 2*a*b*sqrt(-1/(c^2*x^2) + 1) + b^2*arcsin(1/(c*x))^2/(c*x) + 2*a*b*arcsin(1/(c*x))/(c*x) + a^2/(c*x) - 2*b^2/(c*x))*c","B",0
21,1,163,0,0.180967," ","integrate((a+b*arccsc(c*x))^2/x^3,x, algorithm=""giac"")","-\frac{1}{8} \, {\left(4 \, b^{2} c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)^{2} + 8 \, a b c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right) + 2 \, b^{2} c \arcsin\left(\frac{1}{c x}\right)^{2} + 4 \, a^{2} c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} - 2 \, b^{2} c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + 4 \, a b c \arcsin\left(\frac{1}{c x}\right) - b^{2} c + \frac{4 \, b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arcsin\left(\frac{1}{c x}\right)}{x} + \frac{4 \, a b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x}\right)} c"," ",0,"-1/8*(4*b^2*c*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))^2 + 8*a*b*c*(1/(c^2*x^2) - 1)*arcsin(1/(c*x)) + 2*b^2*c*arcsin(1/(c*x))^2 + 4*a^2*c*(1/(c^2*x^2) - 1) - 2*b^2*c*(1/(c^2*x^2) - 1) + 4*a*b*c*arcsin(1/(c*x)) - b^2*c + 4*b^2*sqrt(-1/(c^2*x^2) + 1)*arcsin(1/(c*x))/x + 4*a*b*sqrt(-1/(c^2*x^2) + 1)/x)*c","B",0
22,1,224,0,0.171860," ","integrate((a+b*arccsc(c*x))^2/x^4,x, algorithm=""giac"")","\frac{1}{27} \, {\left(6 \, b^{2} c^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} \arcsin\left(\frac{1}{c x}\right) + 6 \, a b c^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 18 \, b^{2} c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arcsin\left(\frac{1}{c x}\right) - \frac{9 \, b^{2} c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)^{2}}{x} - 18 \, a b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{18 \, a b c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)}{x} - \frac{9 \, b^{2} c \arcsin\left(\frac{1}{c x}\right)^{2}}{x} + \frac{2 \, b^{2} c {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{x} - \frac{18 \, a b c \arcsin\left(\frac{1}{c x}\right)}{x} + \frac{14 \, b^{2} c}{x} - \frac{9 \, a^{2}}{c x^{3}}\right)} c"," ",0,"1/27*(6*b^2*c^2*(-1/(c^2*x^2) + 1)^(3/2)*arcsin(1/(c*x)) + 6*a*b*c^2*(-1/(c^2*x^2) + 1)^(3/2) - 18*b^2*c^2*sqrt(-1/(c^2*x^2) + 1)*arcsin(1/(c*x)) - 9*b^2*c*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))^2/x - 18*a*b*c^2*sqrt(-1/(c^2*x^2) + 1) - 18*a*b*c*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))/x - 9*b^2*c*arcsin(1/(c*x))^2/x + 2*b^2*c*(1/(c^2*x^2) - 1)/x - 18*a*b*c*arcsin(1/(c*x))/x + 14*b^2*c/x - 9*a^2/(c*x^3))*c","B",0
23,1,304,0,0.167127," ","integrate((a+b*arccsc(c*x))^2/x^5,x, algorithm=""giac"")","-\frac{1}{256} \, {\left(64 \, b^{2} c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)^{2} + 128 \, a b c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) + 128 \, b^{2} c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)^{2} - 8 \, b^{2} c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 256 \, a b c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right) + 40 \, b^{2} c^{3} \arcsin\left(\frac{1}{c x}\right)^{2} - 40 \, b^{2} c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + 80 \, a b c^{3} \arcsin\left(\frac{1}{c x}\right) - \frac{32 \, b^{2} c^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} \arcsin\left(\frac{1}{c x}\right)}{x} - 17 \, b^{2} c^{3} - \frac{32 \, a b c^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{x} + \frac{80 \, b^{2} c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arcsin\left(\frac{1}{c x}\right)}{x} + \frac{80 \, a b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x} + \frac{64 \, a^{2}}{c x^{4}}\right)} c"," ",0,"-1/256*(64*b^2*c^3*(1/(c^2*x^2) - 1)^2*arcsin(1/(c*x))^2 + 128*a*b*c^3*(1/(c^2*x^2) - 1)^2*arcsin(1/(c*x)) + 128*b^2*c^3*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))^2 - 8*b^2*c^3*(1/(c^2*x^2) - 1)^2 + 256*a*b*c^3*(1/(c^2*x^2) - 1)*arcsin(1/(c*x)) + 40*b^2*c^3*arcsin(1/(c*x))^2 - 40*b^2*c^3*(1/(c^2*x^2) - 1) + 80*a*b*c^3*arcsin(1/(c*x)) - 32*b^2*c^2*(-1/(c^2*x^2) + 1)^(3/2)*arcsin(1/(c*x))/x - 17*b^2*c^3 - 32*a*b*c^2*(-1/(c^2*x^2) + 1)^(3/2)/x + 80*b^2*c^2*sqrt(-1/(c^2*x^2) + 1)*arcsin(1/(c*x))/x + 80*a*b*c^2*sqrt(-1/(c^2*x^2) + 1)/x + 64*a^2/(c*x^4))*c","B",0
24,0,0,0,0.000000," ","integrate(x^3*(a+b*arccsc(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}^{3} x^{3}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)^3*x^3, x)","F",0
25,0,0,0,0.000000," ","integrate(x^2*(a+b*arccsc(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}^{3} x^{2}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)^3*x^2, x)","F",0
26,0,0,0,0.000000," ","integrate(x*(a+b*arccsc(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}^{3} x\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)^3*x, x)","F",0
27,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)^3, x)","F",0
28,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))^3/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)}^{3}}{x}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)^3/x, x)","F",0
29,1,195,0,0.191307," ","integrate((a+b*arccsc(c*x))^3/x^2,x, algorithm=""giac"")","-{\left(3 \, b^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arcsin\left(\frac{1}{c x}\right)^{2} + 6 \, a b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arcsin\left(\frac{1}{c x}\right) + \frac{b^{3} \arcsin\left(\frac{1}{c x}\right)^{3}}{c x} + 3 \, a^{2} b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 6 \, b^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{3 \, a b^{2} \arcsin\left(\frac{1}{c x}\right)^{2}}{c x} + \frac{3 \, a^{2} b \arcsin\left(\frac{1}{c x}\right)}{c x} - \frac{6 \, b^{3} \arcsin\left(\frac{1}{c x}\right)}{c x} + \frac{a^{3}}{c x} - \frac{6 \, a b^{2}}{c x}\right)} c"," ",0,"-(3*b^3*sqrt(-1/(c^2*x^2) + 1)*arcsin(1/(c*x))^2 + 6*a*b^2*sqrt(-1/(c^2*x^2) + 1)*arcsin(1/(c*x)) + b^3*arcsin(1/(c*x))^3/(c*x) + 3*a^2*b*sqrt(-1/(c^2*x^2) + 1) - 6*b^3*sqrt(-1/(c^2*x^2) + 1) + 3*a*b^2*arcsin(1/(c*x))^2/(c*x) + 3*a^2*b*arcsin(1/(c*x))/(c*x) - 6*b^3*arcsin(1/(c*x))/(c*x) + a^3/(c*x) - 6*a*b^2/(c*x))*c","B",0
30,1,302,0,0.179244," ","integrate((a+b*arccsc(c*x))^3/x^3,x, algorithm=""giac"")","-\frac{1}{8} \, {\left(4 \, b^{3} c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)^{3} + 12 \, a b^{2} c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)^{2} + 2 \, b^{3} c \arcsin\left(\frac{1}{c x}\right)^{3} + 12 \, a^{2} b c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right) - 6 \, b^{3} c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right) + 6 \, a b^{2} c \arcsin\left(\frac{1}{c x}\right)^{2} + 4 \, a^{3} c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} - 6 \, a b^{2} c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + 6 \, a^{2} b c \arcsin\left(\frac{1}{c x}\right) - 3 \, b^{3} c \arcsin\left(\frac{1}{c x}\right) + \frac{6 \, b^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arcsin\left(\frac{1}{c x}\right)^{2}}{x} - 3 \, a b^{2} c + \frac{12 \, a b^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arcsin\left(\frac{1}{c x}\right)}{x} + \frac{6 \, a^{2} b \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x} - \frac{3 \, b^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x}\right)} c"," ",0,"-1/8*(4*b^3*c*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))^3 + 12*a*b^2*c*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))^2 + 2*b^3*c*arcsin(1/(c*x))^3 + 12*a^2*b*c*(1/(c^2*x^2) - 1)*arcsin(1/(c*x)) - 6*b^3*c*(1/(c^2*x^2) - 1)*arcsin(1/(c*x)) + 6*a*b^2*c*arcsin(1/(c*x))^2 + 4*a^3*c*(1/(c^2*x^2) - 1) - 6*a*b^2*c*(1/(c^2*x^2) - 1) + 6*a^2*b*c*arcsin(1/(c*x)) - 3*b^3*c*arcsin(1/(c*x)) + 6*b^3*sqrt(-1/(c^2*x^2) + 1)*arcsin(1/(c*x))^2/x - 3*a*b^2*c + 12*a*b^2*sqrt(-1/(c^2*x^2) + 1)*arcsin(1/(c*x))/x + 6*a^2*b*sqrt(-1/(c^2*x^2) + 1)/x - 3*b^3*sqrt(-1/(c^2*x^2) + 1)/x)*c","B",0
31,1,428,0,0.181599," ","integrate((a+b*arccsc(c*x))^3/x^4,x, algorithm=""giac"")","\frac{1}{27} \, {\left(9 \, b^{3} c^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} \arcsin\left(\frac{1}{c x}\right)^{2} + 18 \, a b^{2} c^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} \arcsin\left(\frac{1}{c x}\right) - 27 \, b^{3} c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arcsin\left(\frac{1}{c x}\right)^{2} - \frac{9 \, b^{3} c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)^{3}}{x} + 9 \, a^{2} b c^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 2 \, b^{3} c^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 54 \, a b^{2} c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arcsin\left(\frac{1}{c x}\right) - \frac{27 \, a b^{2} c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)^{2}}{x} - \frac{9 \, b^{3} c \arcsin\left(\frac{1}{c x}\right)^{3}}{x} - 27 \, a^{2} b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 42 \, b^{3} c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{27 \, a^{2} b c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)}{x} + \frac{6 \, b^{3} c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)}{x} - \frac{27 \, a b^{2} c \arcsin\left(\frac{1}{c x}\right)^{2}}{x} + \frac{6 \, a b^{2} c {\left(\frac{1}{c^{2} x^{2}} - 1\right)}}{x} - \frac{27 \, a^{2} b c \arcsin\left(\frac{1}{c x}\right)}{x} + \frac{42 \, b^{3} c \arcsin\left(\frac{1}{c x}\right)}{x} + \frac{42 \, a b^{2} c}{x} - \frac{9 \, a^{3}}{c x^{3}}\right)} c"," ",0,"1/27*(9*b^3*c^2*(-1/(c^2*x^2) + 1)^(3/2)*arcsin(1/(c*x))^2 + 18*a*b^2*c^2*(-1/(c^2*x^2) + 1)^(3/2)*arcsin(1/(c*x)) - 27*b^3*c^2*sqrt(-1/(c^2*x^2) + 1)*arcsin(1/(c*x))^2 - 9*b^3*c*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))^3/x + 9*a^2*b*c^2*(-1/(c^2*x^2) + 1)^(3/2) - 2*b^3*c^2*(-1/(c^2*x^2) + 1)^(3/2) - 54*a*b^2*c^2*sqrt(-1/(c^2*x^2) + 1)*arcsin(1/(c*x)) - 27*a*b^2*c*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))^2/x - 9*b^3*c*arcsin(1/(c*x))^3/x - 27*a^2*b*c^2*sqrt(-1/(c^2*x^2) + 1) + 42*b^3*c^2*sqrt(-1/(c^2*x^2) + 1) - 27*a^2*b*c*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))/x + 6*b^3*c*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))/x - 27*a*b^2*c*arcsin(1/(c*x))^2/x + 6*a*b^2*c*(1/(c^2*x^2) - 1)/x - 27*a^2*b*c*arcsin(1/(c*x))/x + 42*b^3*c*arcsin(1/(c*x))/x + 42*a*b^2*c/x - 9*a^3/(c*x^3))*c","B",0
32,1,576,0,0.181431," ","integrate((a+b*arccsc(c*x))^3/x^5,x, algorithm=""giac"")","-\frac{1}{256} \, {\left(64 \, b^{3} c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)^{3} + 192 \, a b^{2} c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)^{2} + 128 \, b^{3} c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)^{3} + 192 \, a^{2} b c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) - 24 \, b^{3} c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) + 384 \, a b^{2} c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)^{2} + 40 \, b^{3} c^{3} \arcsin\left(\frac{1}{c x}\right)^{3} - 24 \, a b^{2} c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 384 \, a^{2} b c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right) - 120 \, b^{3} c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right) + 120 \, a b^{2} c^{3} \arcsin\left(\frac{1}{c x}\right)^{2} - \frac{48 \, b^{3} c^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} \arcsin\left(\frac{1}{c x}\right)^{2}}{x} - 120 \, a b^{2} c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + 120 \, a^{2} b c^{3} \arcsin\left(\frac{1}{c x}\right) - 51 \, b^{3} c^{3} \arcsin\left(\frac{1}{c x}\right) - \frac{96 \, a b^{2} c^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} \arcsin\left(\frac{1}{c x}\right)}{x} + \frac{120 \, b^{3} c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arcsin\left(\frac{1}{c x}\right)^{2}}{x} - 51 \, a b^{2} c^{3} - \frac{48 \, a^{2} b c^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{x} + \frac{6 \, b^{3} c^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{x} + \frac{240 \, a b^{2} c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \arcsin\left(\frac{1}{c x}\right)}{x} + \frac{120 \, a^{2} b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x} - \frac{51 \, b^{3} c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{x} + \frac{64 \, a^{3}}{c x^{4}}\right)} c"," ",0,"-1/256*(64*b^3*c^3*(1/(c^2*x^2) - 1)^2*arcsin(1/(c*x))^3 + 192*a*b^2*c^3*(1/(c^2*x^2) - 1)^2*arcsin(1/(c*x))^2 + 128*b^3*c^3*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))^3 + 192*a^2*b*c^3*(1/(c^2*x^2) - 1)^2*arcsin(1/(c*x)) - 24*b^3*c^3*(1/(c^2*x^2) - 1)^2*arcsin(1/(c*x)) + 384*a*b^2*c^3*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))^2 + 40*b^3*c^3*arcsin(1/(c*x))^3 - 24*a*b^2*c^3*(1/(c^2*x^2) - 1)^2 + 384*a^2*b*c^3*(1/(c^2*x^2) - 1)*arcsin(1/(c*x)) - 120*b^3*c^3*(1/(c^2*x^2) - 1)*arcsin(1/(c*x)) + 120*a*b^2*c^3*arcsin(1/(c*x))^2 - 48*b^3*c^2*(-1/(c^2*x^2) + 1)^(3/2)*arcsin(1/(c*x))^2/x - 120*a*b^2*c^3*(1/(c^2*x^2) - 1) + 120*a^2*b*c^3*arcsin(1/(c*x)) - 51*b^3*c^3*arcsin(1/(c*x)) - 96*a*b^2*c^2*(-1/(c^2*x^2) + 1)^(3/2)*arcsin(1/(c*x))/x + 120*b^3*c^2*sqrt(-1/(c^2*x^2) + 1)*arcsin(1/(c*x))^2/x - 51*a*b^2*c^3 - 48*a^2*b*c^2*(-1/(c^2*x^2) + 1)^(3/2)/x + 6*b^3*c^2*(-1/(c^2*x^2) + 1)^(3/2)/x + 240*a*b^2*c^2*sqrt(-1/(c^2*x^2) + 1)*arcsin(1/(c*x))/x + 120*a^2*b*c^2*sqrt(-1/(c^2*x^2) + 1)/x - 51*b^3*c^2*sqrt(-1/(c^2*x^2) + 1)/x + 64*a^3/(c*x^4))*c","B",0
33,0,0,0,0.000000," ","integrate(x/(a+b*arccsc(c*x)),x, algorithm=""giac"")","\int \frac{x}{b \operatorname{arccsc}\left(c x\right) + a}\,{d x}"," ",0,"integrate(x/(b*arccsc(c*x) + a), x)","F",0
34,0,0,0,0.000000," ","integrate(1/(a+b*arccsc(c*x)),x, algorithm=""giac"")","\int \frac{1}{b \operatorname{arccsc}\left(c x\right) + a}\,{d x}"," ",0,"integrate(1/(b*arccsc(c*x) + a), x)","F",0
35,0,0,0,0.000000," ","integrate(1/x/(a+b*arccsc(c*x)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/((b*arccsc(c*x) + a)*x), x)","F",0
36,1,54,0,0.122860," ","integrate(1/x^2/(a+b*arccsc(c*x)),x, algorithm=""giac"")","-c {\left(\frac{\cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(\frac{1}{c x}\right)\right)}{b} + \frac{\sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(\frac{1}{c x}\right)\right)}{b}\right)}"," ",0,"-c*(cos(a/b)*cos_integral(a/b + arcsin(1/(c*x)))/b + sin(a/b)*sin_integral(a/b + arcsin(1/(c*x)))/b)","A",0
37,1,95,0,0.163225," ","integrate(1/x^3/(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{2 \, c \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(\frac{1}{c x}\right)\right) \sin\left(\frac{a}{b}\right)}{b} - \frac{2 \, c \cos\left(\frac{a}{b}\right)^{2} \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(\frac{1}{c x}\right)\right)}{b} + \frac{c \operatorname{Si}\left(\frac{2 \, a}{b} + 2 \, \arcsin\left(\frac{1}{c x}\right)\right)}{b}\right)} c"," ",0,"1/2*(2*c*cos(a/b)*cos_integral(2*a/b + 2*arcsin(1/(c*x)))*sin(a/b)/b - 2*c*cos(a/b)^2*sin_integral(2*a/b + 2*arcsin(1/(c*x)))/b + c*sin_integral(2*a/b + 2*arcsin(1/(c*x)))/b)*c","A",0
38,1,200,0,0.147866," ","integrate(1/x^4/(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{4} \, {\left(\frac{4 \, c^{2} \cos\left(\frac{a}{b}\right)^{3} \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(\frac{1}{c x}\right)\right)}{b} + \frac{4 \, c^{2} \cos\left(\frac{a}{b}\right)^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(\frac{1}{c x}\right)\right)}{b} - \frac{3 \, c^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(\frac{1}{c x}\right)\right)}{b} - \frac{c^{2} \cos\left(\frac{a}{b}\right) \operatorname{Ci}\left(\frac{a}{b} + \arcsin\left(\frac{1}{c x}\right)\right)}{b} - \frac{c^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{3 \, a}{b} + 3 \, \arcsin\left(\frac{1}{c x}\right)\right)}{b} - \frac{c^{2} \sin\left(\frac{a}{b}\right) \operatorname{Si}\left(\frac{a}{b} + \arcsin\left(\frac{1}{c x}\right)\right)}{b}\right)} c"," ",0,"1/4*(4*c^2*cos(a/b)^3*cos_integral(3*a/b + 3*arcsin(1/(c*x)))/b + 4*c^2*cos(a/b)^2*sin(a/b)*sin_integral(3*a/b + 3*arcsin(1/(c*x)))/b - 3*c^2*cos(a/b)*cos_integral(3*a/b + 3*arcsin(1/(c*x)))/b - c^2*cos(a/b)*cos_integral(a/b + arcsin(1/(c*x)))/b - c^2*sin(a/b)*sin_integral(3*a/b + 3*arcsin(1/(c*x)))/b - c^2*sin(a/b)*sin_integral(a/b + arcsin(1/(c*x)))/b)*c","A",0
39,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arccsc(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}^{3} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)^3*(d*x)^m, x)","F",0
40,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arccsc(c*x))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}^{2} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)^2*(d*x)^m, x)","F",0
41,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\int {\left(b \operatorname{arccsc}\left(c x\right) + a\right)} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*(d*x)^m, x)","F",0
42,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arccsc(c*x)),x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{b \operatorname{arccsc}\left(c x\right) + a}\,{d x}"," ",0,"integrate((d*x)^m/(b*arccsc(c*x) + a), x)","F",0
43,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arccsc(c*x))^2,x, algorithm=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x)^m/(b*arccsc(c*x) + a)^2, x)","F",0
44,1,1112,0,2.008189," ","integrate((e*x+d)^3*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{192} \, {\left(\frac{3 \, b x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} \arcsin\left(\frac{1}{c x}\right) e^{3}}{c} + \frac{3 \, a x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} e^{3}}{c} + \frac{24 \, b d x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c} + \frac{24 \, a d x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e^{2}}{c} + \frac{72 \, b d^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) e}{c} + \frac{72 \, a d^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e}{c} + \frac{96 \, b d^{3} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{2 \, b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e^{3}}{c^{2}} + \frac{96 \, a d^{3} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c} + \frac{24 \, b d x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e^{2}}{c^{2}} + \frac{12 \, b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) e^{3}}{c^{3}} + \frac{144 \, b d^{2} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e}{c^{2}} + \frac{12 \, a x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e^{3}}{c^{3}} + \frac{72 \, b d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{3}} + \frac{192 \, b d^{3} \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}} - \frac{192 \, b d^{3} \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{2}} + \frac{72 \, a d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e^{2}}{c^{3}} + \frac{144 \, b d^{2} \arcsin\left(\frac{1}{c x}\right) e}{c^{3}} + \frac{144 \, a d^{2} e}{c^{3}} + \frac{96 \, b d^{3} \arcsin\left(\frac{1}{c x}\right)}{c^{3} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{18 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e^{3}}{c^{4}} + \frac{96 \, b d e^{2} \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{4}} - \frac{96 \, b d e^{2} \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{4}} + \frac{96 \, a d^{3}}{c^{3} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{18 \, b \arcsin\left(\frac{1}{c x}\right) e^{3}}{c^{5}} - \frac{144 \, b d^{2} e}{c^{4} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{18 \, a e^{3}}{c^{5}} + \frac{72 \, b d \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{5} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{72 \, a d e^{2}}{c^{5} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{72 \, b d^{2} \arcsin\left(\frac{1}{c x}\right) e}{c^{5} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{72 \, a d^{2} e}{c^{5} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} - \frac{18 \, b e^{3}}{c^{6} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} - \frac{24 \, b d e^{2}}{c^{6} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{12 \, b \arcsin\left(\frac{1}{c x}\right) e^{3}}{c^{7} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{12 \, a e^{3}}{c^{7} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{24 \, b d \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{7} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{24 \, a d e^{2}}{c^{7} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} - \frac{2 \, b e^{3}}{c^{8} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3 \, b \arcsin\left(\frac{1}{c x}\right) e^{3}}{c^{9} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{3 \, a e^{3}}{c^{9} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}}\right)} c"," ",0,"1/192*(3*b*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*arcsin(1/(c*x))*e^3/c + 3*a*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*e^3/c + 24*b*d*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*arcsin(1/(c*x))*e^2/c + 24*a*d*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e^2/c + 72*b*d^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))*e/c + 72*a*d^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e/c + 96*b*d^3*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))/c + 2*b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e^3/c^2 + 96*a*d^3*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c + 24*b*d*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e^2/c^2 + 12*b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))*e^3/c^3 + 144*b*d^2*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e/c^2 + 12*a*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e^3/c^3 + 72*b*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))*e^2/c^3 + 192*b*d^3*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 - 192*b*d^3*log(1/(abs(c)*abs(x)))/c^2 + 72*a*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e^2/c^3 + 144*b*d^2*arcsin(1/(c*x))*e/c^3 + 144*a*d^2*e/c^3 + 96*b*d^3*arcsin(1/(c*x))/(c^3*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 18*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e^3/c^4 + 96*b*d*e^2*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^4 - 96*b*d*e^2*log(1/(abs(c)*abs(x)))/c^4 + 96*a*d^3/(c^3*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 18*b*arcsin(1/(c*x))*e^3/c^5 - 144*b*d^2*e/(c^4*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 18*a*e^3/c^5 + 72*b*d*arcsin(1/(c*x))*e^2/(c^5*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 72*a*d*e^2/(c^5*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 72*b*d^2*arcsin(1/(c*x))*e/(c^5*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 72*a*d^2*e/(c^5*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) - 18*b*e^3/(c^6*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) - 24*b*d*e^2/(c^6*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 12*b*arcsin(1/(c*x))*e^3/(c^7*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 12*a*e^3/(c^7*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 24*b*d*arcsin(1/(c*x))*e^2/(c^7*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 24*a*d*e^2/(c^7*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) - 2*b*e^3/(c^8*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3*b*arcsin(1/(c*x))*e^3/(c^9*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 3*a*e^3/(c^9*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4))*c","B",0
45,1,595,0,2.927709," ","integrate((e*x+d)^2*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{24} \, {\left(\frac{b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c} + \frac{a x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e^{2}}{c} - \frac{24 \, b d x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right) e}{c} + \frac{12 \, b d^{2} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right)}{c} - \frac{24 \, a d x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} e}{c} + \frac{12 \, a d^{2} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c} + \frac{b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e^{2}}{c^{2}} + \frac{24 \, b d x \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e}{c^{2}} + \frac{3 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{3}} + \frac{24 \, b d^{2} \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}} - \frac{24 \, b d^{2} \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{2}} + \frac{3 \, a x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e^{2}}{c^{3}} + \frac{24 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{3}} + \frac{24 \, a d e}{c^{3}} + \frac{12 \, b d^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{3} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{4 \, b e^{2} \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{4}} - \frac{4 \, b e^{2} \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{4}} + \frac{12 \, a d^{2}}{c^{3} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{5} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3 \, a e^{2}}{c^{5} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} - \frac{b e^{2}}{c^{6} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{7} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{a e^{2}}{c^{7} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}\right)} c"," ",0,"1/24*(b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*arcsin(1/(c*x))*e^2/c + a*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e^2/c - 24*b*d*x^2*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))*e/c + 12*b*d^2*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))/c - 24*a*d*x^2*(1/(c^2*x^2) - 1)*e/c + 12*a*d^2*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c + b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e^2/c^2 + 24*b*d*x*sqrt(-1/(c^2*x^2) + 1)*e/c^2 + 3*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))*e^2/c^3 + 24*b*d^2*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 - 24*b*d^2*log(1/(abs(c)*abs(x)))/c^2 + 3*a*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e^2/c^3 + 24*b*d*arcsin(1/(c*x))*e/c^3 + 24*a*d*e/c^3 + 12*b*d^2*arcsin(1/(c*x))/(c^3*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 4*b*e^2*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^4 - 4*b*e^2*log(1/(abs(c)*abs(x)))/c^4 + 12*a*d^2/(c^3*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3*b*arcsin(1/(c*x))*e^2/(c^5*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3*a*e^2/(c^5*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) - b*e^2/(c^6*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + b*arcsin(1/(c*x))*e^2/(c^7*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + a*e^2/(c^7*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3))*c","B",0
46,1,349,0,0.451190," ","integrate((e*x+d)*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{8} \, {\left(\frac{b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) e}{c} + \frac{a x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e}{c} + \frac{4 \, b d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{4 \, a d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c} + \frac{2 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e}{c^{2}} + \frac{8 \, b d \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}} - \frac{8 \, b d \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{2}} + \frac{2 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{3}} + \frac{2 \, a e}{c^{3}} + \frac{4 \, b d \arcsin\left(\frac{1}{c x}\right)}{c^{3} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{4 \, a d}{c^{3} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} - \frac{2 \, b e}{c^{4} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{b \arcsin\left(\frac{1}{c x}\right) e}{c^{5} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{a e}{c^{5} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}\right)} c"," ",0,"1/8*(b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))*e/c + a*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e/c + 4*b*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))/c + 4*a*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c + 2*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e/c^2 + 8*b*d*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 - 8*b*d*log(1/(abs(c)*abs(x)))/c^2 + 2*b*arcsin(1/(c*x))*e/c^3 + 2*a*e/c^3 + 4*b*d*arcsin(1/(c*x))/(c^3*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 4*a*d/(c^3*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) - 2*b*e/(c^4*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + b*arcsin(1/(c*x))*e/(c^5*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + a*e/(c^5*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2))*c","B",0
47,1,62,0,0.127956," ","integrate(a+b*arccsc(c*x),x, algorithm=""giac"")","\frac{1}{2} \, b c {\left(\frac{2 \, x \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right) - \log\left(-\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}}\right)} + a x"," ",0,"1/2*b*c*(2*x*arcsin(1/(c*x))/c + (log(sqrt(-1/(c^2*x^2) + 1) + 1) - log(-sqrt(-1/(c^2*x^2) + 1) + 1))/c^2) + a*x","B",0
48,-2,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/(e*x+d),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
49,-2,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/(e*x+d)^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
50,-2,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/(e*x+d)^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
51,0,0,0,0.000000," ","integrate(x^2*(a+b*arccsc(c*x))*(e*x+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x + d} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{2}\,{d x}"," ",0,"integrate(sqrt(e*x + d)*(b*arccsc(c*x) + a)*x^2, x)","F",0
52,0,0,0,0.000000," ","integrate(x*(a+b*arccsc(c*x))*(e*x+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x + d} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x\,{d x}"," ",0,"integrate(sqrt(e*x + d)*(b*arccsc(c*x) + a)*x, x)","F",0
53,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))*(e*x+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x + d} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(e*x + d)*(b*arccsc(c*x) + a), x)","F",0
54,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))*(e*x+d)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{e x + d} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}}{x}\,{d x}"," ",0,"integrate(sqrt(e*x + d)*(b*arccsc(c*x) + a)/x, x)","F",0
55,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))*(e*x+d)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{e x + d} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(e*x + d)*(b*arccsc(c*x) + a)/x^2, x)","F",0
56,0,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\int {\left(e x + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}\,{d x}"," ",0,"integrate((e*x + d)^(3/2)*(b*arccsc(c*x) + a), x)","F",0
57,0,0,0,0.000000," ","integrate(x^3*(a+b*arccsc(c*x))/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{3}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^3/sqrt(e*x + d), x)","F",0
58,0,0,0,0.000000," ","integrate(x^2*(a+b*arccsc(c*x))/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{2}}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^2/sqrt(e*x + d), x)","F",0
59,0,0,0,0.000000," ","integrate(x*(a+b*arccsc(c*x))/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x/sqrt(e*x + d), x)","F",0
60,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{\sqrt{e x + d}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/sqrt(e*x + d), x)","F",0
61,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{\sqrt{e x + d} x}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/(sqrt(e*x + d)*x), x)","F",0
62,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x^2/(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{\sqrt{e x + d} x^{2}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/(sqrt(e*x + d)*x^2), x)","F",0
63,0,0,0,0.000000," ","integrate(x^3*(a+b*arccsc(c*x))/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{3}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^3/(e*x + d)^(3/2), x)","F",0
64,0,0,0,0.000000," ","integrate(x^2*(a+b*arccsc(c*x))/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{2}}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^2/(e*x + d)^(3/2), x)","F",0
65,0,0,0,0.000000," ","integrate(x*(a+b*arccsc(c*x))/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x/(e*x + d)^(3/2), x)","F",0
66,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{{\left(e x + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/(e*x + d)^(3/2), x)","F",0
67,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{{\left(e x + d\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/((e*x + d)^(3/2)*x), x)","F",0
68,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x^2/(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{{\left(e x + d\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/((e*x + d)^(3/2)*x^2), x)","F",0
69,0,0,0,0.000000," ","integrate(x^3*(a+b*arccsc(c*x))/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{3}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^3/(e*x + d)^(5/2), x)","F",0
70,0,0,0,0.000000," ","integrate(x^2*(a+b*arccsc(c*x))/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{2}}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^2/(e*x + d)^(5/2), x)","F",0
71,0,0,0,0.000000," ","integrate(x*(a+b*arccsc(c*x))/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x/(e*x + d)^(5/2), x)","F",0
72,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{{\left(e x + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/(e*x + d)^(5/2), x)","F",0
73,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{{\left(e x + d\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/((e*x + d)^(5/2)*x), x)","F",0
74,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x^2/(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{{\left(e x + d\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/((e*x + d)^(5/2)*x^2), x)","F",0
75,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/(e*x+d)^(7/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{{\left(e x + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/(e*x + d)^(7/2), x)","F",0
76,1,1190,0,2.123863," ","integrate(x^4*(e*x^2+d)*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{13440} \, {\left(\frac{15 \, b x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7} \arcsin\left(\frac{1}{c x}\right) e}{c} + \frac{15 \, a x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7} e}{c} + \frac{84 \, b d x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{5 \, b x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} e}{c^{2}} + \frac{84 \, a d x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}{c} + \frac{105 \, b x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} \arcsin\left(\frac{1}{c x}\right) e}{c^{3}} + \frac{105 \, a x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} e}{c^{3}} + \frac{42 \, b d x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}}{c^{2}} + \frac{420 \, b d x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right)}{c^{3}} + \frac{45 \, b x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} e}{c^{4}} + \frac{420 \, a d x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}{c^{3}} + \frac{315 \, b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right) e}{c^{5}} + \frac{315 \, a x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e}{c^{5}} + \frac{336 \, b d x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c^{4}} + \frac{840 \, b d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right)}{c^{5}} + \frac{225 \, b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e}{c^{6}} + \frac{840 \, a d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c^{5}} + \frac{525 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right) e}{c^{7}} + \frac{525 \, a x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e}{c^{7}} + \frac{1008 \, b d \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{6}} - \frac{1008 \, b d \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{6}} + \frac{600 \, b e \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{8}} - \frac{600 \, b e \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{8}} + \frac{840 \, b d \arcsin\left(\frac{1}{c x}\right)}{c^{7} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{840 \, a d}{c^{7} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{525 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{9} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{525 \, a e}{c^{9} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} - \frac{336 \, b d}{c^{8} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{420 \, b d \arcsin\left(\frac{1}{c x}\right)}{c^{9} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} - \frac{225 \, b e}{c^{10} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{420 \, a d}{c^{9} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{315 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{11} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{315 \, a e}{c^{11} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} - \frac{42 \, b d}{c^{10} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{84 \, b d \arcsin\left(\frac{1}{c x}\right)}{c^{11} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} - \frac{45 \, b e}{c^{12} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{84 \, a d}{c^{11} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{105 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{13} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{105 \, a e}{c^{13} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} - \frac{5 \, b e}{c^{14} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}} + \frac{15 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{15} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}} + \frac{15 \, a e}{c^{15} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)} c"," ",0,"1/13440*(15*b*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7*arcsin(1/(c*x))*e/c + 15*a*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7*e/c + 84*b*d*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*arcsin(1/(c*x))/c + 5*b*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*e/c^2 + 84*a*d*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5/c + 105*b*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*arcsin(1/(c*x))*e/c^3 + 105*a*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*e/c^3 + 42*b*d*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4/c^2 + 420*b*d*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*arcsin(1/(c*x))/c^3 + 45*b*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*e/c^4 + 420*a*d*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3/c^3 + 315*b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*arcsin(1/(c*x))*e/c^5 + 315*a*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e/c^5 + 336*b*d*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c^4 + 840*b*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))/c^5 + 225*b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e/c^6 + 840*a*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c^5 + 525*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))*e/c^7 + 525*a*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e/c^7 + 1008*b*d*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^6 - 1008*b*d*log(1/(abs(c)*abs(x)))/c^6 + 600*b*e*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^8 - 600*b*e*log(1/(abs(c)*abs(x)))/c^8 + 840*b*d*arcsin(1/(c*x))/(c^7*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 840*a*d/(c^7*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 525*b*arcsin(1/(c*x))*e/(c^9*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 525*a*e/(c^9*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) - 336*b*d/(c^8*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 420*b*d*arcsin(1/(c*x))/(c^9*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) - 225*b*e/(c^10*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 420*a*d/(c^9*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 315*b*arcsin(1/(c*x))*e/(c^11*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 315*a*e/(c^11*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) - 42*b*d/(c^10*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 84*b*d*arcsin(1/(c*x))/(c^11*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) - 45*b*e/(c^12*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 84*a*d/(c^11*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 105*b*arcsin(1/(c*x))*e/(c^13*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 105*a*e/(c^13*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) - 5*b*e/(c^14*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6) + 15*b*arcsin(1/(c*x))*e/(c^15*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7) + 15*a*e/(c^15*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))*c","B",0
77,1,840,0,1.443611," ","integrate(x^2*(e*x^2+d)*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{960} \, {\left(\frac{6 \, b x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} \arcsin\left(\frac{1}{c x}\right) e}{c} + \frac{6 \, a x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} e}{c} + \frac{40 \, b d x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{3 \, b x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} e}{c^{2}} + \frac{40 \, a d x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}{c} + \frac{30 \, b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right) e}{c^{3}} + \frac{30 \, a x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e}{c^{3}} + \frac{40 \, b d x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c^{2}} + \frac{120 \, b d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right)}{c^{3}} + \frac{24 \, b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e}{c^{4}} + \frac{120 \, a d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c^{3}} + \frac{60 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right) e}{c^{5}} + \frac{60 \, a x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e}{c^{5}} + \frac{160 \, b d \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{4}} - \frac{160 \, b d \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{4}} + \frac{72 \, b e \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{6}} - \frac{72 \, b e \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{6}} + \frac{120 \, b d \arcsin\left(\frac{1}{c x}\right)}{c^{5} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{120 \, a d}{c^{5} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{60 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{7} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{60 \, a e}{c^{7} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} - \frac{40 \, b d}{c^{6} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{40 \, b d \arcsin\left(\frac{1}{c x}\right)}{c^{7} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} - \frac{24 \, b e}{c^{8} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{40 \, a d}{c^{7} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{30 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{9} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{30 \, a e}{c^{9} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} - \frac{3 \, b e}{c^{10} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{6 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{11} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{6 \, a e}{c^{11} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)} c"," ",0,"1/960*(6*b*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*arcsin(1/(c*x))*e/c + 6*a*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*e/c + 40*b*d*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*arcsin(1/(c*x))/c + 3*b*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*e/c^2 + 40*a*d*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3/c + 30*b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*arcsin(1/(c*x))*e/c^3 + 30*a*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e/c^3 + 40*b*d*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c^2 + 120*b*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))/c^3 + 24*b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e/c^4 + 120*a*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c^3 + 60*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))*e/c^5 + 60*a*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e/c^5 + 160*b*d*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^4 - 160*b*d*log(1/(abs(c)*abs(x)))/c^4 + 72*b*e*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^6 - 72*b*e*log(1/(abs(c)*abs(x)))/c^6 + 120*b*d*arcsin(1/(c*x))/(c^5*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 120*a*d/(c^5*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 60*b*arcsin(1/(c*x))*e/(c^7*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 60*a*e/(c^7*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) - 40*b*d/(c^6*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 40*b*d*arcsin(1/(c*x))/(c^7*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) - 24*b*e/(c^8*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 40*a*d/(c^7*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 30*b*arcsin(1/(c*x))*e/(c^9*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 30*a*e/(c^9*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) - 3*b*e/(c^10*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 6*b*arcsin(1/(c*x))*e/(c^11*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 6*a*e/(c^11*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))*c","B",0
78,1,485,0,1.231524," ","integrate((e*x^2+d)*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{24} \, {\left(\frac{b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right) e}{c} + \frac{a x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e}{c} + \frac{12 \, b d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e}{c^{2}} + \frac{12 \, a d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c} + \frac{3 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right) e}{c^{3}} + \frac{3 \, a x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e}{c^{3}} + \frac{24 \, b d \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}} - \frac{24 \, b d \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{2}} + \frac{4 \, b e \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{4}} - \frac{4 \, b e \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{4}} + \frac{12 \, b d \arcsin\left(\frac{1}{c x}\right)}{c^{3} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{12 \, a d}{c^{3} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{5} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3 \, a e}{c^{5} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} - \frac{b e}{c^{6} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{b \arcsin\left(\frac{1}{c x}\right) e}{c^{7} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{a e}{c^{7} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}\right)} c"," ",0,"1/24*(b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*arcsin(1/(c*x))*e/c + a*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e/c + 12*b*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))/c + b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e/c^2 + 12*a*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c + 3*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))*e/c^3 + 3*a*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e/c^3 + 24*b*d*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 - 24*b*d*log(1/(abs(c)*abs(x)))/c^2 + 4*b*e*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^4 - 4*b*e*log(1/(abs(c)*abs(x)))/c^4 + 12*b*d*arcsin(1/(c*x))/(c^3*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 12*a*d/(c^3*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3*b*arcsin(1/(c*x))*e/(c^5*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3*a*e/(c^5*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) - b*e/(c^6*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + b*arcsin(1/(c*x))*e/(c^7*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + a*e/(c^7*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3))*c","B",0
79,1,1062,0,0.458377," ","integrate((e*x^2+d)*(a+b*arccsc(c*x))/x^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{b \arcsin\left(\frac{1}{c x}\right) e}{\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{1}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}} + \frac{a e}{\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{1}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}} - \frac{2 \, b c d}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{1}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}\right)}} + \frac{2 \, b e \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{1}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}\right)}} - \frac{2 \, b e \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{1}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}\right)}} - \frac{4 \, b d \arcsin\left(\frac{1}{c x}\right)}{x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{1}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}\right)}} - \frac{4 \, a d}{x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{1}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}\right)}} + \frac{2 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{1}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}\right)}} + \frac{2 \, a e}{c^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{1}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}\right)}} + \frac{2 \, b d}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{1}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}\right)}} + \frac{2 \, b e \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{3} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{1}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}\right)}} - \frac{2 \, b e \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{3} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{1}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}\right)}} + \frac{b \arcsin\left(\frac{1}{c x}\right) e}{c^{4} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{1}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}\right)}} + \frac{a e}{c^{4} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{1}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}\right)}}\right)} c"," ",0,"1/2*(b*arcsin(1/(c*x))*e/(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 1/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3)) + a*e/(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 1/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3)) - 2*b*c*d/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 1/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3))) + 2*b*e*log(sqrt(-1/(c^2*x^2) + 1) + 1)/(c*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 1/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3))) - 2*b*e*log(1/(abs(c)*abs(x)))/(c*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 1/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3))) - 4*b*d*arcsin(1/(c*x))/(x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 1/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3))) - 4*a*d/(x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 1/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3))) + 2*b*arcsin(1/(c*x))*e/(c^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 1/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3))) + 2*a*e/(c^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 1/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3))) + 2*b*d/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 1/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3))) + 2*b*e*log(sqrt(-1/(c^2*x^2) + 1) + 1)/(c^3*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 1/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3))) - 2*b*e*log(1/(abs(c)*abs(x)))/(c^3*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 1/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3))) + b*arcsin(1/(c*x))*e/(c^4*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 1/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3))) + a*e/(c^4*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 1/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3))))*c","B",0
80,1,139,0,0.144518," ","integrate((e*x^2+d)*(a+b*arccsc(c*x))/x^4,x, algorithm=""giac"")","\frac{1}{9} \, {\left(b c^{2} d {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 3 \, b c^{2} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{3 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)}{x} - \frac{3 \, b c d \arcsin\left(\frac{1}{c x}\right)}{x} - 9 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e - \frac{9 \, b \arcsin\left(\frac{1}{c x}\right) e}{c x} - \frac{9 \, a e}{c x} - \frac{3 \, a d}{c x^{3}}\right)} c"," ",0,"1/9*(b*c^2*d*(-1/(c^2*x^2) + 1)^(3/2) - 3*b*c^2*d*sqrt(-1/(c^2*x^2) + 1) - 3*b*c*d*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))/x - 3*b*c*d*arcsin(1/(c*x))/x - 9*b*sqrt(-1/(c^2*x^2) + 1)*e - 9*b*arcsin(1/(c*x))*e/(c*x) - 9*a*e/(c*x) - 3*a*d/(c*x^3))*c","A",0
81,1,250,0,0.170947," ","integrate((e*x^2+d)*(a+b*arccsc(c*x))/x^6,x, algorithm=""giac"")","-\frac{1}{225} \, {\left(9 \, b c^{4} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 30 \, b c^{4} d {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + \frac{45 \, b c^{3} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)}{x} + 45 \, b c^{4} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{90 \, b c^{3} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)}{x} - 25 \, b c^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e + \frac{45 \, b c^{3} d \arcsin\left(\frac{1}{c x}\right)}{x} + 75 \, b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e + \frac{75 \, b c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right) e}{x} + \frac{75 \, b c \arcsin\left(\frac{1}{c x}\right) e}{x} + \frac{75 \, a e}{c x^{3}} + \frac{45 \, a d}{c x^{5}}\right)} c"," ",0,"-1/225*(9*b*c^4*d*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1) - 30*b*c^4*d*(-1/(c^2*x^2) + 1)^(3/2) + 45*b*c^3*d*(1/(c^2*x^2) - 1)^2*arcsin(1/(c*x))/x + 45*b*c^4*d*sqrt(-1/(c^2*x^2) + 1) + 90*b*c^3*d*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))/x - 25*b*c^2*(-1/(c^2*x^2) + 1)^(3/2)*e + 45*b*c^3*d*arcsin(1/(c*x))/x + 75*b*c^2*sqrt(-1/(c^2*x^2) + 1)*e + 75*b*c*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))*e/x + 75*b*c*arcsin(1/(c*x))*e/x + 75*a*e/(c*x^3) + 45*a*d/(c*x^5))*c","A",0
82,1,374,0,0.157793," ","integrate((e*x^2+d)*(a+b*arccsc(c*x))/x^8,x, algorithm=""giac"")","-\frac{1}{3675} \, {\left(75 \, b c^{6} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 315 \, b c^{6} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{525 \, b c^{5} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right)}{x} - 525 \, b c^{6} d {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + \frac{1575 \, b c^{5} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)}{x} + 525 \, b c^{6} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 147 \, b c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e + \frac{1575 \, b c^{5} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)}{x} - 490 \, b c^{4} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e + \frac{525 \, b c^{5} d \arcsin\left(\frac{1}{c x}\right)}{x} + \frac{735 \, b c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) e}{x} + 735 \, b c^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e + \frac{1470 \, b c^{3} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right) e}{x} + \frac{735 \, b c^{3} \arcsin\left(\frac{1}{c x}\right) e}{x} + \frac{735 \, a e}{c x^{5}} + \frac{525 \, a d}{c x^{7}}\right)} c"," ",0,"-1/3675*(75*b*c^6*d*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1) + 315*b*c^6*d*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1) + 525*b*c^5*d*(1/(c^2*x^2) - 1)^3*arcsin(1/(c*x))/x - 525*b*c^6*d*(-1/(c^2*x^2) + 1)^(3/2) + 1575*b*c^5*d*(1/(c^2*x^2) - 1)^2*arcsin(1/(c*x))/x + 525*b*c^6*d*sqrt(-1/(c^2*x^2) + 1) + 147*b*c^4*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)*e + 1575*b*c^5*d*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))/x - 490*b*c^4*(-1/(c^2*x^2) + 1)^(3/2)*e + 525*b*c^5*d*arcsin(1/(c*x))/x + 735*b*c^3*(1/(c^2*x^2) - 1)^2*arcsin(1/(c*x))*e/x + 735*b*c^4*sqrt(-1/(c^2*x^2) + 1)*e + 1470*b*c^3*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))*e/x + 735*b*c^3*arcsin(1/(c*x))*e/x + 735*a*e/(c*x^5) + 525*a*d/(c*x^7))*c","B",0
83,1,1270,0,0.321978," ","integrate(x^5*(e*x^2+d)*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{645120} \, {\left(\frac{315 \, b x^{8} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{8} \arcsin\left(\frac{1}{c x}\right) e}{c} + \frac{315 \, a x^{8} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{8} e}{c} + \frac{1680 \, b d x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{90 \, b x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7} e}{c^{2}} + \frac{1680 \, a d x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}}{c} + \frac{2520 \, b x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} \arcsin\left(\frac{1}{c x}\right) e}{c^{3}} + \frac{2520 \, a x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} e}{c^{3}} + \frac{672 \, b d x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}{c^{2}} + \frac{10080 \, b d x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} \arcsin\left(\frac{1}{c x}\right)}{c^{3}} + \frac{882 \, b x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} e}{c^{4}} + \frac{10080 \, a d x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}}{c^{3}} + \frac{8820 \, b x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} \arcsin\left(\frac{1}{c x}\right) e}{c^{5}} + \frac{8820 \, a x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} e}{c^{5}} + \frac{5600 \, b d x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}{c^{4}} + \frac{25200 \, b d x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{5}} + \frac{4410 \, b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e}{c^{6}} + \frac{25200 \, a d x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c^{5}} + \frac{17640 \, b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) e}{c^{7}} + \frac{17640 \, a x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e}{c^{7}} + \frac{33600 \, b d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c^{6}} + \frac{33600 \, b d \arcsin\left(\frac{1}{c x}\right)}{c^{7}} + \frac{22050 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e}{c^{8}} + \frac{33600 \, a d}{c^{7}} + \frac{22050 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{9}} + \frac{22050 \, a e}{c^{9}} - \frac{33600 \, b d}{c^{8} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{25200 \, b d \arcsin\left(\frac{1}{c x}\right)}{c^{9} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} - \frac{22050 \, b e}{c^{10} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{25200 \, a d}{c^{9} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{17640 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{11} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{17640 \, a e}{c^{11} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} - \frac{5600 \, b d}{c^{10} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{10080 \, b d \arcsin\left(\frac{1}{c x}\right)}{c^{11} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} - \frac{4410 \, b e}{c^{12} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{10080 \, a d}{c^{11} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{8820 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{13} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{8820 \, a e}{c^{13} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} - \frac{672 \, b d}{c^{12} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1680 \, b d \arcsin\left(\frac{1}{c x}\right)}{c^{13} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}} - \frac{882 \, b e}{c^{14} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1680 \, a d}{c^{13} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}} + \frac{2520 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{15} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}} + \frac{2520 \, a e}{c^{15} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}} - \frac{90 \, b e}{c^{16} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}} + \frac{315 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{17} x^{8} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{8}} + \frac{315 \, a e}{c^{17} x^{8} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{8}}\right)} c"," ",0,"1/645120*(315*b*x^8*(sqrt(-1/(c^2*x^2) + 1) + 1)^8*arcsin(1/(c*x))*e/c + 315*a*x^8*(sqrt(-1/(c^2*x^2) + 1) + 1)^8*e/c + 1680*b*d*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*arcsin(1/(c*x))/c + 90*b*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7*e/c^2 + 1680*a*d*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6/c + 2520*b*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*arcsin(1/(c*x))*e/c^3 + 2520*a*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*e/c^3 + 672*b*d*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5/c^2 + 10080*b*d*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*arcsin(1/(c*x))/c^3 + 882*b*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*e/c^4 + 10080*a*d*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4/c^3 + 8820*b*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*arcsin(1/(c*x))*e/c^5 + 8820*a*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*e/c^5 + 5600*b*d*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3/c^4 + 25200*b*d*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))/c^5 + 4410*b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e/c^6 + 25200*a*d*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c^5 + 17640*b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))*e/c^7 + 17640*a*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e/c^7 + 33600*b*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c^6 + 33600*b*d*arcsin(1/(c*x))/c^7 + 22050*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e/c^8 + 33600*a*d/c^7 + 22050*b*arcsin(1/(c*x))*e/c^9 + 22050*a*e/c^9 - 33600*b*d/(c^8*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 25200*b*d*arcsin(1/(c*x))/(c^9*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) - 22050*b*e/(c^10*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 25200*a*d/(c^9*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 17640*b*arcsin(1/(c*x))*e/(c^11*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 17640*a*e/(c^11*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) - 5600*b*d/(c^10*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 10080*b*d*arcsin(1/(c*x))/(c^11*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) - 4410*b*e/(c^12*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 10080*a*d/(c^11*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 8820*b*arcsin(1/(c*x))*e/(c^13*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 8820*a*e/(c^13*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) - 672*b*d/(c^12*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1680*b*d*arcsin(1/(c*x))/(c^13*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6) - 882*b*e/(c^14*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1680*a*d/(c^13*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6) + 2520*b*arcsin(1/(c*x))*e/(c^15*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6) + 2520*a*e/(c^15*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6) - 90*b*e/(c^16*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7) + 315*b*arcsin(1/(c*x))*e/(c^17*x^8*(sqrt(-1/(c^2*x^2) + 1) + 1)^8) + 315*a*e/(c^17*x^8*(sqrt(-1/(c^2*x^2) + 1) + 1)^8))*c","B",0
84,1,920,0,0.264058," ","integrate(x^3*(e*x^2+d)*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{5760} \, {\left(\frac{15 \, b x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} \arcsin\left(\frac{1}{c x}\right) e}{c} + \frac{15 \, a x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} e}{c} + \frac{90 \, b d x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{6 \, b x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} e}{c^{2}} + \frac{90 \, a d x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}}{c} + \frac{90 \, b x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} \arcsin\left(\frac{1}{c x}\right) e}{c^{3}} + \frac{90 \, a x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} e}{c^{3}} + \frac{60 \, b d x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}{c^{2}} + \frac{360 \, b d x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{3}} + \frac{50 \, b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e}{c^{4}} + \frac{360 \, a d x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c^{3}} + \frac{225 \, b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) e}{c^{5}} + \frac{225 \, a x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e}{c^{5}} + \frac{540 \, b d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c^{4}} + \frac{540 \, b d \arcsin\left(\frac{1}{c x}\right)}{c^{5}} + \frac{300 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e}{c^{6}} + \frac{540 \, a d}{c^{5}} + \frac{300 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{7}} + \frac{300 \, a e}{c^{7}} - \frac{540 \, b d}{c^{6} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{360 \, b d \arcsin\left(\frac{1}{c x}\right)}{c^{7} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} - \frac{300 \, b e}{c^{8} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{360 \, a d}{c^{7} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{225 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{9} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{225 \, a e}{c^{9} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} - \frac{60 \, b d}{c^{8} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{90 \, b d \arcsin\left(\frac{1}{c x}\right)}{c^{9} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} - \frac{50 \, b e}{c^{10} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{90 \, a d}{c^{9} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{90 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{11} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{90 \, a e}{c^{11} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} - \frac{6 \, b e}{c^{12} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{15 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{13} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}} + \frac{15 \, a e}{c^{13} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}}\right)} c"," ",0,"1/5760*(15*b*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*arcsin(1/(c*x))*e/c + 15*a*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*e/c + 90*b*d*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*arcsin(1/(c*x))/c + 6*b*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*e/c^2 + 90*a*d*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4/c + 90*b*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*arcsin(1/(c*x))*e/c^3 + 90*a*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*e/c^3 + 60*b*d*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3/c^2 + 360*b*d*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))/c^3 + 50*b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e/c^4 + 360*a*d*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c^3 + 225*b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))*e/c^5 + 225*a*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e/c^5 + 540*b*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c^4 + 540*b*d*arcsin(1/(c*x))/c^5 + 300*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e/c^6 + 540*a*d/c^5 + 300*b*arcsin(1/(c*x))*e/c^7 + 300*a*e/c^7 - 540*b*d/(c^6*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 360*b*d*arcsin(1/(c*x))/(c^7*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) - 300*b*e/(c^8*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 360*a*d/(c^7*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 225*b*arcsin(1/(c*x))*e/(c^9*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 225*a*e/(c^9*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) - 60*b*d/(c^8*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 90*b*d*arcsin(1/(c*x))/(c^9*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) - 50*b*e/(c^10*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 90*a*d/(c^9*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 90*b*arcsin(1/(c*x))*e/(c^11*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 90*a*e/(c^11*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) - 6*b*e/(c^12*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 15*b*arcsin(1/(c*x))*e/(c^13*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6) + 15*a*e/(c^13*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6))*c","B",0
85,1,570,0,0.223024," ","integrate(x*(e*x^2+d)*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{192} \, {\left(\frac{3 \, b x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} \arcsin\left(\frac{1}{c x}\right) e}{c} + \frac{3 \, a x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} e}{c} + \frac{24 \, b d x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{2 \, b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e}{c^{2}} + \frac{24 \, a d x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c} + \frac{12 \, b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) e}{c^{3}} + \frac{12 \, a x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e}{c^{3}} + \frac{48 \, b d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c^{2}} + \frac{48 \, b d \arcsin\left(\frac{1}{c x}\right)}{c^{3}} + \frac{18 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e}{c^{4}} + \frac{48 \, a d}{c^{3}} + \frac{18 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{5}} + \frac{18 \, a e}{c^{5}} - \frac{48 \, b d}{c^{4} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{24 \, b d \arcsin\left(\frac{1}{c x}\right)}{c^{5} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} - \frac{18 \, b e}{c^{6} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{24 \, a d}{c^{5} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{12 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{7} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{12 \, a e}{c^{7} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} - \frac{2 \, b e}{c^{8} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3 \, b \arcsin\left(\frac{1}{c x}\right) e}{c^{9} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{3 \, a e}{c^{9} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}}\right)} c"," ",0,"1/192*(3*b*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*arcsin(1/(c*x))*e/c + 3*a*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*e/c + 24*b*d*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))/c + 2*b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e/c^2 + 24*a*d*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c + 12*b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))*e/c^3 + 12*a*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e/c^3 + 48*b*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 + 48*b*d*arcsin(1/(c*x))/c^3 + 18*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e/c^4 + 48*a*d/c^3 + 18*b*arcsin(1/(c*x))*e/c^5 + 18*a*e/c^5 - 48*b*d/(c^4*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 24*b*d*arcsin(1/(c*x))/(c^5*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) - 18*b*e/(c^6*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 24*a*d/(c^5*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 12*b*arcsin(1/(c*x))*e/(c^7*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 12*a*e/(c^7*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) - 2*b*e/(c^8*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3*b*arcsin(1/(c*x))*e/(c^9*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 3*a*e/(c^9*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4))*c","B",0
86,-2,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arccsc(c*x))/x,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Undef/Unsigned Inf encountered in limitEvaluation time: 0.55Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
87,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arccsc(c*x))/x^3,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}}{x^{3}}\,{d x}"," ",0,"integrate((e*x^2 + d)*(b*arccsc(c*x) + a)/x^3, x)","F",0
88,1,1573,0,4.953630," ","integrate(x^2*(e*x^2+d)^2*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{13440} \, {\left(\frac{15 \, b x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c} + \frac{15 \, a x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7} e^{2}}{c} + \frac{168 \, b d x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} \arcsin\left(\frac{1}{c x}\right) e}{c} + \frac{5 \, b x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} e^{2}}{c^{2}} + \frac{168 \, a d x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} e}{c} + \frac{105 \, b x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{3}} + \frac{560 \, b d^{2} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{105 \, a x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} e^{2}}{c^{3}} + \frac{84 \, b d x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} e}{c^{2}} + \frac{560 \, a d^{2} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}{c} + \frac{840 \, b d x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right) e}{c^{3}} + \frac{45 \, b x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} e^{2}}{c^{4}} + \frac{840 \, a d x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e}{c^{3}} + \frac{560 \, b d^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c^{2}} + \frac{315 \, b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{5}} + \frac{1680 \, b d^{2} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right)}{c^{3}} + \frac{315 \, a x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e^{2}}{c^{5}} + \frac{672 \, b d x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e}{c^{4}} + \frac{1680 \, a d^{2} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c^{3}} + \frac{1680 \, b d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right) e}{c^{5}} + \frac{225 \, b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e^{2}}{c^{6}} + \frac{1680 \, a d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e}{c^{5}} + \frac{2240 \, b d^{2} \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{4}} - \frac{2240 \, b d^{2} \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{4}} + \frac{525 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{7}} + \frac{2016 \, b d e \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{6}} - \frac{2016 \, b d e \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{6}} + \frac{1680 \, b d^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{5} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{525 \, a x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e^{2}}{c^{7}} + \frac{1680 \, a d^{2}}{c^{5} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{1680 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{7} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{600 \, b e^{2} \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{8}} - \frac{600 \, b e^{2} \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{8}} + \frac{1680 \, a d e}{c^{7} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} - \frac{560 \, b d^{2}}{c^{6} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{525 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{9} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{560 \, b d^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{7} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{525 \, a e^{2}}{c^{9} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} - \frac{672 \, b d e}{c^{8} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{560 \, a d^{2}}{c^{7} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{840 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{9} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} - \frac{225 \, b e^{2}}{c^{10} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{840 \, a d e}{c^{9} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{315 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{11} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{315 \, a e^{2}}{c^{11} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} - \frac{84 \, b d e}{c^{10} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{168 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{11} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} - \frac{45 \, b e^{2}}{c^{12} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{168 \, a d e}{c^{11} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{105 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{13} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{105 \, a e^{2}}{c^{13} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} - \frac{5 \, b e^{2}}{c^{14} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}} + \frac{15 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{15} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}} + \frac{15 \, a e^{2}}{c^{15} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)} c"," ",0,"1/13440*(15*b*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7*arcsin(1/(c*x))*e^2/c + 15*a*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7*e^2/c + 168*b*d*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*arcsin(1/(c*x))*e/c + 5*b*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*e^2/c^2 + 168*a*d*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*e/c + 105*b*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*arcsin(1/(c*x))*e^2/c^3 + 560*b*d^2*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*arcsin(1/(c*x))/c + 105*a*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*e^2/c^3 + 84*b*d*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*e/c^2 + 560*a*d^2*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3/c + 840*b*d*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*arcsin(1/(c*x))*e/c^3 + 45*b*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*e^2/c^4 + 840*a*d*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e/c^3 + 560*b*d^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c^2 + 315*b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*arcsin(1/(c*x))*e^2/c^5 + 1680*b*d^2*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))/c^3 + 315*a*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e^2/c^5 + 672*b*d*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e/c^4 + 1680*a*d^2*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c^3 + 1680*b*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))*e/c^5 + 225*b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e^2/c^6 + 1680*a*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e/c^5 + 2240*b*d^2*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^4 - 2240*b*d^2*log(1/(abs(c)*abs(x)))/c^4 + 525*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))*e^2/c^7 + 2016*b*d*e*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^6 - 2016*b*d*e*log(1/(abs(c)*abs(x)))/c^6 + 1680*b*d^2*arcsin(1/(c*x))/(c^5*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 525*a*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e^2/c^7 + 1680*a*d^2/(c^5*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 1680*b*d*arcsin(1/(c*x))*e/(c^7*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 600*b*e^2*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^8 - 600*b*e^2*log(1/(abs(c)*abs(x)))/c^8 + 1680*a*d*e/(c^7*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) - 560*b*d^2/(c^6*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 525*b*arcsin(1/(c*x))*e^2/(c^9*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 560*b*d^2*arcsin(1/(c*x))/(c^7*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 525*a*e^2/(c^9*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) - 672*b*d*e/(c^8*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 560*a*d^2/(c^7*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 840*b*d*arcsin(1/(c*x))*e/(c^9*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) - 225*b*e^2/(c^10*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 840*a*d*e/(c^9*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 315*b*arcsin(1/(c*x))*e^2/(c^11*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 315*a*e^2/(c^11*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) - 84*b*d*e/(c^10*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 168*b*d*arcsin(1/(c*x))*e/(c^11*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) - 45*b*e^2/(c^12*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 168*a*d*e/(c^11*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 105*b*arcsin(1/(c*x))*e^2/(c^13*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 105*a*e^2/(c^13*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) - 5*b*e^2/(c^14*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6) + 15*b*arcsin(1/(c*x))*e^2/(c^15*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7) + 15*a*e^2/(c^15*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))*c","B",0
89,1,1027,0,3.199710," ","integrate((e*x^2+d)^2*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{960} \, {\left(\frac{6 \, b x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c} + \frac{6 \, a x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} e^{2}}{c} + \frac{80 \, b d x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right) e}{c} + \frac{3 \, b x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} e^{2}}{c^{2}} + \frac{80 \, a d x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e}{c} + \frac{30 \, b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{3}} + \frac{480 \, b d^{2} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{30 \, a x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e^{2}}{c^{3}} + \frac{80 \, b d x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e}{c^{2}} + \frac{480 \, a d^{2} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c} + \frac{240 \, b d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right) e}{c^{3}} + \frac{24 \, b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e^{2}}{c^{4}} + \frac{240 \, a d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e}{c^{3}} + \frac{960 \, b d^{2} \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}} - \frac{960 \, b d^{2} \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{2}} + \frac{60 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{5}} + \frac{320 \, b d e \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{4}} - \frac{320 \, b d e \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{4}} + \frac{480 \, b d^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{3} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{60 \, a x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e^{2}}{c^{5}} + \frac{480 \, a d^{2}}{c^{3} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{240 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{5} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{72 \, b e^{2} \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{6}} - \frac{72 \, b e^{2} \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{6}} + \frac{240 \, a d e}{c^{5} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{60 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{7} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{60 \, a e^{2}}{c^{7} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} - \frac{80 \, b d e}{c^{6} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{80 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{7} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} - \frac{24 \, b e^{2}}{c^{8} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{80 \, a d e}{c^{7} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{30 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{9} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{30 \, a e^{2}}{c^{9} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} - \frac{3 \, b e^{2}}{c^{10} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{6 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{11} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{6 \, a e^{2}}{c^{11} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)} c"," ",0,"1/960*(6*b*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*arcsin(1/(c*x))*e^2/c + 6*a*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*e^2/c + 80*b*d*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*arcsin(1/(c*x))*e/c + 3*b*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*e^2/c^2 + 80*a*d*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e/c + 30*b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*arcsin(1/(c*x))*e^2/c^3 + 480*b*d^2*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))/c + 30*a*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e^2/c^3 + 80*b*d*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e/c^2 + 480*a*d^2*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c + 240*b*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))*e/c^3 + 24*b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e^2/c^4 + 240*a*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e/c^3 + 960*b*d^2*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 - 960*b*d^2*log(1/(abs(c)*abs(x)))/c^2 + 60*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*arcsin(1/(c*x))*e^2/c^5 + 320*b*d*e*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^4 - 320*b*d*e*log(1/(abs(c)*abs(x)))/c^4 + 480*b*d^2*arcsin(1/(c*x))/(c^3*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 60*a*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e^2/c^5 + 480*a*d^2/(c^3*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 240*b*d*arcsin(1/(c*x))*e/(c^5*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 72*b*e^2*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^6 - 72*b*e^2*log(1/(abs(c)*abs(x)))/c^6 + 240*a*d*e/(c^5*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 60*b*arcsin(1/(c*x))*e^2/(c^7*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 60*a*e^2/(c^7*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) - 80*b*d*e/(c^6*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 80*b*d*arcsin(1/(c*x))*e/(c^7*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) - 24*b*e^2/(c^8*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 80*a*d*e/(c^7*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 30*b*arcsin(1/(c*x))*e^2/(c^9*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 30*a*e^2/(c^9*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) - 3*b*e^2/(c^10*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 6*b*arcsin(1/(c*x))*e^2/(c^11*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 6*a*e^2/(c^11*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))*c","B",0
90,1,2494,0,2.153870," ","integrate((e*x^2+d)^2*(a+b*arccsc(c*x))/x^2,x, algorithm=""giac"")","\frac{1}{24} \, {\left(\frac{b \arcsin\left(\frac{1}{c x}\right) e^{2}}{\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}} + \frac{a e^{2}}{\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}} + \frac{24 \, b d \arcsin\left(\frac{1}{c x}\right) e}{x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{b e^{2}}{c x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{24 \, a d e}{x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} - \frac{24 \, b c d^{2}}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{4 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{48 \, b d e \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} - \frac{48 \, b d e \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} - \frac{48 \, b d^{2} \arcsin\left(\frac{1}{c x}\right)}{x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{4 \, a e^{2}}{c^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} - \frac{48 \, a d^{2}}{x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{48 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{2} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{4 \, b e^{2} \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{3} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} - \frac{4 \, b e^{2} \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{3} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{b e^{2}}{c^{3} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{48 \, a d e}{c^{2} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{24 \, b d^{2}}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{6 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{4} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{48 \, b d e \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} - \frac{48 \, b d e \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{6 \, a e^{2}}{c^{4} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{24 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{4} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{4 \, b e^{2} \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{5} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} - \frac{4 \, b e^{2} \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{5} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} - \frac{b e^{2}}{c^{5} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{24 \, a d e}{c^{4} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{4 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{6} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{4 \, a e^{2}}{c^{6} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} - \frac{b e^{2}}{c^{7} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{8} x^{8} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{8} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}} + \frac{a e^{2}}{c^{8} x^{8} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{8} {\left(\frac{c}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{1}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}}\right)}}\right)} c"," ",0,"1/24*(b*arcsin(1/(c*x))*e^2/(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5)) + a*e^2/(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5)) + 24*b*d*arcsin(1/(c*x))*e/(x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + b*e^2/(c*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + 24*a*d*e/(x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) - 24*b*c*d^2/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + 4*b*arcsin(1/(c*x))*e^2/(c^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + 48*b*d*e*log(sqrt(-1/(c^2*x^2) + 1) + 1)/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) - 48*b*d*e*log(1/(abs(c)*abs(x)))/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) - 48*b*d^2*arcsin(1/(c*x))/(x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + 4*a*e^2/(c^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) - 48*a*d^2/(x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + 48*b*d*arcsin(1/(c*x))*e/(c^2*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + 4*b*e^2*log(sqrt(-1/(c^2*x^2) + 1) + 1)/(c^3*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) - 4*b*e^2*log(1/(abs(c)*abs(x)))/(c^3*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + b*e^2/(c^3*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + 48*a*d*e/(c^2*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + 24*b*d^2/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + 6*b*arcsin(1/(c*x))*e^2/(c^4*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + 48*b*d*e*log(sqrt(-1/(c^2*x^2) + 1) + 1)/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) - 48*b*d*e*log(1/(abs(c)*abs(x)))/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + 6*a*e^2/(c^4*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + 24*b*d*arcsin(1/(c*x))*e/(c^4*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + 4*b*e^2*log(sqrt(-1/(c^2*x^2) + 1) + 1)/(c^5*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) - 4*b*e^2*log(1/(abs(c)*abs(x)))/(c^5*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) - b*e^2/(c^5*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + 24*a*d*e/(c^4*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + 4*b*arcsin(1/(c*x))*e^2/(c^6*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + 4*a*e^2/(c^6*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) - b*e^2/(c^7*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + b*arcsin(1/(c*x))*e^2/(c^8*x^8*(sqrt(-1/(c^2*x^2) + 1) + 1)^8*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))) + a*e^2/(c^8*x^8*(sqrt(-1/(c^2*x^2) + 1) + 1)^8*(c/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 1/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5))))*c","B",0
91,1,4280,0,14.422024," ","integrate((e*x^2+d)^2*(a+b*arccsc(c*x))/x^4,x, algorithm=""giac"")","-\frac{1}{18} \, {\left(\frac{4 \, b c^{3} d^{2}}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{9 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}} - \frac{9 \, a e^{2}}{\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}} + \frac{36 \, b c d e}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} + \frac{72 \, b d \arcsin\left(\frac{1}{c x}\right) e}{x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{18 \, b e^{2} \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} + \frac{18 \, b e^{2} \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} + \frac{72 \, a d e}{x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} + \frac{12 \, b c d^{2}}{x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{36 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} + \frac{48 \, b d^{2} \arcsin\left(\frac{1}{c x}\right)}{x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{36 \, a e^{2}}{c^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} + \frac{36 \, b d e}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} + \frac{48 \, a d^{2}}{x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} + \frac{144 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{2} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{54 \, b e^{2} \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{3} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} + \frac{54 \, b e^{2} \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{3} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} + \frac{144 \, a d e}{c^{2} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{12 \, b d^{2}}{c x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{54 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{4} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{54 \, a e^{2}}{c^{4} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{36 \, b d e}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} + \frac{72 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{4} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{54 \, b e^{2} \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{5} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} + \frac{54 \, b e^{2} \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{5} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} + \frac{72 \, a d e}{c^{4} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{4 \, b d^{2}}{c^{3} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{36 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{6} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{36 \, a e^{2}}{c^{6} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{36 \, b d e}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{18 \, b e^{2} \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{7} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} + \frac{18 \, b e^{2} \log\left(\frac{1}{{\left| c \right|} {\left| x \right|}}\right)}{c^{7} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{9 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{8} x^{8} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{8} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}} - \frac{9 \, a e^{2}}{c^{8} x^{8} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{8} {\left(\frac{c}{x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{3}{c x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{3}{c^{3} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{1}{c^{5} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}}\right)}}\right)} c"," ",0,"-1/18*(4*b*c^3*d^2/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 9*b*arcsin(1/(c*x))*e^2/(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7)) - 9*a*e^2/(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7)) + 36*b*c*d*e/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) + 72*b*d*arcsin(1/(c*x))*e/(x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 18*b*e^2*log(sqrt(-1/(c^2*x^2) + 1) + 1)/(c*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) + 18*b*e^2*log(1/(abs(c)*abs(x)))/(c*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) + 72*a*d*e/(x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) + 12*b*c*d^2/(x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 36*b*arcsin(1/(c*x))*e^2/(c^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) + 48*b*d^2*arcsin(1/(c*x))/(x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 36*a*e^2/(c^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) + 36*b*d*e/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) + 48*a*d^2/(x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) + 144*b*d*arcsin(1/(c*x))*e/(c^2*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 54*b*e^2*log(sqrt(-1/(c^2*x^2) + 1) + 1)/(c^3*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) + 54*b*e^2*log(1/(abs(c)*abs(x)))/(c^3*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) + 144*a*d*e/(c^2*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 12*b*d^2/(c*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 54*b*arcsin(1/(c*x))*e^2/(c^4*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 54*a*e^2/(c^4*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 36*b*d*e/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) + 72*b*d*arcsin(1/(c*x))*e/(c^4*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 54*b*e^2*log(sqrt(-1/(c^2*x^2) + 1) + 1)/(c^5*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) + 54*b*e^2*log(1/(abs(c)*abs(x)))/(c^5*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) + 72*a*d*e/(c^4*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 4*b*d^2/(c^3*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 36*b*arcsin(1/(c*x))*e^2/(c^6*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 36*a*e^2/(c^6*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 36*b*d*e/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 18*b*e^2*log(sqrt(-1/(c^2*x^2) + 1) + 1)/(c^7*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) + 18*b*e^2*log(1/(abs(c)*abs(x)))/(c^7*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 9*b*arcsin(1/(c*x))*e^2/(c^8*x^8*(sqrt(-1/(c^2*x^2) + 1) + 1)^8*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))) - 9*a*e^2/(c^8*x^8*(sqrt(-1/(c^2*x^2) + 1) + 1)^8*(c/(x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 3/(c*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 3/(c^3*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 1/(c^5*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7))))*c","B",0
92,1,316,0,0.157527," ","integrate((e*x^2+d)^2*(a+b*arccsc(c*x))/x^6,x, algorithm=""giac"")","-\frac{1}{225} \, {\left(9 \, b c^{4} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 30 \, b c^{4} d^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + \frac{45 \, b c^{3} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)}{x} + 45 \, b c^{4} d^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{90 \, b c^{3} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)}{x} - 50 \, b c^{2} d {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e + \frac{45 \, b c^{3} d^{2} \arcsin\left(\frac{1}{c x}\right)}{x} + 150 \, b c^{2} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e + \frac{150 \, b c d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right) e}{x} + \frac{150 \, b c d \arcsin\left(\frac{1}{c x}\right) e}{x} + 225 \, b \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2} + \frac{225 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c x} + \frac{225 \, a e^{2}}{c x} + \frac{150 \, a d e}{c x^{3}} + \frac{45 \, a d^{2}}{c x^{5}}\right)} c"," ",0,"-1/225*(9*b*c^4*d^2*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1) - 30*b*c^4*d^2*(-1/(c^2*x^2) + 1)^(3/2) + 45*b*c^3*d^2*(1/(c^2*x^2) - 1)^2*arcsin(1/(c*x))/x + 45*b*c^4*d^2*sqrt(-1/(c^2*x^2) + 1) + 90*b*c^3*d^2*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))/x - 50*b*c^2*d*(-1/(c^2*x^2) + 1)^(3/2)*e + 45*b*c^3*d^2*arcsin(1/(c*x))/x + 150*b*c^2*d*sqrt(-1/(c^2*x^2) + 1)*e + 150*b*c*d*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))*e/x + 150*b*c*d*arcsin(1/(c*x))*e/x + 225*b*sqrt(-1/(c^2*x^2) + 1)*e^2 + 225*b*arcsin(1/(c*x))*e^2/(c*x) + 225*a*e^2/(c*x) + 150*a*d*e/(c*x^3) + 45*a*d^2/(c*x^5))*c","A",0
93,1,493,0,0.173559," ","integrate((e*x^2+d)^2*(a+b*arccsc(c*x))/x^8,x, algorithm=""giac"")","-\frac{1}{11025} \, {\left(225 \, b c^{6} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 945 \, b c^{6} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{1575 \, b c^{5} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} \arcsin\left(\frac{1}{c x}\right)}{x} - 1575 \, b c^{6} d^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + \frac{4725 \, b c^{5} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)}{x} + 1575 \, b c^{6} d^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 882 \, b c^{4} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e + \frac{4725 \, b c^{5} d^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right)}{x} - 2940 \, b c^{4} d {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e + \frac{1575 \, b c^{5} d^{2} \arcsin\left(\frac{1}{c x}\right)}{x} + \frac{4410 \, b c^{3} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) e}{x} + 4410 \, b c^{4} d \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e + \frac{8820 \, b c^{3} d {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right) e}{x} + \frac{4410 \, b c^{3} d \arcsin\left(\frac{1}{c x}\right) e}{x} - 1225 \, b c^{2} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} e^{2} + 3675 \, b c^{2} \sqrt{-\frac{1}{c^{2} x^{2}} + 1} e^{2} + \frac{3675 \, b c {\left(\frac{1}{c^{2} x^{2}} - 1\right)} \arcsin\left(\frac{1}{c x}\right) e^{2}}{x} + \frac{3675 \, b c \arcsin\left(\frac{1}{c x}\right) e^{2}}{x} + \frac{3675 \, a e^{2}}{c x^{3}} + \frac{4410 \, a d e}{c x^{5}} + \frac{1575 \, a d^{2}}{c x^{7}}\right)} c"," ",0,"-1/11025*(225*b*c^6*d^2*(1/(c^2*x^2) - 1)^3*sqrt(-1/(c^2*x^2) + 1) + 945*b*c^6*d^2*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1) + 1575*b*c^5*d^2*(1/(c^2*x^2) - 1)^3*arcsin(1/(c*x))/x - 1575*b*c^6*d^2*(-1/(c^2*x^2) + 1)^(3/2) + 4725*b*c^5*d^2*(1/(c^2*x^2) - 1)^2*arcsin(1/(c*x))/x + 1575*b*c^6*d^2*sqrt(-1/(c^2*x^2) + 1) + 882*b*c^4*d*(1/(c^2*x^2) - 1)^2*sqrt(-1/(c^2*x^2) + 1)*e + 4725*b*c^5*d^2*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))/x - 2940*b*c^4*d*(-1/(c^2*x^2) + 1)^(3/2)*e + 1575*b*c^5*d^2*arcsin(1/(c*x))/x + 4410*b*c^3*d*(1/(c^2*x^2) - 1)^2*arcsin(1/(c*x))*e/x + 4410*b*c^4*d*sqrt(-1/(c^2*x^2) + 1)*e + 8820*b*c^3*d*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))*e/x + 4410*b*c^3*d*arcsin(1/(c*x))*e/x - 1225*b*c^2*(-1/(c^2*x^2) + 1)^(3/2)*e^2 + 3675*b*c^2*sqrt(-1/(c^2*x^2) + 1)*e^2 + 3675*b*c*(1/(c^2*x^2) - 1)*arcsin(1/(c*x))*e^2/x + 3675*b*c*arcsin(1/(c*x))*e^2/x + 3675*a*e^2/(c*x^3) + 4410*a*d*e/(c*x^5) + 1575*a*d^2/(c*x^7))*c","B",0
94,1,1700,0,0.445828," ","integrate(x^3*(e*x^2+d)^2*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{645120} \, {\left(\frac{315 \, b x^{8} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{8} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c} + \frac{315 \, a x^{8} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{8} e^{2}}{c} + \frac{3360 \, b d x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} \arcsin\left(\frac{1}{c x}\right) e}{c} + \frac{90 \, b x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7} e^{2}}{c^{2}} + \frac{3360 \, a d x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} e}{c} + \frac{2520 \, b x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{3}} + \frac{10080 \, b d^{2} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{2520 \, a x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} e^{2}}{c^{3}} + \frac{1344 \, b d x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} e}{c^{2}} + \frac{10080 \, a d^{2} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}}{c} + \frac{20160 \, b d x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} \arcsin\left(\frac{1}{c x}\right) e}{c^{3}} + \frac{882 \, b x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} e^{2}}{c^{4}} + \frac{20160 \, a d x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} e}{c^{3}} + \frac{6720 \, b d^{2} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}}{c^{2}} + \frac{8820 \, b x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{5}} + \frac{40320 \, b d^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{3}} + \frac{8820 \, a x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} e^{2}}{c^{5}} + \frac{11200 \, b d x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e}{c^{4}} + \frac{40320 \, a d^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c^{3}} + \frac{50400 \, b d x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) e}{c^{5}} + \frac{4410 \, b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e^{2}}{c^{6}} + \frac{50400 \, a d x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e}{c^{5}} + \frac{60480 \, b d^{2} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c^{4}} + \frac{17640 \, b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{7}} + \frac{60480 \, b d^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{5}} + \frac{17640 \, a x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e^{2}}{c^{7}} + \frac{67200 \, b d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e}{c^{6}} + \frac{60480 \, a d^{2}}{c^{5}} + \frac{67200 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{7}} + \frac{22050 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e^{2}}{c^{8}} + \frac{67200 \, a d e}{c^{7}} - \frac{60480 \, b d^{2}}{c^{6} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{22050 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{9}} + \frac{40320 \, b d^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{7} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{22050 \, a e^{2}}{c^{9}} - \frac{67200 \, b d e}{c^{8} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{40320 \, a d^{2}}{c^{7} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{50400 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{9} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} - \frac{22050 \, b e^{2}}{c^{10} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{50400 \, a d e}{c^{9} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} - \frac{6720 \, b d^{2}}{c^{8} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{17640 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{11} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{10080 \, b d^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{9} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{17640 \, a e^{2}}{c^{11} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} - \frac{11200 \, b d e}{c^{10} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{10080 \, a d^{2}}{c^{9} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{20160 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{11} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} - \frac{4410 \, b e^{2}}{c^{12} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{20160 \, a d e}{c^{11} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{8820 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{13} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{8820 \, a e^{2}}{c^{13} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} - \frac{1344 \, b d e}{c^{12} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{3360 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{13} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}} - \frac{882 \, b e^{2}}{c^{14} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{3360 \, a d e}{c^{13} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}} + \frac{2520 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{15} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}} + \frac{2520 \, a e^{2}}{c^{15} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}} - \frac{90 \, b e^{2}}{c^{16} x^{7} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{7}} + \frac{315 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{17} x^{8} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{8}} + \frac{315 \, a e^{2}}{c^{17} x^{8} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{8}}\right)} c"," ",0,"1/645120*(315*b*x^8*(sqrt(-1/(c^2*x^2) + 1) + 1)^8*arcsin(1/(c*x))*e^2/c + 315*a*x^8*(sqrt(-1/(c^2*x^2) + 1) + 1)^8*e^2/c + 3360*b*d*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*arcsin(1/(c*x))*e/c + 90*b*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7*e^2/c^2 + 3360*a*d*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*e/c + 2520*b*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*arcsin(1/(c*x))*e^2/c^3 + 10080*b*d^2*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*arcsin(1/(c*x))/c + 2520*a*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*e^2/c^3 + 1344*b*d*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*e/c^2 + 10080*a*d^2*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4/c + 20160*b*d*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*arcsin(1/(c*x))*e/c^3 + 882*b*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*e^2/c^4 + 20160*a*d*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*e/c^3 + 6720*b*d^2*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3/c^2 + 8820*b*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*arcsin(1/(c*x))*e^2/c^5 + 40320*b*d^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))/c^3 + 8820*a*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*e^2/c^5 + 11200*b*d*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e/c^4 + 40320*a*d^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c^3 + 50400*b*d*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))*e/c^5 + 4410*b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e^2/c^6 + 50400*a*d*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e/c^5 + 60480*b*d^2*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c^4 + 17640*b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))*e^2/c^7 + 60480*b*d^2*arcsin(1/(c*x))/c^5 + 17640*a*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e^2/c^7 + 67200*b*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e/c^6 + 60480*a*d^2/c^5 + 67200*b*d*arcsin(1/(c*x))*e/c^7 + 22050*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e^2/c^8 + 67200*a*d*e/c^7 - 60480*b*d^2/(c^6*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 22050*b*arcsin(1/(c*x))*e^2/c^9 + 40320*b*d^2*arcsin(1/(c*x))/(c^7*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 22050*a*e^2/c^9 - 67200*b*d*e/(c^8*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 40320*a*d^2/(c^7*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 50400*b*d*arcsin(1/(c*x))*e/(c^9*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) - 22050*b*e^2/(c^10*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 50400*a*d*e/(c^9*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) - 6720*b*d^2/(c^8*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 17640*b*arcsin(1/(c*x))*e^2/(c^11*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 10080*b*d^2*arcsin(1/(c*x))/(c^9*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 17640*a*e^2/(c^11*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) - 11200*b*d*e/(c^10*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 10080*a*d^2/(c^9*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 20160*b*d*arcsin(1/(c*x))*e/(c^11*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) - 4410*b*e^2/(c^12*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 20160*a*d*e/(c^11*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 8820*b*arcsin(1/(c*x))*e^2/(c^13*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 8820*a*e^2/(c^13*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) - 1344*b*d*e/(c^12*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 3360*b*d*arcsin(1/(c*x))*e/(c^13*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6) - 882*b*e^2/(c^14*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 3360*a*d*e/(c^13*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6) + 2520*b*arcsin(1/(c*x))*e^2/(c^15*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6) + 2520*a*e^2/(c^15*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6) - 90*b*e^2/(c^16*x^7*(sqrt(-1/(c^2*x^2) + 1) + 1)^7) + 315*b*arcsin(1/(c*x))*e^2/(c^17*x^8*(sqrt(-1/(c^2*x^2) + 1) + 1)^8) + 315*a*e^2/(c^17*x^8*(sqrt(-1/(c^2*x^2) + 1) + 1)^8))*c","B",0
95,1,1154,0,0.321487," ","integrate(x*(e*x^2+d)^2*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\frac{1}{5760} \, {\left(\frac{15 \, b x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c} + \frac{15 \, a x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6} e^{2}}{c} + \frac{180 \, b d x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} \arcsin\left(\frac{1}{c x}\right) e}{c} + \frac{6 \, b x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5} e^{2}}{c^{2}} + \frac{180 \, a d x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} e}{c} + \frac{90 \, b x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{3}} + \frac{720 \, b d^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right)}{c} + \frac{90 \, a x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4} e^{2}}{c^{3}} + \frac{120 \, b d x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e}{c^{2}} + \frac{720 \, a d^{2} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}}{c} + \frac{720 \, b d x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) e}{c^{3}} + \frac{50 \, b x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3} e^{2}}{c^{4}} + \frac{720 \, a d x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e}{c^{3}} + \frac{1440 \, b d^{2} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}}{c^{2}} + \frac{225 \, b x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{5}} + \frac{1440 \, b d^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{3}} + \frac{225 \, a x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2} e^{2}}{c^{5}} + \frac{1080 \, b d x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e}{c^{4}} + \frac{1440 \, a d^{2}}{c^{3}} + \frac{1080 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{5}} + \frac{300 \, b x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)} e^{2}}{c^{6}} + \frac{1080 \, a d e}{c^{5}} - \frac{1440 \, b d^{2}}{c^{4} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{300 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{7}} + \frac{720 \, b d^{2} \arcsin\left(\frac{1}{c x}\right)}{c^{5} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{300 \, a e^{2}}{c^{7}} - \frac{1080 \, b d e}{c^{6} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{720 \, a d^{2}}{c^{5} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{720 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{7} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} - \frac{300 \, b e^{2}}{c^{8} x {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}} + \frac{720 \, a d e}{c^{7} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{225 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{9} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} + \frac{225 \, a e^{2}}{c^{9} x^{2} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{2}} - \frac{120 \, b d e}{c^{8} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{180 \, b d \arcsin\left(\frac{1}{c x}\right) e}{c^{9} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} - \frac{50 \, b e^{2}}{c^{10} x^{3} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{3}} + \frac{180 \, a d e}{c^{9} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{90 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{11} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} + \frac{90 \, a e^{2}}{c^{11} x^{4} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{4}} - \frac{6 \, b e^{2}}{c^{12} x^{5} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{5}} + \frac{15 \, b \arcsin\left(\frac{1}{c x}\right) e^{2}}{c^{13} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}} + \frac{15 \, a e^{2}}{c^{13} x^{6} {\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}^{6}}\right)} c"," ",0,"1/5760*(15*b*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*arcsin(1/(c*x))*e^2/c + 15*a*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6*e^2/c + 180*b*d*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*arcsin(1/(c*x))*e/c + 6*b*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5*e^2/c^2 + 180*a*d*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*e/c + 90*b*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*arcsin(1/(c*x))*e^2/c^3 + 720*b*d^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))/c + 90*a*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4*e^2/c^3 + 120*b*d*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e/c^2 + 720*a*d^2*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2/c + 720*b*d*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))*e/c^3 + 50*b*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3*e^2/c^4 + 720*a*d*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e/c^3 + 1440*b*d^2*x*(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 + 225*b*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*arcsin(1/(c*x))*e^2/c^5 + 1440*b*d^2*arcsin(1/(c*x))/c^3 + 225*a*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2*e^2/c^5 + 1080*b*d*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e/c^4 + 1440*a*d^2/c^3 + 1080*b*d*arcsin(1/(c*x))*e/c^5 + 300*b*x*(sqrt(-1/(c^2*x^2) + 1) + 1)*e^2/c^6 + 1080*a*d*e/c^5 - 1440*b*d^2/(c^4*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 300*b*arcsin(1/(c*x))*e^2/c^7 + 720*b*d^2*arcsin(1/(c*x))/(c^5*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 300*a*e^2/c^7 - 1080*b*d*e/(c^6*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 720*a*d^2/(c^5*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 720*b*d*arcsin(1/(c*x))*e/(c^7*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) - 300*b*e^2/(c^8*x*(sqrt(-1/(c^2*x^2) + 1) + 1)) + 720*a*d*e/(c^7*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 225*b*arcsin(1/(c*x))*e^2/(c^9*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) + 225*a*e^2/(c^9*x^2*(sqrt(-1/(c^2*x^2) + 1) + 1)^2) - 120*b*d*e/(c^8*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 180*b*d*arcsin(1/(c*x))*e/(c^9*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) - 50*b*e^2/(c^10*x^3*(sqrt(-1/(c^2*x^2) + 1) + 1)^3) + 180*a*d*e/(c^9*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 90*b*arcsin(1/(c*x))*e^2/(c^11*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) + 90*a*e^2/(c^11*x^4*(sqrt(-1/(c^2*x^2) + 1) + 1)^4) - 6*b*e^2/(c^12*x^5*(sqrt(-1/(c^2*x^2) + 1) + 1)^5) + 15*b*arcsin(1/(c*x))*e^2/(c^13*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6) + 15*a*e^2/(c^13*x^6*(sqrt(-1/(c^2*x^2) + 1) + 1)^6))*c","B",0
96,-2,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arccsc(c*x))/x,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]Undef/Unsigned Inf encountered in limitEvaluation time: 5.5Limit: Max order reached or unable to make series expansion Error: Bad Argument Value","F(-2)",0
97,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arccsc(c*x))/x^3,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{2} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}}{x^{3}}\,{d x}"," ",0,"integrate((e*x^2 + d)^2*(b*arccsc(c*x) + a)/x^3, x)","F",0
98,-1,0,0,0.000000," ","integrate(x^2*(a+b*arccsc(c*x))/(e*x^2+d),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-2,0,0,0.000000," ","integrate(x*(a+b*arccsc(c*x))/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
100,-2,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
101,-2,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
102,-2,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x^2/(e*x^2+d),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
103,-1,0,0,0.000000," ","integrate(x^5*(a+b*arccsc(c*x))/(e*x^2+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate(x^3*(a+b*arccsc(c*x))/(e*x^2+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-2,0,0,0.000000," ","integrate(x*(a+b*arccsc(c*x))/(e*x^2+d)^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
106,-2,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x/(e*x^2+d)^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
107,-1,0,0,0.000000," ","integrate(x^4*(a+b*arccsc(c*x))/(e*x^2+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-2,0,0,0.000000," ","integrate(x^2*(a+b*arccsc(c*x))/(e*x^2+d)^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
109,-2,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/(e*x^2+d)^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
110,-1,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x^2/(e*x^2+d)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate(x^5*(a+b*arccsc(c*x))/(e*x^2+d)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-2,0,0,0.000000," ","integrate(x^3*(a+b*arccsc(c*x))/(e*x^2+d)^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
113,-2,0,0,0.000000," ","integrate(x*(a+b*arccsc(c*x))/(e*x^2+d)^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
114,-2,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x/(e*x^2+d)^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
115,-2,0,0,0.000000," ","integrate(x^4*(a+b*arccsc(c*x))/(e*x^2+d)^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
116,-2,0,0,0.000000," ","integrate(x^2*(a+b*arccsc(c*x))/(e*x^2+d)^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
117,-2,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/(e*x^2+d)^3,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(x)]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
118,0,0,0,0.000000," ","integrate(x^5*(a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x^{2} + d} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{5}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arccsc(c*x) + a)*x^5, x)","F",0
119,0,0,0,0.000000," ","integrate(x^3*(a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x^{2} + d} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{3}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arccsc(c*x) + a)*x^3, x)","F",0
120,0,0,0,0.000000," ","integrate(x*(a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x^{2} + d} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arccsc(c*x) + a)*x, x)","F",0
121,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))*(e*x^2+d)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}}{x}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arccsc(c*x) + a)/x, x)","F",0
122,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))*(e*x^2+d)^(1/2)/x^3,x, algorithm=""giac"")","\int \frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arccsc(c*x) + a)/x^3, x)","F",0
123,0,0,0,0.000000," ","integrate(x^2*(a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x^{2} + d} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{2}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arccsc(c*x) + a)*x^2, x)","F",0
124,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x^{2} + d} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arccsc(c*x) + a), x)","F",0
125,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))*(e*x^2+d)^(1/2)/x^2,x, algorithm=""giac"")","\int \frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arccsc(c*x) + a)/x^2, x)","F",0
126,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))*(e*x^2+d)^(1/2)/x^4,x, algorithm=""giac"")","\int \frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}}{x^{4}}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arccsc(c*x) + a)/x^4, x)","F",0
127,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))*(e*x^2+d)^(1/2)/x^6,x, algorithm=""giac"")","\int \frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}}{x^{6}}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arccsc(c*x) + a)/x^6, x)","F",0
128,0,0,0,0.000000," ","integrate(x^3*(e*x^2+d)^(3/2)*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\int {\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{3}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arccsc(c*x) + a)*x^3, x)","F",0
129,0,0,0,0.000000," ","integrate(x*(e*x^2+d)^(3/2)*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\int {\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arccsc(c*x) + a)*x, x)","F",0
130,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}}{x}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arccsc(c*x) + a)/x, x)","F",0
131,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x^3,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}}{x^{3}}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arccsc(c*x) + a)/x^3, x)","F",0
132,0,0,0,0.000000," ","integrate(x^2*(e*x^2+d)^(3/2)*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\int {\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{2}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arccsc(c*x) + a)*x^2, x)","F",0
133,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\int {\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arccsc(c*x) + a), x)","F",0
134,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x^2,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}}{x^{2}}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arccsc(c*x) + a)/x^2, x)","F",0
135,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x^4,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}}{x^{4}}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arccsc(c*x) + a)/x^4, x)","F",0
136,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x^6,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}}{x^{6}}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arccsc(c*x) + a)/x^6, x)","F",0
137,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arccsc(c*x))/x^8,x, algorithm=""giac"")","\int \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)}}{x^{8}}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arccsc(c*x) + a)/x^8, x)","F",0
138,0,0,0,0.000000," ","integrate(x^5*(a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{5}}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^5/sqrt(e*x^2 + d), x)","F",0
139,0,0,0,0.000000," ","integrate(x^3*(a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{3}}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^3/sqrt(e*x^2 + d), x)","F",0
140,0,0,0,0.000000," ","integrate(x*(a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x/sqrt(e*x^2 + d), x)","F",0
141,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{\sqrt{e x^{2} + d} x}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/(sqrt(e*x^2 + d)*x), x)","F",0
142,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x^3/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{\sqrt{e x^{2} + d} x^{3}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/(sqrt(e*x^2 + d)*x^3), x)","F",0
143,0,0,0,0.000000," ","integrate(x^2*(a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{2}}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^2/sqrt(e*x^2 + d), x)","F",0
144,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/sqrt(e*x^2 + d), x)","F",0
145,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x^2/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{\sqrt{e x^{2} + d} x^{2}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/(sqrt(e*x^2 + d)*x^2), x)","F",0
146,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x^4/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{\sqrt{e x^{2} + d} x^{4}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/(sqrt(e*x^2 + d)*x^4), x)","F",0
147,0,0,0,0.000000," ","integrate(x^5*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{5}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^5/(e*x^2 + d)^(3/2), x)","F",0
148,0,0,0,0.000000," ","integrate(x^3*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{3}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^3/(e*x^2 + d)^(3/2), x)","F",0
149,0,0,0,0.000000," ","integrate(x*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x/(e*x^2 + d)^(3/2), x)","F",0
150,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/((e*x^2 + d)^(3/2)*x), x)","F",0
151,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x^3/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/((e*x^2 + d)^(3/2)*x^3), x)","F",0
152,0,0,0,0.000000," ","integrate(x^4*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{4}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^4/(e*x^2 + d)^(3/2), x)","F",0
153,0,0,0,0.000000," ","integrate(x^2*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{2}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^2/(e*x^2 + d)^(3/2), x)","F",0
154,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/(e*x^2 + d)^(3/2), x)","F",0
155,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x^2/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/((e*x^2 + d)^(3/2)*x^2), x)","F",0
156,0,0,0,0.000000," ","integrate(x^5*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{5}}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^5/(e*x^2 + d)^(5/2), x)","F",0
157,0,0,0,0.000000," ","integrate(x^3*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{3}}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^3/(e*x^2 + d)^(5/2), x)","F",0
158,0,0,0,0.000000," ","integrate(x*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x/(e*x^2 + d)^(5/2), x)","F",0
159,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{{\left(e x^{2} + d\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/((e*x^2 + d)^(5/2)*x), x)","F",0
160,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x^3/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{{\left(e x^{2} + d\right)}^{\frac{5}{2}} x^{3}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/((e*x^2 + d)^(5/2)*x^3), x)","F",0
161,0,0,0,0.000000," ","integrate(x^6*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{6}}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^6/(e*x^2 + d)^(5/2), x)","F",0
162,0,0,0,0.000000," ","integrate(x^4*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{4}}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^4/(e*x^2 + d)^(5/2), x)","F",0
163,0,0,0,0.000000," ","integrate(x^2*(a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{2}}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^2/(e*x^2 + d)^(5/2), x)","F",0
164,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/(e*x^2+d)^(5/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/(e*x^2 + d)^(5/2), x)","F",0
165,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^3*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\int {\left(e x^{2} + d\right)}^{3} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((e*x^2 + d)^3*(b*arccsc(c*x) + a)*(f*x)^m, x)","F",0
166,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^2*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\int {\left(e x^{2} + d\right)}^{2} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((e*x^2 + d)^2*(b*arccsc(c*x) + a)*(f*x)^m, x)","F",0
167,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\int {\left(e x^{2} + d\right)} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((e*x^2 + d)*(b*arccsc(c*x) + a)*(f*x)^m, x)","F",0
168,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccsc(c*x))/(e*x^2+d),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} \left(f x\right)^{m}}{e x^{2} + d}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*(f*x)^m/(e*x^2 + d), x)","F",0
169,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccsc(c*x))/(e*x^2+d)^2,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*(f*x)^m/(e*x^2 + d)^2, x)","F",0
170,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^(3/2)*(a+b*arccsc(c*x)),x, algorithm=""giac"")","\int {\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arccsc(c*x) + a)*(f*x)^m, x)","F",0
171,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccsc(c*x))*(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{e x^{2} + d} {\left(b \operatorname{arccsc}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arccsc(c*x) + a)*(f*x)^m, x)","F",0
172,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccsc(c*x))/(e*x^2+d)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} \left(f x\right)^{m}}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*(f*x)^m/sqrt(e*x^2 + d), x)","F",0
173,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccsc(c*x))/(e*x^2+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*(f*x)^m/(e*x^2 + d)^(3/2), x)","F",0
174,-2,0,0,0.000000," ","integrate(x^11*(a+b*arccsc(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
175,-2,0,0,0.000000," ","integrate(x^7*(a+b*arccsc(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
176,0,0,0,0.000000," ","integrate(x^3*(a+b*arccsc(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{arccsc}\left(c x\right) + a\right)} x^{3}}{\sqrt{-c^{4} x^{4} + 1}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)*x^3/sqrt(-c^4*x^4 + 1), x)","F",0
177,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x/(-c^4*x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{\sqrt{-c^{4} x^{4} + 1} x}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/(sqrt(-c^4*x^4 + 1)*x), x)","F",0
178,0,0,0,0.000000," ","integrate((a+b*arccsc(c*x))/x^5/(-c^4*x^4+1)^(1/2),x, algorithm=""giac"")","\int \frac{b \operatorname{arccsc}\left(c x\right) + a}{\sqrt{-c^{4} x^{4} + 1} x^{5}}\,{d x}"," ",0,"integrate((b*arccsc(c*x) + a)/(sqrt(-c^4*x^4 + 1)*x^5), x)","F",0
