1,1,184,0,0.341593," ","integrate(x^4*(-c^2*d*x^2+d)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{7} \, a c^{2} d x^{7} + \frac{1}{5} \, a d x^{5} - \frac{1}{245} \, {\left(35 \, x^{7} \operatorname{arcosh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{c^{2} x^{2} - 1}}{c^{8}}\right)} c\right)} b c^{2} d + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b d"," ",0,"-1/7*a*c^2*d*x^7 + 1/5*a*d*x^5 - 1/245*(35*x^7*arccosh(c*x) - (5*sqrt(c^2*x^2 - 1)*x^6/c^2 + 6*sqrt(c^2*x^2 - 1)*x^4/c^4 + 8*sqrt(c^2*x^2 - 1)*x^2/c^6 + 16*sqrt(c^2*x^2 - 1)/c^8)*c)*b*c^2*d + 1/75*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*d","A",0
2,1,202,0,0.334595," ","integrate(x^3*(-c^2*d*x^2+d)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{6} \, a c^{2} d x^{6} + \frac{1}{4} \, a d x^{4} - \frac{1}{288} \, {\left(48 \, x^{6} \operatorname{arcosh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} - 1} x}{c^{6}} + \frac{15 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{7}}\right)} c\right)} b c^{2} d + \frac{1}{32} \, {\left(8 \, x^{4} \operatorname{arcosh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{c^{2} x^{2} - 1} x}{c^{4}} + \frac{3 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{5}}\right)} c\right)} b d"," ",0,"-1/6*a*c^2*d*x^6 + 1/4*a*d*x^4 - 1/288*(48*x^6*arccosh(c*x) - (8*sqrt(c^2*x^2 - 1)*x^5/c^2 + 10*sqrt(c^2*x^2 - 1)*x^3/c^4 + 15*sqrt(c^2*x^2 - 1)*x/c^6 + 15*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^7)*c)*b*c^2*d + 1/32*(8*x^4*arccosh(c*x) - (2*sqrt(c^2*x^2 - 1)*x^3/c^2 + 3*sqrt(c^2*x^2 - 1)*x/c^4 + 3*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5)*c)*b*d","A",0
3,1,145,0,0.324634," ","integrate(x^2*(-c^2*d*x^2+d)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{5} \, a c^{2} d x^{5} - \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b c^{2} d + \frac{1}{3} \, a d x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b d"," ",0,"-1/5*a*c^2*d*x^5 - 1/75*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*c^2*d + 1/3*a*d*x^3 + 1/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*d","A",0
4,1,162,0,0.317205," ","integrate(x*(-c^2*d*x^2+d)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{4} \, a c^{2} d x^{4} - \frac{1}{32} \, {\left(8 \, x^{4} \operatorname{arcosh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{c^{2} x^{2} - 1} x}{c^{4}} + \frac{3 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{5}}\right)} c\right)} b c^{2} d + \frac{1}{2} \, a d x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x}{c^{2}} + \frac{\log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{3}}\right)}\right)} b d"," ",0,"-1/4*a*c^2*d*x^4 - 1/32*(8*x^4*arccosh(c*x) - (2*sqrt(c^2*x^2 - 1)*x^3/c^2 + 3*sqrt(c^2*x^2 - 1)*x/c^4 + 3*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5)*c)*b*c^2*d + 1/2*a*d*x^2 + 1/4*(2*x^2*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x/c^2 + log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3))*b*d","A",0
5,1,97,0,0.334173," ","integrate((-c^2*d*x^2+d)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{3} \, a c^{2} d x^{3} - \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b c^{2} d + a d x + \frac{{\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b d}{c}"," ",0,"-1/3*a*c^2*d*x^3 - 1/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*c^2*d + a*d*x + (c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*d/c","A",0
6,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)*(a+b*arccosh(c*x))/x,x, algorithm=""maxima"")","-\frac{1}{2} \, a c^{2} d x^{2} + a d \log\left(x\right) - \int b c^{2} d x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) - \frac{b d \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"-1/2*a*c^2*d*x^2 + a*d*log(x) - integrate(b*c^2*d*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) - b*d*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
7,1,66,0,0.445058," ","integrate((-c^2*d*x^2+d)*(a+b*arccosh(c*x))/x^2,x, algorithm=""maxima"")","-a c^{2} d x - {\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b c d - {\left(c \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arcosh}\left(c x\right)}{x}\right)} b d - \frac{a d}{x}"," ",0,"-a*c^2*d*x - (c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*c*d - (c*arcsin(1/(c*abs(x))) + arccosh(c*x)/x)*b*d - a*d/x","A",0
8,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)*(a+b*arccosh(c*x))/x^3,x, algorithm=""maxima"")","-b c^{2} d \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x} - a c^{2} d \log\left(x\right) + \frac{1}{2} \, b d {\left(\frac{\sqrt{c^{2} x^{2} - 1} c}{x} - \frac{\operatorname{arcosh}\left(c x\right)}{x^{2}}\right)} - \frac{a d}{2 \, x^{2}}"," ",0,"-b*c^2*d*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x) - a*c^2*d*log(x) + 1/2*b*d*(sqrt(c^2*x^2 - 1)*c/x - arccosh(c*x)/x^2) - 1/2*a*d/x^2","F",0
9,1,89,0,0.486760," ","integrate((-c^2*d*x^2+d)*(a+b*arccosh(c*x))/x^4,x, algorithm=""maxima"")","{\left(c \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arcosh}\left(c x\right)}{x}\right)} b c^{2} d - \frac{1}{6} \, {\left({\left(c^{2} \arcsin\left(\frac{1}{c {\left| x \right|}}\right) - \frac{\sqrt{c^{2} x^{2} - 1}}{x^{2}}\right)} c + \frac{2 \, \operatorname{arcosh}\left(c x\right)}{x^{3}}\right)} b d + \frac{a c^{2} d}{x} - \frac{a d}{3 \, x^{3}}"," ",0,"(c*arcsin(1/(c*abs(x))) + arccosh(c*x)/x)*b*c^2*d - 1/6*((c^2*arcsin(1/(c*abs(x))) - sqrt(c^2*x^2 - 1)/x^2)*c + 2*arccosh(c*x)/x^3)*b*d + a*c^2*d/x - 1/3*a*d/x^3","A",0
10,1,319,0,0.354369," ","integrate(x^4*(-c^2*d*x^2+d)^2*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{9} \, a c^{4} d^{2} x^{9} - \frac{2}{7} \, a c^{2} d^{2} x^{7} + \frac{1}{2835} \, {\left(315 \, x^{9} \operatorname{arcosh}\left(c x\right) - {\left(\frac{35 \, \sqrt{c^{2} x^{2} - 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} - 1}}{c^{10}}\right)} c\right)} b c^{4} d^{2} + \frac{1}{5} \, a d^{2} x^{5} - \frac{2}{245} \, {\left(35 \, x^{7} \operatorname{arcosh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{c^{2} x^{2} - 1}}{c^{8}}\right)} c\right)} b c^{2} d^{2} + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b d^{2}"," ",0,"1/9*a*c^4*d^2*x^9 - 2/7*a*c^2*d^2*x^7 + 1/2835*(315*x^9*arccosh(c*x) - (35*sqrt(c^2*x^2 - 1)*x^8/c^2 + 40*sqrt(c^2*x^2 - 1)*x^6/c^4 + 48*sqrt(c^2*x^2 - 1)*x^4/c^6 + 64*sqrt(c^2*x^2 - 1)*x^2/c^8 + 128*sqrt(c^2*x^2 - 1)/c^10)*c)*b*c^4*d^2 + 1/5*a*d^2*x^5 - 2/245*(35*x^7*arccosh(c*x) - (5*sqrt(c^2*x^2 - 1)*x^6/c^2 + 6*sqrt(c^2*x^2 - 1)*x^4/c^4 + 8*sqrt(c^2*x^2 - 1)*x^2/c^6 + 16*sqrt(c^2*x^2 - 1)/c^8)*c)*b*c^2*d^2 + 1/75*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*d^2","A",0
11,1,346,0,0.329894," ","integrate(x^3*(-c^2*d*x^2+d)^2*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, a c^{4} d^{2} x^{8} - \frac{1}{3} \, a c^{2} d^{2} x^{6} + \frac{1}{3072} \, {\left(384 \, x^{8} \operatorname{arcosh}\left(c x\right) - {\left(\frac{48 \, \sqrt{c^{2} x^{2} - 1} x^{7}}{c^{2}} + \frac{56 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{6}} + \frac{105 \, \sqrt{c^{2} x^{2} - 1} x}{c^{8}} + \frac{105 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{9}}\right)} c\right)} b c^{4} d^{2} + \frac{1}{4} \, a d^{2} x^{4} - \frac{1}{144} \, {\left(48 \, x^{6} \operatorname{arcosh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} - 1} x}{c^{6}} + \frac{15 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{7}}\right)} c\right)} b c^{2} d^{2} + \frac{1}{32} \, {\left(8 \, x^{4} \operatorname{arcosh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{c^{2} x^{2} - 1} x}{c^{4}} + \frac{3 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{5}}\right)} c\right)} b d^{2}"," ",0,"1/8*a*c^4*d^2*x^8 - 1/3*a*c^2*d^2*x^6 + 1/3072*(384*x^8*arccosh(c*x) - (48*sqrt(c^2*x^2 - 1)*x^7/c^2 + 56*sqrt(c^2*x^2 - 1)*x^5/c^4 + 70*sqrt(c^2*x^2 - 1)*x^3/c^6 + 105*sqrt(c^2*x^2 - 1)*x/c^8 + 105*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^9)*c)*b*c^4*d^2 + 1/4*a*d^2*x^4 - 1/144*(48*x^6*arccosh(c*x) - (8*sqrt(c^2*x^2 - 1)*x^5/c^2 + 10*sqrt(c^2*x^2 - 1)*x^3/c^4 + 15*sqrt(c^2*x^2 - 1)*x/c^6 + 15*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^7)*c)*b*c^2*d^2 + 1/32*(8*x^4*arccosh(c*x) - (2*sqrt(c^2*x^2 - 1)*x^3/c^2 + 3*sqrt(c^2*x^2 - 1)*x/c^4 + 3*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5)*c)*b*d^2","B",0
12,1,261,0,0.343773," ","integrate(x^2*(-c^2*d*x^2+d)^2*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a c^{4} d^{2} x^{7} - \frac{2}{5} \, a c^{2} d^{2} x^{5} + \frac{1}{245} \, {\left(35 \, x^{7} \operatorname{arcosh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{c^{2} x^{2} - 1}}{c^{8}}\right)} c\right)} b c^{4} d^{2} - \frac{2}{75} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b c^{2} d^{2} + \frac{1}{3} \, a d^{2} x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b d^{2}"," ",0,"1/7*a*c^4*d^2*x^7 - 2/5*a*c^2*d^2*x^5 + 1/245*(35*x^7*arccosh(c*x) - (5*sqrt(c^2*x^2 - 1)*x^6/c^2 + 6*sqrt(c^2*x^2 - 1)*x^4/c^4 + 8*sqrt(c^2*x^2 - 1)*x^2/c^6 + 16*sqrt(c^2*x^2 - 1)/c^8)*c)*b*c^4*d^2 - 2/75*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*c^2*d^2 + 1/3*a*d^2*x^3 + 1/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*d^2","A",0
13,1,287,0,0.455585," ","integrate(x*(-c^2*d*x^2+d)^2*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a c^{4} d^{2} x^{6} - \frac{1}{2} \, a c^{2} d^{2} x^{4} + \frac{1}{288} \, {\left(48 \, x^{6} \operatorname{arcosh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} - 1} x}{c^{6}} + \frac{15 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{7}}\right)} c\right)} b c^{4} d^{2} - \frac{1}{16} \, {\left(8 \, x^{4} \operatorname{arcosh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{c^{2} x^{2} - 1} x}{c^{4}} + \frac{3 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{5}}\right)} c\right)} b c^{2} d^{2} + \frac{1}{2} \, a d^{2} x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x}{c^{2}} + \frac{\log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{3}}\right)}\right)} b d^{2}"," ",0,"1/6*a*c^4*d^2*x^6 - 1/2*a*c^2*d^2*x^4 + 1/288*(48*x^6*arccosh(c*x) - (8*sqrt(c^2*x^2 - 1)*x^5/c^2 + 10*sqrt(c^2*x^2 - 1)*x^3/c^4 + 15*sqrt(c^2*x^2 - 1)*x/c^6 + 15*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^7)*c)*b*c^4*d^2 - 1/16*(8*x^4*arccosh(c*x) - (2*sqrt(c^2*x^2 - 1)*x^3/c^2 + 3*sqrt(c^2*x^2 - 1)*x/c^4 + 3*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5)*c)*b*c^2*d^2 + 1/2*a*d^2*x^2 + 1/4*(2*x^2*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x/c^2 + log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3))*b*d^2","B",0
14,1,194,0,0.374157," ","integrate((-c^2*d*x^2+d)^2*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a c^{4} d^{2} x^{5} + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b c^{4} d^{2} - \frac{2}{3} \, a c^{2} d^{2} x^{3} - \frac{2}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b c^{2} d^{2} + a d^{2} x + \frac{{\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b d^{2}}{c}"," ",0,"1/5*a*c^4*d^2*x^5 + 1/75*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*c^4*d^2 - 2/3*a*c^2*d^2*x^3 - 2/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*c^2*d^2 + a*d^2*x + (c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*d^2/c","A",0
15,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^2*(a+b*arccosh(c*x))/x,x, algorithm=""maxima"")","\frac{1}{4} \, a c^{4} d^{2} x^{4} - a c^{2} d^{2} x^{2} + a d^{2} \log\left(x\right) + \int b c^{4} d^{2} x^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) - 2 \, b c^{2} d^{2} x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + \frac{b d^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"1/4*a*c^4*d^2*x^4 - a*c^2*d^2*x^2 + a*d^2*log(x) + integrate(b*c^4*d^2*x^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) - 2*b*c^2*d^2*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + b*d^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
16,1,143,0,0.462046," ","integrate((-c^2*d*x^2+d)^2*(a+b*arccosh(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{3} \, a c^{4} d^{2} x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b c^{4} d^{2} - 2 \, a c^{2} d^{2} x - 2 \, {\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b c d^{2} - {\left(c \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arcosh}\left(c x\right)}{x}\right)} b d^{2} - \frac{a d^{2}}{x}"," ",0,"1/3*a*c^4*d^2*x^3 + 1/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*c^4*d^2 - 2*a*c^2*d^2*x - 2*(c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*c*d^2 - (c*arcsin(1/(c*abs(x))) + arccosh(c*x)/x)*b*d^2 - a*d^2/x","A",0
17,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^2*(a+b*arccosh(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, a c^{4} d^{2} x^{2} - 2 \, a c^{2} d^{2} \log\left(x\right) + \frac{1}{2} \, b d^{2} {\left(\frac{\sqrt{c^{2} x^{2} - 1} c}{x} - \frac{\operatorname{arcosh}\left(c x\right)}{x^{2}}\right)} - \frac{a d^{2}}{2 \, x^{2}} + \int b c^{4} d^{2} x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) - \frac{2 \, b c^{2} d^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"1/2*a*c^4*d^2*x^2 - 2*a*c^2*d^2*log(x) + 1/2*b*d^2*(sqrt(c^2*x^2 - 1)*c/x - arccosh(c*x)/x^2) - 1/2*a*d^2/x^2 + integrate(b*c^4*d^2*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) - 2*b*c^2*d^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
18,1,137,0,0.458992," ","integrate((-c^2*d*x^2+d)^2*(a+b*arccosh(c*x))/x^4,x, algorithm=""maxima"")","a c^{4} d^{2} x + {\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b c^{3} d^{2} + 2 \, {\left(c \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arcosh}\left(c x\right)}{x}\right)} b c^{2} d^{2} - \frac{1}{6} \, {\left({\left(c^{2} \arcsin\left(\frac{1}{c {\left| x \right|}}\right) - \frac{\sqrt{c^{2} x^{2} - 1}}{x^{2}}\right)} c + \frac{2 \, \operatorname{arcosh}\left(c x\right)}{x^{3}}\right)} b d^{2} + \frac{2 \, a c^{2} d^{2}}{x} - \frac{a d^{2}}{3 \, x^{3}}"," ",0,"a*c^4*d^2*x + (c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*c^3*d^2 + 2*(c*arcsin(1/(c*abs(x))) + arccosh(c*x)/x)*b*c^2*d^2 - 1/6*((c^2*arcsin(1/(c*abs(x))) - sqrt(c^2*x^2 - 1)/x^2)*c + 2*arccosh(c*x)/x^3)*b*d^2 + 2*a*c^2*d^2/x - 1/3*a*d^2/x^3","A",0
19,1,465,0,0.363094," ","integrate(x^4*(-c^2*d*x^2+d)^3*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{11} \, a c^{6} d^{3} x^{11} + \frac{1}{3} \, a c^{4} d^{3} x^{9} - \frac{3}{7} \, a c^{2} d^{3} x^{7} - \frac{1}{7623} \, {\left(693 \, x^{11} \operatorname{arcosh}\left(c x\right) - {\left(\frac{63 \, \sqrt{c^{2} x^{2} - 1} x^{10}}{c^{2}} + \frac{70 \, \sqrt{c^{2} x^{2} - 1} x^{8}}{c^{4}} + \frac{80 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{6}} + \frac{96 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{10}} + \frac{256 \, \sqrt{c^{2} x^{2} - 1}}{c^{12}}\right)} c\right)} b c^{6} d^{3} + \frac{1}{945} \, {\left(315 \, x^{9} \operatorname{arcosh}\left(c x\right) - {\left(\frac{35 \, \sqrt{c^{2} x^{2} - 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} - 1}}{c^{10}}\right)} c\right)} b c^{4} d^{3} + \frac{1}{5} \, a d^{3} x^{5} - \frac{3}{245} \, {\left(35 \, x^{7} \operatorname{arcosh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{c^{2} x^{2} - 1}}{c^{8}}\right)} c\right)} b c^{2} d^{3} + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b d^{3}"," ",0,"-1/11*a*c^6*d^3*x^11 + 1/3*a*c^4*d^3*x^9 - 3/7*a*c^2*d^3*x^7 - 1/7623*(693*x^11*arccosh(c*x) - (63*sqrt(c^2*x^2 - 1)*x^10/c^2 + 70*sqrt(c^2*x^2 - 1)*x^8/c^4 + 80*sqrt(c^2*x^2 - 1)*x^6/c^6 + 96*sqrt(c^2*x^2 - 1)*x^4/c^8 + 128*sqrt(c^2*x^2 - 1)*x^2/c^10 + 256*sqrt(c^2*x^2 - 1)/c^12)*c)*b*c^6*d^3 + 1/945*(315*x^9*arccosh(c*x) - (35*sqrt(c^2*x^2 - 1)*x^8/c^2 + 40*sqrt(c^2*x^2 - 1)*x^6/c^4 + 48*sqrt(c^2*x^2 - 1)*x^4/c^6 + 64*sqrt(c^2*x^2 - 1)*x^2/c^8 + 128*sqrt(c^2*x^2 - 1)/c^10)*c)*b*c^4*d^3 + 1/5*a*d^3*x^5 - 3/245*(35*x^7*arccosh(c*x) - (5*sqrt(c^2*x^2 - 1)*x^6/c^2 + 6*sqrt(c^2*x^2 - 1)*x^4/c^4 + 8*sqrt(c^2*x^2 - 1)*x^2/c^6 + 16*sqrt(c^2*x^2 - 1)/c^8)*c)*b*c^2*d^3 + 1/75*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*d^3","B",0
20,1,501,0,0.369441," ","integrate(x^3*(-c^2*d*x^2+d)^3*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{10} \, a c^{6} d^{3} x^{10} + \frac{3}{8} \, a c^{4} d^{3} x^{8} - \frac{1}{2} \, a c^{2} d^{3} x^{6} - \frac{1}{12800} \, {\left(1280 \, x^{10} \operatorname{arcosh}\left(c x\right) - {\left(\frac{128 \, \sqrt{c^{2} x^{2} - 1} x^{9}}{c^{2}} + \frac{144 \, \sqrt{c^{2} x^{2} - 1} x^{7}}{c^{4}} + \frac{168 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{6}} + \frac{210 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{8}} + \frac{315 \, \sqrt{c^{2} x^{2} - 1} x}{c^{10}} + \frac{315 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{11}}\right)} c\right)} b c^{6} d^{3} + \frac{1}{1024} \, {\left(384 \, x^{8} \operatorname{arcosh}\left(c x\right) - {\left(\frac{48 \, \sqrt{c^{2} x^{2} - 1} x^{7}}{c^{2}} + \frac{56 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{6}} + \frac{105 \, \sqrt{c^{2} x^{2} - 1} x}{c^{8}} + \frac{105 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{9}}\right)} c\right)} b c^{4} d^{3} + \frac{1}{4} \, a d^{3} x^{4} - \frac{1}{96} \, {\left(48 \, x^{6} \operatorname{arcosh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} - 1} x}{c^{6}} + \frac{15 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{7}}\right)} c\right)} b c^{2} d^{3} + \frac{1}{32} \, {\left(8 \, x^{4} \operatorname{arcosh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{c^{2} x^{2} - 1} x}{c^{4}} + \frac{3 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{5}}\right)} c\right)} b d^{3}"," ",0,"-1/10*a*c^6*d^3*x^10 + 3/8*a*c^4*d^3*x^8 - 1/2*a*c^2*d^3*x^6 - 1/12800*(1280*x^10*arccosh(c*x) - (128*sqrt(c^2*x^2 - 1)*x^9/c^2 + 144*sqrt(c^2*x^2 - 1)*x^7/c^4 + 168*sqrt(c^2*x^2 - 1)*x^5/c^6 + 210*sqrt(c^2*x^2 - 1)*x^3/c^8 + 315*sqrt(c^2*x^2 - 1)*x/c^10 + 315*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^11)*c)*b*c^6*d^3 + 1/1024*(384*x^8*arccosh(c*x) - (48*sqrt(c^2*x^2 - 1)*x^7/c^2 + 56*sqrt(c^2*x^2 - 1)*x^5/c^4 + 70*sqrt(c^2*x^2 - 1)*x^3/c^6 + 105*sqrt(c^2*x^2 - 1)*x/c^8 + 105*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^9)*c)*b*c^4*d^3 + 1/4*a*d^3*x^4 - 1/96*(48*x^6*arccosh(c*x) - (8*sqrt(c^2*x^2 - 1)*x^5/c^2 + 10*sqrt(c^2*x^2 - 1)*x^3/c^4 + 15*sqrt(c^2*x^2 - 1)*x/c^6 + 15*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^7)*c)*b*c^2*d^3 + 1/32*(8*x^4*arccosh(c*x) - (2*sqrt(c^2*x^2 - 1)*x^3/c^2 + 3*sqrt(c^2*x^2 - 1)*x/c^4 + 3*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5)*c)*b*d^3","B",0
21,1,388,0,0.370124," ","integrate(x^2*(-c^2*d*x^2+d)^3*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{9} \, a c^{6} d^{3} x^{9} + \frac{3}{7} \, a c^{4} d^{3} x^{7} - \frac{1}{2835} \, {\left(315 \, x^{9} \operatorname{arcosh}\left(c x\right) - {\left(\frac{35 \, \sqrt{c^{2} x^{2} - 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} - 1}}{c^{10}}\right)} c\right)} b c^{6} d^{3} - \frac{3}{5} \, a c^{2} d^{3} x^{5} + \frac{3}{245} \, {\left(35 \, x^{7} \operatorname{arcosh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{c^{2} x^{2} - 1}}{c^{8}}\right)} c\right)} b c^{4} d^{3} - \frac{1}{25} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b c^{2} d^{3} + \frac{1}{3} \, a d^{3} x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b d^{3}"," ",0,"-1/9*a*c^6*d^3*x^9 + 3/7*a*c^4*d^3*x^7 - 1/2835*(315*x^9*arccosh(c*x) - (35*sqrt(c^2*x^2 - 1)*x^8/c^2 + 40*sqrt(c^2*x^2 - 1)*x^6/c^4 + 48*sqrt(c^2*x^2 - 1)*x^4/c^6 + 64*sqrt(c^2*x^2 - 1)*x^2/c^8 + 128*sqrt(c^2*x^2 - 1)/c^10)*c)*b*c^6*d^3 - 3/5*a*c^2*d^3*x^5 + 3/245*(35*x^7*arccosh(c*x) - (5*sqrt(c^2*x^2 - 1)*x^6/c^2 + 6*sqrt(c^2*x^2 - 1)*x^4/c^4 + 8*sqrt(c^2*x^2 - 1)*x^2/c^6 + 16*sqrt(c^2*x^2 - 1)/c^8)*c)*b*c^4*d^3 - 1/25*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*c^2*d^3 + 1/3*a*d^3*x^3 + 1/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*d^3","B",0
22,1,423,0,0.365703," ","integrate(x*(-c^2*d*x^2+d)^3*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{8} \, a c^{6} d^{3} x^{8} + \frac{1}{2} \, a c^{4} d^{3} x^{6} - \frac{1}{3072} \, {\left(384 \, x^{8} \operatorname{arcosh}\left(c x\right) - {\left(\frac{48 \, \sqrt{c^{2} x^{2} - 1} x^{7}}{c^{2}} + \frac{56 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{6}} + \frac{105 \, \sqrt{c^{2} x^{2} - 1} x}{c^{8}} + \frac{105 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{9}}\right)} c\right)} b c^{6} d^{3} - \frac{3}{4} \, a c^{2} d^{3} x^{4} + \frac{1}{96} \, {\left(48 \, x^{6} \operatorname{arcosh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} - 1} x}{c^{6}} + \frac{15 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{7}}\right)} c\right)} b c^{4} d^{3} - \frac{3}{32} \, {\left(8 \, x^{4} \operatorname{arcosh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{c^{2} x^{2} - 1} x}{c^{4}} + \frac{3 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{5}}\right)} c\right)} b c^{2} d^{3} + \frac{1}{2} \, a d^{3} x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x}{c^{2}} + \frac{\log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{3}}\right)}\right)} b d^{3}"," ",0,"-1/8*a*c^6*d^3*x^8 + 1/2*a*c^4*d^3*x^6 - 1/3072*(384*x^8*arccosh(c*x) - (48*sqrt(c^2*x^2 - 1)*x^7/c^2 + 56*sqrt(c^2*x^2 - 1)*x^5/c^4 + 70*sqrt(c^2*x^2 - 1)*x^3/c^6 + 105*sqrt(c^2*x^2 - 1)*x/c^8 + 105*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^9)*c)*b*c^6*d^3 - 3/4*a*c^2*d^3*x^4 + 1/96*(48*x^6*arccosh(c*x) - (8*sqrt(c^2*x^2 - 1)*x^5/c^2 + 10*sqrt(c^2*x^2 - 1)*x^3/c^4 + 15*sqrt(c^2*x^2 - 1)*x/c^6 + 15*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^7)*c)*b*c^4*d^3 - 3/32*(8*x^4*arccosh(c*x) - (2*sqrt(c^2*x^2 - 1)*x^3/c^2 + 3*sqrt(c^2*x^2 - 1)*x/c^4 + 3*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5)*c)*b*c^2*d^3 + 1/2*a*d^3*x^2 + 1/4*(2*x^2*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x/c^2 + log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3))*b*d^3","B",0
23,1,302,0,0.349756," ","integrate((-c^2*d*x^2+d)^3*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{7} \, a c^{6} d^{3} x^{7} + \frac{3}{5} \, a c^{4} d^{3} x^{5} - \frac{1}{245} \, {\left(35 \, x^{7} \operatorname{arcosh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{c^{2} x^{2} - 1}}{c^{8}}\right)} c\right)} b c^{6} d^{3} + \frac{1}{25} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b c^{4} d^{3} - a c^{2} d^{3} x^{3} - \frac{1}{3} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b c^{2} d^{3} + a d^{3} x + \frac{{\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b d^{3}}{c}"," ",0,"-1/7*a*c^6*d^3*x^7 + 3/5*a*c^4*d^3*x^5 - 1/245*(35*x^7*arccosh(c*x) - (5*sqrt(c^2*x^2 - 1)*x^6/c^2 + 6*sqrt(c^2*x^2 - 1)*x^4/c^4 + 8*sqrt(c^2*x^2 - 1)*x^2/c^6 + 16*sqrt(c^2*x^2 - 1)/c^8)*c)*b*c^6*d^3 + 1/25*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*c^4*d^3 - a*c^2*d^3*x^3 - 1/3*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*c^2*d^3 + a*d^3*x + (c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*d^3/c","A",0
24,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^3*(a+b*arccosh(c*x))/x,x, algorithm=""maxima"")","-\frac{1}{6} \, a c^{6} d^{3} x^{6} + \frac{3}{4} \, a c^{4} d^{3} x^{4} - \frac{3}{2} \, a c^{2} d^{3} x^{2} + a d^{3} \log\left(x\right) - \int b c^{6} d^{3} x^{5} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) - 3 \, b c^{4} d^{3} x^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 3 \, b c^{2} d^{3} x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) - \frac{b d^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"-1/6*a*c^6*d^3*x^6 + 3/4*a*c^4*d^3*x^4 - 3/2*a*c^2*d^3*x^2 + a*d^3*log(x) - integrate(b*c^6*d^3*x^5*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) - 3*b*c^4*d^3*x^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 3*b*c^2*d^3*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) - b*d^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
25,1,231,0,0.466188," ","integrate((-c^2*d*x^2+d)^3*(a+b*arccosh(c*x))/x^2,x, algorithm=""maxima"")","-\frac{1}{5} \, a c^{6} d^{3} x^{5} - \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b c^{6} d^{3} + a c^{4} d^{3} x^{3} + \frac{1}{3} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b c^{4} d^{3} - 3 \, a c^{2} d^{3} x - 3 \, {\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b c d^{3} - {\left(c \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arcosh}\left(c x\right)}{x}\right)} b d^{3} - \frac{a d^{3}}{x}"," ",0,"-1/5*a*c^6*d^3*x^5 - 1/75*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*c^6*d^3 + a*c^4*d^3*x^3 + 1/3*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*c^4*d^3 - 3*a*c^2*d^3*x - 3*(c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*c*d^3 - (c*arcsin(1/(c*abs(x))) + arccosh(c*x)/x)*b*d^3 - a*d^3/x","A",0
26,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^3*(a+b*arccosh(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a c^{6} d^{3} x^{4} + \frac{3}{2} \, a c^{4} d^{3} x^{2} - 3 \, a c^{2} d^{3} \log\left(x\right) + \frac{1}{2} \, b d^{3} {\left(\frac{\sqrt{c^{2} x^{2} - 1} c}{x} - \frac{\operatorname{arcosh}\left(c x\right)}{x^{2}}\right)} - \frac{a d^{3}}{2 \, x^{2}} - \int b c^{6} d^{3} x^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) - 3 \, b c^{4} d^{3} x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + \frac{3 \, b c^{2} d^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"-1/4*a*c^6*d^3*x^4 + 3/2*a*c^4*d^3*x^2 - 3*a*c^2*d^3*log(x) + 1/2*b*d^3*(sqrt(c^2*x^2 - 1)*c/x - arccosh(c*x)/x^2) - 1/2*a*d^3/x^2 - integrate(b*c^6*d^3*x^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) - 3*b*c^4*d^3*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 3*b*c^2*d^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
27,1,208,0,0.562154," ","integrate((-c^2*d*x^2+d)^3*(a+b*arccosh(c*x))/x^4,x, algorithm=""maxima"")","-\frac{1}{3} \, a c^{6} d^{3} x^{3} - \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b c^{6} d^{3} + 3 \, a c^{4} d^{3} x + 3 \, {\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b c^{3} d^{3} + 3 \, {\left(c \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arcosh}\left(c x\right)}{x}\right)} b c^{2} d^{3} - \frac{1}{6} \, {\left({\left(c^{2} \arcsin\left(\frac{1}{c {\left| x \right|}}\right) - \frac{\sqrt{c^{2} x^{2} - 1}}{x^{2}}\right)} c + \frac{2 \, \operatorname{arcosh}\left(c x\right)}{x^{3}}\right)} b d^{3} + \frac{3 \, a c^{2} d^{3}}{x} - \frac{a d^{3}}{3 \, x^{3}}"," ",0,"-1/3*a*c^6*d^3*x^3 - 1/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*c^6*d^3 + 3*a*c^4*d^3*x + 3*(c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*c^3*d^3 + 3*(c*arcsin(1/(c*abs(x))) + arccosh(c*x)/x)*b*c^2*d^3 - 1/6*((c^2*arcsin(1/(c*abs(x))) - sqrt(c^2*x^2 - 1)/x^2)*c + 2*arccosh(c*x)/x^3)*b*d^3 + 3*a*c^2*d^3/x - 1/3*a*d^3/x^3","A",0
28,0,0,0,0.000000," ","integrate(x^4*(a+b*arccosh(c*x))/(-c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{72} \, {\left(4 \, c^{4} {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{8} d} - \frac{3 \, \log\left(c x + 1\right)}{c^{9} d} + \frac{3 \, \log\left(c x - 1\right)}{c^{9} d}\right)} + 36 \, c^{2} {\left(\frac{2 \, x}{c^{6} d} - \frac{\log\left(c x + 1\right)}{c^{7} d} + \frac{\log\left(c x - 1\right)}{c^{7} d}\right)} + 648 \, c \int \frac{x \log\left(c x - 1\right)}{12 \, {\left(c^{6} d x^{2} - c^{4} d\right)}}\,{d x} - \frac{3 \, {\left(4 \, {\left(2 \, c^{3} x^{3} + 6 \, c x - 3 \, \log\left(c x + 1\right) + 3 \, \log\left(c x - 1\right)\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 3 \, \log\left(c x + 1\right)^{2} + 6 \, \log\left(c x + 1\right) \log\left(c x - 1\right)\right)}}{c^{5} d} + 72 \, \int -\frac{2 \, c^{3} x^{3} + 6 \, c x - 3 \, \log\left(c x + 1\right) + 3 \, \log\left(c x - 1\right)}{6 \, {\left(c^{7} d x^{3} - c^{5} d x + {\left(c^{6} d x^{2} - c^{4} d\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x} - 216 \, \int \frac{\log\left(c x - 1\right)}{12 \, {\left(c^{6} d x^{2} - c^{4} d\right)}}\,{d x}\right)} b - \frac{1}{6} \, a {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4} d} - \frac{3 \, \log\left(c x + 1\right)}{c^{5} d} + \frac{3 \, \log\left(c x - 1\right)}{c^{5} d}\right)}"," ",0,"1/72*(4*c^4*(2*(c^2*x^3 + 3*x)/(c^8*d) - 3*log(c*x + 1)/(c^9*d) + 3*log(c*x - 1)/(c^9*d)) + 36*c^2*(2*x/(c^6*d) - log(c*x + 1)/(c^7*d) + log(c*x - 1)/(c^7*d)) + 648*c*integrate(1/12*x*log(c*x - 1)/(c^6*d*x^2 - c^4*d), x) - 3*(4*(2*c^3*x^3 + 6*c*x - 3*log(c*x + 1) + 3*log(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 3*log(c*x + 1)^2 + 6*log(c*x + 1)*log(c*x - 1))/(c^5*d) + 72*integrate(-1/6*(2*c^3*x^3 + 6*c*x - 3*log(c*x + 1) + 3*log(c*x - 1))/(c^7*d*x^3 - c^5*d*x + (c^6*d*x^2 - c^4*d)*sqrt(c*x + 1)*sqrt(c*x - 1)), x) - 216*integrate(1/12*log(c*x - 1)/(c^6*d*x^2 - c^4*d), x))*b - 1/6*a*(2*(c^2*x^3 + 3*x)/(c^4*d) - 3*log(c*x + 1)/(c^5*d) + 3*log(c*x - 1)/(c^5*d))","F",0
29,0,0,0,0.000000," ","integrate(x^3*(a+b*arccosh(c*x))/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{x^{2}}{c^{2} d} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4} d}\right)} + \frac{1}{8} \, b {\left(\frac{2 \, c^{2} x^{2} - 4 \, {\left(c^{2} x^{2} + \log\left(c x + 1\right) + \log\left(c x - 1\right)\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 2 \, {\left(\log\left(c x - 1\right) + 1\right)} \log\left(c x + 1\right) + \log\left(c x + 1\right)^{2} + \log\left(c x - 1\right)^{2} + 2 \, \log\left(c x - 1\right)}{c^{4} d} - 8 \, \int \frac{c^{2} x^{2} + \log\left(c x + 1\right) + \log\left(c x - 1\right)}{2 \, {\left(c^{6} d x^{3} - c^{4} d x + {\left(c^{5} d x^{2} - c^{3} d\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)}\right)}}\,{d x}\right)}"," ",0,"-1/2*a*(x^2/(c^2*d) + log(c^2*x^2 - 1)/(c^4*d)) + 1/8*b*((2*c^2*x^2 - 4*(c^2*x^2 + log(c*x + 1) + log(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 2*(log(c*x - 1) + 1)*log(c*x + 1) + log(c*x + 1)^2 + log(c*x - 1)^2 + 2*log(c*x - 1))/(c^4*d) - 8*integrate(1/2*(c^2*x^2 + log(c*x + 1) + log(c*x - 1))/(c^6*d*x^3 - c^4*d*x + (c^5*d*x^2 - c^3*d)*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1))), x))","F",0
30,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))/(-c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(4 \, c^{2} {\left(\frac{2 \, x}{c^{4} d} - \frac{\log\left(c x + 1\right)}{c^{5} d} + \frac{\log\left(c x - 1\right)}{c^{5} d}\right)} + 24 \, c \int \frac{x \log\left(c x - 1\right)}{4 \, {\left(c^{4} d x^{2} - c^{2} d\right)}}\,{d x} - \frac{4 \, {\left(2 \, c x - \log\left(c x + 1\right) + \log\left(c x - 1\right)\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + \log\left(c x + 1\right)^{2} + 2 \, \log\left(c x + 1\right) \log\left(c x - 1\right)}{c^{3} d} + 8 \, \int -\frac{2 \, c x - \log\left(c x + 1\right) + \log\left(c x - 1\right)}{2 \, {\left(c^{5} d x^{3} - c^{3} d x + {\left(c^{4} d x^{2} - c^{2} d\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x} - 8 \, \int \frac{\log\left(c x - 1\right)}{4 \, {\left(c^{4} d x^{2} - c^{2} d\right)}}\,{d x}\right)} b - \frac{1}{2} \, a {\left(\frac{2 \, x}{c^{2} d} - \frac{\log\left(c x + 1\right)}{c^{3} d} + \frac{\log\left(c x - 1\right)}{c^{3} d}\right)}"," ",0,"1/8*(4*c^2*(2*x/(c^4*d) - log(c*x + 1)/(c^5*d) + log(c*x - 1)/(c^5*d)) + 24*c*integrate(1/4*x*log(c*x - 1)/(c^4*d*x^2 - c^2*d), x) - (4*(2*c*x - log(c*x + 1) + log(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + log(c*x + 1)^2 + 2*log(c*x + 1)*log(c*x - 1))/(c^3*d) + 8*integrate(-1/2*(2*c*x - log(c*x + 1) + log(c*x - 1))/(c^5*d*x^3 - c^3*d*x + (c^4*d*x^2 - c^2*d)*sqrt(c*x + 1)*sqrt(c*x - 1)), x) - 8*integrate(1/4*log(c*x - 1)/(c^4*d*x^2 - c^2*d), x))*b - 1/2*a*(2*x/(c^2*d) - log(c*x + 1)/(c^3*d) + log(c*x - 1)/(c^3*d))","F",0
31,0,0,0,0.000000," ","integrate(x*(a+b*arccosh(c*x))/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{8} \, b {\left(\frac{4 \, {\left(\log\left(c x + 1\right) + \log\left(c x - 1\right)\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) - \log\left(c x + 1\right)^{2} - 2 \, \log\left(c x + 1\right) \log\left(c x - 1\right) - \log\left(c x - 1\right)^{2}}{c^{2} d} + 8 \, \int \frac{\log\left(c x + 1\right) + \log\left(c x - 1\right)}{2 \, {\left(c^{4} d x^{3} - c^{2} d x + {\left(c^{3} d x^{2} - c d\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)}\right)}}\,{d x}\right)} - \frac{a \log\left(c^{2} d x^{2} - d\right)}{2 \, c^{2} d}"," ",0,"-1/8*b*((4*(log(c*x + 1) + log(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) - log(c*x + 1)^2 - 2*log(c*x + 1)*log(c*x - 1) - log(c*x - 1)^2)/(c^2*d) + 8*integrate(1/2*(log(c*x + 1) + log(c*x - 1))/(c^4*d*x^3 - c^2*d*x + (c^3*d*x^2 - c*d)*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1))), x)) - 1/2*a*log(c^2*d*x^2 - d)/(c^2*d)","F",0
32,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(-c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{8} \, b {\left(\frac{4 \, {\left(\log\left(c x + 1\right) - \log\left(c x - 1\right)\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) - \log\left(c x + 1\right)^{2} - 2 \, \log\left(c x + 1\right) \log\left(c x - 1\right)}{c d} + 8 \, \int \frac{{\left(3 \, c x - 1\right)} \log\left(c x - 1\right)}{4 \, {\left(c^{2} d x^{2} - d\right)}}\,{d x} + 8 \, \int \frac{\log\left(c x + 1\right) - \log\left(c x - 1\right)}{2 \, {\left(c^{3} d x^{3} - c d x + {\left(c^{2} d x^{2} - d\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x}\right)} + \frac{1}{2} \, a {\left(\frac{\log\left(c x + 1\right)}{c d} - \frac{\log\left(c x - 1\right)}{c d}\right)}"," ",0,"1/8*b*((4*(log(c*x + 1) - log(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) - log(c*x + 1)^2 - 2*log(c*x + 1)*log(c*x - 1))/(c*d) + 8*integrate(1/4*(3*c*x - 1)*log(c*x - 1)/(c^2*d*x^2 - d), x) + 8*integrate(1/2*(log(c*x + 1) - log(c*x - 1))/(c^3*d*x^3 - c*d*x + (c^2*d*x^2 - d)*sqrt(c*x + 1)*sqrt(c*x - 1)), x)) + 1/2*a*(log(c*x + 1)/(c*d) - log(c*x - 1)/(c*d))","F",0
33,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\log\left(c x + 1\right)}{d} + \frac{\log\left(c x - 1\right)}{d} - \frac{2 \, \log\left(x\right)}{d}\right)} - b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{2} d x^{3} - d x}\,{d x}"," ",0,"-1/2*a*(log(c*x + 1)/d + log(c*x - 1)/d - 2*log(x)/d) - b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*d*x^3 - d*x), x)","F",0
34,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^2/(-c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(24 \, c^{3} \int \frac{x \log\left(c x - 1\right)}{4 \, {\left(c^{2} d x^{2} - d\right)}}\,{d x} - 4 \, c^{2} {\left(\frac{\log\left(c x + 1\right)}{c d} - \frac{\log\left(c x - 1\right)}{c d}\right)} - 8 \, c^{2} \int \frac{\log\left(c x - 1\right)}{4 \, {\left(c^{2} d x^{2} - d\right)}}\,{d x} - \frac{c x \log\left(c x + 1\right)^{2} + 2 \, c x \log\left(c x + 1\right) \log\left(c x - 1\right) - 4 \, {\left(c x \log\left(c x + 1\right) - c x \log\left(c x - 1\right) - 2\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{d x} + 8 \, \int \frac{c^{2} x \log\left(c x + 1\right) - c^{2} x \log\left(c x - 1\right) - 2 \, c}{2 \, {\left(c^{3} d x^{4} - c d x^{2} + {\left(c^{2} d x^{3} - d x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x}\right)} b + \frac{1}{2} \, a {\left(\frac{c \log\left(c x + 1\right)}{d} - \frac{c \log\left(c x - 1\right)}{d} - \frac{2}{d x}\right)}"," ",0,"1/8*(24*c^3*integrate(1/4*x*log(c*x - 1)/(c^2*d*x^2 - d), x) - 4*c^2*(log(c*x + 1)/(c*d) - log(c*x - 1)/(c*d)) - 8*c^2*integrate(1/4*log(c*x - 1)/(c^2*d*x^2 - d), x) - (c*x*log(c*x + 1)^2 + 2*c*x*log(c*x + 1)*log(c*x - 1) - 4*(c*x*log(c*x + 1) - c*x*log(c*x - 1) - 2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)))/(d*x) + 8*integrate(1/2*(c^2*x*log(c*x + 1) - c^2*x*log(c*x - 1) - 2*c)/(c^3*d*x^4 - c*d*x^2 + (c^2*d*x^3 - d*x)*sqrt(c*x + 1)*sqrt(c*x - 1)), x))*b + 1/2*a*(c*log(c*x + 1)/d - c*log(c*x - 1)/d - 2/(d*x))","F",0
35,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^3/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{c^{2} \log\left(c x + 1\right)}{d} + \frac{c^{2} \log\left(c x - 1\right)}{d} - \frac{2 \, c^{2} \log\left(x\right)}{d} + \frac{1}{d x^{2}}\right)} a - b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{2} d x^{5} - d x^{3}}\,{d x}"," ",0,"-1/2*(c^2*log(c*x + 1)/d + c^2*log(c*x - 1)/d - 2*c^2*log(x)/d + 1/(d*x^2))*a - b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*d*x^5 - d*x^3), x)","F",0
36,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^4/(-c^2*d*x^2+d),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{3 \, c^{3} \log\left(c x + 1\right)}{d} - \frac{3 \, c^{3} \log\left(c x - 1\right)}{d} - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{d x^{3}}\right)} a + \frac{1}{24} \, {\left(216 \, c^{5} \int \frac{x^{3} \log\left(c x - 1\right)}{12 \, {\left(c^{2} d x^{4} - d x^{2}\right)}}\,{d x} - 12 \, c^{4} {\left(\frac{\log\left(c x + 1\right)}{c d} - \frac{\log\left(c x - 1\right)}{c d}\right)} - 72 \, c^{4} \int \frac{x^{2} \log\left(c x - 1\right)}{12 \, {\left(c^{2} d x^{4} - d x^{2}\right)}}\,{d x} - 4 \, c^{2} {\left(\frac{c \log\left(c x + 1\right)}{d} - \frac{c \log\left(c x - 1\right)}{d} - \frac{2}{d x}\right)} - \frac{3 \, c^{3} x^{3} \log\left(c x + 1\right)^{2} + 6 \, c^{3} x^{3} \log\left(c x + 1\right) \log\left(c x - 1\right) - 4 \, {\left(3 \, c^{3} x^{3} \log\left(c x + 1\right) - 3 \, c^{3} x^{3} \log\left(c x - 1\right) - 6 \, c^{2} x^{2} - 2\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{d x^{3}} + 24 \, \int \frac{3 \, c^{4} x^{3} \log\left(c x + 1\right) - 3 \, c^{4} x^{3} \log\left(c x - 1\right) - 6 \, c^{3} x^{2} - 2 \, c}{6 \, {\left(c^{3} d x^{6} - c d x^{4} + {\left(c^{2} d x^{5} - d x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x}\right)} b"," ",0,"1/6*(3*c^3*log(c*x + 1)/d - 3*c^3*log(c*x - 1)/d - 2*(3*c^2*x^2 + 1)/(d*x^3))*a + 1/24*(216*c^5*integrate(1/12*x^3*log(c*x - 1)/(c^2*d*x^4 - d*x^2), x) - 12*c^4*(log(c*x + 1)/(c*d) - log(c*x - 1)/(c*d)) - 72*c^4*integrate(1/12*x^2*log(c*x - 1)/(c^2*d*x^4 - d*x^2), x) - 4*c^2*(c*log(c*x + 1)/d - c*log(c*x - 1)/d - 2/(d*x)) - (3*c^3*x^3*log(c*x + 1)^2 + 6*c^3*x^3*log(c*x + 1)*log(c*x - 1) - 4*(3*c^3*x^3*log(c*x + 1) - 3*c^3*x^3*log(c*x - 1) - 6*c^2*x^2 - 2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)))/(d*x^3) + 24*integrate(1/6*(3*c^4*x^3*log(c*x + 1) - 3*c^4*x^3*log(c*x - 1) - 6*c^3*x^2 - 2*c)/(c^3*d*x^6 - c*d*x^4 + (c^2*d*x^5 - d*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1)), x))*b","F",0
37,0,0,0,0.000000," ","integrate(x^4*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{64} \, {\left(16 \, c^{4} {\left(\frac{2 \, x}{c^{10} d^{2} x^{2} - c^{8} d^{2}} - \frac{4 \, x}{c^{8} d^{2}} + \frac{3 \, \log\left(c x + 1\right)}{c^{9} d^{2}} - \frac{3 \, \log\left(c x - 1\right)}{c^{9} d^{2}}\right)} - 576 \, c^{3} \int \frac{x^{3} \log\left(c x - 1\right)}{8 \, {\left(c^{8} d^{2} x^{4} - 2 \, c^{6} d^{2} x^{2} + c^{4} d^{2}\right)}}\,{d x} - 24 \, c^{2} {\left(\frac{2 \, x}{c^{8} d^{2} x^{2} - c^{6} d^{2}} + \frac{\log\left(c x + 1\right)}{c^{7} d^{2}} - \frac{\log\left(c x - 1\right)}{c^{7} d^{2}}\right)} + 192 \, c^{2} \int \frac{x^{2} \log\left(c x - 1\right)}{8 \, {\left(c^{8} d^{2} x^{4} - 2 \, c^{6} d^{2} x^{2} + c^{4} d^{2}\right)}}\,{d x} - 9 \, {\left(c {\left(\frac{2}{c^{8} d^{2} x - c^{7} d^{2}} - \frac{\log\left(c x + 1\right)}{c^{7} d^{2}} + \frac{\log\left(c x - 1\right)}{c^{7} d^{2}}\right)} + \frac{4 \, \log\left(c x - 1\right)}{c^{8} d^{2} x^{2} - c^{6} d^{2}}\right)} c + \frac{4 \, {\left(3 \, {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right)^{2} + 6 \, {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) \log\left(c x - 1\right) + 4 \, {\left(4 \, c^{3} x^{3} - 6 \, c x - 3 \, {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) + 3 \, {\left(c^{2} x^{2} - 1\right)} \log\left(c x - 1\right)\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\right)}}{c^{7} d^{2} x^{2} - c^{5} d^{2}} - 64 \, \int -\frac{4 \, c^{3} x^{3} - 6 \, c x - 3 \, {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) + 3 \, {\left(c^{2} x^{2} - 1\right)} \log\left(c x - 1\right)}{4 \, {\left(c^{9} d^{2} x^{5} - 2 \, c^{7} d^{2} x^{3} + c^{5} d^{2} x + {\left(c^{8} d^{2} x^{4} - 2 \, c^{6} d^{2} x^{2} + c^{4} d^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x} - 192 \, \int \frac{\log\left(c x - 1\right)}{8 \, {\left(c^{8} d^{2} x^{4} - 2 \, c^{6} d^{2} x^{2} + c^{4} d^{2}\right)}}\,{d x}\right)} b - \frac{1}{4} \, a {\left(\frac{2 \, x}{c^{6} d^{2} x^{2} - c^{4} d^{2}} - \frac{4 \, x}{c^{4} d^{2}} + \frac{3 \, \log\left(c x + 1\right)}{c^{5} d^{2}} - \frac{3 \, \log\left(c x - 1\right)}{c^{5} d^{2}}\right)}"," ",0,"1/64*(16*c^4*(2*x/(c^10*d^2*x^2 - c^8*d^2) - 4*x/(c^8*d^2) + 3*log(c*x + 1)/(c^9*d^2) - 3*log(c*x - 1)/(c^9*d^2)) - 576*c^3*integrate(1/8*x^3*log(c*x - 1)/(c^8*d^2*x^4 - 2*c^6*d^2*x^2 + c^4*d^2), x) - 24*c^2*(2*x/(c^8*d^2*x^2 - c^6*d^2) + log(c*x + 1)/(c^7*d^2) - log(c*x - 1)/(c^7*d^2)) + 192*c^2*integrate(1/8*x^2*log(c*x - 1)/(c^8*d^2*x^4 - 2*c^6*d^2*x^2 + c^4*d^2), x) - 9*(c*(2/(c^8*d^2*x - c^7*d^2) - log(c*x + 1)/(c^7*d^2) + log(c*x - 1)/(c^7*d^2)) + 4*log(c*x - 1)/(c^8*d^2*x^2 - c^6*d^2))*c + 4*(3*(c^2*x^2 - 1)*log(c*x + 1)^2 + 6*(c^2*x^2 - 1)*log(c*x + 1)*log(c*x - 1) + 4*(4*c^3*x^3 - 6*c*x - 3*(c^2*x^2 - 1)*log(c*x + 1) + 3*(c^2*x^2 - 1)*log(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)))/(c^7*d^2*x^2 - c^5*d^2) - 64*integrate(-1/4*(4*c^3*x^3 - 6*c*x - 3*(c^2*x^2 - 1)*log(c*x + 1) + 3*(c^2*x^2 - 1)*log(c*x - 1))/(c^9*d^2*x^5 - 2*c^7*d^2*x^3 + c^5*d^2*x + (c^8*d^2*x^4 - 2*c^6*d^2*x^2 + c^4*d^2)*sqrt(c*x + 1)*sqrt(c*x - 1)), x) - 192*integrate(1/8*log(c*x - 1)/(c^8*d^2*x^4 - 2*c^6*d^2*x^2 + c^4*d^2), x))*b - 1/4*a*(2*x/(c^6*d^2*x^2 - c^4*d^2) - 4*x/(c^4*d^2) + 3*log(c*x + 1)/(c^5*d^2) - 3*log(c*x - 1)/(c^5*d^2))","F",0
38,0,0,0,0.000000," ","integrate(x^3*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{8} \, b {\left(\frac{{\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right)^{2} + 2 \, {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) \log\left(c x - 1\right) + {\left(c^{2} x^{2} - 1\right)} \log\left(c x - 1\right)^{2} - 4 \, {\left({\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) + {\left(c^{2} x^{2} - 1\right)} \log\left(c x - 1\right) - 1\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 2}{c^{6} d^{2} x^{2} - c^{4} d^{2}} - 8 \, \int \frac{{\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) + {\left(c^{2} x^{2} - 1\right)} \log\left(c x - 1\right) - 1}{2 \, {\left(c^{8} d^{2} x^{5} - 2 \, c^{6} d^{2} x^{3} + c^{4} d^{2} x + {\left(c^{7} d^{2} x^{4} - 2 \, c^{5} d^{2} x^{2} + c^{3} d^{2}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)}\right)}}\,{d x}\right)} - \frac{1}{2} \, a {\left(\frac{1}{c^{6} d^{2} x^{2} - c^{4} d^{2}} - \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4} d^{2}}\right)}"," ",0,"-1/8*b*(((c^2*x^2 - 1)*log(c*x + 1)^2 + 2*(c^2*x^2 - 1)*log(c*x + 1)*log(c*x - 1) + (c^2*x^2 - 1)*log(c*x - 1)^2 - 4*((c^2*x^2 - 1)*log(c*x + 1) + (c^2*x^2 - 1)*log(c*x - 1) - 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 2)/(c^6*d^2*x^2 - c^4*d^2) - 8*integrate(1/2*((c^2*x^2 - 1)*log(c*x + 1) + (c^2*x^2 - 1)*log(c*x - 1) - 1)/(c^8*d^2*x^5 - 2*c^6*d^2*x^3 + c^4*d^2*x + (c^7*d^2*x^4 - 2*c^5*d^2*x^2 + c^3*d^2)*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1))), x)) - 1/2*a*(1/(c^6*d^2*x^2 - c^4*d^2) - log(c^2*x^2 - 1)/(c^4*d^2))","F",0
39,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{64} \, {\left(192 \, c^{3} \int \frac{x^{3} \log\left(c x - 1\right)}{8 \, {\left(c^{6} d^{2} x^{4} - 2 \, c^{4} d^{2} x^{2} + c^{2} d^{2}\right)}}\,{d x} + 8 \, c^{2} {\left(\frac{2 \, x}{c^{6} d^{2} x^{2} - c^{4} d^{2}} + \frac{\log\left(c x + 1\right)}{c^{5} d^{2}} - \frac{\log\left(c x - 1\right)}{c^{5} d^{2}}\right)} - 64 \, c^{2} \int \frac{x^{2} \log\left(c x - 1\right)}{8 \, {\left(c^{6} d^{2} x^{4} - 2 \, c^{4} d^{2} x^{2} + c^{2} d^{2}\right)}}\,{d x} + 3 \, {\left(c {\left(\frac{2}{c^{6} d^{2} x - c^{5} d^{2}} - \frac{\log\left(c x + 1\right)}{c^{5} d^{2}} + \frac{\log\left(c x - 1\right)}{c^{5} d^{2}}\right)} + \frac{4 \, \log\left(c x - 1\right)}{c^{6} d^{2} x^{2} - c^{4} d^{2}}\right)} c - \frac{4 \, {\left({\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right)^{2} + 2 \, {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) \log\left(c x - 1\right) - 4 \, {\left(2 \, c x + {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) - {\left(c^{2} x^{2} - 1\right)} \log\left(c x - 1\right)\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\right)}}{c^{5} d^{2} x^{2} - c^{3} d^{2}} + 64 \, \int \frac{2 \, c x + {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) - {\left(c^{2} x^{2} - 1\right)} \log\left(c x - 1\right)}{4 \, {\left(c^{7} d^{2} x^{5} - 2 \, c^{5} d^{2} x^{3} + c^{3} d^{2} x + {\left(c^{6} d^{2} x^{4} - 2 \, c^{4} d^{2} x^{2} + c^{2} d^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x} + 64 \, \int \frac{\log\left(c x - 1\right)}{8 \, {\left(c^{6} d^{2} x^{4} - 2 \, c^{4} d^{2} x^{2} + c^{2} d^{2}\right)}}\,{d x}\right)} b - \frac{1}{4} \, a {\left(\frac{2 \, x}{c^{4} d^{2} x^{2} - c^{2} d^{2}} + \frac{\log\left(c x + 1\right)}{c^{3} d^{2}} - \frac{\log\left(c x - 1\right)}{c^{3} d^{2}}\right)}"," ",0,"-1/64*(192*c^3*integrate(1/8*x^3*log(c*x - 1)/(c^6*d^2*x^4 - 2*c^4*d^2*x^2 + c^2*d^2), x) + 8*c^2*(2*x/(c^6*d^2*x^2 - c^4*d^2) + log(c*x + 1)/(c^5*d^2) - log(c*x - 1)/(c^5*d^2)) - 64*c^2*integrate(1/8*x^2*log(c*x - 1)/(c^6*d^2*x^4 - 2*c^4*d^2*x^2 + c^2*d^2), x) + 3*(c*(2/(c^6*d^2*x - c^5*d^2) - log(c*x + 1)/(c^5*d^2) + log(c*x - 1)/(c^5*d^2)) + 4*log(c*x - 1)/(c^6*d^2*x^2 - c^4*d^2))*c - 4*((c^2*x^2 - 1)*log(c*x + 1)^2 + 2*(c^2*x^2 - 1)*log(c*x + 1)*log(c*x - 1) - 4*(2*c*x + (c^2*x^2 - 1)*log(c*x + 1) - (c^2*x^2 - 1)*log(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)))/(c^5*d^2*x^2 - c^3*d^2) + 64*integrate(1/4*(2*c*x + (c^2*x^2 - 1)*log(c*x + 1) - (c^2*x^2 - 1)*log(c*x - 1))/(c^7*d^2*x^5 - 2*c^5*d^2*x^3 + c^3*d^2*x + (c^6*d^2*x^4 - 2*c^4*d^2*x^2 + c^2*d^2)*sqrt(c*x + 1)*sqrt(c*x - 1)), x) + 64*integrate(1/8*log(c*x - 1)/(c^6*d^2*x^4 - 2*c^4*d^2*x^2 + c^2*d^2), x))*b - 1/4*a*(2*x/(c^4*d^2*x^2 - c^2*d^2) + log(c*x + 1)/(c^3*d^2) - log(c*x - 1)/(c^3*d^2))","F",0
40,1,134,0,0.372314," ","integrate(x*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left({\left(\frac{\sqrt{c^{2} x^{2} - 1} c^{2} d^{2}}{c^{7} d^{4} x + c^{6} d^{4}} + \frac{\sqrt{c^{2} x^{2} - 1} c^{2} d^{2}}{c^{7} d^{4} x - c^{6} d^{4}}\right)} c^{2} + \frac{2 \, \operatorname{arcosh}\left(c x\right)}{c^{4} d^{2} x^{2} - c^{2} d^{2}}\right)} b - \frac{a}{2 \, {\left(c^{4} d^{2} x^{2} - c^{2} d^{2}\right)}}"," ",0,"-1/4*((sqrt(c^2*x^2 - 1)*c^2*d^2/(c^7*d^4*x + c^6*d^4) + sqrt(c^2*x^2 - 1)*c^2*d^2/(c^7*d^4*x - c^6*d^4))*c^2 + 2*arccosh(c*x)/(c^4*d^2*x^2 - c^2*d^2))*b - 1/2*a/(c^4*d^2*x^2 - c^2*d^2)","B",0
41,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{64} \, {\left(192 \, c^{3} \int \frac{x^{3} \log\left(c x - 1\right)}{8 \, {\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)}}\,{d x} - 8 \, c^{2} {\left(\frac{2 \, x}{c^{4} d^{2} x^{2} - c^{2} d^{2}} + \frac{\log\left(c x + 1\right)}{c^{3} d^{2}} - \frac{\log\left(c x - 1\right)}{c^{3} d^{2}}\right)} - 64 \, c^{2} \int \frac{x^{2} \log\left(c x - 1\right)}{8 \, {\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)}}\,{d x} + 3 \, {\left(c {\left(\frac{2}{c^{4} d^{2} x - c^{3} d^{2}} - \frac{\log\left(c x + 1\right)}{c^{3} d^{2}} + \frac{\log\left(c x - 1\right)}{c^{3} d^{2}}\right)} + \frac{4 \, \log\left(c x - 1\right)}{c^{4} d^{2} x^{2} - c^{2} d^{2}}\right)} c - \frac{4 \, {\left({\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right)^{2} + 2 \, {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) \log\left(c x - 1\right) + 4 \, {\left(2 \, c x - {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) + {\left(c^{2} x^{2} - 1\right)} \log\left(c x - 1\right)\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\right)}}{c^{3} d^{2} x^{2} - c d^{2}} + 64 \, \int -\frac{2 \, c x - {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) + {\left(c^{2} x^{2} - 1\right)} \log\left(c x - 1\right)}{4 \, {\left(c^{5} d^{2} x^{5} - 2 \, c^{3} d^{2} x^{3} + c d^{2} x + {\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x} + 64 \, \int \frac{\log\left(c x - 1\right)}{8 \, {\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)}}\,{d x}\right)} b - \frac{1}{4} \, a {\left(\frac{2 \, x}{c^{2} d^{2} x^{2} - d^{2}} - \frac{\log\left(c x + 1\right)}{c d^{2}} + \frac{\log\left(c x - 1\right)}{c d^{2}}\right)}"," ",0,"1/64*(192*c^3*integrate(1/8*x^3*log(c*x - 1)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x) - 8*c^2*(2*x/(c^4*d^2*x^2 - c^2*d^2) + log(c*x + 1)/(c^3*d^2) - log(c*x - 1)/(c^3*d^2)) - 64*c^2*integrate(1/8*x^2*log(c*x - 1)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x) + 3*(c*(2/(c^4*d^2*x - c^3*d^2) - log(c*x + 1)/(c^3*d^2) + log(c*x - 1)/(c^3*d^2)) + 4*log(c*x - 1)/(c^4*d^2*x^2 - c^2*d^2))*c - 4*((c^2*x^2 - 1)*log(c*x + 1)^2 + 2*(c^2*x^2 - 1)*log(c*x + 1)*log(c*x - 1) + 4*(2*c*x - (c^2*x^2 - 1)*log(c*x + 1) + (c^2*x^2 - 1)*log(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)))/(c^3*d^2*x^2 - c*d^2) + 64*integrate(-1/4*(2*c*x - (c^2*x^2 - 1)*log(c*x + 1) + (c^2*x^2 - 1)*log(c*x - 1))/(c^5*d^2*x^5 - 2*c^3*d^2*x^3 + c*d^2*x + (c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2)*sqrt(c*x + 1)*sqrt(c*x - 1)), x) + 64*integrate(1/8*log(c*x - 1)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x))*b - 1/4*a*(2*x/(c^2*d^2*x^2 - d^2) - log(c*x + 1)/(c*d^2) + log(c*x - 1)/(c*d^2))","F",0
42,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{1}{c^{2} d^{2} x^{2} - d^{2}} + \frac{\log\left(c x + 1\right)}{d^{2}} + \frac{\log\left(c x - 1\right)}{d^{2}} - \frac{2 \, \log\left(x\right)}{d^{2}}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{4} d^{2} x^{5} - 2 \, c^{2} d^{2} x^{3} + d^{2} x}\,{d x}"," ",0,"-1/2*a*(1/(c^2*d^2*x^2 - d^2) + log(c*x + 1)/d^2 + log(c*x - 1)/d^2 - 2*log(x)/d^2) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c^4*d^2*x^5 - 2*c^2*d^2*x^3 + d^2*x), x)","F",0
43,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^2/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{64} \, {\left(576 \, c^{5} \int \frac{x^{3} \log\left(c x - 1\right)}{8 \, {\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)}}\,{d x} - 24 \, c^{4} {\left(\frac{2 \, x}{c^{4} d^{2} x^{2} - c^{2} d^{2}} + \frac{\log\left(c x + 1\right)}{c^{3} d^{2}} - \frac{\log\left(c x - 1\right)}{c^{3} d^{2}}\right)} - 192 \, c^{4} \int \frac{x^{2} \log\left(c x - 1\right)}{8 \, {\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)}}\,{d x} + 9 \, {\left(c {\left(\frac{2}{c^{4} d^{2} x - c^{3} d^{2}} - \frac{\log\left(c x + 1\right)}{c^{3} d^{2}} + \frac{\log\left(c x - 1\right)}{c^{3} d^{2}}\right)} + \frac{4 \, \log\left(c x - 1\right)}{c^{4} d^{2} x^{2} - c^{2} d^{2}}\right)} c^{3} + 16 \, c^{2} {\left(\frac{2 \, x}{c^{2} d^{2} x^{2} - d^{2}} - \frac{\log\left(c x + 1\right)}{c d^{2}} + \frac{\log\left(c x - 1\right)}{c d^{2}}\right)} + 192 \, c^{2} \int \frac{\log\left(c x - 1\right)}{8 \, {\left(c^{4} d^{2} x^{4} - 2 \, c^{2} d^{2} x^{2} + d^{2}\right)}}\,{d x} - \frac{4 \, {\left(3 \, {\left(c^{3} x^{3} - c x\right)} \log\left(c x + 1\right)^{2} + 6 \, {\left(c^{3} x^{3} - c x\right)} \log\left(c x + 1\right) \log\left(c x - 1\right) + 4 \, {\left(6 \, c^{2} x^{2} - 3 \, {\left(c^{3} x^{3} - c x\right)} \log\left(c x + 1\right) + 3 \, {\left(c^{3} x^{3} - c x\right)} \log\left(c x - 1\right) - 4\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\right)}}{c^{2} d^{2} x^{3} - d^{2} x} + 64 \, \int -\frac{6 \, c^{3} x^{2} - 3 \, {\left(c^{4} x^{3} - c^{2} x\right)} \log\left(c x + 1\right) + 3 \, {\left(c^{4} x^{3} - c^{2} x\right)} \log\left(c x - 1\right) - 4 \, c}{4 \, {\left(c^{5} d^{2} x^{6} - 2 \, c^{3} d^{2} x^{4} + c d^{2} x^{2} + {\left(c^{4} d^{2} x^{5} - 2 \, c^{2} d^{2} x^{3} + d^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x}\right)} b - \frac{1}{4} \, a {\left(\frac{2 \, {\left(3 \, c^{2} x^{2} - 2\right)}}{c^{2} d^{2} x^{3} - d^{2} x} - \frac{3 \, c \log\left(c x + 1\right)}{d^{2}} + \frac{3 \, c \log\left(c x - 1\right)}{d^{2}}\right)}"," ",0,"1/64*(576*c^5*integrate(1/8*x^3*log(c*x - 1)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x) - 24*c^4*(2*x/(c^4*d^2*x^2 - c^2*d^2) + log(c*x + 1)/(c^3*d^2) - log(c*x - 1)/(c^3*d^2)) - 192*c^4*integrate(1/8*x^2*log(c*x - 1)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x) + 9*(c*(2/(c^4*d^2*x - c^3*d^2) - log(c*x + 1)/(c^3*d^2) + log(c*x - 1)/(c^3*d^2)) + 4*log(c*x - 1)/(c^4*d^2*x^2 - c^2*d^2))*c^3 + 16*c^2*(2*x/(c^2*d^2*x^2 - d^2) - log(c*x + 1)/(c*d^2) + log(c*x - 1)/(c*d^2)) + 192*c^2*integrate(1/8*log(c*x - 1)/(c^4*d^2*x^4 - 2*c^2*d^2*x^2 + d^2), x) - 4*(3*(c^3*x^3 - c*x)*log(c*x + 1)^2 + 6*(c^3*x^3 - c*x)*log(c*x + 1)*log(c*x - 1) + 4*(6*c^2*x^2 - 3*(c^3*x^3 - c*x)*log(c*x + 1) + 3*(c^3*x^3 - c*x)*log(c*x - 1) - 4)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)))/(c^2*d^2*x^3 - d^2*x) + 64*integrate(-1/4*(6*c^3*x^2 - 3*(c^4*x^3 - c^2*x)*log(c*x + 1) + 3*(c^4*x^3 - c^2*x)*log(c*x - 1) - 4*c)/(c^5*d^2*x^6 - 2*c^3*d^2*x^4 + c*d^2*x^2 + (c^4*d^2*x^5 - 2*c^2*d^2*x^3 + d^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1)), x))*b - 1/4*a*(2*(3*c^2*x^2 - 2)/(c^2*d^2*x^3 - d^2*x) - 3*c*log(c*x + 1)/d^2 + 3*c*log(c*x - 1)/d^2)","F",0
44,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^3/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, c^{2} \log\left(c x + 1\right)}{d^{2}} + \frac{2 \, c^{2} \log\left(c x - 1\right)}{d^{2}} - \frac{4 \, c^{2} \log\left(x\right)}{d^{2}} + \frac{2 \, c^{2} x^{2} - 1}{c^{2} d^{2} x^{4} - d^{2} x^{2}}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{4} d^{2} x^{7} - 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}}\,{d x}"," ",0,"-1/2*a*(2*c^2*log(c*x + 1)/d^2 + 2*c^2*log(c*x - 1)/d^2 - 4*c^2*log(x)/d^2 + (2*c^2*x^2 - 1)/(c^2*d^2*x^4 - d^2*x^2)) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c^4*d^2*x^7 - 2*c^2*d^2*x^5 + d^2*x^3), x)","F",0
45,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^4/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{12} \, {\left(\frac{15 \, c^{3} \log\left(c x + 1\right)}{d^{2}} - \frac{15 \, c^{3} \log\left(c x - 1\right)}{d^{2}} - \frac{2 \, {\left(15 \, c^{4} x^{4} - 10 \, c^{2} x^{2} - 2\right)}}{c^{2} d^{2} x^{5} - d^{2} x^{3}}\right)} a + \frac{1}{192} \, {\left(8640 \, c^{7} \int \frac{x^{5} \log\left(c x - 1\right)}{24 \, {\left(c^{4} d^{2} x^{6} - 2 \, c^{2} d^{2} x^{4} + d^{2} x^{2}\right)}}\,{d x} - 120 \, c^{6} {\left(\frac{2 \, x}{c^{4} d^{2} x^{2} - c^{2} d^{2}} + \frac{\log\left(c x + 1\right)}{c^{3} d^{2}} - \frac{\log\left(c x - 1\right)}{c^{3} d^{2}}\right)} - 2880 \, c^{6} \int \frac{x^{4} \log\left(c x - 1\right)}{24 \, {\left(c^{4} d^{2} x^{6} - 2 \, c^{2} d^{2} x^{4} + d^{2} x^{2}\right)}}\,{d x} + 45 \, {\left(c {\left(\frac{2}{c^{4} d^{2} x - c^{3} d^{2}} - \frac{\log\left(c x + 1\right)}{c^{3} d^{2}} + \frac{\log\left(c x - 1\right)}{c^{3} d^{2}}\right)} + \frac{4 \, \log\left(c x - 1\right)}{c^{4} d^{2} x^{2} - c^{2} d^{2}}\right)} c^{5} + 80 \, c^{4} {\left(\frac{2 \, x}{c^{2} d^{2} x^{2} - d^{2}} - \frac{\log\left(c x + 1\right)}{c d^{2}} + \frac{\log\left(c x - 1\right)}{c d^{2}}\right)} + 2880 \, c^{4} \int \frac{x^{2} \log\left(c x - 1\right)}{24 \, {\left(c^{4} d^{2} x^{6} - 2 \, c^{2} d^{2} x^{4} + d^{2} x^{2}\right)}}\,{d x} + 16 \, c^{2} {\left(\frac{2 \, {\left(3 \, c^{2} x^{2} - 2\right)}}{c^{2} d^{2} x^{3} - d^{2} x} - \frac{3 \, c \log\left(c x + 1\right)}{d^{2}} + \frac{3 \, c \log\left(c x - 1\right)}{d^{2}}\right)} - \frac{4 \, {\left(15 \, {\left(c^{5} x^{5} - c^{3} x^{3}\right)} \log\left(c x + 1\right)^{2} + 30 \, {\left(c^{5} x^{5} - c^{3} x^{3}\right)} \log\left(c x + 1\right) \log\left(c x - 1\right) + 4 \, {\left(30 \, c^{4} x^{4} - 20 \, c^{2} x^{2} - 15 \, {\left(c^{5} x^{5} - c^{3} x^{3}\right)} \log\left(c x + 1\right) + 15 \, {\left(c^{5} x^{5} - c^{3} x^{3}\right)} \log\left(c x - 1\right) - 4\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\right)}}{c^{2} d^{2} x^{5} - d^{2} x^{3}} + 192 \, \int -\frac{30 \, c^{5} x^{4} - 20 \, c^{3} x^{2} - 15 \, {\left(c^{6} x^{5} - c^{4} x^{3}\right)} \log\left(c x + 1\right) + 15 \, {\left(c^{6} x^{5} - c^{4} x^{3}\right)} \log\left(c x - 1\right) - 4 \, c}{12 \, {\left(c^{5} d^{2} x^{8} - 2 \, c^{3} d^{2} x^{6} + c d^{2} x^{4} + {\left(c^{4} d^{2} x^{7} - 2 \, c^{2} d^{2} x^{5} + d^{2} x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x}\right)} b"," ",0,"1/12*(15*c^3*log(c*x + 1)/d^2 - 15*c^3*log(c*x - 1)/d^2 - 2*(15*c^4*x^4 - 10*c^2*x^2 - 2)/(c^2*d^2*x^5 - d^2*x^3))*a + 1/192*(8640*c^7*integrate(1/24*x^5*log(c*x - 1)/(c^4*d^2*x^6 - 2*c^2*d^2*x^4 + d^2*x^2), x) - 120*c^6*(2*x/(c^4*d^2*x^2 - c^2*d^2) + log(c*x + 1)/(c^3*d^2) - log(c*x - 1)/(c^3*d^2)) - 2880*c^6*integrate(1/24*x^4*log(c*x - 1)/(c^4*d^2*x^6 - 2*c^2*d^2*x^4 + d^2*x^2), x) + 45*(c*(2/(c^4*d^2*x - c^3*d^2) - log(c*x + 1)/(c^3*d^2) + log(c*x - 1)/(c^3*d^2)) + 4*log(c*x - 1)/(c^4*d^2*x^2 - c^2*d^2))*c^5 + 80*c^4*(2*x/(c^2*d^2*x^2 - d^2) - log(c*x + 1)/(c*d^2) + log(c*x - 1)/(c*d^2)) + 2880*c^4*integrate(1/24*x^2*log(c*x - 1)/(c^4*d^2*x^6 - 2*c^2*d^2*x^4 + d^2*x^2), x) + 16*c^2*(2*(3*c^2*x^2 - 2)/(c^2*d^2*x^3 - d^2*x) - 3*c*log(c*x + 1)/d^2 + 3*c*log(c*x - 1)/d^2) - 4*(15*(c^5*x^5 - c^3*x^3)*log(c*x + 1)^2 + 30*(c^5*x^5 - c^3*x^3)*log(c*x + 1)*log(c*x - 1) + 4*(30*c^4*x^4 - 20*c^2*x^2 - 15*(c^5*x^5 - c^3*x^3)*log(c*x + 1) + 15*(c^5*x^5 - c^3*x^3)*log(c*x - 1) - 4)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)))/(c^2*d^2*x^5 - d^2*x^3) + 192*integrate(-1/12*(30*c^5*x^4 - 20*c^3*x^2 - 15*(c^6*x^5 - c^4*x^3)*log(c*x + 1) + 15*(c^6*x^5 - c^4*x^3)*log(c*x - 1) - 4*c)/(c^5*d^2*x^8 - 2*c^3*d^2*x^6 + c*d^2*x^4 + (c^4*d^2*x^7 - 2*c^2*d^2*x^5 + d^2*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1)), x))*b","F",0
46,0,0,0,0.000000," ","integrate(x^4*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{2048} \, {\left(18432 \, c^{5} \int \frac{x^{5} \log\left(c x - 1\right)}{32 \, {\left(c^{10} d^{3} x^{6} - 3 \, c^{8} d^{3} x^{4} + 3 \, c^{6} d^{3} x^{2} - c^{4} d^{3}\right)}}\,{d x} + 80 \, c^{4} {\left(\frac{2 \, {\left(5 \, c^{2} x^{3} - 3 \, x\right)}}{c^{12} d^{3} x^{4} - 2 \, c^{10} d^{3} x^{2} + c^{8} d^{3}} + \frac{3 \, \log\left(c x + 1\right)}{c^{9} d^{3}} - \frac{3 \, \log\left(c x - 1\right)}{c^{9} d^{3}}\right)} - 6144 \, c^{4} \int \frac{x^{4} \log\left(c x - 1\right)}{32 \, {\left(c^{10} d^{3} x^{6} - 3 \, c^{8} d^{3} x^{4} + 3 \, c^{6} d^{3} x^{2} - c^{4} d^{3}\right)}}\,{d x} + 18 \, {\left(c {\left(\frac{2 \, {\left(5 \, c^{2} x^{2} + 3 \, c x - 6\right)}}{c^{12} d^{3} x^{3} - c^{11} d^{3} x^{2} - c^{10} d^{3} x + c^{9} d^{3}} - \frac{5 \, \log\left(c x + 1\right)}{c^{9} d^{3}} + \frac{5 \, \log\left(c x - 1\right)}{c^{9} d^{3}}\right)} + \frac{16 \, {\left(2 \, c^{2} x^{2} - 1\right)} \log\left(c x - 1\right)}{c^{12} d^{3} x^{4} - 2 \, c^{10} d^{3} x^{2} + c^{8} d^{3}}\right)} c^{3} - 48 \, c^{2} {\left(\frac{2 \, {\left(c^{2} x^{3} + x\right)}}{c^{10} d^{3} x^{4} - 2 \, c^{8} d^{3} x^{2} + c^{6} d^{3}} - \frac{\log\left(c x + 1\right)}{c^{7} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{7} d^{3}}\right)} + 12288 \, c^{2} \int \frac{x^{2} \log\left(c x - 1\right)}{32 \, {\left(c^{10} d^{3} x^{6} - 3 \, c^{8} d^{3} x^{4} + 3 \, c^{6} d^{3} x^{2} - c^{4} d^{3}\right)}}\,{d x} + 9 \, {\left(c {\left(\frac{2 \, {\left(3 \, c^{2} x^{2} - 3 \, c x - 2\right)}}{c^{10} d^{3} x^{3} - c^{9} d^{3} x^{2} - c^{8} d^{3} x + c^{7} d^{3}} - \frac{3 \, \log\left(c x + 1\right)}{c^{7} d^{3}} + \frac{3 \, \log\left(c x - 1\right)}{c^{7} d^{3}}\right)} - \frac{16 \, \log\left(c x - 1\right)}{c^{10} d^{3} x^{4} - 2 \, c^{8} d^{3} x^{2} + c^{6} d^{3}}\right)} c - \frac{32 \, {\left(3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x + 1\right)^{2} + 6 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x + 1\right) \log\left(c x - 1\right) - 4 \, {\left(10 \, c^{3} x^{3} - 6 \, c x + 3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x + 1\right) - 3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x - 1\right)\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\right)}}{c^{9} d^{3} x^{4} - 2 \, c^{7} d^{3} x^{2} + c^{5} d^{3}} + 2048 \, \int \frac{10 \, c^{3} x^{3} - 6 \, c x + 3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x + 1\right) - 3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x - 1\right)}{16 \, {\left(c^{11} d^{3} x^{7} - 3 \, c^{9} d^{3} x^{5} + 3 \, c^{7} d^{3} x^{3} - c^{5} d^{3} x + {\left(c^{10} d^{3} x^{6} - 3 \, c^{8} d^{3} x^{4} + 3 \, c^{6} d^{3} x^{2} - c^{4} d^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x} - 6144 \, \int \frac{\log\left(c x - 1\right)}{32 \, {\left(c^{10} d^{3} x^{6} - 3 \, c^{8} d^{3} x^{4} + 3 \, c^{6} d^{3} x^{2} - c^{4} d^{3}\right)}}\,{d x}\right)} b + \frac{1}{16} \, a {\left(\frac{2 \, {\left(5 \, c^{2} x^{3} - 3 \, x\right)}}{c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}} + \frac{3 \, \log\left(c x + 1\right)}{c^{5} d^{3}} - \frac{3 \, \log\left(c x - 1\right)}{c^{5} d^{3}}\right)}"," ",0,"1/2048*(18432*c^5*integrate(1/32*x^5*log(c*x - 1)/(c^10*d^3*x^6 - 3*c^8*d^3*x^4 + 3*c^6*d^3*x^2 - c^4*d^3), x) + 80*c^4*(2*(5*c^2*x^3 - 3*x)/(c^12*d^3*x^4 - 2*c^10*d^3*x^2 + c^8*d^3) + 3*log(c*x + 1)/(c^9*d^3) - 3*log(c*x - 1)/(c^9*d^3)) - 6144*c^4*integrate(1/32*x^4*log(c*x - 1)/(c^10*d^3*x^6 - 3*c^8*d^3*x^4 + 3*c^6*d^3*x^2 - c^4*d^3), x) + 18*(c*(2*(5*c^2*x^2 + 3*c*x - 6)/(c^12*d^3*x^3 - c^11*d^3*x^2 - c^10*d^3*x + c^9*d^3) - 5*log(c*x + 1)/(c^9*d^3) + 5*log(c*x - 1)/(c^9*d^3)) + 16*(2*c^2*x^2 - 1)*log(c*x - 1)/(c^12*d^3*x^4 - 2*c^10*d^3*x^2 + c^8*d^3))*c^3 - 48*c^2*(2*(c^2*x^3 + x)/(c^10*d^3*x^4 - 2*c^8*d^3*x^2 + c^6*d^3) - log(c*x + 1)/(c^7*d^3) + log(c*x - 1)/(c^7*d^3)) + 12288*c^2*integrate(1/32*x^2*log(c*x - 1)/(c^10*d^3*x^6 - 3*c^8*d^3*x^4 + 3*c^6*d^3*x^2 - c^4*d^3), x) + 9*(c*(2*(3*c^2*x^2 - 3*c*x - 2)/(c^10*d^3*x^3 - c^9*d^3*x^2 - c^8*d^3*x + c^7*d^3) - 3*log(c*x + 1)/(c^7*d^3) + 3*log(c*x - 1)/(c^7*d^3)) - 16*log(c*x - 1)/(c^10*d^3*x^4 - 2*c^8*d^3*x^2 + c^6*d^3))*c - 32*(3*(c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x + 1)^2 + 6*(c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x + 1)*log(c*x - 1) - 4*(10*c^3*x^3 - 6*c*x + 3*(c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x + 1) - 3*(c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)))/(c^9*d^3*x^4 - 2*c^7*d^3*x^2 + c^5*d^3) + 2048*integrate(1/16*(10*c^3*x^3 - 6*c*x + 3*(c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x + 1) - 3*(c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x - 1))/(c^11*d^3*x^7 - 3*c^9*d^3*x^5 + 3*c^7*d^3*x^3 - c^5*d^3*x + (c^10*d^3*x^6 - 3*c^8*d^3*x^4 + 3*c^6*d^3*x^2 - c^4*d^3)*sqrt(c*x + 1)*sqrt(c*x - 1)), x) - 6144*integrate(1/32*log(c*x - 1)/(c^10*d^3*x^6 - 3*c^8*d^3*x^4 + 3*c^6*d^3*x^2 - c^4*d^3), x))*b + 1/16*a*(2*(5*c^2*x^3 - 3*x)/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3) + 3*log(c*x + 1)/(c^5*d^3) - 3*log(c*x - 1)/(c^5*d^3))","F",0
47,0,0,0,0.000000," ","integrate(x^3*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{16} \, b {\left(\frac{4 \, c^{2} x^{2} + 4 \, {\left(2 \, c^{2} x^{2} - 1\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) - 3}{c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}} + 16 \, \int \frac{2 \, c^{2} x^{2} - 1}{4 \, {\left(c^{10} d^{3} x^{7} - 3 \, c^{8} d^{3} x^{5} + 3 \, c^{6} d^{3} x^{3} - c^{4} d^{3} x + {\left(c^{9} d^{3} x^{6} - 3 \, c^{7} d^{3} x^{4} + 3 \, c^{5} d^{3} x^{2} - c^{3} d^{3}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)}\right)}}\,{d x}\right)} + \frac{{\left(2 \, c^{2} x^{2} - 1\right)} a}{4 \, {\left(c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}\right)}}"," ",0,"1/16*b*((4*c^2*x^2 + 4*(2*c^2*x^2 - 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) - 3)/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3) + 16*integrate(1/4*(2*c^2*x^2 - 1)/(c^10*d^3*x^7 - 3*c^8*d^3*x^5 + 3*c^6*d^3*x^3 - c^4*d^3*x + (c^9*d^3*x^6 - 3*c^7*d^3*x^4 + 3*c^5*d^3*x^2 - c^3*d^3)*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1))), x)) + 1/4*(2*c^2*x^2 - 1)*a/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3)","F",0
48,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{2048} \, {\left(6144 \, c^{5} \int \frac{x^{5} \log\left(c x - 1\right)}{32 \, {\left(c^{8} d^{3} x^{6} - 3 \, c^{6} d^{3} x^{4} + 3 \, c^{4} d^{3} x^{2} - c^{2} d^{3}\right)}}\,{d x} - 16 \, c^{4} {\left(\frac{2 \, {\left(5 \, c^{2} x^{3} - 3 \, x\right)}}{c^{10} d^{3} x^{4} - 2 \, c^{8} d^{3} x^{2} + c^{6} d^{3}} + \frac{3 \, \log\left(c x + 1\right)}{c^{7} d^{3}} - \frac{3 \, \log\left(c x - 1\right)}{c^{7} d^{3}}\right)} - 2048 \, c^{4} \int \frac{x^{4} \log\left(c x - 1\right)}{32 \, {\left(c^{8} d^{3} x^{6} - 3 \, c^{6} d^{3} x^{4} + 3 \, c^{4} d^{3} x^{2} - c^{2} d^{3}\right)}}\,{d x} + 6 \, {\left(c {\left(\frac{2 \, {\left(5 \, c^{2} x^{2} + 3 \, c x - 6\right)}}{c^{10} d^{3} x^{3} - c^{9} d^{3} x^{2} - c^{8} d^{3} x + c^{7} d^{3}} - \frac{5 \, \log\left(c x + 1\right)}{c^{7} d^{3}} + \frac{5 \, \log\left(c x - 1\right)}{c^{7} d^{3}}\right)} + \frac{16 \, {\left(2 \, c^{2} x^{2} - 1\right)} \log\left(c x - 1\right)}{c^{10} d^{3} x^{4} - 2 \, c^{8} d^{3} x^{2} + c^{6} d^{3}}\right)} c^{3} - 16 \, c^{2} {\left(\frac{2 \, {\left(c^{2} x^{3} + x\right)}}{c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}} - \frac{\log\left(c x + 1\right)}{c^{5} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{5} d^{3}}\right)} + 4096 \, c^{2} \int \frac{x^{2} \log\left(c x - 1\right)}{32 \, {\left(c^{8} d^{3} x^{6} - 3 \, c^{6} d^{3} x^{4} + 3 \, c^{4} d^{3} x^{2} - c^{2} d^{3}\right)}}\,{d x} + 3 \, {\left(c {\left(\frac{2 \, {\left(3 \, c^{2} x^{2} - 3 \, c x - 2\right)}}{c^{8} d^{3} x^{3} - c^{7} d^{3} x^{2} - c^{6} d^{3} x + c^{5} d^{3}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5} d^{3}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5} d^{3}}\right)} - \frac{16 \, \log\left(c x - 1\right)}{c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}}\right)} c - \frac{32 \, {\left({\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x + 1\right)^{2} + 2 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x + 1\right) \log\left(c x - 1\right) + 4 \, {\left(2 \, c^{3} x^{3} + 2 \, c x - {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x + 1\right) + {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x - 1\right)\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\right)}}{c^{7} d^{3} x^{4} - 2 \, c^{5} d^{3} x^{2} + c^{3} d^{3}} + 2048 \, \int -\frac{2 \, c^{3} x^{3} + 2 \, c x - {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x + 1\right) + {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x - 1\right)}{16 \, {\left(c^{9} d^{3} x^{7} - 3 \, c^{7} d^{3} x^{5} + 3 \, c^{5} d^{3} x^{3} - c^{3} d^{3} x + {\left(c^{8} d^{3} x^{6} - 3 \, c^{6} d^{3} x^{4} + 3 \, c^{4} d^{3} x^{2} - c^{2} d^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x} - 2048 \, \int \frac{\log\left(c x - 1\right)}{32 \, {\left(c^{8} d^{3} x^{6} - 3 \, c^{6} d^{3} x^{4} + 3 \, c^{4} d^{3} x^{2} - c^{2} d^{3}\right)}}\,{d x}\right)} b + \frac{1}{16} \, a {\left(\frac{2 \, {\left(c^{2} x^{3} + x\right)}}{c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}} - \frac{\log\left(c x + 1\right)}{c^{3} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{3} d^{3}}\right)}"," ",0,"-1/2048*(6144*c^5*integrate(1/32*x^5*log(c*x - 1)/(c^8*d^3*x^6 - 3*c^6*d^3*x^4 + 3*c^4*d^3*x^2 - c^2*d^3), x) - 16*c^4*(2*(5*c^2*x^3 - 3*x)/(c^10*d^3*x^4 - 2*c^8*d^3*x^2 + c^6*d^3) + 3*log(c*x + 1)/(c^7*d^3) - 3*log(c*x - 1)/(c^7*d^3)) - 2048*c^4*integrate(1/32*x^4*log(c*x - 1)/(c^8*d^3*x^6 - 3*c^6*d^3*x^4 + 3*c^4*d^3*x^2 - c^2*d^3), x) + 6*(c*(2*(5*c^2*x^2 + 3*c*x - 6)/(c^10*d^3*x^3 - c^9*d^3*x^2 - c^8*d^3*x + c^7*d^3) - 5*log(c*x + 1)/(c^7*d^3) + 5*log(c*x - 1)/(c^7*d^3)) + 16*(2*c^2*x^2 - 1)*log(c*x - 1)/(c^10*d^3*x^4 - 2*c^8*d^3*x^2 + c^6*d^3))*c^3 - 16*c^2*(2*(c^2*x^3 + x)/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3) - log(c*x + 1)/(c^5*d^3) + log(c*x - 1)/(c^5*d^3)) + 4096*c^2*integrate(1/32*x^2*log(c*x - 1)/(c^8*d^3*x^6 - 3*c^6*d^3*x^4 + 3*c^4*d^3*x^2 - c^2*d^3), x) + 3*(c*(2*(3*c^2*x^2 - 3*c*x - 2)/(c^8*d^3*x^3 - c^7*d^3*x^2 - c^6*d^3*x + c^5*d^3) - 3*log(c*x + 1)/(c^5*d^3) + 3*log(c*x - 1)/(c^5*d^3)) - 16*log(c*x - 1)/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3))*c - 32*((c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x + 1)^2 + 2*(c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x + 1)*log(c*x - 1) + 4*(2*c^3*x^3 + 2*c*x - (c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x + 1) + (c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)))/(c^7*d^3*x^4 - 2*c^5*d^3*x^2 + c^3*d^3) + 2048*integrate(-1/16*(2*c^3*x^3 + 2*c*x - (c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x + 1) + (c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x - 1))/(c^9*d^3*x^7 - 3*c^7*d^3*x^5 + 3*c^5*d^3*x^3 - c^3*d^3*x + (c^8*d^3*x^6 - 3*c^6*d^3*x^4 + 3*c^4*d^3*x^2 - c^2*d^3)*sqrt(c*x + 1)*sqrt(c*x - 1)), x) - 2048*integrate(1/32*log(c*x - 1)/(c^8*d^3*x^6 - 3*c^6*d^3*x^4 + 3*c^4*d^3*x^2 - c^2*d^3), x))*b + 1/16*a*(2*(c^2*x^3 + x)/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3) - log(c*x + 1)/(c^3*d^3) + log(c*x - 1)/(c^3*d^3))","F",0
49,0,0,0,0.000000," ","integrate(x*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{16} \, b {\left(\frac{4 \, \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 1}{c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}} + 16 \, \int \frac{1}{4 \, {\left(c^{8} d^{3} x^{7} - 3 \, c^{6} d^{3} x^{5} + 3 \, c^{4} d^{3} x^{3} - c^{2} d^{3} x + {\left(c^{7} d^{3} x^{6} - 3 \, c^{5} d^{3} x^{4} + 3 \, c^{3} d^{3} x^{2} - c d^{3}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)}\right)}}\,{d x}\right)} + \frac{a}{4 \, {\left(c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}\right)}}"," ",0,"1/16*b*((4*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 1)/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3) + 16*integrate(1/4/(c^8*d^3*x^7 - 3*c^6*d^3*x^5 + 3*c^4*d^3*x^3 - c^2*d^3*x + (c^7*d^3*x^6 - 3*c^5*d^3*x^4 + 3*c^3*d^3*x^2 - c*d^3)*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1))), x)) + 1/4*a/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3)","F",0
50,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{2048} \, {\left(18432 \, c^{5} \int \frac{x^{5} \log\left(c x - 1\right)}{32 \, {\left(c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}\right)}}\,{d x} - 48 \, c^{4} {\left(\frac{2 \, {\left(5 \, c^{2} x^{3} - 3 \, x\right)}}{c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}} + \frac{3 \, \log\left(c x + 1\right)}{c^{5} d^{3}} - \frac{3 \, \log\left(c x - 1\right)}{c^{5} d^{3}}\right)} - 6144 \, c^{4} \int \frac{x^{4} \log\left(c x - 1\right)}{32 \, {\left(c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}\right)}}\,{d x} + 18 \, {\left(c {\left(\frac{2 \, {\left(5 \, c^{2} x^{2} + 3 \, c x - 6\right)}}{c^{8} d^{3} x^{3} - c^{7} d^{3} x^{2} - c^{6} d^{3} x + c^{5} d^{3}} - \frac{5 \, \log\left(c x + 1\right)}{c^{5} d^{3}} + \frac{5 \, \log\left(c x - 1\right)}{c^{5} d^{3}}\right)} + \frac{16 \, {\left(2 \, c^{2} x^{2} - 1\right)} \log\left(c x - 1\right)}{c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}}\right)} c^{3} + 80 \, c^{2} {\left(\frac{2 \, {\left(c^{2} x^{3} + x\right)}}{c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}} - \frac{\log\left(c x + 1\right)}{c^{3} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{3} d^{3}}\right)} + 12288 \, c^{2} \int \frac{x^{2} \log\left(c x - 1\right)}{32 \, {\left(c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}\right)}}\,{d x} + 9 \, {\left(c {\left(\frac{2 \, {\left(3 \, c^{2} x^{2} - 3 \, c x - 2\right)}}{c^{6} d^{3} x^{3} - c^{5} d^{3} x^{2} - c^{4} d^{3} x + c^{3} d^{3}} - \frac{3 \, \log\left(c x + 1\right)}{c^{3} d^{3}} + \frac{3 \, \log\left(c x - 1\right)}{c^{3} d^{3}}\right)} - \frac{16 \, \log\left(c x - 1\right)}{c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}}\right)} c - \frac{32 \, {\left(3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x + 1\right)^{2} + 6 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x + 1\right) \log\left(c x - 1\right) + 4 \, {\left(6 \, c^{3} x^{3} - 10 \, c x - 3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x + 1\right) + 3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x - 1\right)\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\right)}}{c^{5} d^{3} x^{4} - 2 \, c^{3} d^{3} x^{2} + c d^{3}} + 2048 \, \int -\frac{6 \, c^{3} x^{3} - 10 \, c x - 3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x + 1\right) + 3 \, {\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} \log\left(c x - 1\right)}{16 \, {\left(c^{7} d^{3} x^{7} - 3 \, c^{5} d^{3} x^{5} + 3 \, c^{3} d^{3} x^{3} - c d^{3} x + {\left(c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x} - 6144 \, \int \frac{\log\left(c x - 1\right)}{32 \, {\left(c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}\right)}}\,{d x}\right)} b - \frac{1}{16} \, a {\left(\frac{2 \, {\left(3 \, c^{2} x^{3} - 5 \, x\right)}}{c^{4} d^{3} x^{4} - 2 \, c^{2} d^{3} x^{2} + d^{3}} - \frac{3 \, \log\left(c x + 1\right)}{c d^{3}} + \frac{3 \, \log\left(c x - 1\right)}{c d^{3}}\right)}"," ",0,"1/2048*(18432*c^5*integrate(1/32*x^5*log(c*x - 1)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x) - 48*c^4*(2*(5*c^2*x^3 - 3*x)/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3) + 3*log(c*x + 1)/(c^5*d^3) - 3*log(c*x - 1)/(c^5*d^3)) - 6144*c^4*integrate(1/32*x^4*log(c*x - 1)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x) + 18*(c*(2*(5*c^2*x^2 + 3*c*x - 6)/(c^8*d^3*x^3 - c^7*d^3*x^2 - c^6*d^3*x + c^5*d^3) - 5*log(c*x + 1)/(c^5*d^3) + 5*log(c*x - 1)/(c^5*d^3)) + 16*(2*c^2*x^2 - 1)*log(c*x - 1)/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3))*c^3 + 80*c^2*(2*(c^2*x^3 + x)/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3) - log(c*x + 1)/(c^3*d^3) + log(c*x - 1)/(c^3*d^3)) + 12288*c^2*integrate(1/32*x^2*log(c*x - 1)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x) + 9*(c*(2*(3*c^2*x^2 - 3*c*x - 2)/(c^6*d^3*x^3 - c^5*d^3*x^2 - c^4*d^3*x + c^3*d^3) - 3*log(c*x + 1)/(c^3*d^3) + 3*log(c*x - 1)/(c^3*d^3)) - 16*log(c*x - 1)/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3))*c - 32*(3*(c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x + 1)^2 + 6*(c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x + 1)*log(c*x - 1) + 4*(6*c^3*x^3 - 10*c*x - 3*(c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x + 1) + 3*(c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)))/(c^5*d^3*x^4 - 2*c^3*d^3*x^2 + c*d^3) + 2048*integrate(-1/16*(6*c^3*x^3 - 10*c*x - 3*(c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x + 1) + 3*(c^4*x^4 - 2*c^2*x^2 + 1)*log(c*x - 1))/(c^7*d^3*x^7 - 3*c^5*d^3*x^5 + 3*c^3*d^3*x^3 - c*d^3*x + (c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3)*sqrt(c*x + 1)*sqrt(c*x - 1)), x) - 6144*integrate(1/32*log(c*x - 1)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x))*b - 1/16*a*(2*(3*c^2*x^3 - 5*x)/(c^4*d^3*x^4 - 2*c^2*d^3*x^2 + d^3) - 3*log(c*x + 1)/(c*d^3) + 3*log(c*x - 1)/(c*d^3))","F",0
51,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{2 \, c^{2} x^{2} - 3}{c^{4} d^{3} x^{4} - 2 \, c^{2} d^{3} x^{2} + d^{3}} + \frac{2 \, \log\left(c x + 1\right)}{d^{3}} + \frac{2 \, \log\left(c x - 1\right)}{d^{3}} - \frac{4 \, \log\left(x\right)}{d^{3}}\right)} - b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{6} d^{3} x^{7} - 3 \, c^{4} d^{3} x^{5} + 3 \, c^{2} d^{3} x^{3} - d^{3} x}\,{d x}"," ",0,"-1/4*a*((2*c^2*x^2 - 3)/(c^4*d^3*x^4 - 2*c^2*d^3*x^2 + d^3) + 2*log(c*x + 1)/d^3 + 2*log(c*x - 1)/d^3 - 4*log(x)/d^3) - b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c^6*d^3*x^7 - 3*c^4*d^3*x^5 + 3*c^2*d^3*x^3 - d^3*x), x)","F",0
52,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^2/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{2048} \, {\left(92160 \, c^{7} \int \frac{x^{5} \log\left(c x - 1\right)}{32 \, {\left(c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}\right)}}\,{d x} - 240 \, c^{6} {\left(\frac{2 \, {\left(5 \, c^{2} x^{3} - 3 \, x\right)}}{c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}} + \frac{3 \, \log\left(c x + 1\right)}{c^{5} d^{3}} - \frac{3 \, \log\left(c x - 1\right)}{c^{5} d^{3}}\right)} - 30720 \, c^{6} \int \frac{x^{4} \log\left(c x - 1\right)}{32 \, {\left(c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}\right)}}\,{d x} + 90 \, {\left(c {\left(\frac{2 \, {\left(5 \, c^{2} x^{2} + 3 \, c x - 6\right)}}{c^{8} d^{3} x^{3} - c^{7} d^{3} x^{2} - c^{6} d^{3} x + c^{5} d^{3}} - \frac{5 \, \log\left(c x + 1\right)}{c^{5} d^{3}} + \frac{5 \, \log\left(c x - 1\right)}{c^{5} d^{3}}\right)} + \frac{16 \, {\left(2 \, c^{2} x^{2} - 1\right)} \log\left(c x - 1\right)}{c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}}\right)} c^{5} + 400 \, c^{4} {\left(\frac{2 \, {\left(c^{2} x^{3} + x\right)}}{c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}} - \frac{\log\left(c x + 1\right)}{c^{3} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{3} d^{3}}\right)} + 61440 \, c^{4} \int \frac{x^{2} \log\left(c x - 1\right)}{32 \, {\left(c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}\right)}}\,{d x} + 45 \, {\left(c {\left(\frac{2 \, {\left(3 \, c^{2} x^{2} - 3 \, c x - 2\right)}}{c^{6} d^{3} x^{3} - c^{5} d^{3} x^{2} - c^{4} d^{3} x + c^{3} d^{3}} - \frac{3 \, \log\left(c x + 1\right)}{c^{3} d^{3}} + \frac{3 \, \log\left(c x - 1\right)}{c^{3} d^{3}}\right)} - \frac{16 \, \log\left(c x - 1\right)}{c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}}\right)} c^{3} + 128 \, c^{2} {\left(\frac{2 \, {\left(3 \, c^{2} x^{3} - 5 \, x\right)}}{c^{4} d^{3} x^{4} - 2 \, c^{2} d^{3} x^{2} + d^{3}} - \frac{3 \, \log\left(c x + 1\right)}{c d^{3}} + \frac{3 \, \log\left(c x - 1\right)}{c d^{3}}\right)} - 30720 \, c^{2} \int \frac{\log\left(c x - 1\right)}{32 \, {\left(c^{6} d^{3} x^{6} - 3 \, c^{4} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{2} - d^{3}\right)}}\,{d x} - \frac{32 \, {\left(15 \, {\left(c^{5} x^{5} - 2 \, c^{3} x^{3} + c x\right)} \log\left(c x + 1\right)^{2} + 30 \, {\left(c^{5} x^{5} - 2 \, c^{3} x^{3} + c x\right)} \log\left(c x + 1\right) \log\left(c x - 1\right) + 4 \, {\left(30 \, c^{4} x^{4} - 50 \, c^{2} x^{2} - 15 \, {\left(c^{5} x^{5} - 2 \, c^{3} x^{3} + c x\right)} \log\left(c x + 1\right) + 15 \, {\left(c^{5} x^{5} - 2 \, c^{3} x^{3} + c x\right)} \log\left(c x - 1\right) + 16\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\right)}}{c^{4} d^{3} x^{5} - 2 \, c^{2} d^{3} x^{3} + d^{3} x} + 2048 \, \int -\frac{30 \, c^{5} x^{4} - 50 \, c^{3} x^{2} - 15 \, {\left(c^{6} x^{5} - 2 \, c^{4} x^{3} + c^{2} x\right)} \log\left(c x + 1\right) + 15 \, {\left(c^{6} x^{5} - 2 \, c^{4} x^{3} + c^{2} x\right)} \log\left(c x - 1\right) + 16 \, c}{16 \, {\left(c^{7} d^{3} x^{8} - 3 \, c^{5} d^{3} x^{6} + 3 \, c^{3} d^{3} x^{4} - c d^{3} x^{2} + {\left(c^{6} d^{3} x^{7} - 3 \, c^{4} d^{3} x^{5} + 3 \, c^{2} d^{3} x^{3} - d^{3} x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x}\right)} b - \frac{1}{16} \, a {\left(\frac{2 \, {\left(15 \, c^{4} x^{4} - 25 \, c^{2} x^{2} + 8\right)}}{c^{4} d^{3} x^{5} - 2 \, c^{2} d^{3} x^{3} + d^{3} x} - \frac{15 \, c \log\left(c x + 1\right)}{d^{3}} + \frac{15 \, c \log\left(c x - 1\right)}{d^{3}}\right)}"," ",0,"1/2048*(92160*c^7*integrate(1/32*x^5*log(c*x - 1)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x) - 240*c^6*(2*(5*c^2*x^3 - 3*x)/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3) + 3*log(c*x + 1)/(c^5*d^3) - 3*log(c*x - 1)/(c^5*d^3)) - 30720*c^6*integrate(1/32*x^4*log(c*x - 1)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x) + 90*(c*(2*(5*c^2*x^2 + 3*c*x - 6)/(c^8*d^3*x^3 - c^7*d^3*x^2 - c^6*d^3*x + c^5*d^3) - 5*log(c*x + 1)/(c^5*d^3) + 5*log(c*x - 1)/(c^5*d^3)) + 16*(2*c^2*x^2 - 1)*log(c*x - 1)/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3))*c^5 + 400*c^4*(2*(c^2*x^3 + x)/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3) - log(c*x + 1)/(c^3*d^3) + log(c*x - 1)/(c^3*d^3)) + 61440*c^4*integrate(1/32*x^2*log(c*x - 1)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x) + 45*(c*(2*(3*c^2*x^2 - 3*c*x - 2)/(c^6*d^3*x^3 - c^5*d^3*x^2 - c^4*d^3*x + c^3*d^3) - 3*log(c*x + 1)/(c^3*d^3) + 3*log(c*x - 1)/(c^3*d^3)) - 16*log(c*x - 1)/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3))*c^3 + 128*c^2*(2*(3*c^2*x^3 - 5*x)/(c^4*d^3*x^4 - 2*c^2*d^3*x^2 + d^3) - 3*log(c*x + 1)/(c*d^3) + 3*log(c*x - 1)/(c*d^3)) - 30720*c^2*integrate(1/32*log(c*x - 1)/(c^6*d^3*x^6 - 3*c^4*d^3*x^4 + 3*c^2*d^3*x^2 - d^3), x) - 32*(15*(c^5*x^5 - 2*c^3*x^3 + c*x)*log(c*x + 1)^2 + 30*(c^5*x^5 - 2*c^3*x^3 + c*x)*log(c*x + 1)*log(c*x - 1) + 4*(30*c^4*x^4 - 50*c^2*x^2 - 15*(c^5*x^5 - 2*c^3*x^3 + c*x)*log(c*x + 1) + 15*(c^5*x^5 - 2*c^3*x^3 + c*x)*log(c*x - 1) + 16)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)))/(c^4*d^3*x^5 - 2*c^2*d^3*x^3 + d^3*x) + 2048*integrate(-1/16*(30*c^5*x^4 - 50*c^3*x^2 - 15*(c^6*x^5 - 2*c^4*x^3 + c^2*x)*log(c*x + 1) + 15*(c^6*x^5 - 2*c^4*x^3 + c^2*x)*log(c*x - 1) + 16*c)/(c^7*d^3*x^8 - 3*c^5*d^3*x^6 + 3*c^3*d^3*x^4 - c*d^3*x^2 + (c^6*d^3*x^7 - 3*c^4*d^3*x^5 + 3*c^2*d^3*x^3 - d^3*x)*sqrt(c*x + 1)*sqrt(c*x - 1)), x))*b - 1/16*a*(2*(15*c^4*x^4 - 25*c^2*x^2 + 8)/(c^4*d^3*x^5 - 2*c^2*d^3*x^3 + d^3*x) - 15*c*log(c*x + 1)/d^3 + 15*c*log(c*x - 1)/d^3)","F",0
53,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^3/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{6 \, c^{4} x^{4} - 9 \, c^{2} x^{2} + 2}{c^{4} d^{3} x^{6} - 2 \, c^{2} d^{3} x^{4} + d^{3} x^{2}} + \frac{6 \, c^{2} \log\left(c x + 1\right)}{d^{3}} + \frac{6 \, c^{2} \log\left(c x - 1\right)}{d^{3}} - \frac{12 \, c^{2} \log\left(x\right)}{d^{3}}\right)} - b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{6} d^{3} x^{9} - 3 \, c^{4} d^{3} x^{7} + 3 \, c^{2} d^{3} x^{5} - d^{3} x^{3}}\,{d x}"," ",0,"-1/4*a*((6*c^4*x^4 - 9*c^2*x^2 + 2)/(c^4*d^3*x^6 - 2*c^2*d^3*x^4 + d^3*x^2) + 6*c^2*log(c*x + 1)/d^3 + 6*c^2*log(c*x - 1)/d^3 - 12*c^2*log(x)/d^3) - b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c^6*d^3*x^9 - 3*c^4*d^3*x^7 + 3*c^2*d^3*x^5 - d^3*x^3), x)","F",0
54,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^4/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{6144} \, {\left(1935360 \, c^{9} \int \frac{x^{7} \log\left(c x - 1\right)}{96 \, {\left(c^{6} d^{3} x^{8} - 3 \, c^{4} d^{3} x^{6} + 3 \, c^{2} d^{3} x^{4} - d^{3} x^{2}\right)}}\,{d x} - 1680 \, c^{8} {\left(\frac{2 \, {\left(5 \, c^{2} x^{3} - 3 \, x\right)}}{c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}} + \frac{3 \, \log\left(c x + 1\right)}{c^{5} d^{3}} - \frac{3 \, \log\left(c x - 1\right)}{c^{5} d^{3}}\right)} - 645120 \, c^{8} \int \frac{x^{6} \log\left(c x - 1\right)}{96 \, {\left(c^{6} d^{3} x^{8} - 3 \, c^{4} d^{3} x^{6} + 3 \, c^{2} d^{3} x^{4} - d^{3} x^{2}\right)}}\,{d x} + 630 \, {\left(c {\left(\frac{2 \, {\left(5 \, c^{2} x^{2} + 3 \, c x - 6\right)}}{c^{8} d^{3} x^{3} - c^{7} d^{3} x^{2} - c^{6} d^{3} x + c^{5} d^{3}} - \frac{5 \, \log\left(c x + 1\right)}{c^{5} d^{3}} + \frac{5 \, \log\left(c x - 1\right)}{c^{5} d^{3}}\right)} + \frac{16 \, {\left(2 \, c^{2} x^{2} - 1\right)} \log\left(c x - 1\right)}{c^{8} d^{3} x^{4} - 2 \, c^{6} d^{3} x^{2} + c^{4} d^{3}}\right)} c^{7} + 2800 \, c^{6} {\left(\frac{2 \, {\left(c^{2} x^{3} + x\right)}}{c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}} - \frac{\log\left(c x + 1\right)}{c^{3} d^{3}} + \frac{\log\left(c x - 1\right)}{c^{3} d^{3}}\right)} + 1290240 \, c^{6} \int \frac{x^{4} \log\left(c x - 1\right)}{96 \, {\left(c^{6} d^{3} x^{8} - 3 \, c^{4} d^{3} x^{6} + 3 \, c^{2} d^{3} x^{4} - d^{3} x^{2}\right)}}\,{d x} + 315 \, {\left(c {\left(\frac{2 \, {\left(3 \, c^{2} x^{2} - 3 \, c x - 2\right)}}{c^{6} d^{3} x^{3} - c^{5} d^{3} x^{2} - c^{4} d^{3} x + c^{3} d^{3}} - \frac{3 \, \log\left(c x + 1\right)}{c^{3} d^{3}} + \frac{3 \, \log\left(c x - 1\right)}{c^{3} d^{3}}\right)} - \frac{16 \, \log\left(c x - 1\right)}{c^{6} d^{3} x^{4} - 2 \, c^{4} d^{3} x^{2} + c^{2} d^{3}}\right)} c^{5} + 896 \, c^{4} {\left(\frac{2 \, {\left(3 \, c^{2} x^{3} - 5 \, x\right)}}{c^{4} d^{3} x^{4} - 2 \, c^{2} d^{3} x^{2} + d^{3}} - \frac{3 \, \log\left(c x + 1\right)}{c d^{3}} + \frac{3 \, \log\left(c x - 1\right)}{c d^{3}}\right)} - 645120 \, c^{4} \int \frac{x^{2} \log\left(c x - 1\right)}{96 \, {\left(c^{6} d^{3} x^{8} - 3 \, c^{4} d^{3} x^{6} + 3 \, c^{2} d^{3} x^{4} - d^{3} x^{2}\right)}}\,{d x} + 128 \, c^{2} {\left(\frac{2 \, {\left(15 \, c^{4} x^{4} - 25 \, c^{2} x^{2} + 8\right)}}{c^{4} d^{3} x^{5} - 2 \, c^{2} d^{3} x^{3} + d^{3} x} - \frac{15 \, c \log\left(c x + 1\right)}{d^{3}} + \frac{15 \, c \log\left(c x - 1\right)}{d^{3}}\right)} - \frac{32 \, {\left(105 \, {\left(c^{7} x^{7} - 2 \, c^{5} x^{5} + c^{3} x^{3}\right)} \log\left(c x + 1\right)^{2} + 210 \, {\left(c^{7} x^{7} - 2 \, c^{5} x^{5} + c^{3} x^{3}\right)} \log\left(c x + 1\right) \log\left(c x - 1\right) + 4 \, {\left(210 \, c^{6} x^{6} - 350 \, c^{4} x^{4} + 112 \, c^{2} x^{2} - 105 \, {\left(c^{7} x^{7} - 2 \, c^{5} x^{5} + c^{3} x^{3}\right)} \log\left(c x + 1\right) + 105 \, {\left(c^{7} x^{7} - 2 \, c^{5} x^{5} + c^{3} x^{3}\right)} \log\left(c x - 1\right) + 16\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\right)}}{c^{4} d^{3} x^{7} - 2 \, c^{2} d^{3} x^{5} + d^{3} x^{3}} + 6144 \, \int -\frac{210 \, c^{7} x^{6} - 350 \, c^{5} x^{4} + 112 \, c^{3} x^{2} - 105 \, {\left(c^{8} x^{7} - 2 \, c^{6} x^{5} + c^{4} x^{3}\right)} \log\left(c x + 1\right) + 105 \, {\left(c^{8} x^{7} - 2 \, c^{6} x^{5} + c^{4} x^{3}\right)} \log\left(c x - 1\right) + 16 \, c}{48 \, {\left(c^{7} d^{3} x^{10} - 3 \, c^{5} d^{3} x^{8} + 3 \, c^{3} d^{3} x^{6} - c d^{3} x^{4} + {\left(c^{6} d^{3} x^{9} - 3 \, c^{4} d^{3} x^{7} + 3 \, c^{2} d^{3} x^{5} - d^{3} x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x}\right)} b + \frac{1}{48} \, a {\left(\frac{105 \, c^{3} \log\left(c x + 1\right)}{d^{3}} - \frac{105 \, c^{3} \log\left(c x - 1\right)}{d^{3}} - \frac{2 \, {\left(105 \, c^{6} x^{6} - 175 \, c^{4} x^{4} + 56 \, c^{2} x^{2} + 8\right)}}{c^{4} d^{3} x^{7} - 2 \, c^{2} d^{3} x^{5} + d^{3} x^{3}}\right)}"," ",0,"1/6144*(1935360*c^9*integrate(1/96*x^7*log(c*x - 1)/(c^6*d^3*x^8 - 3*c^4*d^3*x^6 + 3*c^2*d^3*x^4 - d^3*x^2), x) - 1680*c^8*(2*(5*c^2*x^3 - 3*x)/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3) + 3*log(c*x + 1)/(c^5*d^3) - 3*log(c*x - 1)/(c^5*d^3)) - 645120*c^8*integrate(1/96*x^6*log(c*x - 1)/(c^6*d^3*x^8 - 3*c^4*d^3*x^6 + 3*c^2*d^3*x^4 - d^3*x^2), x) + 630*(c*(2*(5*c^2*x^2 + 3*c*x - 6)/(c^8*d^3*x^3 - c^7*d^3*x^2 - c^6*d^3*x + c^5*d^3) - 5*log(c*x + 1)/(c^5*d^3) + 5*log(c*x - 1)/(c^5*d^3)) + 16*(2*c^2*x^2 - 1)*log(c*x - 1)/(c^8*d^3*x^4 - 2*c^6*d^3*x^2 + c^4*d^3))*c^7 + 2800*c^6*(2*(c^2*x^3 + x)/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3) - log(c*x + 1)/(c^3*d^3) + log(c*x - 1)/(c^3*d^3)) + 1290240*c^6*integrate(1/96*x^4*log(c*x - 1)/(c^6*d^3*x^8 - 3*c^4*d^3*x^6 + 3*c^2*d^3*x^4 - d^3*x^2), x) + 315*(c*(2*(3*c^2*x^2 - 3*c*x - 2)/(c^6*d^3*x^3 - c^5*d^3*x^2 - c^4*d^3*x + c^3*d^3) - 3*log(c*x + 1)/(c^3*d^3) + 3*log(c*x - 1)/(c^3*d^3)) - 16*log(c*x - 1)/(c^6*d^3*x^4 - 2*c^4*d^3*x^2 + c^2*d^3))*c^5 + 896*c^4*(2*(3*c^2*x^3 - 5*x)/(c^4*d^3*x^4 - 2*c^2*d^3*x^2 + d^3) - 3*log(c*x + 1)/(c*d^3) + 3*log(c*x - 1)/(c*d^3)) - 645120*c^4*integrate(1/96*x^2*log(c*x - 1)/(c^6*d^3*x^8 - 3*c^4*d^3*x^6 + 3*c^2*d^3*x^4 - d^3*x^2), x) + 128*c^2*(2*(15*c^4*x^4 - 25*c^2*x^2 + 8)/(c^4*d^3*x^5 - 2*c^2*d^3*x^3 + d^3*x) - 15*c*log(c*x + 1)/d^3 + 15*c*log(c*x - 1)/d^3) - 32*(105*(c^7*x^7 - 2*c^5*x^5 + c^3*x^3)*log(c*x + 1)^2 + 210*(c^7*x^7 - 2*c^5*x^5 + c^3*x^3)*log(c*x + 1)*log(c*x - 1) + 4*(210*c^6*x^6 - 350*c^4*x^4 + 112*c^2*x^2 - 105*(c^7*x^7 - 2*c^5*x^5 + c^3*x^3)*log(c*x + 1) + 105*(c^7*x^7 - 2*c^5*x^5 + c^3*x^3)*log(c*x - 1) + 16)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)))/(c^4*d^3*x^7 - 2*c^2*d^3*x^5 + d^3*x^3) + 6144*integrate(-1/48*(210*c^7*x^6 - 350*c^5*x^4 + 112*c^3*x^2 - 105*(c^8*x^7 - 2*c^6*x^5 + c^4*x^3)*log(c*x + 1) + 105*(c^8*x^7 - 2*c^6*x^5 + c^4*x^3)*log(c*x - 1) + 16*c)/(c^7*d^3*x^10 - 3*c^5*d^3*x^8 + 3*c^3*d^3*x^6 - c*d^3*x^4 + (c^6*d^3*x^9 - 3*c^4*d^3*x^7 + 3*c^2*d^3*x^5 - d^3*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1)), x))*b + 1/48*a*(105*c^3*log(c*x + 1)/d^3 - 105*c^3*log(c*x - 1)/d^3 - 2*(105*c^6*x^6 - 175*c^4*x^4 + 56*c^2*x^2 + 8)/(c^4*d^3*x^7 - 2*c^2*d^3*x^5 + d^3*x^3))","F",0
55,0,0,0,0.000000," ","integrate(arccosh(a*x)/(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{4 \, {\left(\log\left(a x + 1\right) - \log\left(a x - 1\right)\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right) - \log\left(a x + 1\right)^{2} - 2 \, \log\left(a x + 1\right) \log\left(a x - 1\right) + \log\left(a x - 1\right)^{2}}{8 \, a c} + \frac{\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)}{2 \, a c} + \int \frac{\log\left(a x + 1\right) - \log\left(a x - 1\right)}{2 \, {\left(a^{3} c x^{3} - a c x + {\left(a^{2} c x^{2} - c\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)}}\,{d x}"," ",0,"1/8*(4*(log(a*x + 1) - log(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)) - log(a*x + 1)^2 - 2*log(a*x + 1)*log(a*x - 1) + log(a*x - 1)^2)/(a*c) + 1/2*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/(a*c) + integrate(1/2*(log(a*x + 1) - log(a*x - 1))/(a^3*c*x^3 - a*c*x + (a^2*c*x^2 - c)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
56,0,0,0,0.000000," ","integrate(arccosh(a*x)/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{{\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right)^{2} + 2 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)^{2} + 4 \, a x + 4 \, {\left(2 \, a x - {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right) - 2 \, {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)}{16 \, {\left(a^{3} c^{2} x^{2} - a c^{2}\right)}} + \frac{\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)}{4 \, a c^{2}} - \frac{\log\left(a x + 1\right)}{8 \, a c^{2}} + \int -\frac{2 \, a x - {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)}{4 \, {\left(a^{5} c^{2} x^{5} - 2 \, a^{3} c^{2} x^{3} + a c^{2} x + {\left(a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)}}\,{d x}"," ",0,"-1/16*((a^2*x^2 - 1)*log(a*x + 1)^2 + 2*(a^2*x^2 - 1)*log(a*x + 1)*log(a*x - 1) - (a^2*x^2 - 1)*log(a*x - 1)^2 + 4*a*x + 4*(2*a*x - (a^2*x^2 - 1)*log(a*x + 1) + (a^2*x^2 - 1)*log(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)) - 2*(a^2*x^2 - 1)*log(a*x - 1))/(a^3*c^2*x^2 - a*c^2) + 1/4*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/(a*c^2) - 1/8*log(a*x + 1)/(a*c^2) + integrate(-1/4*(2*a*x - (a^2*x^2 - 1)*log(a*x + 1) + (a^2*x^2 - 1)*log(a*x - 1))/(a^5*c^2*x^5 - 2*a^3*c^2*x^3 + a*c^2*x + (a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
57,0,0,0,0.000000," ","integrate(arccosh(a*x)/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{10 \, a^{3} x^{3} + 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right)^{2} + 6 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) \log\left(a x - 1\right) - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)^{2} - 14 \, a x + 4 \, {\left(6 \, a^{3} x^{3} - 10 \, a x - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) + 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right) - 7 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)}{64 \, {\left(a^{5} c^{3} x^{4} - 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}} + \frac{3 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{16 \, a c^{3}} - \frac{7 \, \log\left(a x + 1\right)}{64 \, a c^{3}} + \int -\frac{6 \, a^{3} x^{3} - 10 \, a x - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) + 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)}{16 \, {\left(a^{7} c^{3} x^{7} - 3 \, a^{5} c^{3} x^{5} + 3 \, a^{3} c^{3} x^{3} - a c^{3} x + {\left(a^{6} c^{3} x^{6} - 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - c^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)}}\,{d x}"," ",0,"-1/64*(10*a^3*x^3 + 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)^2 + 6*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1)*log(a*x - 1) - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1)^2 - 14*a*x + 4*(6*a^3*x^3 - 10*a*x - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1) + 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)) - 7*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1))/(a^5*c^3*x^4 - 2*a^3*c^3*x^2 + a*c^3) + 3/16*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/(a*c^3) - 7/64*log(a*x + 1)/(a*c^3) + integrate(-1/16*(6*a^3*x^3 - 10*a*x - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1) + 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1))/(a^7*c^3*x^7 - 3*a^5*c^3*x^5 + 3*a^3*c^3*x^3 - a*c^3*x + (a^6*c^3*x^6 - 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - c^3)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
58,0,0,0,0.000000," ","integrate(x^4*(a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{48} \, {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{3}}{c^{2} d} - \frac{3 \, \sqrt{-c^{2} d x^{2} + d} x}{c^{4}} + \frac{6 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}{c^{4} d} - \frac{3 \, \sqrt{d} \arcsin\left(c x\right)}{c^{5}}\right)} a + b \int \sqrt{-c^{2} d x^{2} + d} x^{4} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"-1/48*(8*(-c^2*d*x^2 + d)^(3/2)*x^3/(c^2*d) - 3*sqrt(-c^2*d*x^2 + d)*x/c^4 + 6*(-c^2*d*x^2 + d)^(3/2)*x/(c^4*d) - 3*sqrt(d)*arcsin(c*x)/c^5)*a + b*integrate(sqrt(-c^2*d*x^2 + d)*x^4*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
59,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x}{c^{2}} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}{c^{2} d} + \frac{\sqrt{d} \arcsin\left(c x\right)}{c^{3}}\right)} + b \int \sqrt{-c^{2} d x^{2} + d} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/8*a*(sqrt(-c^2*d*x^2 + d)*x/c^2 - 2*(-c^2*d*x^2 + d)^(3/2)*x/(c^2*d) + sqrt(d)*arcsin(c*x)/c^3) + b*integrate(sqrt(-c^2*d*x^2 + d)*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
60,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\sqrt{-c^{2} d x^{2} + d} x + \frac{\sqrt{d} \arcsin\left(c x\right)}{c}\right)} a + b \int \sqrt{-c^{2} d x^{2} + d} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/2*(sqrt(-c^2*d*x^2 + d)*x + sqrt(d)*arcsin(c*x)/c)*a + b*integrate(sqrt(-c^2*d*x^2 + d)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
61,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/x^2,x, algorithm=""maxima"")","-{\left(c \sqrt{d} \arcsin\left(c x\right) + \frac{\sqrt{-c^{2} d x^{2} + d}}{x}\right)} a + b \int \frac{\sqrt{-c^{2} d x^{2} + d} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{2}}\,{d x}"," ",0,"-(c*sqrt(d)*arcsin(c*x) + sqrt(-c^2*d*x^2 + d)/x)*a + b*integrate(sqrt(-c^2*d*x^2 + d)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^2, x)","F",0
62,1,150,0,0.488986," ","integrate((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/x^4,x, algorithm=""maxima"")","\frac{{\left(c^{4} d^{2} \sqrt{-\frac{1}{c^{4} d}} \log\left(x^{2} - \frac{1}{c^{2}}\right) + i \, \left(-1\right)^{-2 \, c^{2} d x^{2} + 2 \, d} c^{2} d^{\frac{3}{2}} \log\left(-2 \, c^{2} d + \frac{2 \, d}{x^{2}}\right) + \frac{\sqrt{-c^{4} d x^{4} + 2 \, c^{2} d x^{2} - d} d}{x^{2}}\right)} b c}{6 \, d} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b \operatorname{arcosh}\left(c x\right)}{3 \, d x^{3}} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a}{3 \, d x^{3}}"," ",0,"1/6*(c^4*d^2*sqrt(-1/(c^4*d))*log(x^2 - 1/c^2) + I*(-1)^(-2*c^2*d*x^2 + 2*d)*c^2*d^(3/2)*log(-2*c^2*d + 2*d/x^2) + sqrt(-c^4*d*x^4 + 2*c^2*d*x^2 - d)*d/x^2)*b*c/d - 1/3*(-c^2*d*x^2 + d)^(3/2)*b*arccosh(c*x)/(d*x^3) - 1/3*(-c^2*d*x^2 + d)^(3/2)*a/(d*x^3)","C",0
63,1,146,0,0.453889," ","integrate((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/x^6,x, algorithm=""maxima"")","-\frac{1}{60} \, {\left(8 \, c^{4} \sqrt{-d} \log\left(x\right) - \frac{2 \, c^{2} \sqrt{-d} x^{2} - 3 \, \sqrt{-d}}{x^{4}}\right)} b c - \frac{1}{15} \, b {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2}}{d x^{3}} + \frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{d x^{5}}\right)} \operatorname{arcosh}\left(c x\right) - \frac{1}{15} \, a {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2}}{d x^{3}} + \frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{d x^{5}}\right)}"," ",0,"-1/60*(8*c^4*sqrt(-d)*log(x) - (2*c^2*sqrt(-d)*x^2 - 3*sqrt(-d))/x^4)*b*c - 1/15*b*(2*(-c^2*d*x^2 + d)^(3/2)*c^2/(d*x^3) + 3*(-c^2*d*x^2 + d)^(3/2)/(d*x^5))*arccosh(c*x) - 1/15*a*(2*(-c^2*d*x^2 + d)^(3/2)*c^2/(d*x^3) + 3*(-c^2*d*x^2 + d)^(3/2)/(d*x^5))","A",0
64,1,207,0,0.439981," ","integrate((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/x^8,x, algorithm=""maxima"")","-\frac{1}{420} \, {\left(32 \, c^{6} \sqrt{-d} \log\left(x\right) - \frac{8 \, c^{4} \sqrt{-d} x^{4} + 3 \, c^{2} \sqrt{-d} x^{2} - 10 \, \sqrt{-d}}{x^{6}}\right)} b c - \frac{1}{105} \, {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4}}{d x^{3}} + \frac{12 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2}}{d x^{5}} + \frac{15 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{d x^{7}}\right)} b \operatorname{arcosh}\left(c x\right) - \frac{1}{105} \, {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4}}{d x^{3}} + \frac{12 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2}}{d x^{5}} + \frac{15 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{d x^{7}}\right)} a"," ",0,"-1/420*(32*c^6*sqrt(-d)*log(x) - (8*c^4*sqrt(-d)*x^4 + 3*c^2*sqrt(-d)*x^2 - 10*sqrt(-d))/x^6)*b*c - 1/105*(8*(-c^2*d*x^2 + d)^(3/2)*c^4/(d*x^3) + 12*(-c^2*d*x^2 + d)^(3/2)*c^2/(d*x^5) + 15*(-c^2*d*x^2 + d)^(3/2)/(d*x^7))*b*arccosh(c*x) - 1/105*(8*(-c^2*d*x^2 + d)^(3/2)*c^4/(d*x^3) + 12*(-c^2*d*x^2 + d)^(3/2)*c^2/(d*x^5) + 15*(-c^2*d*x^2 + d)^(3/2)/(d*x^7))*a","A",0
65,1,205,0,0.452380," ","integrate(x^5*(a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{105} \, {\left(\frac{15 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{4}}{c^{2} d} + \frac{12 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{4} d} + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{6} d}\right)} b \operatorname{arcosh}\left(c x\right) - \frac{1}{105} \, {\left(\frac{15 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{4}}{c^{2} d} + \frac{12 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{4} d} + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{6} d}\right)} a - \frac{{\left(225 \, c^{6} \sqrt{-d} x^{7} - 63 \, c^{4} \sqrt{-d} x^{5} - 140 \, c^{2} \sqrt{-d} x^{3} - 840 \, \sqrt{-d} x\right)} b}{11025 \, c^{5}}"," ",0,"-1/105*(15*(-c^2*d*x^2 + d)^(3/2)*x^4/(c^2*d) + 12*(-c^2*d*x^2 + d)^(3/2)*x^2/(c^4*d) + 8*(-c^2*d*x^2 + d)^(3/2)/(c^6*d))*b*arccosh(c*x) - 1/105*(15*(-c^2*d*x^2 + d)^(3/2)*x^4/(c^2*d) + 12*(-c^2*d*x^2 + d)^(3/2)*x^2/(c^4*d) + 8*(-c^2*d*x^2 + d)^(3/2)/(c^6*d))*a - 1/11025*(225*c^6*sqrt(-d)*x^7 - 63*c^4*sqrt(-d)*x^5 - 140*c^2*sqrt(-d)*x^3 - 840*sqrt(-d)*x)*b/c^5","A",0
66,1,144,0,0.512162," ","integrate(x^3*(a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{15} \, b {\left(\frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{4} d}\right)} \operatorname{arcosh}\left(c x\right) - \frac{1}{15} \, a {\left(\frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{4} d}\right)} - \frac{{\left(9 \, c^{4} \sqrt{-d} x^{5} - 5 \, c^{2} \sqrt{-d} x^{3} - 30 \, \sqrt{-d} x\right)} b}{225 \, c^{3}}"," ",0,"-1/15*b*(3*(-c^2*d*x^2 + d)^(3/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(3/2)/(c^4*d))*arccosh(c*x) - 1/15*a*(3*(-c^2*d*x^2 + d)^(3/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(3/2)/(c^4*d)) - 1/225*(9*c^4*sqrt(-d)*x^5 - 5*c^2*sqrt(-d)*x^3 - 30*sqrt(-d)*x)*b/c^3","A",0
67,1,81,0,0.342408," ","integrate(x*(a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b \operatorname{arcosh}\left(c x\right)}{3 \, c^{2} d} - \frac{{\left(c^{2} \sqrt{-d} d x^{3} - 3 \, \sqrt{-d} d x\right)} b}{9 \, c d} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a}{3 \, c^{2} d}"," ",0,"-1/3*(-c^2*d*x^2 + d)^(3/2)*b*arccosh(c*x)/(c^2*d) - 1/9*(c^2*sqrt(-d)*d*x^3 - 3*sqrt(-d)*d*x)*b/(c*d) - 1/3*(-c^2*d*x^2 + d)^(3/2)*a/(c^2*d)","A",0
68,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/x,x, algorithm=""maxima"")","-{\left(\sqrt{d} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - \sqrt{-c^{2} d x^{2} + d}\right)} a + b \int \frac{\sqrt{-c^{2} d x^{2} + d} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"-(sqrt(d)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - sqrt(-c^2*d*x^2 + d))*a + b*integrate(sqrt(-c^2*d*x^2 + d)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
69,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(c^{2} \sqrt{d} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - \sqrt{-c^{2} d x^{2} + d} c^{2} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{d x^{2}}\right)} a + b \int \frac{\sqrt{-c^{2} d x^{2} + d} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{3}}\,{d x}"," ",0,"1/2*(c^2*sqrt(d)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - sqrt(-c^2*d*x^2 + d)*c^2 - (-c^2*d*x^2 + d)^(3/2)/(d*x^2))*a + b*integrate(sqrt(-c^2*d*x^2 + d)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^3, x)","F",0
70,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))*(-c^2*d*x^2+d)^(1/2)/x^5,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(c^{4} \sqrt{d} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - \sqrt{-c^{2} d x^{2} + d} c^{4} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2}}{d x^{2}} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{d x^{4}}\right)} a + b \int \frac{\sqrt{-c^{2} d x^{2} + d} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{5}}\,{d x}"," ",0,"1/8*(c^4*sqrt(d)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - sqrt(-c^2*d*x^2 + d)*c^4 - (-c^2*d*x^2 + d)^(3/2)*c^2/(d*x^2) - 2*(-c^2*d*x^2 + d)^(3/2)/(d*x^4))*a + b*integrate(sqrt(-c^2*d*x^2 + d)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^5, x)","F",0
71,0,0,0,0.000000," ","integrate(x^4*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{128} \, {\left(\frac{16 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{3}}{c^{2} d} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}{c^{4}} + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}{c^{4} d} - \frac{3 \, \sqrt{-c^{2} d x^{2} + d} d x}{c^{4}} - \frac{3 \, d^{\frac{3}{2}} \arcsin\left(c x\right)}{c^{5}}\right)} a + b \int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{4} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"-1/128*(16*(-c^2*d*x^2 + d)^(5/2)*x^3/(c^2*d) - 2*(-c^2*d*x^2 + d)^(3/2)*x/c^4 + 8*(-c^2*d*x^2 + d)^(5/2)*x/(c^4*d) - 3*sqrt(-c^2*d*x^2 + d)*d*x/c^4 - 3*d^(3/2)*arcsin(c*x)/c^5)*a + b*integrate((-c^2*d*x^2 + d)^(3/2)*x^4*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
72,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{48} \, a {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}{c^{2}} - \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}{c^{2} d} + \frac{3 \, \sqrt{-c^{2} d x^{2} + d} d x}{c^{2}} + \frac{3 \, d^{\frac{3}{2}} \arcsin\left(c x\right)}{c^{3}}\right)} + b \int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/48*a*(2*(-c^2*d*x^2 + d)^(3/2)*x/c^2 - 8*(-c^2*d*x^2 + d)^(5/2)*x/(c^2*d) + 3*sqrt(-c^2*d*x^2 + d)*d*x/c^2 + 3*d^(3/2)*arcsin(c*x)/c^3) + b*integrate((-c^2*d*x^2 + d)^(3/2)*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
73,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x + 3 \, \sqrt{-c^{2} d x^{2} + d} d x + \frac{3 \, d^{\frac{3}{2}} \arcsin\left(c x\right)}{c}\right)} a + b \int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/8*(2*(-c^2*d*x^2 + d)^(3/2)*x + 3*sqrt(-c^2*d*x^2 + d)*d*x + 3*d^(3/2)*arcsin(c*x)/c)*a + b*integrate((-c^2*d*x^2 + d)^(3/2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
74,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(3 \, \sqrt{-c^{2} d x^{2} + d} c^{2} d x + 3 \, c d^{\frac{3}{2}} \arcsin\left(c x\right) + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{x}\right)} a + b \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{2}}\,{d x}"," ",0,"-1/2*(3*sqrt(-c^2*d*x^2 + d)*c^2*d*x + 3*c*d^(3/2)*arcsin(c*x) + 2*(-c^2*d*x^2 + d)^(3/2)/x)*a + b*integrate((-c^2*d*x^2 + d)^(3/2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^2, x)","F",0
75,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(3 \, \sqrt{-c^{2} d x^{2} + d} c^{4} d x + 3 \, c^{3} d^{\frac{3}{2}} \arcsin\left(c x\right) + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2}}{x} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{3}}\right)} a + b \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{4}}\,{d x}"," ",0,"1/3*(3*sqrt(-c^2*d*x^2 + d)*c^4*d*x + 3*c^3*d^(3/2)*arcsin(c*x) + 2*(-c^2*d*x^2 + d)^(3/2)*c^2/x - (-c^2*d*x^2 + d)^(5/2)/(d*x^3))*a + b*integrate((-c^2*d*x^2 + d)^(3/2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^4, x)","F",0
76,1,189,0,0.464914," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x^6,x, algorithm=""maxima"")","-\frac{{\left(2 \, c^{6} d^{3} \sqrt{-\frac{1}{c^{4} d}} \log\left(x^{2} - \frac{1}{c^{2}}\right) + 2 i \, \left(-1\right)^{-2 \, c^{2} d x^{2} + 2 \, d} c^{4} d^{\frac{5}{2}} \log\left(-2 \, c^{2} d + \frac{2 \, d}{x^{2}}\right) + \frac{3 \, \sqrt{-c^{4} d x^{4} + 2 \, c^{2} d x^{2} - d} c^{2} d^{2}}{x^{2}} - \frac{\sqrt{-c^{4} d x^{4} + 2 \, c^{2} d x^{2} - d} d^{2}}{x^{4}}\right)} b c}{20 \, d} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b \operatorname{arcosh}\left(c x\right)}{5 \, d x^{5}} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a}{5 \, d x^{5}}"," ",0,"-1/20*(2*c^6*d^3*sqrt(-1/(c^4*d))*log(x^2 - 1/c^2) + 2*I*(-1)^(-2*c^2*d*x^2 + 2*d)*c^4*d^(5/2)*log(-2*c^2*d + 2*d/x^2) + 3*sqrt(-c^4*d*x^4 + 2*c^2*d*x^2 - d)*c^2*d^2/x^2 - sqrt(-c^4*d*x^4 + 2*c^2*d*x^2 - d)*d^2/x^4)*b*c/d - 1/5*(-c^2*d*x^2 + d)^(5/2)*b*arccosh(c*x)/(d*x^5) - 1/5*(-c^2*d*x^2 + d)^(5/2)*a/(d*x^5)","C",0
77,1,163,0,0.471592," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x^8,x, algorithm=""maxima"")","\frac{1}{210} \, {\left(12 \, c^{6} \sqrt{-d} d \log\left(x\right) - \frac{3 \, c^{4} \sqrt{-d} d x^{4} - 12 \, c^{2} \sqrt{-d} d x^{2} + 5 \, \sqrt{-d} d}{x^{6}}\right)} b c - \frac{1}{35} \, b {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{d x^{5}} + \frac{5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{7}}\right)} \operatorname{arcosh}\left(c x\right) - \frac{1}{35} \, a {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{d x^{5}} + \frac{5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{7}}\right)}"," ",0,"1/210*(12*c^6*sqrt(-d)*d*log(x) - (3*c^4*sqrt(-d)*d*x^4 - 12*c^2*sqrt(-d)*d*x^2 + 5*sqrt(-d)*d)/x^6)*b*c - 1/35*b*(2*(-c^2*d*x^2 + d)^(5/2)*c^2/(d*x^5) + 5*(-c^2*d*x^2 + d)^(5/2)/(d*x^7))*arccosh(c*x) - 1/35*a*(2*(-c^2*d*x^2 + d)^(5/2)*c^2/(d*x^5) + 5*(-c^2*d*x^2 + d)^(5/2)/(d*x^7))","A",0
78,1,225,0,0.729661," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x^10,x, algorithm=""maxima"")","\frac{1}{7560} \, {\left(192 \, c^{8} \sqrt{-d} d \log\left(x\right) - \frac{48 \, c^{6} \sqrt{-d} d x^{6} + 18 \, c^{4} \sqrt{-d} d x^{4} - 200 \, c^{2} \sqrt{-d} d x^{2} + 105 \, \sqrt{-d} d}{x^{8}}\right)} b c - \frac{1}{315} \, b {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{4}}{d x^{5}} + \frac{20 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{d x^{7}} + \frac{35 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{9}}\right)} \operatorname{arcosh}\left(c x\right) - \frac{1}{315} \, a {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{4}}{d x^{5}} + \frac{20 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{d x^{7}} + \frac{35 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{9}}\right)}"," ",0,"1/7560*(192*c^8*sqrt(-d)*d*log(x) - (48*c^6*sqrt(-d)*d*x^6 + 18*c^4*sqrt(-d)*d*x^4 - 200*c^2*sqrt(-d)*d*x^2 + 105*sqrt(-d)*d)/x^8)*b*c - 1/315*b*(8*(-c^2*d*x^2 + d)^(5/2)*c^4/(d*x^5) + 20*(-c^2*d*x^2 + d)^(5/2)*c^2/(d*x^7) + 35*(-c^2*d*x^2 + d)^(5/2)/(d*x^9))*arccosh(c*x) - 1/315*a*(8*(-c^2*d*x^2 + d)^(5/2)*c^4/(d*x^5) + 20*(-c^2*d*x^2 + d)^(5/2)*c^2/(d*x^7) + 35*(-c^2*d*x^2 + d)^(5/2)/(d*x^9))","A",0
79,1,287,0,0.714826," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x^12,x, algorithm=""maxima"")","\frac{1}{6930} \, {\left(96 \, c^{10} \sqrt{-d} d \log\left(x\right) - \frac{24 \, c^{8} \sqrt{-d} d x^{8} + 9 \, c^{6} \sqrt{-d} d x^{6} + 5 \, c^{4} \sqrt{-d} d x^{4} - 105 \, c^{2} \sqrt{-d} d x^{2} + 63 \, \sqrt{-d} d}{x^{10}}\right)} b c - \frac{1}{1155} \, {\left(\frac{16 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{6}}{d x^{5}} + \frac{40 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{4}}{d x^{7}} + \frac{70 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{d x^{9}} + \frac{105 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{11}}\right)} b \operatorname{arcosh}\left(c x\right) - \frac{1}{1155} \, {\left(\frac{16 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{6}}{d x^{5}} + \frac{40 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{4}}{d x^{7}} + \frac{70 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{d x^{9}} + \frac{105 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{11}}\right)} a"," ",0,"1/6930*(96*c^10*sqrt(-d)*d*log(x) - (24*c^8*sqrt(-d)*d*x^8 + 9*c^6*sqrt(-d)*d*x^6 + 5*c^4*sqrt(-d)*d*x^4 - 105*c^2*sqrt(-d)*d*x^2 + 63*sqrt(-d)*d)/x^10)*b*c - 1/1155*(16*(-c^2*d*x^2 + d)^(5/2)*c^6/(d*x^5) + 40*(-c^2*d*x^2 + d)^(5/2)*c^4/(d*x^7) + 70*(-c^2*d*x^2 + d)^(5/2)*c^2/(d*x^9) + 105*(-c^2*d*x^2 + d)^(5/2)/(d*x^11))*b*arccosh(c*x) - 1/1155*(16*(-c^2*d*x^2 + d)^(5/2)*c^6/(d*x^5) + 40*(-c^2*d*x^2 + d)^(5/2)*c^4/(d*x^7) + 70*(-c^2*d*x^2 + d)^(5/2)*c^2/(d*x^9) + 105*(-c^2*d*x^2 + d)^(5/2)/(d*x^11))*a","A",0
80,1,285,0,0.925302," ","integrate(x^7*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{1155} \, {\left(\frac{105 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{6}}{c^{2} d} + \frac{70 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{4}}{c^{4} d} + \frac{40 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{6} d} + \frac{16 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{8} d}\right)} b \operatorname{arcosh}\left(c x\right) - \frac{1}{1155} \, {\left(\frac{105 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{6}}{c^{2} d} + \frac{70 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{4}}{c^{4} d} + \frac{40 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{6} d} + \frac{16 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{8} d}\right)} a + \frac{{\left(33075 \, c^{10} \sqrt{-d} d x^{11} - 53900 \, c^{8} \sqrt{-d} d x^{9} + 2475 \, c^{6} \sqrt{-d} d x^{7} + 4158 \, c^{4} \sqrt{-d} d x^{5} + 9240 \, c^{2} \sqrt{-d} d x^{3} + 55440 \, \sqrt{-d} d x\right)} b}{4002075 \, c^{7}}"," ",0,"-1/1155*(105*(-c^2*d*x^2 + d)^(5/2)*x^6/(c^2*d) + 70*(-c^2*d*x^2 + d)^(5/2)*x^4/(c^4*d) + 40*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^6*d) + 16*(-c^2*d*x^2 + d)^(5/2)/(c^8*d))*b*arccosh(c*x) - 1/1155*(105*(-c^2*d*x^2 + d)^(5/2)*x^6/(c^2*d) + 70*(-c^2*d*x^2 + d)^(5/2)*x^4/(c^4*d) + 40*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^6*d) + 16*(-c^2*d*x^2 + d)^(5/2)/(c^8*d))*a + 1/4002075*(33075*c^10*sqrt(-d)*d*x^11 - 53900*c^8*sqrt(-d)*d*x^9 + 2475*c^6*sqrt(-d)*d*x^7 + 4158*c^4*sqrt(-d)*d*x^5 + 9240*c^2*sqrt(-d)*d*x^3 + 55440*sqrt(-d)*d*x)*b/c^7","A",0
81,1,223,0,1.360084," ","integrate(x^5*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{315} \, {\left(\frac{35 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{4}}{c^{2} d} + \frac{20 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{4} d} + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{6} d}\right)} b \operatorname{arcosh}\left(c x\right) - \frac{1}{315} \, {\left(\frac{35 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{4}}{c^{2} d} + \frac{20 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{4} d} + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{6} d}\right)} a + \frac{{\left(1225 \, c^{8} \sqrt{-d} d x^{9} - 2250 \, c^{6} \sqrt{-d} d x^{7} + 189 \, c^{4} \sqrt{-d} d x^{5} + 420 \, c^{2} \sqrt{-d} d x^{3} + 2520 \, \sqrt{-d} d x\right)} b}{99225 \, c^{5}}"," ",0,"-1/315*(35*(-c^2*d*x^2 + d)^(5/2)*x^4/(c^2*d) + 20*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^4*d) + 8*(-c^2*d*x^2 + d)^(5/2)/(c^6*d))*b*arccosh(c*x) - 1/315*(35*(-c^2*d*x^2 + d)^(5/2)*x^4/(c^2*d) + 20*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^4*d) + 8*(-c^2*d*x^2 + d)^(5/2)/(c^6*d))*a + 1/99225*(1225*c^8*sqrt(-d)*d*x^9 - 2250*c^6*sqrt(-d)*d*x^7 + 189*c^4*sqrt(-d)*d*x^5 + 420*c^2*sqrt(-d)*d*x^3 + 2520*sqrt(-d)*d*x)*b/c^5","A",0
82,1,161,0,1.091033," ","integrate(x^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{35} \, {\left(\frac{5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{4} d}\right)} b \operatorname{arcosh}\left(c x\right) - \frac{1}{35} \, {\left(\frac{5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{4} d}\right)} a + \frac{{\left(75 \, c^{6} \sqrt{-d} d x^{7} - 168 \, c^{4} \sqrt{-d} d x^{5} + 35 \, c^{2} \sqrt{-d} d x^{3} + 210 \, \sqrt{-d} d x\right)} b}{3675 \, c^{3}}"," ",0,"-1/35*(5*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(5/2)/(c^4*d))*b*arccosh(c*x) - 1/35*(5*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(5/2)/(c^4*d))*a + 1/3675*(75*c^6*sqrt(-d)*d*x^7 - 168*c^4*sqrt(-d)*d*x^5 + 35*c^2*sqrt(-d)*d*x^3 + 210*sqrt(-d)*d*x)*b/c^3","A",0
83,1,102,0,0.768636," ","integrate(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b \operatorname{arcosh}\left(c x\right)}{5 \, c^{2} d} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a}{5 \, c^{2} d} + \frac{{\left(3 \, c^{4} \sqrt{-d} d^{2} x^{5} - 10 \, c^{2} \sqrt{-d} d^{2} x^{3} + 15 \, \sqrt{-d} d^{2} x\right)} b}{75 \, c d}"," ",0,"-1/5*(-c^2*d*x^2 + d)^(5/2)*b*arccosh(c*x)/(c^2*d) - 1/5*(-c^2*d*x^2 + d)^(5/2)*a/(c^2*d) + 1/75*(3*c^4*sqrt(-d)*d^2*x^5 - 10*c^2*sqrt(-d)*d^2*x^3 + 15*sqrt(-d)*d^2*x)*b/(c*d)","A",0
84,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(3 \, d^{\frac{3}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{-c^{2} d x^{2} + d} d\right)} a + b \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"-1/3*(3*d^(3/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - (-c^2*d*x^2 + d)^(3/2) - 3*sqrt(-c^2*d*x^2 + d)*d)*a + b*integrate((-c^2*d*x^2 + d)^(3/2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
85,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(3 \, c^{2} d^{\frac{3}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} - 3 \, \sqrt{-c^{2} d x^{2} + d} c^{2} d - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{2}}\right)} a + b \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{3}}\,{d x}"," ",0,"1/2*(3*c^2*d^(3/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - (-c^2*d*x^2 + d)^(3/2)*c^2 - 3*sqrt(-c^2*d*x^2 + d)*c^2*d - (-c^2*d*x^2 + d)^(5/2)/(d*x^2))*a + b*integrate((-c^2*d*x^2 + d)^(3/2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^3, x)","F",0
86,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))/x^5,x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(3 \, c^{4} d^{\frac{3}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} - 3 \, \sqrt{-c^{2} d x^{2} + d} c^{4} d - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{d x^{2}} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{4}}\right)} a + b \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{5}}\,{d x}"," ",0,"-1/8*(3*c^4*d^(3/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - (-c^2*d*x^2 + d)^(3/2)*c^4 - 3*sqrt(-c^2*d*x^2 + d)*c^4*d - (-c^2*d*x^2 + d)^(5/2)*c^2/(d*x^2) + 2*(-c^2*d*x^2 + d)^(5/2)/(d*x^4))*a + b*integrate((-c^2*d*x^2 + d)^(3/2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^5, x)","F",0
87,0,0,0,0.000000," ","integrate(x^4*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{1280} \, {\left(\frac{128 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{3}}{c^{2} d} - \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}{c^{4}} + \frac{48 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x}{c^{4} d} - \frac{10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x}{c^{4}} - \frac{15 \, \sqrt{-c^{2} d x^{2} + d} d^{2} x}{c^{4}} - \frac{15 \, d^{\frac{5}{2}} \arcsin\left(c x\right)}{c^{5}}\right)} a + b \int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{4} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"-1/1280*(128*(-c^2*d*x^2 + d)^(7/2)*x^3/(c^2*d) - 8*(-c^2*d*x^2 + d)^(5/2)*x/c^4 + 48*(-c^2*d*x^2 + d)^(7/2)*x/(c^4*d) - 10*(-c^2*d*x^2 + d)^(3/2)*d*x/c^4 - 15*sqrt(-c^2*d*x^2 + d)*d^2*x/c^4 - 15*d^(5/2)*arcsin(c*x)/c^5)*a + b*integrate((-c^2*d*x^2 + d)^(5/2)*x^4*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
88,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{384} \, {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}{c^{2}} - \frac{48 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x}{c^{2} d} + \frac{10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x}{c^{2}} + \frac{15 \, \sqrt{-c^{2} d x^{2} + d} d^{2} x}{c^{2}} + \frac{15 \, d^{\frac{5}{2}} \arcsin\left(c x\right)}{c^{3}}\right)} a + b \int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/384*(8*(-c^2*d*x^2 + d)^(5/2)*x/c^2 - 48*(-c^2*d*x^2 + d)^(7/2)*x/(c^2*d) + 10*(-c^2*d*x^2 + d)^(3/2)*d*x/c^2 + 15*sqrt(-c^2*d*x^2 + d)*d^2*x/c^2 + 15*d^(5/2)*arcsin(c*x)/c^3)*a + b*integrate((-c^2*d*x^2 + d)^(5/2)*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
89,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{48} \, {\left(8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x + 10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} d^{2} x + \frac{15 \, d^{\frac{5}{2}} \arcsin\left(c x\right)}{c}\right)} a + b \int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/48*(8*(-c^2*d*x^2 + d)^(5/2)*x + 10*(-c^2*d*x^2 + d)^(3/2)*d*x + 15*sqrt(-c^2*d*x^2 + d)*d^2*x + 15*d^(5/2)*arcsin(c*x)/c)*a + b*integrate((-c^2*d*x^2 + d)^(5/2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
90,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x^2,x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} c^{2} d^{2} x + 15 \, c d^{\frac{5}{2}} \arcsin\left(c x\right) + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{x}\right)} a + b \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{2}}\,{d x}"," ",0,"-1/8*(10*(-c^2*d*x^2 + d)^(3/2)*c^2*d*x + 15*sqrt(-c^2*d*x^2 + d)*c^2*d^2*x + 15*c*d^(5/2)*arcsin(c*x) + 8*(-c^2*d*x^2 + d)^(5/2)/x)*a + b*integrate((-c^2*d*x^2 + d)^(5/2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^2, x)","F",0
91,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x^4,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} c^{4} d^{2} x + 15 \, c^{3} d^{\frac{5}{2}} \arcsin\left(c x\right) + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{x} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{3}}\right)} a + b \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{4}}\,{d x}"," ",0,"1/6*(10*(-c^2*d*x^2 + d)^(3/2)*c^4*d*x + 15*sqrt(-c^2*d*x^2 + d)*c^4*d^2*x + 15*c^3*d^(5/2)*arcsin(c*x) + 8*(-c^2*d*x^2 + d)^(5/2)*c^2/x - 2*(-c^2*d*x^2 + d)^(7/2)/(d*x^3))*a + b*integrate((-c^2*d*x^2 + d)^(5/2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^4, x)","F",0
92,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x^6,x, algorithm=""maxima"")","-\frac{1}{15} \, {\left(10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{6} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} c^{6} d^{2} x + 15 \, c^{5} d^{\frac{5}{2}} \arcsin\left(c x\right) + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{4}}{x} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} c^{2}}{d x^{3}} + \frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{5}}\right)} a + b \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{6}}\,{d x}"," ",0,"-1/15*(10*(-c^2*d*x^2 + d)^(3/2)*c^6*d*x + 15*sqrt(-c^2*d*x^2 + d)*c^6*d^2*x + 15*c^5*d^(5/2)*arcsin(c*x) + 8*(-c^2*d*x^2 + d)^(5/2)*c^4/x - 2*(-c^2*d*x^2 + d)^(7/2)*c^2/(d*x^3) + 3*(-c^2*d*x^2 + d)^(7/2)/(d*x^5))*a + b*integrate((-c^2*d*x^2 + d)^(5/2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^6, x)","F",0
93,1,224,0,0.958908," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x^8,x, algorithm=""maxima"")","\frac{{\left(6 \, c^{8} d^{4} \sqrt{-\frac{1}{c^{4} d}} \log\left(x^{2} - \frac{1}{c^{2}}\right) + 6 i \, \left(-1\right)^{-2 \, c^{2} d x^{2} + 2 \, d} c^{6} d^{\frac{7}{2}} \log\left(-2 \, c^{2} d + \frac{2 \, d}{x^{2}}\right) + \frac{11 \, \sqrt{-c^{4} d x^{4} + 2 \, c^{2} d x^{2} - d} c^{4} d^{3}}{x^{2}} - \frac{7 \, \sqrt{-c^{4} d x^{4} + 2 \, c^{2} d x^{2} - d} c^{2} d^{3}}{x^{4}} + \frac{2 \, \sqrt{-c^{4} d x^{4} + 2 \, c^{2} d x^{2} - d} d^{3}}{x^{6}}\right)} b c}{84 \, d} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} b \operatorname{arcosh}\left(c x\right)}{7 \, d x^{7}} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a}{7 \, d x^{7}}"," ",0,"1/84*(6*c^8*d^4*sqrt(-1/(c^4*d))*log(x^2 - 1/c^2) + 6*I*(-1)^(-2*c^2*d*x^2 + 2*d)*c^6*d^(7/2)*log(-2*c^2*d + 2*d/x^2) + 11*sqrt(-c^4*d*x^4 + 2*c^2*d*x^2 - d)*c^4*d^3/x^2 - 7*sqrt(-c^4*d*x^4 + 2*c^2*d*x^2 - d)*c^2*d^3/x^4 + 2*sqrt(-c^4*d*x^4 + 2*c^2*d*x^2 - d)*d^3/x^6)*b*c/d - 1/7*(-c^2*d*x^2 + d)^(7/2)*b*arccosh(c*x)/(d*x^7) - 1/7*(-c^2*d*x^2 + d)^(7/2)*a/(d*x^7)","C",0
94,1,187,0,0.518480," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x^10,x, algorithm=""maxima"")","-\frac{1}{1512} \, {\left(48 \, c^{8} \sqrt{-d} d^{2} \log\left(x\right) - \frac{12 \, c^{6} \sqrt{-d} d^{2} x^{6} - 90 \, c^{4} \sqrt{-d} d^{2} x^{4} + 76 \, c^{2} \sqrt{-d} d^{2} x^{2} - 21 \, \sqrt{-d} d^{2}}{x^{8}}\right)} b c - \frac{1}{63} \, b {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} c^{2}}{d x^{7}} + \frac{7 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{9}}\right)} \operatorname{arcosh}\left(c x\right) - \frac{1}{63} \, a {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} c^{2}}{d x^{7}} + \frac{7 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{9}}\right)}"," ",0,"-1/1512*(48*c^8*sqrt(-d)*d^2*log(x) - (12*c^6*sqrt(-d)*d^2*x^6 - 90*c^4*sqrt(-d)*d^2*x^4 + 76*c^2*sqrt(-d)*d^2*x^2 - 21*sqrt(-d)*d^2)/x^8)*b*c - 1/63*b*(2*(-c^2*d*x^2 + d)^(7/2)*c^2/(d*x^7) + 7*(-c^2*d*x^2 + d)^(7/2)/(d*x^9))*arccosh(c*x) - 1/63*a*(2*(-c^2*d*x^2 + d)^(7/2)*c^2/(d*x^7) + 7*(-c^2*d*x^2 + d)^(7/2)/(d*x^9))","A",0
95,1,251,0,0.800533," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x^12,x, algorithm=""maxima"")","-\frac{1}{83160} \, {\left(960 \, c^{10} \sqrt{-d} d^{2} \log\left(x\right) - \frac{240 \, c^{8} \sqrt{-d} d^{2} x^{8} + 90 \, c^{6} \sqrt{-d} d^{2} x^{6} - 2260 \, c^{4} \sqrt{-d} d^{2} x^{4} + 2415 \, c^{2} \sqrt{-d} d^{2} x^{2} - 756 \, \sqrt{-d} d^{2}}{x^{10}}\right)} b c - \frac{1}{693} \, b {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} c^{4}}{d x^{7}} + \frac{28 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} c^{2}}{d x^{9}} + \frac{63 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{11}}\right)} \operatorname{arcosh}\left(c x\right) - \frac{1}{693} \, a {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} c^{4}}{d x^{7}} + \frac{28 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} c^{2}}{d x^{9}} + \frac{63 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{11}}\right)}"," ",0,"-1/83160*(960*c^10*sqrt(-d)*d^2*log(x) - (240*c^8*sqrt(-d)*d^2*x^8 + 90*c^6*sqrt(-d)*d^2*x^6 - 2260*c^4*sqrt(-d)*d^2*x^4 + 2415*c^2*sqrt(-d)*d^2*x^2 - 756*sqrt(-d)*d^2)/x^10)*b*c - 1/693*b*(8*(-c^2*d*x^2 + d)^(7/2)*c^4/(d*x^7) + 28*(-c^2*d*x^2 + d)^(7/2)*c^2/(d*x^9) + 63*(-c^2*d*x^2 + d)^(7/2)/(d*x^11))*arccosh(c*x) - 1/693*a*(8*(-c^2*d*x^2 + d)^(7/2)*c^4/(d*x^7) + 28*(-c^2*d*x^2 + d)^(7/2)*c^2/(d*x^9) + 63*(-c^2*d*x^2 + d)^(7/2)/(d*x^11))","A",0
96,1,313,0,0.951566," ","integrate(x^7*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{3003} \, {\left(\frac{231 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{6}}{c^{2} d} + \frac{126 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{4}}{c^{4} d} + \frac{56 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{6} d} + \frac{16 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{8} d}\right)} b \operatorname{arcosh}\left(c x\right) - \frac{1}{3003} \, {\left(\frac{231 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{6}}{c^{2} d} + \frac{126 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{4}}{c^{4} d} + \frac{56 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{6} d} + \frac{16 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{8} d}\right)} a - \frac{{\left(800415 \, c^{12} \sqrt{-d} d^{2} x^{13} - 2321865 \, c^{10} \sqrt{-d} d^{2} x^{11} + 1856855 \, c^{8} \sqrt{-d} d^{2} x^{9} - 32175 \, c^{6} \sqrt{-d} d^{2} x^{7} - 54054 \, c^{4} \sqrt{-d} d^{2} x^{5} - 120120 \, c^{2} \sqrt{-d} d^{2} x^{3} - 720720 \, \sqrt{-d} d^{2} x\right)} b}{135270135 \, c^{7}}"," ",0,"-1/3003*(231*(-c^2*d*x^2 + d)^(7/2)*x^6/(c^2*d) + 126*(-c^2*d*x^2 + d)^(7/2)*x^4/(c^4*d) + 56*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^6*d) + 16*(-c^2*d*x^2 + d)^(7/2)/(c^8*d))*b*arccosh(c*x) - 1/3003*(231*(-c^2*d*x^2 + d)^(7/2)*x^6/(c^2*d) + 126*(-c^2*d*x^2 + d)^(7/2)*x^4/(c^4*d) + 56*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^6*d) + 16*(-c^2*d*x^2 + d)^(7/2)/(c^8*d))*a - 1/135270135*(800415*c^12*sqrt(-d)*d^2*x^13 - 2321865*c^10*sqrt(-d)*d^2*x^11 + 1856855*c^8*sqrt(-d)*d^2*x^9 - 32175*c^6*sqrt(-d)*d^2*x^7 - 54054*c^4*sqrt(-d)*d^2*x^5 - 120120*c^2*sqrt(-d)*d^2*x^3 - 720720*sqrt(-d)*d^2*x)*b/c^7","A",0
97,1,249,0,0.883209," ","integrate(x^5*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{693} \, {\left(\frac{63 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{4}}{c^{2} d} + \frac{28 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{4} d} + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{6} d}\right)} b \operatorname{arcosh}\left(c x\right) - \frac{1}{693} \, {\left(\frac{63 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{4}}{c^{2} d} + \frac{28 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{4} d} + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{6} d}\right)} a - \frac{{\left(19845 \, c^{10} \sqrt{-d} d^{2} x^{11} - 61985 \, c^{8} \sqrt{-d} d^{2} x^{9} + 55935 \, c^{6} \sqrt{-d} d^{2} x^{7} - 2079 \, c^{4} \sqrt{-d} d^{2} x^{5} - 4620 \, c^{2} \sqrt{-d} d^{2} x^{3} - 27720 \, \sqrt{-d} d^{2} x\right)} b}{2401245 \, c^{5}}"," ",0,"-1/693*(63*(-c^2*d*x^2 + d)^(7/2)*x^4/(c^2*d) + 28*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^4*d) + 8*(-c^2*d*x^2 + d)^(7/2)/(c^6*d))*b*arccosh(c*x) - 1/693*(63*(-c^2*d*x^2 + d)^(7/2)*x^4/(c^2*d) + 28*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^4*d) + 8*(-c^2*d*x^2 + d)^(7/2)/(c^6*d))*a - 1/2401245*(19845*c^10*sqrt(-d)*d^2*x^11 - 61985*c^8*sqrt(-d)*d^2*x^9 + 55935*c^6*sqrt(-d)*d^2*x^7 - 2079*c^4*sqrt(-d)*d^2*x^5 - 4620*c^2*sqrt(-d)*d^2*x^3 - 27720*sqrt(-d)*d^2*x)*b/c^5","A",0
98,1,185,0,0.950176," ","integrate(x^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{1}{63} \, {\left(\frac{7 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{4} d}\right)} b \operatorname{arcosh}\left(c x\right) - \frac{1}{63} \, {\left(\frac{7 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{4} d}\right)} a - \frac{{\left(49 \, c^{8} \sqrt{-d} d^{2} x^{9} - 171 \, c^{6} \sqrt{-d} d^{2} x^{7} + 189 \, c^{4} \sqrt{-d} d^{2} x^{5} - 21 \, c^{2} \sqrt{-d} d^{2} x^{3} - 126 \, \sqrt{-d} d^{2} x\right)} b}{3969 \, c^{3}}"," ",0,"-1/63*(7*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(7/2)/(c^4*d))*b*arccosh(c*x) - 1/63*(7*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(7/2)/(c^4*d))*a - 1/3969*(49*c^8*sqrt(-d)*d^2*x^9 - 171*c^6*sqrt(-d)*d^2*x^7 + 189*c^4*sqrt(-d)*d^2*x^5 - 21*c^2*sqrt(-d)*d^2*x^3 - 126*sqrt(-d)*d^2*x)*b/c^3","A",0
99,1,118,0,0.683864," ","integrate(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} b \operatorname{arcosh}\left(c x\right)}{7 \, c^{2} d} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a}{7 \, c^{2} d} - \frac{{\left(5 \, c^{6} \sqrt{-d} d^{3} x^{7} - 21 \, c^{4} \sqrt{-d} d^{3} x^{5} + 35 \, c^{2} \sqrt{-d} d^{3} x^{3} - 35 \, \sqrt{-d} d^{3} x\right)} b}{245 \, c d}"," ",0,"-1/7*(-c^2*d*x^2 + d)^(7/2)*b*arccosh(c*x)/(c^2*d) - 1/7*(-c^2*d*x^2 + d)^(7/2)*a/(c^2*d) - 1/245*(5*c^6*sqrt(-d)*d^3*x^7 - 21*c^4*sqrt(-d)*d^3*x^5 + 35*c^2*sqrt(-d)*d^3*x^3 - 35*sqrt(-d)*d^3*x)*b/(c*d)","A",0
100,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x,x, algorithm=""maxima"")","-\frac{1}{15} \, {\left(15 \, d^{\frac{5}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - 3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} - 5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d - 15 \, \sqrt{-c^{2} d x^{2} + d} d^{2}\right)} a + b \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"-1/15*(15*d^(5/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - 3*(-c^2*d*x^2 + d)^(5/2) - 5*(-c^2*d*x^2 + d)^(3/2)*d - 15*sqrt(-c^2*d*x^2 + d)*d^2)*a + b*integrate((-c^2*d*x^2 + d)^(5/2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
101,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(15 \, c^{2} d^{\frac{5}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - 3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2} - 5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d - 15 \, \sqrt{-c^{2} d x^{2} + d} c^{2} d^{2} - \frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{2}}\right)} a + b \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{3}}\,{d x}"," ",0,"1/6*(15*c^2*d^(5/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - 3*(-c^2*d*x^2 + d)^(5/2)*c^2 - 5*(-c^2*d*x^2 + d)^(3/2)*c^2*d - 15*sqrt(-c^2*d*x^2 + d)*c^2*d^2 - 3*(-c^2*d*x^2 + d)^(7/2)/(d*x^2))*a + b*integrate((-c^2*d*x^2 + d)^(5/2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^3, x)","F",0
102,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))/x^5,x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(15 \, c^{4} d^{\frac{5}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - 3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{4} - 5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d - 15 \, \sqrt{-c^{2} d x^{2} + d} c^{4} d^{2} - \frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} c^{2}}{d x^{2}} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{4}}\right)} a + b \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{5}}\,{d x}"," ",0,"-1/8*(15*c^4*d^(5/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - 3*(-c^2*d*x^2 + d)^(5/2)*c^4 - 5*(-c^2*d*x^2 + d)^(3/2)*c^4*d - 15*sqrt(-c^2*d*x^2 + d)*c^4*d^2 - 3*(-c^2*d*x^2 + d)^(7/2)*c^2/(d*x^2) + 2*(-c^2*d*x^2 + d)^(7/2)/(d*x^4))*a + b*integrate((-c^2*d*x^2 + d)^(5/2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^5, x)","F",0
103,-2,0,0,0.000000," ","integrate(arccosh(x)*(-x^2+1)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
104,1,195,0,0.926834," ","integrate(x^5*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{15} \, {\left(\frac{3 \, \sqrt{-c^{2} d x^{2} + d} x^{4}}{c^{2} d} + \frac{4 \, \sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{4} d} + \frac{8 \, \sqrt{-c^{2} d x^{2} + d}}{c^{6} d}\right)} b \operatorname{arcosh}\left(c x\right) - \frac{1}{15} \, {\left(\frac{3 \, \sqrt{-c^{2} d x^{2} + d} x^{4}}{c^{2} d} + \frac{4 \, \sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{4} d} + \frac{8 \, \sqrt{-c^{2} d x^{2} + d}}{c^{6} d}\right)} a + \frac{{\left(9 \, c^{4} \sqrt{-d} x^{5} + 20 \, c^{2} \sqrt{-d} x^{3} + 120 \, \sqrt{-d} x\right)} b}{225 \, c^{5} d}"," ",0,"-1/15*(3*sqrt(-c^2*d*x^2 + d)*x^4/(c^2*d) + 4*sqrt(-c^2*d*x^2 + d)*x^2/(c^4*d) + 8*sqrt(-c^2*d*x^2 + d)/(c^6*d))*b*arccosh(c*x) - 1/15*(3*sqrt(-c^2*d*x^2 + d)*x^4/(c^2*d) + 4*sqrt(-c^2*d*x^2 + d)*x^2/(c^4*d) + 8*sqrt(-c^2*d*x^2 + d)/(c^6*d))*a + 1/225*(9*c^4*sqrt(-d)*x^5 + 20*c^2*sqrt(-d)*x^3 + 120*sqrt(-d)*x)*b/(c^5*d)","A",0
105,0,0,0,0.000000," ","integrate(x^4*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} x^{3}}{c^{2} d} + \frac{3 \, \sqrt{-c^{2} d x^{2} + d} x}{c^{4} d} - \frac{3 \, \arcsin\left(c x\right)}{c^{5} \sqrt{d}}\right)} + b \int \frac{x^{4} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"-1/8*a*(2*sqrt(-c^2*d*x^2 + d)*x^3/(c^2*d) + 3*sqrt(-c^2*d*x^2 + d)*x/(c^4*d) - 3*arcsin(c*x)/(c^5*sqrt(d))) + b*integrate(x^4*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c^2*d*x^2 + d), x)","F",0
106,1,131,0,0.843241," ","integrate(x^3*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, b {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{2} d} + \frac{2 \, \sqrt{-c^{2} d x^{2} + d}}{c^{4} d}\right)} \operatorname{arcosh}\left(c x\right) - \frac{1}{3} \, a {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{2} d} + \frac{2 \, \sqrt{-c^{2} d x^{2} + d}}{c^{4} d}\right)} + \frac{{\left(c^{2} \sqrt{-d} x^{3} + 6 \, \sqrt{-d} x\right)} b}{9 \, c^{3} d}"," ",0,"-1/3*b*(sqrt(-c^2*d*x^2 + d)*x^2/(c^2*d) + 2*sqrt(-c^2*d*x^2 + d)/(c^4*d))*arccosh(c*x) - 1/3*a*(sqrt(-c^2*d*x^2 + d)*x^2/(c^2*d) + 2*sqrt(-c^2*d*x^2 + d)/(c^4*d)) + 1/9*(c^2*sqrt(-d)*x^3 + 6*sqrt(-d)*x)*b/(c^3*d)","A",0
107,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x}{c^{2} d} - \frac{\arcsin\left(c x\right)}{c^{3} \sqrt{d}}\right)} + b \int \frac{x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"-1/2*a*(sqrt(-c^2*d*x^2 + d)*x/(c^2*d) - arcsin(c*x)/(c^3*sqrt(d))) + b*integrate(x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c^2*d*x^2 + d), x)","F",0
108,1,63,0,1.251160," ","integrate(x*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{b \sqrt{-d} x}{c d} - \frac{\sqrt{-c^{2} d x^{2} + d} b \operatorname{arcosh}\left(c x\right)}{c^{2} d} - \frac{\sqrt{-c^{2} d x^{2} + d} a}{c^{2} d}"," ",0,"b*sqrt(-d)*x/(c*d) - sqrt(-c^2*d*x^2 + d)*b*arccosh(c*x)/(c^2*d) - sqrt(-c^2*d*x^2 + d)*a/(c^2*d)","A",0
109,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d}}\,{d x} + \frac{a \arcsin\left(c x\right)}{c \sqrt{d}}"," ",0,"b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c^2*d*x^2 + d), x) + a*arcsin(c*x)/(c*sqrt(d))","F",0
110,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d} x}\,{d x} - \frac{a \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{\sqrt{d}}"," ",0,"b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(sqrt(-c^2*d*x^2 + d)*x), x) - a*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/sqrt(d)","F",0
111,1,116,0,0.541238," ","integrate((a+b*arccosh(c*x))/x^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(c^{2} d \sqrt{-\frac{1}{c^{4} d}} \log\left(x^{2} - \frac{1}{c^{2}}\right) + i \, \left(-1\right)^{-2 \, c^{2} d x^{2} + 2 \, d} \sqrt{d} \log\left(-2 \, c^{2} d + \frac{2 \, d}{x^{2}}\right)\right)} b c}{2 \, d} - \frac{\sqrt{-c^{2} d x^{2} + d} b \operatorname{arcosh}\left(c x\right)}{d x} - \frac{\sqrt{-c^{2} d x^{2} + d} a}{d x}"," ",0,"-1/2*(c^2*d*sqrt(-1/(c^4*d))*log(x^2 - 1/c^2) + I*(-1)^(-2*c^2*d*x^2 + 2*d)*sqrt(d)*log(-2*c^2*d + 2*d/x^2))*b*c/d - sqrt(-c^2*d*x^2 + d)*b*arccosh(c*x)/(d*x) - sqrt(-c^2*d*x^2 + d)*a/(d*x)","C",0
112,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^3/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{\sqrt{d}} + \frac{\sqrt{-c^{2} d x^{2} + d}}{d x^{2}}\right)} a + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d} x^{3}}\,{d x}"," ",0,"-1/2*(c^2*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/sqrt(d) + sqrt(-c^2*d*x^2 + d)/(d*x^2))*a + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(sqrt(-c^2*d*x^2 + d)*x^3), x)","F",0
113,1,134,0,0.971686," ","integrate((a+b*arccosh(c*x))/x^4/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{4 \, c^{2} \sqrt{-d} \log\left(x\right)}{d} - \frac{\sqrt{-d}}{d x^{2}}\right)} b c - \frac{1}{3} \, b {\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} c^{2}}{d x} + \frac{\sqrt{-c^{2} d x^{2} + d}}{d x^{3}}\right)} \operatorname{arcosh}\left(c x\right) - \frac{1}{3} \, a {\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} c^{2}}{d x} + \frac{\sqrt{-c^{2} d x^{2} + d}}{d x^{3}}\right)}"," ",0,"1/6*(4*c^2*sqrt(-d)*log(x)/d - sqrt(-d)/(d*x^2))*b*c - 1/3*b*(2*sqrt(-c^2*d*x^2 + d)*c^2/(d*x) + sqrt(-c^2*d*x^2 + d)/(d*x^3))*arccosh(c*x) - 1/3*a*(2*sqrt(-c^2*d*x^2 + d)*c^2/(d*x) + sqrt(-c^2*d*x^2 + d)/(d*x^3))","A",0
114,0,0,0,0.000000," ","integrate(x^5*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{x^{4}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} + \frac{4 \, x^{2}}{\sqrt{-c^{2} d x^{2} + d} c^{4} d} - \frac{8}{\sqrt{-c^{2} d x^{2} + d} c^{6} d}\right)} + \frac{1}{9} \, b {\left(\frac{\frac{{\left(c^{4} \sqrt{d} x^{4} + 16 \, c^{2} \sqrt{d} x^{2} - 8 \, \sqrt{d}\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{\sqrt{-c x + 1}} - \frac{3 \, {\left(c^{5} \sqrt{d} x^{5} + 4 \, c^{3} \sqrt{d} x^{3} - 8 \, c \sqrt{d} x + {\left(c^{4} \sqrt{d} x^{4} + 4 \, c^{2} \sqrt{d} x^{2} - 8 \, \sqrt{d}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c x + 1}}}{\sqrt{c x + 1} c^{7} d^{2} x + {\left(c x + 1\right)} \sqrt{c x - 1} c^{6} d^{2}} + 9 \, \int \frac{3 \, c^{7} \sqrt{d} x^{7} + 9 \, c^{5} \sqrt{d} x^{5} - 36 \, c^{3} \sqrt{d} x^{3} + 24 \, c \sqrt{d} x + {\left(3 \, c^{6} \sqrt{d} x^{6} + 8 \, c^{4} \sqrt{d} x^{4} - 52 \, c^{2} \sqrt{d} x^{2} + 32 \, \sqrt{d}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)}}{9 \, \sqrt{-c x + 1} {\left({\left(c^{7} d^{2} x^{2} - c^{5} d^{2}\right)} e^{\left(\frac{3}{2} \, \log\left(c x + 1\right) + \log\left(c x - 1\right)\right)} + 2 \, {\left(c^{8} d^{2} x^{3} - c^{6} d^{2} x\right)} e^{\left(\log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)} + {\left(c^{9} d^{2} x^{4} - c^{7} d^{2} x^{2}\right)} \sqrt{c x + 1}\right)}}\,{d x}\right)}"," ",0,"-1/3*a*(x^4/(sqrt(-c^2*d*x^2 + d)*c^2*d) + 4*x^2/(sqrt(-c^2*d*x^2 + d)*c^4*d) - 8/(sqrt(-c^2*d*x^2 + d)*c^6*d)) + 1/9*b*(((c^4*sqrt(d)*x^4 + 16*c^2*sqrt(d)*x^2 - 8*sqrt(d))*sqrt(c*x + 1)*sqrt(c*x - 1)/sqrt(-c*x + 1) - 3*(c^5*sqrt(d)*x^5 + 4*c^3*sqrt(d)*x^3 - 8*c*sqrt(d)*x + (c^4*sqrt(d)*x^4 + 4*c^2*sqrt(d)*x^2 - 8*sqrt(d))*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c*x + 1))/(sqrt(c*x + 1)*c^7*d^2*x + (c*x + 1)*sqrt(c*x - 1)*c^6*d^2) + 9*integrate(1/9*(3*c^7*sqrt(d)*x^7 + 9*c^5*sqrt(d)*x^5 - 36*c^3*sqrt(d)*x^3 + 24*c*sqrt(d)*x + (3*c^6*sqrt(d)*x^6 + 8*c^4*sqrt(d)*x^4 - 52*c^2*sqrt(d)*x^2 + 32*sqrt(d))*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1)))/(sqrt(-c*x + 1)*((c^7*d^2*x^2 - c^5*d^2)*e^(3/2*log(c*x + 1) + log(c*x - 1)) + 2*(c^8*d^2*x^3 - c^6*d^2*x)*e^(log(c*x + 1) + 1/2*log(c*x - 1)) + (c^9*d^2*x^4 - c^7*d^2*x^2)*sqrt(c*x + 1))), x))","F",0
115,0,0,0,0.000000," ","integrate(x^4*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{x^{3}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{3 \, x}{\sqrt{-c^{2} d x^{2} + d} c^{4} d} + \frac{3 \, \arcsin\left(c x\right)}{c^{5} d^{\frac{3}{2}}}\right)} + b \int \frac{x^{4} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-1/2*a*(x^3/(sqrt(-c^2*d*x^2 + d)*c^2*d) - 3*x/(sqrt(-c^2*d*x^2 + d)*c^4*d) + 3*arcsin(c*x)/(c^5*d^(3/2))) + b*integrate(x^4*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(-c^2*d*x^2 + d)^(3/2), x)","F",0
116,1,157,0,0.928884," ","integrate(x^3*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, b c {\left(\frac{2 \, \sqrt{-d} x}{c^{4} d^{2}} + \frac{\sqrt{-d} \log\left(c x + 1\right)}{c^{5} d^{2}} - \frac{\sqrt{-d} \log\left(c x - 1\right)}{c^{5} d^{2}}\right)} - b {\left(\frac{x^{2}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{2}{\sqrt{-c^{2} d x^{2} + d} c^{4} d}\right)} \operatorname{arcosh}\left(c x\right) - a {\left(\frac{x^{2}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{2}{\sqrt{-c^{2} d x^{2} + d} c^{4} d}\right)}"," ",0,"-1/2*b*c*(2*sqrt(-d)*x/(c^4*d^2) + sqrt(-d)*log(c*x + 1)/(c^5*d^2) - sqrt(-d)*log(c*x - 1)/(c^5*d^2)) - b*(x^2/(sqrt(-c^2*d*x^2 + d)*c^2*d) - 2/(sqrt(-c^2*d*x^2 + d)*c^4*d))*arccosh(c*x) - a*(x^2/(sqrt(-c^2*d*x^2 + d)*c^2*d) - 2/(sqrt(-c^2*d*x^2 + d)*c^4*d))","A",0
117,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","a {\left(\frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{\arcsin\left(c x\right)}{c^{3} d^{\frac{3}{2}}}\right)} + b \int \frac{x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"a*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d) - arcsin(c*x)/(c^3*d^(3/2))) + b*integrate(x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(-c^2*d*x^2 + d)^(3/2), x)","F",0
118,0,0,0,0.000000," ","integrate(x*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","b {\left(\frac{\frac{{\left(c \sqrt{d} x + \sqrt{c x + 1} \sqrt{c x - 1} \sqrt{d}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c x + 1}} + \frac{\sqrt{c x + 1} \sqrt{c x - 1} \sqrt{d}}{\sqrt{-c x + 1}}}{\sqrt{c x + 1} c^{3} d^{2} x + {\left(c x + 1\right)} \sqrt{c x - 1} c^{2} d^{2}} - \int \frac{c^{2} x^{3} + c x^{2} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)} - x}{\sqrt{-c x + 1} {\left({\left(c^{2} d^{\frac{3}{2}} x^{2} - d^{\frac{3}{2}}\right)} e^{\left(\frac{3}{2} \, \log\left(c x + 1\right) + \log\left(c x - 1\right)\right)} + 2 \, {\left(c^{3} d^{\frac{3}{2}} x^{3} - c d^{\frac{3}{2}} x\right)} e^{\left(\log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)} + {\left(c^{4} d^{\frac{3}{2}} x^{4} - c^{2} d^{\frac{3}{2}} x^{2}\right)} \sqrt{c x + 1}\right)}}\,{d x}\right)} + \frac{a}{\sqrt{-c^{2} d x^{2} + d} c^{2} d}"," ",0,"b*(((c*sqrt(d)*x + sqrt(c*x + 1)*sqrt(c*x - 1)*sqrt(d))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c*x + 1) + sqrt(c*x + 1)*sqrt(c*x - 1)*sqrt(d)/sqrt(-c*x + 1))/(sqrt(c*x + 1)*c^3*d^2*x + (c*x + 1)*sqrt(c*x - 1)*c^2*d^2) - integrate((c^2*x^3 + c*x^2*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1)) - x)/(sqrt(-c*x + 1)*((c^2*d^(3/2)*x^2 - d^(3/2))*e^(3/2*log(c*x + 1) + log(c*x - 1)) + 2*(c^3*d^(3/2)*x^3 - c*d^(3/2)*x)*e^(log(c*x + 1) + 1/2*log(c*x - 1)) + (c^4*d^(3/2)*x^4 - c^2*d^(3/2)*x^2)*sqrt(c*x + 1))), x)) + a/(sqrt(-c^2*d*x^2 + d)*c^2*d)","F",0
119,1,70,0,0.703569," ","integrate((a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{b c \sqrt{-\frac{1}{c^{4} d}} \log\left(x^{2} - \frac{1}{c^{2}}\right)}{2 \, d} + \frac{b x \operatorname{arcosh}\left(c x\right)}{\sqrt{-c^{2} d x^{2} + d} d} + \frac{a x}{\sqrt{-c^{2} d x^{2} + d} d}"," ",0,"-1/2*b*c*sqrt(-1/(c^4*d))*log(x^2 - 1/c^2)/d + b*x*arccosh(c*x)/(sqrt(-c^2*d*x^2 + d)*d) + a*x/(sqrt(-c^2*d*x^2 + d)*d)","A",0
120,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{\log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{1}{\sqrt{-c^{2} d x^{2} + d} d}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"-a*(log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/d^(3/2) - 1/(sqrt(-c^2*d*x^2 + d)*d)) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/((-c^2*d*x^2 + d)^(3/2)*x), x)","F",0
121,1,144,0,0.742075," ","integrate((a+b*arccosh(c*x))/x^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, b c {\left(\frac{\sqrt{-d} \log\left(c x + 1\right)}{d^{2}} + \frac{\sqrt{-d} \log\left(c x - 1\right)}{d^{2}} + \frac{2 \, \sqrt{-d} \log\left(x\right)}{d^{2}}\right)} + {\left(\frac{2 \, c^{2} x}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{1}{\sqrt{-c^{2} d x^{2} + d} d x}\right)} b \operatorname{arcosh}\left(c x\right) + {\left(\frac{2 \, c^{2} x}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{1}{\sqrt{-c^{2} d x^{2} + d} d x}\right)} a"," ",0,"1/2*b*c*(sqrt(-d)*log(c*x + 1)/d^2 + sqrt(-d)*log(c*x - 1)/d^2 + 2*sqrt(-d)*log(x)/d^2) + (2*c^2*x/(sqrt(-c^2*d*x^2 + d)*d) - 1/(sqrt(-c^2*d*x^2 + d)*d*x))*b*arccosh(c*x) + (2*c^2*x/(sqrt(-c^2*d*x^2 + d)*d) - 1/(sqrt(-c^2*d*x^2 + d)*d*x))*a","A",0
122,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^3/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{3 \, c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{3 \, c^{2}}{\sqrt{-c^{2} d x^{2} + d} d} + \frac{1}{\sqrt{-c^{2} d x^{2} + d} d x^{2}}\right)} a + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"-1/2*(3*c^2*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/d^(3/2) - 3*c^2/(sqrt(-c^2*d*x^2 + d)*d) + 1/(sqrt(-c^2*d*x^2 + d)*d*x^2))*a + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/((-c^2*d*x^2 + d)^(3/2)*x^3), x)","F",0
123,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^4/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{8 \, c^{4} x}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{4 \, c^{2}}{\sqrt{-c^{2} d x^{2} + d} d x} - \frac{1}{\sqrt{-c^{2} d x^{2} + d} d x^{3}}\right)} a + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"1/3*(8*c^4*x/(sqrt(-c^2*d*x^2 + d)*d) - 4*c^2/(sqrt(-c^2*d*x^2 + d)*d*x) - 1/(sqrt(-c^2*d*x^2 + d)*d*x^3))*a + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/((-c^2*d*x^2 + d)^(3/2)*x^4), x)","F",0
124,0,0,0,0.000000," ","integrate(x^5*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{9} \, b {\left(\frac{\frac{{\left(9 \, c^{4} \sqrt{d} x^{4} - 8 \, \sqrt{d}\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{\sqrt{-c x + 1}} - \frac{3 \, {\left(3 \, c^{5} \sqrt{d} x^{5} - 12 \, c^{3} \sqrt{d} x^{3} + 8 \, c \sqrt{d} x + {\left(3 \, c^{4} \sqrt{d} x^{4} - 12 \, c^{2} \sqrt{d} x^{2} + 8 \, \sqrt{d}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c x + 1}}}{{\left(c^{8} d^{3} x^{2} - c^{6} d^{3}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{9} d^{3} x^{3} - c^{7} d^{3} x\right)} \sqrt{c x + 1}} + 9 \, \int \frac{9 \, c^{7} \sqrt{d} x^{7} - 45 \, c^{5} \sqrt{d} x^{5} + 60 \, c^{3} \sqrt{d} x^{3} - 24 \, c \sqrt{d} x + {\left(9 \, c^{6} \sqrt{d} x^{6} - 54 \, c^{4} \sqrt{d} x^{4} + 60 \, c^{2} \sqrt{d} x^{2} - 16 \, \sqrt{d}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)}}{9 \, \sqrt{-c x + 1} {\left({\left(c^{9} d^{3} x^{4} - 2 \, c^{7} d^{3} x^{2} + c^{5} d^{3}\right)} e^{\left(\frac{3}{2} \, \log\left(c x + 1\right) + \log\left(c x - 1\right)\right)} + 2 \, {\left(c^{10} d^{3} x^{5} - 2 \, c^{8} d^{3} x^{3} + c^{6} d^{3} x\right)} e^{\left(\log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)} + {\left(c^{11} d^{3} x^{6} - 2 \, c^{9} d^{3} x^{4} + c^{7} d^{3} x^{2}\right)} \sqrt{c x + 1}\right)}}\,{d x}\right)} - \frac{1}{3} \, a {\left(\frac{3 \, x^{4}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} - \frac{12 \, x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d} + \frac{8}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{6} d}\right)}"," ",0,"-1/9*b*(((9*c^4*sqrt(d)*x^4 - 8*sqrt(d))*sqrt(c*x + 1)*sqrt(c*x - 1)/sqrt(-c*x + 1) - 3*(3*c^5*sqrt(d)*x^5 - 12*c^3*sqrt(d)*x^3 + 8*c*sqrt(d)*x + (3*c^4*sqrt(d)*x^4 - 12*c^2*sqrt(d)*x^2 + 8*sqrt(d))*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c*x + 1))/((c^8*d^3*x^2 - c^6*d^3)*(c*x + 1)*sqrt(c*x - 1) + (c^9*d^3*x^3 - c^7*d^3*x)*sqrt(c*x + 1)) + 9*integrate(1/9*(9*c^7*sqrt(d)*x^7 - 45*c^5*sqrt(d)*x^5 + 60*c^3*sqrt(d)*x^3 - 24*c*sqrt(d)*x + (9*c^6*sqrt(d)*x^6 - 54*c^4*sqrt(d)*x^4 + 60*c^2*sqrt(d)*x^2 - 16*sqrt(d))*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1)))/(sqrt(-c*x + 1)*((c^9*d^3*x^4 - 2*c^7*d^3*x^2 + c^5*d^3)*e^(3/2*log(c*x + 1) + log(c*x - 1)) + 2*(c^10*d^3*x^5 - 2*c^8*d^3*x^3 + c^6*d^3*x)*e^(log(c*x + 1) + 1/2*log(c*x - 1)) + (c^11*d^3*x^6 - 2*c^9*d^3*x^4 + c^7*d^3*x^2)*sqrt(c*x + 1))), x)) - 1/3*a*(3*x^4/((-c^2*d*x^2 + d)^(3/2)*c^2*d) - 12*x^2/((-c^2*d*x^2 + d)^(3/2)*c^4*d) + 8/((-c^2*d*x^2 + d)^(3/2)*c^6*d))","F",0
125,0,0,0,0.000000," ","integrate(x^4*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(x {\left(\frac{3 \, x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} - \frac{2}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)} - \frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{4} d^{2}} + \frac{3 \, \arcsin\left(c x\right)}{c^{5} d^{\frac{5}{2}}}\right)} a + b \int \frac{x^{4} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/3*(x*(3*x^2/((-c^2*d*x^2 + d)^(3/2)*c^2*d) - 2/((-c^2*d*x^2 + d)^(3/2)*c^4*d)) - x/(sqrt(-c^2*d*x^2 + d)*c^4*d^2) + 3*arcsin(c*x)/(c^5*d^(5/2)))*a + b*integrate(x^4*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(-c^2*d*x^2 + d)^(5/2), x)","F",0
126,1,175,0,0.695108," ","integrate(x^3*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{12} \, b c {\left(\frac{2 \, \sqrt{-d} x}{c^{6} d^{3} x^{2} - c^{4} d^{3}} + \frac{5 \, \sqrt{-d} \log\left(c x + 1\right)}{c^{5} d^{3}} - \frac{5 \, \sqrt{-d} \log\left(c x - 1\right)}{c^{5} d^{3}}\right)} + \frac{1}{3} \, b {\left(\frac{3 \, x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} - \frac{2}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)} \operatorname{arcosh}\left(c x\right) + \frac{1}{3} \, a {\left(\frac{3 \, x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} - \frac{2}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)}"," ",0,"1/12*b*c*(2*sqrt(-d)*x/(c^6*d^3*x^2 - c^4*d^3) + 5*sqrt(-d)*log(c*x + 1)/(c^5*d^3) - 5*sqrt(-d)*log(c*x - 1)/(c^5*d^3)) + 1/3*b*(3*x^2/((-c^2*d*x^2 + d)^(3/2)*c^2*d) - 2/((-c^2*d*x^2 + d)^(3/2)*c^4*d))*arccosh(c*x) + 1/3*a*(3*x^2/((-c^2*d*x^2 + d)^(3/2)*c^2*d) - 2/((-c^2*d*x^2 + d)^(3/2)*c^4*d))","A",0
127,1,169,0,0.679057," ","integrate(x^2*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, b c {\left(\frac{\sqrt{-d}}{c^{6} d^{3} x^{2} - c^{4} d^{3}} - \frac{\sqrt{-d} \log\left(c x + 1\right)}{c^{4} d^{3}} - \frac{\sqrt{-d} \log\left(c x - 1\right)}{c^{4} d^{3}}\right)} - \frac{1}{3} \, b {\left(\frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{2} d^{2}} - \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}\right)} \operatorname{arcosh}\left(c x\right) - \frac{1}{3} \, a {\left(\frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{2} d^{2}} - \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}\right)}"," ",0,"1/6*b*c*(sqrt(-d)/(c^6*d^3*x^2 - c^4*d^3) - sqrt(-d)*log(c*x + 1)/(c^4*d^3) - sqrt(-d)*log(c*x - 1)/(c^4*d^3)) - 1/3*b*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d^2) - x/((-c^2*d*x^2 + d)^(3/2)*c^2*d))*arccosh(c*x) - 1/3*a*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d^2) - x/((-c^2*d*x^2 + d)^(3/2)*c^2*d))","A",0
128,0,0,0,0.000000," ","integrate(x*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","b \int \frac{x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x} + \frac{a}{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}"," ",0,"b*integrate(x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(-c^2*d*x^2 + d)^(5/2), x) + 1/3*a/((-c^2*d*x^2 + d)^(3/2)*c^2*d)","F",0
129,1,157,0,0.705327," ","integrate((a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, b c {\left(\frac{\sqrt{-d}}{c^{4} d^{3} x^{2} - c^{2} d^{3}} + \frac{2 \, \sqrt{-d} \log\left(c x + 1\right)}{c^{2} d^{3}} + \frac{2 \, \sqrt{-d} \log\left(c x - 1\right)}{c^{2} d^{3}}\right)} + \frac{1}{3} \, b {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} \operatorname{arcosh}\left(c x\right) + \frac{1}{3} \, a {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)}"," ",0,"1/6*b*c*(sqrt(-d)/(c^4*d^3*x^2 - c^2*d^3) + 2*sqrt(-d)*log(c*x + 1)/(c^2*d^3) + 2*sqrt(-d)*log(c*x - 1)/(c^2*d^3)) + 1/3*b*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d))*arccosh(c*x) + 1/3*a*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d))","A",0
130,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{3 \, \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{3}{\sqrt{-c^{2} d x^{2} + d} d^{2}} - \frac{1}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"-1/3*a*(3*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/d^(5/2) - 3/(sqrt(-c^2*d*x^2 + d)*d^2) - 1/((-c^2*d*x^2 + d)^(3/2)*d)) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/((-c^2*d*x^2 + d)^(5/2)*x), x)","F",0
131,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{8 \, c^{2} x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{4 \, c^{2} x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} - \frac{3}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"1/3*a*(8*c^2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + 4*c^2*x/((-c^2*d*x^2 + d)^(3/2)*d) - 3/((-c^2*d*x^2 + d)^(3/2)*d*x)) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/((-c^2*d*x^2 + d)^(5/2)*x^2), x)","F",0
132,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^3/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{6} \, a {\left(\frac{15 \, c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{15 \, c^{2}}{\sqrt{-c^{2} d x^{2} + d} d^{2}} - \frac{5 \, c^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} + \frac{3}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{2}}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{3}}\,{d x}"," ",0,"-1/6*a*(15*c^2*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/d^(5/2) - 15*c^2/(sqrt(-c^2*d*x^2 + d)*d^2) - 5*c^2/((-c^2*d*x^2 + d)^(3/2)*d) + 3/((-c^2*d*x^2 + d)^(3/2)*d*x^2)) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/((-c^2*d*x^2 + d)^(5/2)*x^3), x)","F",0
133,1,276,0,0.707915," ","integrate((a+b*arccosh(c*x))/x^4/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, b c {\left(\frac{8 \, c^{2} \sqrt{-d} \log\left(c x + 1\right)}{d^{3}} + \frac{8 \, c^{2} \sqrt{-d} \log\left(c x - 1\right)}{d^{3}} + \frac{16 \, c^{2} \sqrt{-d} \log\left(x\right)}{d^{3}} + \frac{\sqrt{-d}}{c^{2} d^{3} x^{4} - d^{3} x^{2}}\right)} + \frac{1}{3} \, {\left(\frac{16 \, c^{4} x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{8 \, c^{4} x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} - \frac{6 \, c^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x} - \frac{1}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{3}}\right)} b \operatorname{arcosh}\left(c x\right) + \frac{1}{3} \, {\left(\frac{16 \, c^{4} x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{8 \, c^{4} x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} - \frac{6 \, c^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x} - \frac{1}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{3}}\right)} a"," ",0,"1/6*b*c*(8*c^2*sqrt(-d)*log(c*x + 1)/d^3 + 8*c^2*sqrt(-d)*log(c*x - 1)/d^3 + 16*c^2*sqrt(-d)*log(x)/d^3 + sqrt(-d)/(c^2*d^3*x^4 - d^3*x^2)) + 1/3*(16*c^4*x/(sqrt(-c^2*d*x^2 + d)*d^2) + 8*c^4*x/((-c^2*d*x^2 + d)^(3/2)*d) - 6*c^2/((-c^2*d*x^2 + d)^(3/2)*d*x) - 1/((-c^2*d*x^2 + d)^(3/2)*d*x^3))*b*arccosh(c*x) + 1/3*(16*c^4*x/(sqrt(-c^2*d*x^2 + d)*d^2) + 8*c^4*x/((-c^2*d*x^2 + d)^(3/2)*d) - 6*c^2/((-c^2*d*x^2 + d)^(3/2)*d*x) - 1/((-c^2*d*x^2 + d)^(3/2)*d*x^3))*a","A",0
134,1,191,0,0.443802," ","integrate(arccosh(a*x)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","-\frac{1}{60} \, a {\left(\frac{16 \, \sqrt{-\frac{1}{a^{4} c}} \log\left(x^{2} - \frac{1}{a^{2}}\right)}{c^{3}} + \frac{3}{{\left(a^{6} c^{3} x^{4} \sqrt{-\frac{1}{c}} - 2 \, a^{4} c^{3} x^{2} \sqrt{-\frac{1}{c}} + a^{2} c^{3} \sqrt{-\frac{1}{c}}\right)} c} - \frac{8}{{\left(a^{4} c^{2} x^{2} \sqrt{-\frac{1}{c}} - a^{2} c^{2} \sqrt{-\frac{1}{c}}\right)} c^{2}}\right)} + \frac{1}{15} \, {\left(\frac{8 \, x}{\sqrt{-a^{2} c x^{2} + c} c^{3}} + \frac{4 \, x}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} c^{2}} + \frac{3 \, x}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} c}\right)} \operatorname{arcosh}\left(a x\right)"," ",0,"-1/60*a*(16*sqrt(-1/(a^4*c))*log(x^2 - 1/a^2)/c^3 + 3/((a^6*c^3*x^4*sqrt(-1/c) - 2*a^4*c^3*x^2*sqrt(-1/c) + a^2*c^3*sqrt(-1/c))*c) - 8/((a^4*c^2*x^2*sqrt(-1/c) - a^2*c^2*sqrt(-1/c))*c^2)) + 1/15*(8*x/(sqrt(-a^2*c*x^2 + c)*c^3) + 4*x/((-a^2*c*x^2 + c)^(3/2)*c^2) + 3*x/((-a^2*c*x^2 + c)^(5/2)*c))*arccosh(a*x)","A",0
135,-2,0,0,0.000000," ","integrate(x^4*arccosh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
136,1,62,0,0.899052," ","integrate(x^3*arccosh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{1}{9} \, a {\left(\frac{i \, x^{3}}{a^{2}} + \frac{6 i \, x}{a^{4}}\right)} - \frac{1}{3} \, {\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{a^{2}} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{a^{4}}\right)} \operatorname{arcosh}\left(a x\right)"," ",0,"1/9*a*(I*x^3/a^2 + 6*I*x/a^4) - 1/3*(sqrt(-a^2*x^2 + 1)*x^2/a^2 + 2*sqrt(-a^2*x^2 + 1)/a^4)*arccosh(a*x)","C",0
137,-2,0,0,0.000000," ","integrate(x^2*arccosh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
138,1,28,0,0.664488," ","integrate(x*arccosh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{i \, x}{a} - \frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{arcosh}\left(a x\right)}{a^{2}}"," ",0,"I*x/a - sqrt(-a^2*x^2 + 1)*arccosh(a*x)/a^2","C",0
139,0,0,0,0.000000," ","integrate(arccosh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(arccosh(a*x)/sqrt(-a^2*x^2 + 1), x)","F",0
140,0,0,0,0.000000," ","integrate(arccosh(a*x)/x/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate(arccosh(a*x)/(sqrt(-a^2*x^2 + 1)*x), x)","F",0
141,1,73,0,0.856254," ","integrate(arccosh(a*x)/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(a^{2} \sqrt{-\frac{1}{a^{4}}} \log\left(x^{2} - \frac{1}{a^{2}}\right) + i \, \left(-1\right)^{-2 \, a^{2} x^{2} + 2} \log\left(-2 \, a^{2} + \frac{2}{x^{2}}\right)\right)} a - \frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{arcosh}\left(a x\right)}{x}"," ",0,"-1/2*(a^2*sqrt(-1/a^4)*log(x^2 - 1/a^2) + I*(-1)^(-2*a^2*x^2 + 2)*log(-2*a^2 + 2/x^2))*a - sqrt(-a^2*x^2 + 1)*arccosh(a*x)/x","C",0
142,0,0,0,0.000000," ","integrate(arccosh(a*x)/x^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate(arccosh(a*x)/(sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
143,0,0,0,0.000000," ","integrate((f*x)^(3/2)*(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(f x\right)^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}{\sqrt{-c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((f*x)^(3/2)*(b*arccosh(c*x) + a)/sqrt(-c^2*x^2 + 1), x)","F",0
144,0,0,0,0.000000," ","integrate((f*x)^(3/2)*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(f x\right)^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((f*x)^(3/2)*(b*arccosh(c*x) + a)/sqrt(-c^2*d*x^2 + d), x)","F",0
145,0,0,0,0.000000," ","integrate((f*x)^m*(-c^2*d*x^2+d)^3*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{a c^{6} d^{3} f^{m} x^{7} x^{m}}{m + 7} + \frac{3 \, a c^{4} d^{3} f^{m} x^{5} x^{m}}{m + 5} - \frac{3 \, a c^{2} d^{3} f^{m} x^{3} x^{m}}{m + 3} + \frac{\left(f x\right)^{m + 1} a d^{3}}{f {\left(m + 1\right)}} - \frac{{\left({\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} b c^{6} d^{3} f^{m} x^{7} - 3 \, {\left(m^{3} + 11 \, m^{2} + 31 \, m + 21\right)} b c^{4} d^{3} f^{m} x^{5} + 3 \, {\left(m^{3} + 13 \, m^{2} + 47 \, m + 35\right)} b c^{2} d^{3} f^{m} x^{3} - {\left(m^{3} + 15 \, m^{2} + 71 \, m + 105\right)} b d^{3} f^{m} x\right)} x^{m} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105} - \int \frac{{\left({\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} b c^{7} d^{3} f^{m} x^{7} - 3 \, {\left(m^{3} + 11 \, m^{2} + 31 \, m + 21\right)} b c^{5} d^{3} f^{m} x^{5} + 3 \, {\left(m^{3} + 13 \, m^{2} + 47 \, m + 35\right)} b c^{3} d^{3} f^{m} x^{3} - {\left(m^{3} + 15 \, m^{2} + 71 \, m + 105\right)} b c d^{3} f^{m} x\right)} x^{m}}{{\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} c^{3} x^{3} - {\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} c x + {\left({\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} c^{2} x^{2} - m^{4} - 16 \, m^{3} - 86 \, m^{2} - 176 \, m - 105\right)} \sqrt{c x + 1} \sqrt{c x - 1}}\,{d x} + \int \frac{{\left({\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} b c^{8} d^{3} f^{m} x^{8} - 3 \, {\left(m^{3} + 11 \, m^{2} + 31 \, m + 21\right)} b c^{6} d^{3} f^{m} x^{6} + 3 \, {\left(m^{3} + 13 \, m^{2} + 47 \, m + 35\right)} b c^{4} d^{3} f^{m} x^{4} - {\left(m^{3} + 15 \, m^{2} + 71 \, m + 105\right)} b c^{2} d^{3} f^{m} x^{2}\right)} x^{m}}{{\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} c^{2} x^{2} - m^{4} - 16 \, m^{3} - 86 \, m^{2} - 176 \, m - 105}\,{d x}"," ",0,"-a*c^6*d^3*f^m*x^7*x^m/(m + 7) + 3*a*c^4*d^3*f^m*x^5*x^m/(m + 5) - 3*a*c^2*d^3*f^m*x^3*x^m/(m + 3) + (f*x)^(m + 1)*a*d^3/(f*(m + 1)) - ((m^3 + 9*m^2 + 23*m + 15)*b*c^6*d^3*f^m*x^7 - 3*(m^3 + 11*m^2 + 31*m + 21)*b*c^4*d^3*f^m*x^5 + 3*(m^3 + 13*m^2 + 47*m + 35)*b*c^2*d^3*f^m*x^3 - (m^3 + 15*m^2 + 71*m + 105)*b*d^3*f^m*x)*x^m*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105) - integrate(((m^3 + 9*m^2 + 23*m + 15)*b*c^7*d^3*f^m*x^7 - 3*(m^3 + 11*m^2 + 31*m + 21)*b*c^5*d^3*f^m*x^5 + 3*(m^3 + 13*m^2 + 47*m + 35)*b*c^3*d^3*f^m*x^3 - (m^3 + 15*m^2 + 71*m + 105)*b*c*d^3*f^m*x)*x^m/((m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*c^3*x^3 - (m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*c*x + ((m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*c^2*x^2 - m^4 - 16*m^3 - 86*m^2 - 176*m - 105)*sqrt(c*x + 1)*sqrt(c*x - 1)), x) + integrate(((m^3 + 9*m^2 + 23*m + 15)*b*c^8*d^3*f^m*x^8 - 3*(m^3 + 11*m^2 + 31*m + 21)*b*c^6*d^3*f^m*x^6 + 3*(m^3 + 13*m^2 + 47*m + 35)*b*c^4*d^3*f^m*x^4 - (m^3 + 15*m^2 + 71*m + 105)*b*c^2*d^3*f^m*x^2)*x^m/((m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*c^2*x^2 - m^4 - 16*m^3 - 86*m^2 - 176*m - 105), x)","F",0
146,0,0,0,0.000000," ","integrate((f*x)^m*(-c^2*d*x^2+d)^2*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{a c^{4} d^{2} f^{m} x^{5} x^{m}}{m + 5} - \frac{2 \, a c^{2} d^{2} f^{m} x^{3} x^{m}}{m + 3} + \frac{\left(f x\right)^{m + 1} a d^{2}}{f {\left(m + 1\right)}} + \frac{{\left({\left(m^{2} + 4 \, m + 3\right)} b c^{4} d^{2} f^{m} x^{5} - 2 \, {\left(m^{2} + 6 \, m + 5\right)} b c^{2} d^{2} f^{m} x^{3} + {\left(m^{2} + 8 \, m + 15\right)} b d^{2} f^{m} x\right)} x^{m} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{m^{3} + 9 \, m^{2} + 23 \, m + 15} + \int \frac{{\left({\left(m^{2} + 4 \, m + 3\right)} b c^{5} d^{2} f^{m} x^{5} - 2 \, {\left(m^{2} + 6 \, m + 5\right)} b c^{3} d^{2} f^{m} x^{3} + {\left(m^{2} + 8 \, m + 15\right)} b c d^{2} f^{m} x\right)} x^{m}}{{\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} c^{3} x^{3} - {\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} c x + {\left({\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} c^{2} x^{2} - m^{3} - 9 \, m^{2} - 23 \, m - 15\right)} \sqrt{c x + 1} \sqrt{c x - 1}}\,{d x} - \int \frac{{\left({\left(m^{2} + 4 \, m + 3\right)} b c^{6} d^{2} f^{m} x^{6} - 2 \, {\left(m^{2} + 6 \, m + 5\right)} b c^{4} d^{2} f^{m} x^{4} + {\left(m^{2} + 8 \, m + 15\right)} b c^{2} d^{2} f^{m} x^{2}\right)} x^{m}}{{\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} c^{2} x^{2} - m^{3} - 9 \, m^{2} - 23 \, m - 15}\,{d x}"," ",0,"a*c^4*d^2*f^m*x^5*x^m/(m + 5) - 2*a*c^2*d^2*f^m*x^3*x^m/(m + 3) + (f*x)^(m + 1)*a*d^2/(f*(m + 1)) + ((m^2 + 4*m + 3)*b*c^4*d^2*f^m*x^5 - 2*(m^2 + 6*m + 5)*b*c^2*d^2*f^m*x^3 + (m^2 + 8*m + 15)*b*d^2*f^m*x)*x^m*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(m^3 + 9*m^2 + 23*m + 15) + integrate(((m^2 + 4*m + 3)*b*c^5*d^2*f^m*x^5 - 2*(m^2 + 6*m + 5)*b*c^3*d^2*f^m*x^3 + (m^2 + 8*m + 15)*b*c*d^2*f^m*x)*x^m/((m^3 + 9*m^2 + 23*m + 15)*c^3*x^3 - (m^3 + 9*m^2 + 23*m + 15)*c*x + ((m^3 + 9*m^2 + 23*m + 15)*c^2*x^2 - m^3 - 9*m^2 - 23*m - 15)*sqrt(c*x + 1)*sqrt(c*x - 1)), x) - integrate(((m^2 + 4*m + 3)*b*c^6*d^2*f^m*x^6 - 2*(m^2 + 6*m + 5)*b*c^4*d^2*f^m*x^4 + (m^2 + 8*m + 15)*b*c^2*d^2*f^m*x^2)*x^m/((m^3 + 9*m^2 + 23*m + 15)*c^2*x^2 - m^3 - 9*m^2 - 23*m - 15), x)","F",0
147,0,0,0,0.000000," ","integrate((f*x)^m*(-c^2*d*x^2+d)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","-\frac{a c^{2} d f^{m} x^{3} x^{m}}{m + 3} - \frac{{\left(b c^{2} d f^{m} {\left(m + 1\right)} x^{3} - b d f^{m} {\left(m + 3\right)} x\right)} x^{m} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{m^{2} + 4 \, m + 3} + \frac{\left(f x\right)^{m + 1} a d}{f {\left(m + 1\right)}} - \int \frac{{\left(b c^{3} d f^{m} {\left(m + 1\right)} x^{3} - b c d f^{m} {\left(m + 3\right)} x\right)} x^{m}}{{\left(m^{2} + 4 \, m + 3\right)} c^{3} x^{3} - {\left(m^{2} + 4 \, m + 3\right)} c x + {\left({\left(m^{2} + 4 \, m + 3\right)} c^{2} x^{2} - m^{2} - 4 \, m - 3\right)} \sqrt{c x + 1} \sqrt{c x - 1}}\,{d x} + \int \frac{{\left(b c^{4} d f^{m} {\left(m + 1\right)} x^{4} - b c^{2} d f^{m} {\left(m + 3\right)} x^{2}\right)} x^{m}}{{\left(m^{2} + 4 \, m + 3\right)} c^{2} x^{2} - m^{2} - 4 \, m - 3}\,{d x}"," ",0,"-a*c^2*d*f^m*x^3*x^m/(m + 3) - (b*c^2*d*f^m*(m + 1)*x^3 - b*d*f^m*(m + 3)*x)*x^m*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(m^2 + 4*m + 3) + (f*x)^(m + 1)*a*d/(f*(m + 1)) - integrate((b*c^3*d*f^m*(m + 1)*x^3 - b*c*d*f^m*(m + 3)*x)*x^m/((m^2 + 4*m + 3)*c^3*x^3 - (m^2 + 4*m + 3)*c*x + ((m^2 + 4*m + 3)*c^2*x^2 - m^2 - 4*m - 3)*sqrt(c*x + 1)*sqrt(c*x - 1)), x) + integrate((b*c^4*d*f^m*(m + 1)*x^4 - b*c^2*d*f^m*(m + 3)*x^2)*x^m/((m^2 + 4*m + 3)*c^2*x^2 - m^2 - 4*m - 3), x)","F",0
148,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}}{c^{2} d x^{2} - d}\,{d x}"," ",0,"-integrate((b*arccosh(c*x) + a)*(f*x)^m/(c^2*d*x^2 - d), x)","F",0
149,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(c^{2} d x^{2} - d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)*(f*x)^m/(c^2*d*x^2 - d)^2, x)","F",0
150,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^3,x, algorithm=""maxima"")","-\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(c^{2} d x^{2} - d\right)}^{3}}\,{d x}"," ",0,"-integrate((b*arccosh(c*x) + a)*(f*x)^m/(c^2*d*x^2 - d)^3, x)","F",0
151,0,0,0,0.000000," ","integrate((f*x)^m*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(5/2)*(b*arccosh(c*x) + a)*(f*x)^m, x)","F",0
152,0,0,0,0.000000," ","integrate((f*x)^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(3/2)*(b*arccosh(c*x) + a)*(f*x)^m, x)","F",0
153,0,0,0,0.000000," ","integrate((f*x)^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \sqrt{-c^{2} d x^{2} + d} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(-c^2*d*x^2 + d)*(b*arccosh(c*x) + a)*(f*x)^m, x)","F",0
154,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)*(f*x)^m/sqrt(-c^2*d*x^2 + d), x)","F",0
155,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)*(f*x)^m/(-c^2*d*x^2 + d)^(3/2), x)","F",0
156,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)*(f*x)^m/(-c^2*d*x^2 + d)^(5/2), x)","F",0
157,0,0,0,0.000000," ","integrate((f*x)^m*(c*d1*x+d1)^(5/2)*(-c*d2*x+d2)^(5/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int {\left(c d_{1} x + d_{1}\right)}^{\frac{5}{2}} {\left(-c d_{2} x + d_{2}\right)}^{\frac{5}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((c*d1*x + d1)^(5/2)*(-c*d2*x + d2)^(5/2)*(b*arccosh(c*x) + a)*(f*x)^m, x)","F",0
158,0,0,0,0.000000," ","integrate((f*x)^m*(c*d1*x+d1)^(3/2)*(-c*d2*x+d2)^(3/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int {\left(c d_{1} x + d_{1}\right)}^{\frac{3}{2}} {\left(-c d_{2} x + d_{2}\right)}^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((c*d1*x + d1)^(3/2)*(-c*d2*x + d2)^(3/2)*(b*arccosh(c*x) + a)*(f*x)^m, x)","F",0
159,0,0,0,0.000000," ","integrate((f*x)^m*(c*d1*x+d1)^(1/2)*(-c*d2*x+d2)^(1/2)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \sqrt{c d_{1} x + d_{1}} \sqrt{-c d_{2} x + d_{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(c*d1*x + d1)*sqrt(-c*d2*x + d2)*(b*arccosh(c*x) + a)*(f*x)^m, x)","F",0
160,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))/(c*d1*x+d1)^(1/2)/(-c*d2*x+d2)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}}{\sqrt{c d_{1} x + d_{1}} \sqrt{-c d_{2} x + d_{2}}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)*(f*x)^m/(sqrt(c*d1*x + d1)*sqrt(-c*d2*x + d2)), x)","F",0
161,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))/(c*d1*x+d1)^(3/2)/(-c*d2*x+d2)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(c d_{1} x + d_{1}\right)}^{\frac{3}{2}} {\left(-c d_{2} x + d_{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)*(f*x)^m/((c*d1*x + d1)^(3/2)*(-c*d2*x + d2)^(3/2)), x)","F",0
162,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))/(c*d1*x+d1)^(5/2)/(-c*d2*x+d2)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(c d_{1} x + d_{1}\right)}^{\frac{5}{2}} {\left(-c d_{2} x + d_{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)*(f*x)^m/((c*d1*x + d1)^(5/2)*(-c*d2*x + d2)^(5/2)), x)","F",0
163,0,0,0,0.000000," ","integrate((f*x)^m*arccosh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(f x\right)^{m} \operatorname{arcosh}\left(a x\right)}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((f*x)^m*arccosh(a*x)/sqrt(-a^2*x^2 + 1), x)","F",0
164,1,178,0,0.851622," ","integrate((-a^2*c*x^2+c)^3*arccosh(a*x)^2,x, algorithm=""maxima"")","-\frac{2}{343} \, a^{6} c^{3} x^{7} + \frac{234}{6125} \, a^{4} c^{3} x^{5} - \frac{1514}{11025} \, a^{2} c^{3} x^{3} + \frac{4322}{3675} \, c^{3} x + \frac{2}{3675} \, {\left(75 \, \sqrt{a^{2} x^{2} - 1} a^{4} c^{3} x^{6} - 351 \, \sqrt{a^{2} x^{2} - 1} a^{2} c^{3} x^{4} + 757 \, \sqrt{a^{2} x^{2} - 1} c^{3} x^{2} - \frac{2161 \, \sqrt{a^{2} x^{2} - 1} c^{3}}{a^{2}}\right)} a \operatorname{arcosh}\left(a x\right) - \frac{1}{35} \, {\left(5 \, a^{6} c^{3} x^{7} - 21 \, a^{4} c^{3} x^{5} + 35 \, a^{2} c^{3} x^{3} - 35 \, c^{3} x\right)} \operatorname{arcosh}\left(a x\right)^{2}"," ",0,"-2/343*a^6*c^3*x^7 + 234/6125*a^4*c^3*x^5 - 1514/11025*a^2*c^3*x^3 + 4322/3675*c^3*x + 2/3675*(75*sqrt(a^2*x^2 - 1)*a^4*c^3*x^6 - 351*sqrt(a^2*x^2 - 1)*a^2*c^3*x^4 + 757*sqrt(a^2*x^2 - 1)*c^3*x^2 - 2161*sqrt(a^2*x^2 - 1)*c^3/a^2)*a*arccosh(a*x) - 1/35*(5*a^6*c^3*x^7 - 21*a^4*c^3*x^5 + 35*a^2*c^3*x^3 - 35*c^3*x)*arccosh(a*x)^2","A",0
165,1,134,0,0.822347," ","integrate((-a^2*c*x^2+c)^2*arccosh(a*x)^2,x, algorithm=""maxima"")","\frac{2}{125} \, a^{4} c^{2} x^{5} - \frac{76}{675} \, a^{2} c^{2} x^{3} + \frac{298}{225} \, c^{2} x - \frac{2}{225} \, {\left(9 \, \sqrt{a^{2} x^{2} - 1} a^{2} c^{2} x^{4} - 38 \, \sqrt{a^{2} x^{2} - 1} c^{2} x^{2} + \frac{149 \, \sqrt{a^{2} x^{2} - 1} c^{2}}{a^{2}}\right)} a \operatorname{arcosh}\left(a x\right) + \frac{1}{15} \, {\left(3 \, a^{4} c^{2} x^{5} - 10 \, a^{2} c^{2} x^{3} + 15 \, c^{2} x\right)} \operatorname{arcosh}\left(a x\right)^{2}"," ",0,"2/125*a^4*c^2*x^5 - 76/675*a^2*c^2*x^3 + 298/225*c^2*x - 2/225*(9*sqrt(a^2*x^2 - 1)*a^2*c^2*x^4 - 38*sqrt(a^2*x^2 - 1)*c^2*x^2 + 149*sqrt(a^2*x^2 - 1)*c^2/a^2)*a*arccosh(a*x) + 1/15*(3*a^4*c^2*x^5 - 10*a^2*c^2*x^3 + 15*c^2*x)*arccosh(a*x)^2","A",0
166,1,76,0,1.075863," ","integrate((-a^2*c*x^2+c)*arccosh(a*x)^2,x, algorithm=""maxima"")","-\frac{2}{27} \, a^{2} c x^{3} + \frac{2}{9} \, {\left(\sqrt{a^{2} x^{2} - 1} c x^{2} - \frac{7 \, \sqrt{a^{2} x^{2} - 1} c}{a^{2}}\right)} a \operatorname{arcosh}\left(a x\right) - \frac{1}{3} \, {\left(a^{2} c x^{3} - 3 \, c x\right)} \operatorname{arcosh}\left(a x\right)^{2} + \frac{14}{9} \, c x"," ",0,"-2/27*a^2*c*x^3 + 2/9*(sqrt(a^2*x^2 - 1)*c*x^2 - 7*sqrt(a^2*x^2 - 1)*c/a^2)*a*arccosh(a*x) - 1/3*(a^2*c*x^3 - 3*c*x)*arccosh(a*x)^2 + 14/9*c*x","A",0
167,0,0,0,0.000000," ","integrate(arccosh(a*x)^2/(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{{\left(\log\left(a x + 1\right) - \log\left(a x - 1\right)\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{2 \, a c} - \int \frac{{\left({\left(a x \log\left(a x + 1\right) - a x \log\left(a x - 1\right)\right)} \sqrt{a x + 1} \sqrt{a x - 1} + {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) - {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{a^{3} c x^{3} - a c x + {\left(a^{2} c x^{2} - c\right)} \sqrt{a x + 1} \sqrt{a x - 1}}\,{d x}"," ",0,"1/2*(log(a*x + 1) - log(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/(a*c) - integrate(((a*x*log(a*x + 1) - a*x*log(a*x - 1))*sqrt(a*x + 1)*sqrt(a*x - 1) + (a^2*x^2 - 1)*log(a*x + 1) - (a^2*x^2 - 1)*log(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))/(a^3*c*x^3 - a*c*x + (a^2*c*x^2 - c)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
168,0,0,0,0.000000," ","integrate(arccosh(a*x)^2/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{{\left(2 \, a x - {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{4 \, {\left(a^{3} c^{2} x^{2} - a c^{2}\right)}} - \int -\frac{{\left(2 \, a^{3} x^{3} + {\left(2 \, a^{2} x^{2} - {\left(a^{3} x^{3} - a x\right)} \log\left(a x + 1\right) + {\left(a^{3} x^{3} - a x\right)} \log\left(a x - 1\right)\right)} \sqrt{a x + 1} \sqrt{a x - 1} - 2 \, a x - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{2 \, {\left(a^{5} c^{2} x^{5} - 2 \, a^{3} c^{2} x^{3} + a c^{2} x + {\left(a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)}}\,{d x}"," ",0,"-1/4*(2*a*x - (a^2*x^2 - 1)*log(a*x + 1) + (a^2*x^2 - 1)*log(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/(a^3*c^2*x^2 - a*c^2) - integrate(-1/2*(2*a^3*x^3 + (2*a^2*x^2 - (a^3*x^3 - a*x)*log(a*x + 1) + (a^3*x^3 - a*x)*log(a*x - 1))*sqrt(a*x + 1)*sqrt(a*x - 1) - 2*a*x - (a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1) + (a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))/(a^5*c^2*x^5 - 2*a^3*c^2*x^3 + a*c^2*x + (a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
169,0,0,0,0.000000," ","integrate(arccosh(a*x)^2/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{{\left(6 \, a^{3} x^{3} - 10 \, a x - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) + 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{16 \, {\left(a^{5} c^{3} x^{4} - 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}} - \int -\frac{{\left(6 \, a^{5} x^{5} - 16 \, a^{3} x^{3} + {\left(6 \, a^{4} x^{4} - 10 \, a^{2} x^{2} - 3 \, {\left(a^{5} x^{5} - 2 \, a^{3} x^{3} + a x\right)} \log\left(a x + 1\right) + 3 \, {\left(a^{5} x^{5} - 2 \, a^{3} x^{3} + a x\right)} \log\left(a x - 1\right)\right)} \sqrt{a x + 1} \sqrt{a x - 1} + 10 \, a x - 3 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) + 3 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{8 \, {\left(a^{7} c^{3} x^{7} - 3 \, a^{5} c^{3} x^{5} + 3 \, a^{3} c^{3} x^{3} - a c^{3} x + {\left(a^{6} c^{3} x^{6} - 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - c^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)}}\,{d x}"," ",0,"-1/16*(6*a^3*x^3 - 10*a*x - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1) + 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/(a^5*c^3*x^4 - 2*a^3*c^3*x^2 + a*c^3) - integrate(-1/8*(6*a^5*x^5 - 16*a^3*x^3 + (6*a^4*x^4 - 10*a^2*x^2 - 3*(a^5*x^5 - 2*a^3*x^3 + a*x)*log(a*x + 1) + 3*(a^5*x^5 - 2*a^3*x^3 + a*x)*log(a*x - 1))*sqrt(a*x + 1)*sqrt(a*x - 1) + 10*a*x - 3*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1) + 3*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))/(a^7*c^3*x^7 - 3*a^5*c^3*x^5 + 3*a^3*c^3*x^3 - a*c^3*x + (a^6*c^3*x^6 - 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - c^3)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
170,1,326,0,0.998544," ","integrate(x^3*(a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{15} \, b^{2} {\left(\frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{4} d}\right)} \operatorname{arcosh}\left(c x\right)^{2} - \frac{2}{15} \, a b {\left(\frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{4} d}\right)} \operatorname{arcosh}\left(c x\right) - \frac{1}{15} \, a^{2} {\left(\frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{c^{4} d}\right)} + \frac{2}{3375} \, b^{2} {\left(\frac{27 \, \sqrt{c^{2} x^{2} - 1} c^{2} \sqrt{-d} x^{4} + 11 \, \sqrt{c^{2} x^{2} - 1} \sqrt{-d} x^{2} - \frac{428 \, \sqrt{c^{2} x^{2} - 1} \sqrt{-d}}{c^{2}}}{c^{2}} - \frac{15 \, {\left(9 \, c^{4} \sqrt{-d} x^{5} - 5 \, c^{2} \sqrt{-d} x^{3} - 30 \, \sqrt{-d} x\right)} \operatorname{arcosh}\left(c x\right)}{c^{3}}\right)} - \frac{2 \, {\left(9 \, c^{4} \sqrt{-d} x^{5} - 5 \, c^{2} \sqrt{-d} x^{3} - 30 \, \sqrt{-d} x\right)} a b}{225 \, c^{3}}"," ",0,"-1/15*b^2*(3*(-c^2*d*x^2 + d)^(3/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(3/2)/(c^4*d))*arccosh(c*x)^2 - 2/15*a*b*(3*(-c^2*d*x^2 + d)^(3/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(3/2)/(c^4*d))*arccosh(c*x) - 1/15*a^2*(3*(-c^2*d*x^2 + d)^(3/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(3/2)/(c^4*d)) + 2/3375*b^2*((27*sqrt(c^2*x^2 - 1)*c^2*sqrt(-d)*x^4 + 11*sqrt(c^2*x^2 - 1)*sqrt(-d)*x^2 - 428*sqrt(c^2*x^2 - 1)*sqrt(-d)/c^2)/c^2 - 15*(9*c^4*sqrt(-d)*x^5 - 5*c^2*sqrt(-d)*x^3 - 30*sqrt(-d)*x)*arccosh(c*x)/c^3) - 2/225*(9*c^4*sqrt(-d)*x^5 - 5*c^2*sqrt(-d)*x^3 - 30*sqrt(-d)*x)*a*b/c^3","A",0
171,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{8} \, a^{2} {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x}{c^{2}} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}{c^{2} d} + \frac{\sqrt{d} \arcsin\left(c x\right)}{c^{3}}\right)} + \int \sqrt{-c^{2} d x^{2} + d} b^{2} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 2 \, \sqrt{-c^{2} d x^{2} + d} a b x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/8*a^2*(sqrt(-c^2*d*x^2 + d)*x/c^2 - 2*(-c^2*d*x^2 + d)^(3/2)*x/(c^2*d) + sqrt(d)*arcsin(c*x)/c^3) + integrate(sqrt(-c^2*d*x^2 + d)*b^2*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 2*sqrt(-c^2*d*x^2 + d)*a*b*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
172,1,204,0,1.236052," ","integrate(x*(a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{2}{27} \, b^{2} {\left(\frac{\sqrt{c^{2} x^{2} - 1} \sqrt{-d} d x^{2} - \frac{7 \, \sqrt{c^{2} x^{2} - 1} \sqrt{-d} d}{c^{2}}}{d} - \frac{3 \, {\left(c^{2} \sqrt{-d} d x^{3} - 3 \, \sqrt{-d} d x\right)} \operatorname{arcosh}\left(c x\right)}{c d}\right)} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b^{2} \operatorname{arcosh}\left(c x\right)^{2}}{3 \, c^{2} d} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a b \operatorname{arcosh}\left(c x\right)}{3 \, c^{2} d} - \frac{2 \, {\left(c^{2} \sqrt{-d} d x^{3} - 3 \, \sqrt{-d} d x\right)} a b}{9 \, c d} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a^{2}}{3 \, c^{2} d}"," ",0,"2/27*b^2*((sqrt(c^2*x^2 - 1)*sqrt(-d)*d*x^2 - 7*sqrt(c^2*x^2 - 1)*sqrt(-d)*d/c^2)/d - 3*(c^2*sqrt(-d)*d*x^3 - 3*sqrt(-d)*d*x)*arccosh(c*x)/(c*d)) - 1/3*(-c^2*d*x^2 + d)^(3/2)*b^2*arccosh(c*x)^2/(c^2*d) - 2/3*(-c^2*d*x^2 + d)^(3/2)*a*b*arccosh(c*x)/(c^2*d) - 2/9*(c^2*sqrt(-d)*d*x^3 - 3*sqrt(-d)*d*x)*a*b/(c*d) - 1/3*(-c^2*d*x^2 + d)^(3/2)*a^2/(c^2*d)","A",0
173,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\sqrt{-c^{2} d x^{2} + d} x + \frac{\sqrt{d} \arcsin\left(c x\right)}{c}\right)} a^{2} + \int \sqrt{-c^{2} d x^{2} + d} b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 2 \, \sqrt{-c^{2} d x^{2} + d} a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/2*(sqrt(-c^2*d*x^2 + d)*x + sqrt(d)*arcsin(c*x)/c)*a^2 + integrate(sqrt(-c^2*d*x^2 + d)*b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 2*sqrt(-c^2*d*x^2 + d)*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
174,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2)/x,x, algorithm=""maxima"")","-{\left(\sqrt{d} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - \sqrt{-c^{2} d x^{2} + d}\right)} a^{2} + \int \frac{\sqrt{-c^{2} d x^{2} + d} b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{x} + \frac{2 \, \sqrt{-c^{2} d x^{2} + d} a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"-(sqrt(d)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - sqrt(-c^2*d*x^2 + d))*a^2 + integrate(sqrt(-c^2*d*x^2 + d)*b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/x + 2*sqrt(-c^2*d*x^2 + d)*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
175,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2)/x^2,x, algorithm=""maxima"")","-{\left(c \sqrt{d} \arcsin\left(c x\right) + \frac{\sqrt{-c^{2} d x^{2} + d}}{x}\right)} a^{2} + \int \frac{\sqrt{-c^{2} d x^{2} + d} b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{x^{2}} + \frac{2 \, \sqrt{-c^{2} d x^{2} + d} a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{2}}\,{d x}"," ",0,"-(c*sqrt(d)*arcsin(c*x) + sqrt(-c^2*d*x^2 + d)/x)*a^2 + integrate(sqrt(-c^2*d*x^2 + d)*b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/x^2 + 2*sqrt(-c^2*d*x^2 + d)*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^2, x)","F",0
176,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2)/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(c^{2} \sqrt{d} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - \sqrt{-c^{2} d x^{2} + d} c^{2} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{d x^{2}}\right)} a^{2} + \int \frac{\sqrt{-c^{2} d x^{2} + d} b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{x^{3}} + \frac{2 \, \sqrt{-c^{2} d x^{2} + d} a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{3}}\,{d x}"," ",0,"1/2*(c^2*sqrt(d)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - sqrt(-c^2*d*x^2 + d)*c^2 - (-c^2*d*x^2 + d)^(3/2)/(d*x^2))*a^2 + integrate(sqrt(-c^2*d*x^2 + d)*b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/x^3 + 2*sqrt(-c^2*d*x^2 + d)*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^3, x)","F",0
177,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2*(-c^2*d*x^2+d)^(1/2)/x^4,x, algorithm=""maxima"")","\frac{{\left(c^{4} d^{2} \sqrt{-\frac{1}{c^{4} d}} \log\left(x^{2} - \frac{1}{c^{2}}\right) + i \, \left(-1\right)^{-2 \, c^{2} d x^{2} + 2 \, d} c^{2} d^{\frac{3}{2}} \log\left(-2 \, c^{2} d + \frac{2 \, d}{x^{2}}\right) + \frac{\sqrt{-c^{4} d x^{4} + 2 \, c^{2} d x^{2} - d} d}{x^{2}}\right)} a b c}{3 \, d} + \frac{1}{3} \, b^{2} {\left(\frac{{\left(c^{2} \sqrt{d} x^{2} - \sqrt{d}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{x^{3}} - 3 \, \int \frac{2 \, {\left({\left(c x + 1\right)} \sqrt{c x - 1} c^{2} \sqrt{d} x + {\left(c^{3} \sqrt{d} x^{2} - c \sqrt{d}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{3 \, {\left(c x^{4} + \sqrt{c x + 1} \sqrt{c x - 1} x^{3}\right)}}\,{d x}\right)} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a b \operatorname{arcosh}\left(c x\right)}{3 \, d x^{3}} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a^{2}}{3 \, d x^{3}}"," ",0,"1/3*(c^4*d^2*sqrt(-1/(c^4*d))*log(x^2 - 1/c^2) + I*(-1)^(-2*c^2*d*x^2 + 2*d)*c^2*d^(3/2)*log(-2*c^2*d + 2*d/x^2) + sqrt(-c^4*d*x^4 + 2*c^2*d*x^2 - d)*d/x^2)*a*b*c/d + 1/3*b^2*((c^2*sqrt(d)*x^2 - sqrt(d))*sqrt(c*x + 1)*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/x^3 - 3*integrate(2/3*((c*x + 1)*sqrt(c*x - 1)*c^2*sqrt(d)*x + (c^3*sqrt(d)*x^2 - c*sqrt(d))*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c*x^4 + sqrt(c*x + 1)*sqrt(c*x - 1)*x^3), x)) - 2/3*(-c^2*d*x^2 + d)^(3/2)*a*b*arccosh(c*x)/(d*x^3) - 1/3*(-c^2*d*x^2 + d)^(3/2)*a^2/(d*x^3)","F",0
178,1,388,0,1.196801," ","integrate(x^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{35} \, {\left(\frac{5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{4} d}\right)} b^{2} \operatorname{arcosh}\left(c x\right)^{2} - \frac{2}{35} \, {\left(\frac{5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{4} d}\right)} a b \operatorname{arcosh}\left(c x\right) - \frac{1}{35} \, {\left(\frac{5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{c^{4} d}\right)} a^{2} - \frac{2}{385875} \, b^{2} {\left(\frac{1125 \, \sqrt{c^{2} x^{2} - 1} c^{4} \sqrt{-d} d x^{6} - 2178 \, \sqrt{c^{2} x^{2} - 1} c^{2} \sqrt{-d} d x^{4} - 1679 \, \sqrt{c^{2} x^{2} - 1} \sqrt{-d} d x^{2} + \frac{18692 \, \sqrt{c^{2} x^{2} - 1} \sqrt{-d} d}{c^{2}}}{c^{2}} - \frac{105 \, {\left(75 \, c^{6} \sqrt{-d} d x^{7} - 168 \, c^{4} \sqrt{-d} d x^{5} + 35 \, c^{2} \sqrt{-d} d x^{3} + 210 \, \sqrt{-d} d x\right)} \operatorname{arcosh}\left(c x\right)}{c^{3}}\right)} + \frac{2 \, {\left(75 \, c^{6} \sqrt{-d} d x^{7} - 168 \, c^{4} \sqrt{-d} d x^{5} + 35 \, c^{2} \sqrt{-d} d x^{3} + 210 \, \sqrt{-d} d x\right)} a b}{3675 \, c^{3}}"," ",0,"-1/35*(5*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(5/2)/(c^4*d))*b^2*arccosh(c*x)^2 - 2/35*(5*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(5/2)/(c^4*d))*a*b*arccosh(c*x) - 1/35*(5*(-c^2*d*x^2 + d)^(5/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(5/2)/(c^4*d))*a^2 - 2/385875*b^2*((1125*sqrt(c^2*x^2 - 1)*c^4*sqrt(-d)*d*x^6 - 2178*sqrt(c^2*x^2 - 1)*c^2*sqrt(-d)*d*x^4 - 1679*sqrt(c^2*x^2 - 1)*sqrt(-d)*d*x^2 + 18692*sqrt(c^2*x^2 - 1)*sqrt(-d)*d/c^2)/c^2 - 105*(75*c^6*sqrt(-d)*d*x^7 - 168*c^4*sqrt(-d)*d*x^5 + 35*c^2*sqrt(-d)*d*x^3 + 210*sqrt(-d)*d*x)*arccosh(c*x)/c^3) + 2/3675*(75*c^6*sqrt(-d)*d*x^7 - 168*c^4*sqrt(-d)*d*x^5 + 35*c^2*sqrt(-d)*d*x^3 + 210*sqrt(-d)*d*x)*a*b/c^3","A",0
179,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{48} \, a^{2} {\left(\frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}{c^{2}} - \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}{c^{2} d} + \frac{3 \, \sqrt{-c^{2} d x^{2} + d} d x}{c^{2}} + \frac{3 \, d^{\frac{3}{2}} \arcsin\left(c x\right)}{c^{3}}\right)} + \int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b^{2} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a b x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/48*a^2*(2*(-c^2*d*x^2 + d)^(3/2)*x/c^2 - 8*(-c^2*d*x^2 + d)^(5/2)*x/(c^2*d) + 3*sqrt(-c^2*d*x^2 + d)*d*x/c^2 + 3*d^(3/2)*arcsin(c*x)/c^3) + integrate((-c^2*d*x^2 + d)^(3/2)*b^2*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 2*(-c^2*d*x^2 + d)^(3/2)*a*b*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
180,1,278,0,0.747272," ","integrate(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b^{2} \operatorname{arcosh}\left(c x\right)^{2}}{5 \, c^{2} d} - \frac{2}{1125} \, b^{2} {\left(\frac{9 \, \sqrt{c^{2} x^{2} - 1} c^{2} \sqrt{-d} d^{2} x^{4} - 38 \, \sqrt{c^{2} x^{2} - 1} \sqrt{-d} d^{2} x^{2} + \frac{149 \, \sqrt{c^{2} x^{2} - 1} \sqrt{-d} d^{2}}{c^{2}}}{d} - \frac{15 \, {\left(3 \, c^{4} \sqrt{-d} d^{2} x^{5} - 10 \, c^{2} \sqrt{-d} d^{2} x^{3} + 15 \, \sqrt{-d} d^{2} x\right)} \operatorname{arcosh}\left(c x\right)}{c d}\right)} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a b \operatorname{arcosh}\left(c x\right)}{5 \, c^{2} d} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a^{2}}{5 \, c^{2} d} + \frac{2 \, {\left(3 \, c^{4} \sqrt{-d} d^{2} x^{5} - 10 \, c^{2} \sqrt{-d} d^{2} x^{3} + 15 \, \sqrt{-d} d^{2} x\right)} a b}{75 \, c d}"," ",0,"-1/5*(-c^2*d*x^2 + d)^(5/2)*b^2*arccosh(c*x)^2/(c^2*d) - 2/1125*b^2*((9*sqrt(c^2*x^2 - 1)*c^2*sqrt(-d)*d^2*x^4 - 38*sqrt(c^2*x^2 - 1)*sqrt(-d)*d^2*x^2 + 149*sqrt(c^2*x^2 - 1)*sqrt(-d)*d^2/c^2)/d - 15*(3*c^4*sqrt(-d)*d^2*x^5 - 10*c^2*sqrt(-d)*d^2*x^3 + 15*sqrt(-d)*d^2*x)*arccosh(c*x)/(c*d)) - 2/5*(-c^2*d*x^2 + d)^(5/2)*a*b*arccosh(c*x)/(c^2*d) - 1/5*(-c^2*d*x^2 + d)^(5/2)*a^2/(c^2*d) + 2/75*(3*c^4*sqrt(-d)*d^2*x^5 - 10*c^2*sqrt(-d)*d^2*x^3 + 15*sqrt(-d)*d^2*x)*a*b/(c*d)","A",0
181,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x + 3 \, \sqrt{-c^{2} d x^{2} + d} d x + \frac{3 \, d^{\frac{3}{2}} \arcsin\left(c x\right)}{c}\right)} a^{2} + \int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/8*(2*(-c^2*d*x^2 + d)^(3/2)*x + 3*sqrt(-c^2*d*x^2 + d)*d*x + 3*d^(3/2)*arcsin(c*x)/c)*a^2 + integrate((-c^2*d*x^2 + d)^(3/2)*b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 2*(-c^2*d*x^2 + d)^(3/2)*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
182,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2/x,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(3 \, d^{\frac{3}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{-c^{2} d x^{2} + d} d\right)} a^{2} + \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{x} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"-1/3*(3*d^(3/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - (-c^2*d*x^2 + d)^(3/2) - 3*sqrt(-c^2*d*x^2 + d)*d)*a^2 + integrate((-c^2*d*x^2 + d)^(3/2)*b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/x + 2*(-c^2*d*x^2 + d)^(3/2)*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
183,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(3 \, \sqrt{-c^{2} d x^{2} + d} c^{2} d x + 3 \, c d^{\frac{3}{2}} \arcsin\left(c x\right) + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}{x}\right)} a^{2} + \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{x^{2}} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{2}}\,{d x}"," ",0,"-1/2*(3*sqrt(-c^2*d*x^2 + d)*c^2*d*x + 3*c*d^(3/2)*arcsin(c*x) + 2*(-c^2*d*x^2 + d)^(3/2)/x)*a^2 + integrate((-c^2*d*x^2 + d)^(3/2)*b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/x^2 + 2*(-c^2*d*x^2 + d)^(3/2)*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^2, x)","F",0
184,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(3 \, c^{2} d^{\frac{3}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} - 3 \, \sqrt{-c^{2} d x^{2} + d} c^{2} d - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{2}}\right)} a^{2} + \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{x^{3}} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{3}}\,{d x}"," ",0,"1/2*(3*c^2*d^(3/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - (-c^2*d*x^2 + d)^(3/2)*c^2 - 3*sqrt(-c^2*d*x^2 + d)*c^2*d - (-c^2*d*x^2 + d)^(5/2)/(d*x^2))*a^2 + integrate((-c^2*d*x^2 + d)^(3/2)*b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/x^3 + 2*(-c^2*d*x^2 + d)^(3/2)*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^3, x)","F",0
185,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(3 \, \sqrt{-c^{2} d x^{2} + d} c^{4} d x + 3 \, c^{3} d^{\frac{3}{2}} \arcsin\left(c x\right) + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2}}{x} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{d x^{3}}\right)} a^{2} + \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{x^{4}} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{4}}\,{d x}"," ",0,"1/3*(3*sqrt(-c^2*d*x^2 + d)*c^4*d*x + 3*c^3*d^(3/2)*arcsin(c*x) + 2*(-c^2*d*x^2 + d)^(3/2)*c^2/x - (-c^2*d*x^2 + d)^(5/2)/(d*x^3))*a^2 + integrate((-c^2*d*x^2 + d)^(3/2)*b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/x^4 + 2*(-c^2*d*x^2 + d)^(3/2)*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^4, x)","F",0
186,1,471,0,0.806228," ","integrate(x^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{63} \, {\left(\frac{7 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{4} d}\right)} b^{2} \operatorname{arcosh}\left(c x\right)^{2} - \frac{2}{63} \, {\left(\frac{7 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{4} d}\right)} a b \operatorname{arcosh}\left(c x\right) - \frac{1}{63} \, {\left(\frac{7 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x^{2}}{c^{2} d} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{c^{4} d}\right)} a^{2} + \frac{2}{250047} \, b^{2} {\left(\frac{343 \, \sqrt{c^{2} x^{2} - 1} c^{6} \sqrt{-d} d^{2} x^{8} - 1147 \, \sqrt{c^{2} x^{2} - 1} c^{4} \sqrt{-d} d^{2} x^{6} + 1005 \, \sqrt{c^{2} x^{2} - 1} c^{2} \sqrt{-d} d^{2} x^{4} + 899 \, \sqrt{c^{2} x^{2} - 1} \sqrt{-d} d^{2} x^{2} - \frac{6140 \, \sqrt{c^{2} x^{2} - 1} \sqrt{-d} d^{2}}{c^{2}}}{c^{2}} - \frac{63 \, {\left(49 \, c^{8} \sqrt{-d} d^{2} x^{9} - 171 \, c^{6} \sqrt{-d} d^{2} x^{7} + 189 \, c^{4} \sqrt{-d} d^{2} x^{5} - 21 \, c^{2} \sqrt{-d} d^{2} x^{3} - 126 \, \sqrt{-d} d^{2} x\right)} \operatorname{arcosh}\left(c x\right)}{c^{3}}\right)} - \frac{2 \, {\left(49 \, c^{8} \sqrt{-d} d^{2} x^{9} - 171 \, c^{6} \sqrt{-d} d^{2} x^{7} + 189 \, c^{4} \sqrt{-d} d^{2} x^{5} - 21 \, c^{2} \sqrt{-d} d^{2} x^{3} - 126 \, \sqrt{-d} d^{2} x\right)} a b}{3969 \, c^{3}}"," ",0,"-1/63*(7*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(7/2)/(c^4*d))*b^2*arccosh(c*x)^2 - 2/63*(7*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(7/2)/(c^4*d))*a*b*arccosh(c*x) - 1/63*(7*(-c^2*d*x^2 + d)^(7/2)*x^2/(c^2*d) + 2*(-c^2*d*x^2 + d)^(7/2)/(c^4*d))*a^2 + 2/250047*b^2*((343*sqrt(c^2*x^2 - 1)*c^6*sqrt(-d)*d^2*x^8 - 1147*sqrt(c^2*x^2 - 1)*c^4*sqrt(-d)*d^2*x^6 + 1005*sqrt(c^2*x^2 - 1)*c^2*sqrt(-d)*d^2*x^4 + 899*sqrt(c^2*x^2 - 1)*sqrt(-d)*d^2*x^2 - 6140*sqrt(c^2*x^2 - 1)*sqrt(-d)*d^2/c^2)/c^2 - 63*(49*c^8*sqrt(-d)*d^2*x^9 - 171*c^6*sqrt(-d)*d^2*x^7 + 189*c^4*sqrt(-d)*d^2*x^5 - 21*c^2*sqrt(-d)*d^2*x^3 - 126*sqrt(-d)*d^2*x)*arccosh(c*x)/c^3) - 2/3969*(49*c^8*sqrt(-d)*d^2*x^9 - 171*c^6*sqrt(-d)*d^2*x^7 + 189*c^4*sqrt(-d)*d^2*x^5 - 21*c^2*sqrt(-d)*d^2*x^3 - 126*sqrt(-d)*d^2*x)*a*b/c^3","A",0
187,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{384} \, {\left(\frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}{c^{2}} - \frac{48 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} x}{c^{2} d} + \frac{10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x}{c^{2}} + \frac{15 \, \sqrt{-c^{2} d x^{2} + d} d^{2} x}{c^{2}} + \frac{15 \, d^{\frac{5}{2}} \arcsin\left(c x\right)}{c^{3}}\right)} a^{2} + \int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b^{2} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a b x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/384*(8*(-c^2*d*x^2 + d)^(5/2)*x/c^2 - 48*(-c^2*d*x^2 + d)^(7/2)*x/(c^2*d) + 10*(-c^2*d*x^2 + d)^(3/2)*d*x/c^2 + 15*sqrt(-c^2*d*x^2 + d)*d^2*x/c^2 + 15*d^(5/2)*arcsin(c*x)/c^3)*a^2 + integrate((-c^2*d*x^2 + d)^(5/2)*b^2*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 2*(-c^2*d*x^2 + d)^(5/2)*a*b*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
188,1,337,0,0.674093," ","integrate(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} b^{2} \operatorname{arcosh}\left(c x\right)^{2}}{7 \, c^{2} d} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a b \operatorname{arcosh}\left(c x\right)}{7 \, c^{2} d} + \frac{2}{25725} \, b^{2} {\left(\frac{75 \, \sqrt{c^{2} x^{2} - 1} c^{4} \sqrt{-d} d^{3} x^{6} - 351 \, \sqrt{c^{2} x^{2} - 1} c^{2} \sqrt{-d} d^{3} x^{4} + 757 \, \sqrt{c^{2} x^{2} - 1} \sqrt{-d} d^{3} x^{2} - \frac{2161 \, \sqrt{c^{2} x^{2} - 1} \sqrt{-d} d^{3}}{c^{2}}}{d} - \frac{105 \, {\left(5 \, c^{6} \sqrt{-d} d^{3} x^{7} - 21 \, c^{4} \sqrt{-d} d^{3} x^{5} + 35 \, c^{2} \sqrt{-d} d^{3} x^{3} - 35 \, \sqrt{-d} d^{3} x\right)} \operatorname{arcosh}\left(c x\right)}{c d}\right)} - \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}} a^{2}}{7 \, c^{2} d} - \frac{2 \, {\left(5 \, c^{6} \sqrt{-d} d^{3} x^{7} - 21 \, c^{4} \sqrt{-d} d^{3} x^{5} + 35 \, c^{2} \sqrt{-d} d^{3} x^{3} - 35 \, \sqrt{-d} d^{3} x\right)} a b}{245 \, c d}"," ",0,"-1/7*(-c^2*d*x^2 + d)^(7/2)*b^2*arccosh(c*x)^2/(c^2*d) - 2/7*(-c^2*d*x^2 + d)^(7/2)*a*b*arccosh(c*x)/(c^2*d) + 2/25725*b^2*((75*sqrt(c^2*x^2 - 1)*c^4*sqrt(-d)*d^3*x^6 - 351*sqrt(c^2*x^2 - 1)*c^2*sqrt(-d)*d^3*x^4 + 757*sqrt(c^2*x^2 - 1)*sqrt(-d)*d^3*x^2 - 2161*sqrt(c^2*x^2 - 1)*sqrt(-d)*d^3/c^2)/d - 105*(5*c^6*sqrt(-d)*d^3*x^7 - 21*c^4*sqrt(-d)*d^3*x^5 + 35*c^2*sqrt(-d)*d^3*x^3 - 35*sqrt(-d)*d^3*x)*arccosh(c*x)/(c*d)) - 1/7*(-c^2*d*x^2 + d)^(7/2)*a^2/(c^2*d) - 2/245*(5*c^6*sqrt(-d)*d^3*x^7 - 21*c^4*sqrt(-d)*d^3*x^5 + 35*c^2*sqrt(-d)*d^3*x^3 - 35*sqrt(-d)*d^3*x)*a*b/(c*d)","A",0
189,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{48} \, {\left(8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x + 10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} d^{2} x + \frac{15 \, d^{\frac{5}{2}} \arcsin\left(c x\right)}{c}\right)} a^{2} + \int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/48*(8*(-c^2*d*x^2 + d)^(5/2)*x + 10*(-c^2*d*x^2 + d)^(3/2)*d*x + 15*sqrt(-c^2*d*x^2 + d)*d^2*x + 15*d^(5/2)*arcsin(c*x)/c)*a^2 + integrate((-c^2*d*x^2 + d)^(5/2)*b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 2*(-c^2*d*x^2 + d)^(5/2)*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
190,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2/x,x, algorithm=""maxima"")","-\frac{1}{15} \, {\left(15 \, d^{\frac{5}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - 3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} - 5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d - 15 \, \sqrt{-c^{2} d x^{2} + d} d^{2}\right)} a^{2} + \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{x} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"-1/15*(15*d^(5/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - 3*(-c^2*d*x^2 + d)^(5/2) - 5*(-c^2*d*x^2 + d)^(3/2)*d - 15*sqrt(-c^2*d*x^2 + d)*d^2)*a^2 + integrate((-c^2*d*x^2 + d)^(5/2)*b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/x + 2*(-c^2*d*x^2 + d)^(5/2)*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
191,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2/x^2,x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} c^{2} d^{2} x + 15 \, c d^{\frac{5}{2}} \arcsin\left(c x\right) + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}{x}\right)} a^{2} + \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{x^{2}} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{2}}\,{d x}"," ",0,"-1/8*(10*(-c^2*d*x^2 + d)^(3/2)*c^2*d*x + 15*sqrt(-c^2*d*x^2 + d)*c^2*d^2*x + 15*c*d^(5/2)*arcsin(c*x) + 8*(-c^2*d*x^2 + d)^(5/2)/x)*a^2 + integrate((-c^2*d*x^2 + d)^(5/2)*b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/x^2 + 2*(-c^2*d*x^2 + d)^(5/2)*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^2, x)","F",0
192,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2/x^3,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(15 \, c^{2} d^{\frac{5}{2}} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right) - 3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2} - 5 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d - 15 \, \sqrt{-c^{2} d x^{2} + d} c^{2} d^{2} - \frac{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{2}}\right)} a^{2} + \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{x^{3}} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{3}}\,{d x}"," ",0,"1/6*(15*c^2*d^(5/2)*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x)) - 3*(-c^2*d*x^2 + d)^(5/2)*c^2 - 5*(-c^2*d*x^2 + d)^(3/2)*c^2*d - 15*sqrt(-c^2*d*x^2 + d)*c^2*d^2 - 3*(-c^2*d*x^2 + d)^(7/2)/(d*x^2))*a^2 + integrate((-c^2*d*x^2 + d)^(5/2)*b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/x^3 + 2*(-c^2*d*x^2 + d)^(5/2)*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^3, x)","F",0
193,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2/x^4,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(10 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d x + 15 \, \sqrt{-c^{2} d x^{2} + d} c^{4} d^{2} x + 15 \, c^{3} d^{\frac{5}{2}} \arcsin\left(c x\right) + \frac{8 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} c^{2}}{x} - \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{7}{2}}}{d x^{3}}\right)} a^{2} + \int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{x^{4}} + \frac{2 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{4}}\,{d x}"," ",0,"1/6*(10*(-c^2*d*x^2 + d)^(3/2)*c^4*d*x + 15*sqrt(-c^2*d*x^2 + d)*c^4*d^2*x + 15*c^3*d^(5/2)*arcsin(c*x) + 8*(-c^2*d*x^2 + d)^(5/2)*c^2/x - 2*(-c^2*d*x^2 + d)^(7/2)/(d*x^3))*a^2 + integrate((-c^2*d*x^2 + d)^(5/2)*b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/x^4 + 2*(-c^2*d*x^2 + d)^(5/2)*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x^4, x)","F",0
194,1,407,0,1.033035," ","integrate(x^5*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{15} \, {\left(\frac{3 \, \sqrt{-c^{2} d x^{2} + d} x^{4}}{c^{2} d} + \frac{4 \, \sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{4} d} + \frac{8 \, \sqrt{-c^{2} d x^{2} + d}}{c^{6} d}\right)} b^{2} \operatorname{arcosh}\left(c x\right)^{2} - \frac{2}{15} \, {\left(\frac{3 \, \sqrt{-c^{2} d x^{2} + d} x^{4}}{c^{2} d} + \frac{4 \, \sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{4} d} + \frac{8 \, \sqrt{-c^{2} d x^{2} + d}}{c^{6} d}\right)} a b \operatorname{arcosh}\left(c x\right) - \frac{1}{15} \, {\left(\frac{3 \, \sqrt{-c^{2} d x^{2} + d} x^{4}}{c^{2} d} + \frac{4 \, \sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{4} d} + \frac{8 \, \sqrt{-c^{2} d x^{2} + d}}{c^{6} d}\right)} a^{2} - \frac{2}{3375} \, b^{2} {\left(\frac{27 \, \sqrt{c^{2} x^{2} - 1} c^{2} \sqrt{-d} x^{4} + 136 \, \sqrt{c^{2} x^{2} - 1} \sqrt{-d} x^{2} + \frac{2072 \, \sqrt{c^{2} x^{2} - 1} \sqrt{-d}}{c^{2}}}{c^{4} d} - \frac{15 \, {\left(9 \, c^{4} \sqrt{-d} x^{5} + 20 \, c^{2} \sqrt{-d} x^{3} + 120 \, \sqrt{-d} x\right)} \operatorname{arcosh}\left(c x\right)}{c^{5} d}\right)} + \frac{2 \, {\left(9 \, c^{4} \sqrt{-d} x^{5} + 20 \, c^{2} \sqrt{-d} x^{3} + 120 \, \sqrt{-d} x\right)} a b}{225 \, c^{5} d}"," ",0,"-1/15*(3*sqrt(-c^2*d*x^2 + d)*x^4/(c^2*d) + 4*sqrt(-c^2*d*x^2 + d)*x^2/(c^4*d) + 8*sqrt(-c^2*d*x^2 + d)/(c^6*d))*b^2*arccosh(c*x)^2 - 2/15*(3*sqrt(-c^2*d*x^2 + d)*x^4/(c^2*d) + 4*sqrt(-c^2*d*x^2 + d)*x^2/(c^4*d) + 8*sqrt(-c^2*d*x^2 + d)/(c^6*d))*a*b*arccosh(c*x) - 1/15*(3*sqrt(-c^2*d*x^2 + d)*x^4/(c^2*d) + 4*sqrt(-c^2*d*x^2 + d)*x^2/(c^4*d) + 8*sqrt(-c^2*d*x^2 + d)/(c^6*d))*a^2 - 2/3375*b^2*((27*sqrt(c^2*x^2 - 1)*c^2*sqrt(-d)*x^4 + 136*sqrt(c^2*x^2 - 1)*sqrt(-d)*x^2 + 2072*sqrt(c^2*x^2 - 1)*sqrt(-d)/c^2)/(c^4*d) - 15*(9*c^4*sqrt(-d)*x^5 + 20*c^2*sqrt(-d)*x^3 + 120*sqrt(-d)*x)*arccosh(c*x)/(c^5*d)) + 2/225*(9*c^4*sqrt(-d)*x^5 + 20*c^2*sqrt(-d)*x^3 + 120*sqrt(-d)*x)*a*b/(c^5*d)","A",0
195,0,0,0,0.000000," ","integrate(x^4*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{8} \, a^{2} {\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} x^{3}}{c^{2} d} + \frac{3 \, \sqrt{-c^{2} d x^{2} + d} x}{c^{4} d} - \frac{3 \, \arcsin\left(c x\right)}{c^{5} \sqrt{d}}\right)} + \int \frac{b^{2} x^{4} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{\sqrt{-c^{2} d x^{2} + d}} + \frac{2 \, a b x^{4} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"-1/8*a^2*(2*sqrt(-c^2*d*x^2 + d)*x^3/(c^2*d) + 3*sqrt(-c^2*d*x^2 + d)*x/(c^4*d) - 3*arcsin(c*x)/(c^5*sqrt(d))) + integrate(b^2*x^4*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/sqrt(-c^2*d*x^2 + d) + 2*a*b*x^4*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c^2*d*x^2 + d), x)","F",0
196,1,279,0,1.021295," ","integrate(x^3*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, b^{2} {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{2} d} + \frac{2 \, \sqrt{-c^{2} d x^{2} + d}}{c^{4} d}\right)} \operatorname{arcosh}\left(c x\right)^{2} - \frac{2}{3} \, a b {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{2} d} + \frac{2 \, \sqrt{-c^{2} d x^{2} + d}}{c^{4} d}\right)} \operatorname{arcosh}\left(c x\right) - \frac{1}{3} \, a^{2} {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x^{2}}{c^{2} d} + \frac{2 \, \sqrt{-c^{2} d x^{2} + d}}{c^{4} d}\right)} - \frac{2}{27} \, b^{2} {\left(\frac{\sqrt{c^{2} x^{2} - 1} \sqrt{-d} x^{2} + \frac{20 \, \sqrt{c^{2} x^{2} - 1} \sqrt{-d}}{c^{2}}}{c^{2} d} - \frac{3 \, {\left(c^{2} \sqrt{-d} x^{3} + 6 \, \sqrt{-d} x\right)} \operatorname{arcosh}\left(c x\right)}{c^{3} d}\right)} + \frac{2 \, {\left(c^{2} \sqrt{-d} x^{3} + 6 \, \sqrt{-d} x\right)} a b}{9 \, c^{3} d}"," ",0,"-1/3*b^2*(sqrt(-c^2*d*x^2 + d)*x^2/(c^2*d) + 2*sqrt(-c^2*d*x^2 + d)/(c^4*d))*arccosh(c*x)^2 - 2/3*a*b*(sqrt(-c^2*d*x^2 + d)*x^2/(c^2*d) + 2*sqrt(-c^2*d*x^2 + d)/(c^4*d))*arccosh(c*x) - 1/3*a^2*(sqrt(-c^2*d*x^2 + d)*x^2/(c^2*d) + 2*sqrt(-c^2*d*x^2 + d)/(c^4*d)) - 2/27*b^2*((sqrt(c^2*x^2 - 1)*sqrt(-d)*x^2 + 20*sqrt(c^2*x^2 - 1)*sqrt(-d)/c^2)/(c^2*d) - 3*(c^2*sqrt(-d)*x^3 + 6*sqrt(-d)*x)*arccosh(c*x)/(c^3*d)) + 2/9*(c^2*sqrt(-d)*x^3 + 6*sqrt(-d)*x)*a*b/(c^3*d)","A",0
197,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{\sqrt{-c^{2} d x^{2} + d} x}{c^{2} d} - \frac{\arcsin\left(c x\right)}{c^{3} \sqrt{d}}\right)} + \int \frac{b^{2} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{\sqrt{-c^{2} d x^{2} + d}} + \frac{2 \, a b x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"-1/2*a^2*(sqrt(-c^2*d*x^2 + d)*x/(c^2*d) - arcsin(c*x)/(c^3*sqrt(d))) + integrate(b^2*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/sqrt(-c^2*d*x^2 + d) + 2*a*b*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c^2*d*x^2 + d), x)","F",0
198,1,145,0,0.390917," ","integrate(x*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","2 \, b^{2} {\left(\frac{\sqrt{-d} x \operatorname{arcosh}\left(c x\right)}{c d} - \frac{\sqrt{c^{2} x^{2} - 1} \sqrt{-d}}{c^{2} d}\right)} + \frac{2 \, a b \sqrt{-d} x}{c d} - \frac{\sqrt{-c^{2} d x^{2} + d} b^{2} \operatorname{arcosh}\left(c x\right)^{2}}{c^{2} d} - \frac{2 \, \sqrt{-c^{2} d x^{2} + d} a b \operatorname{arcosh}\left(c x\right)}{c^{2} d} - \frac{\sqrt{-c^{2} d x^{2} + d} a^{2}}{c^{2} d}"," ",0,"2*b^2*(sqrt(-d)*x*arccosh(c*x)/(c*d) - sqrt(c^2*x^2 - 1)*sqrt(-d)/(c^2*d)) + 2*a*b*sqrt(-d)*x/(c*d) - sqrt(-c^2*d*x^2 + d)*b^2*arccosh(c*x)^2/(c^2*d) - 2*sqrt(-c^2*d*x^2 + d)*a*b*arccosh(c*x)/(c^2*d) - sqrt(-c^2*d*x^2 + d)*a^2/(c^2*d)","A",0
199,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{a^{2} \arcsin\left(c x\right)}{c \sqrt{d}} + \int \frac{b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{\sqrt{-c^{2} d x^{2} + d}} + \frac{2 \, a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"a^2*arcsin(c*x)/(c*sqrt(d)) + integrate(b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/sqrt(-c^2*d*x^2 + d) + 2*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(-c^2*d*x^2 + d), x)","F",0
200,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/x/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{a^{2} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{\sqrt{d}} + \int \frac{b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{\sqrt{-c^{2} d x^{2} + d} x} + \frac{2 \, a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d} x}\,{d x}"," ",0,"-a^2*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/sqrt(d) + integrate(b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(sqrt(-c^2*d*x^2 + d)*x) + 2*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(sqrt(-c^2*d*x^2 + d)*x), x)","F",0
201,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/x^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(c^{2} d \sqrt{-\frac{1}{c^{4} d}} \log\left(x^{2} - \frac{1}{c^{2}}\right) + i \, \left(-1\right)^{-2 \, c^{2} d x^{2} + 2 \, d} \sqrt{d} \log\left(-2 \, c^{2} d + \frac{2 \, d}{x^{2}}\right)\right)} a b c}{d} + b^{2} \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{\sqrt{-c^{2} d x^{2} + d} x^{2}}\,{d x} - \frac{2 \, \sqrt{-c^{2} d x^{2} + d} a b \operatorname{arcosh}\left(c x\right)}{d x} - \frac{\sqrt{-c^{2} d x^{2} + d} a^{2}}{d x}"," ",0,"-(c^2*d*sqrt(-1/(c^4*d))*log(x^2 - 1/c^2) + I*(-1)^(-2*c^2*d*x^2 + 2*d)*sqrt(d)*log(-2*c^2*d + 2*d/x^2))*a*b*c/d + b^2*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(sqrt(-c^2*d*x^2 + d)*x^2), x) - 2*sqrt(-c^2*d*x^2 + d)*a*b*arccosh(c*x)/(d*x) - sqrt(-c^2*d*x^2 + d)*a^2/(d*x)","F",0
202,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/x^3/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{\sqrt{d}} + \frac{\sqrt{-c^{2} d x^{2} + d}}{d x^{2}}\right)} a^{2} + \int \frac{b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{\sqrt{-c^{2} d x^{2} + d} x^{3}} + \frac{2 \, a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{-c^{2} d x^{2} + d} x^{3}}\,{d x}"," ",0,"-1/2*(c^2*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/sqrt(d) + sqrt(-c^2*d*x^2 + d)/(d*x^2))*a^2 + integrate(b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(sqrt(-c^2*d*x^2 + d)*x^3) + 2*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(sqrt(-c^2*d*x^2 + d)*x^3), x)","F",0
203,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/x^4/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{4 \, c^{2} \sqrt{-d} \log\left(x\right)}{d} - \frac{\sqrt{-d}}{d x^{2}}\right)} a b c - \frac{2}{3} \, a b {\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} c^{2}}{d x} + \frac{\sqrt{-c^{2} d x^{2} + d}}{d x^{3}}\right)} \operatorname{arcosh}\left(c x\right) - \frac{1}{3} \, a^{2} {\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} c^{2}}{d x} + \frac{\sqrt{-c^{2} d x^{2} + d}}{d x^{3}}\right)} + b^{2} \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{\sqrt{-c^{2} d x^{2} + d} x^{4}}\,{d x}"," ",0,"1/3*(4*c^2*sqrt(-d)*log(x)/d - sqrt(-d)/(d*x^2))*a*b*c - 2/3*a*b*(2*sqrt(-c^2*d*x^2 + d)*c^2/(d*x) + sqrt(-c^2*d*x^2 + d)/(d*x^3))*arccosh(c*x) - 1/3*a^2*(2*sqrt(-c^2*d*x^2 + d)*c^2/(d*x) + sqrt(-c^2*d*x^2 + d)/(d*x^3)) + b^2*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(sqrt(-c^2*d*x^2 + d)*x^4), x)","F",0
204,0,0,0,0.000000," ","integrate(x^5*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} {\left(\frac{x^{4}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} + \frac{4 \, x^{2}}{\sqrt{-c^{2} d x^{2} + d} c^{4} d} - \frac{8}{\sqrt{-c^{2} d x^{2} + d} c^{6} d}\right)} + \frac{{\left(b^{2} c^{4} \sqrt{d} x^{4} + 4 \, b^{2} c^{2} \sqrt{d} x^{2} - 8 \, b^{2} \sqrt{d}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{3 \, {\left(c^{8} d^{2} x^{2} - c^{6} d^{2}\right)}} + \int -\frac{2 \, {\left({\left(4 \, b^{2} c^{3} x^{3} - {\left(3 \, a b c^{5} - b^{2} c^{5}\right)} x^{5} - 8 \, b^{2} c x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(3 \, b^{2} c^{4} x^{4} - {\left(3 \, a b c^{6} - b^{2} c^{6}\right)} x^{6} - 12 \, b^{2} c^{2} x^{2} + 8 \, b^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{3 \, {\left(c^{10} d^{\frac{3}{2}} x^{5} - 2 \, c^{8} d^{\frac{3}{2}} x^{3} + c^{6} d^{\frac{3}{2}} x + {\left(c^{9} d^{\frac{3}{2}} x^{4} - 2 \, c^{7} d^{\frac{3}{2}} x^{2} + c^{5} d^{\frac{3}{2}}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x}"," ",0,"-1/3*a^2*(x^4/(sqrt(-c^2*d*x^2 + d)*c^2*d) + 4*x^2/(sqrt(-c^2*d*x^2 + d)*c^4*d) - 8/(sqrt(-c^2*d*x^2 + d)*c^6*d)) + 1/3*(b^2*c^4*sqrt(d)*x^4 + 4*b^2*c^2*sqrt(d)*x^2 - 8*b^2*sqrt(d))*sqrt(c*x + 1)*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(c^8*d^2*x^2 - c^6*d^2) + integrate(-2/3*((4*b^2*c^3*x^3 - (3*a*b*c^5 - b^2*c^5)*x^5 - 8*b^2*c*x)*(c*x + 1)*sqrt(c*x - 1) + (3*b^2*c^4*x^4 - (3*a*b*c^6 - b^2*c^6)*x^6 - 12*b^2*c^2*x^2 + 8*b^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c^10*d^(3/2)*x^5 - 2*c^8*d^(3/2)*x^3 + c^6*d^(3/2)*x + (c^9*d^(3/2)*x^4 - 2*c^7*d^(3/2)*x^2 + c^5*d^(3/2))*sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
205,0,0,0,0.000000," ","integrate(x^4*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} {\left(\frac{x^{3}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{3 \, x}{\sqrt{-c^{2} d x^{2} + d} c^{4} d} + \frac{3 \, \arcsin\left(c x\right)}{c^{5} d^{\frac{3}{2}}}\right)} + \int \frac{b^{2} x^{4} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}} + \frac{2 \, a b x^{4} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-1/2*a^2*(x^3/(sqrt(-c^2*d*x^2 + d)*c^2*d) - 3*x/(sqrt(-c^2*d*x^2 + d)*c^4*d) + 3*arcsin(c*x)/(c^5*d^(3/2))) + integrate(b^2*x^4*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(-c^2*d*x^2 + d)^(3/2) + 2*a*b*x^4*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(-c^2*d*x^2 + d)^(3/2), x)","F",0
206,0,0,0,0.000000," ","integrate(x^3*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-a b c {\left(\frac{2 \, \sqrt{-d} x}{c^{4} d^{2}} + \frac{\sqrt{-d} \log\left(c x + 1\right)}{c^{5} d^{2}} - \frac{\sqrt{-d} \log\left(c x - 1\right)}{c^{5} d^{2}}\right)} - 2 \, a b {\left(\frac{x^{2}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{2}{\sqrt{-c^{2} d x^{2} + d} c^{4} d}\right)} \operatorname{arcosh}\left(c x\right) - a^{2} {\left(\frac{x^{2}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{2}{\sqrt{-c^{2} d x^{2} + d} c^{4} d}\right)} - b^{2} {\left(\frac{{\left(c^{2} x^{2} - 2\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{\sqrt{c x + 1} \sqrt{-c x + 1} c^{4} d^{\frac{3}{2}}} - \int \frac{2 \, {\left(c^{4} x^{4} - 3 \, c^{2} x^{2} + {\left(c^{3} x^{3} - 2 \, c x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + 2\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left({\left(c^{5} d^{\frac{3}{2}} x^{2} - c^{3} d^{\frac{3}{2}}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{6} d^{\frac{3}{2}} x^{3} - c^{4} d^{\frac{3}{2}} x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}\right)}"," ",0,"-a*b*c*(2*sqrt(-d)*x/(c^4*d^2) + sqrt(-d)*log(c*x + 1)/(c^5*d^2) - sqrt(-d)*log(c*x - 1)/(c^5*d^2)) - 2*a*b*(x^2/(sqrt(-c^2*d*x^2 + d)*c^2*d) - 2/(sqrt(-c^2*d*x^2 + d)*c^4*d))*arccosh(c*x) - a^2*(x^2/(sqrt(-c^2*d*x^2 + d)*c^2*d) - 2/(sqrt(-c^2*d*x^2 + d)*c^4*d)) - b^2*((c^2*x^2 - 2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(sqrt(c*x + 1)*sqrt(-c*x + 1)*c^4*d^(3/2)) - integrate(2*(c^4*x^4 - 3*c^2*x^2 + (c^3*x^3 - 2*c*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + 2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(((c^5*d^(3/2)*x^2 - c^3*d^(3/2))*(c*x + 1)*sqrt(c*x - 1) + (c^6*d^(3/2)*x^3 - c^4*d^(3/2)*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x))","F",0
207,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","a^{2} {\left(\frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} - \frac{\arcsin\left(c x\right)}{c^{3} d^{\frac{3}{2}}}\right)} + \int \frac{b^{2} x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}} + \frac{2 \, a b x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"a^2*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d) - arcsin(c*x)/(c^3*d^(3/2))) + integrate(b^2*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(-c^2*d*x^2 + d)^(3/2) + 2*a*b*x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(-c^2*d*x^2 + d)^(3/2), x)","F",0
208,0,0,0,0.000000," ","integrate(x*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{a^{2}}{\sqrt{-c^{2} d x^{2} + d} c^{2} d} + \int \frac{b^{2} x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}} + \frac{2 \, a b x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"a^2/(sqrt(-c^2*d*x^2 + d)*c^2*d) + integrate(b^2*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(-c^2*d*x^2 + d)^(3/2) + 2*a*b*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(-c^2*d*x^2 + d)^(3/2), x)","F",0
209,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{a b c \sqrt{-\frac{1}{c^{4} d}} \log\left(x^{2} - \frac{1}{c^{2}}\right)}{d} + b^{2} \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x} + \frac{2 \, a b x \operatorname{arcosh}\left(c x\right)}{\sqrt{-c^{2} d x^{2} + d} d} + \frac{a^{2} x}{\sqrt{-c^{2} d x^{2} + d} d}"," ",0,"-a*b*c*sqrt(-1/(c^4*d))*log(x^2 - 1/c^2)/d + b^2*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(-c^2*d*x^2 + d)^(3/2), x) + 2*a*b*x*arccosh(c*x)/(sqrt(-c^2*d*x^2 + d)*d) + a^2*x/(sqrt(-c^2*d*x^2 + d)*d)","F",0
210,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/x/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-a^{2} {\left(\frac{\log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{1}{\sqrt{-c^{2} d x^{2} + d} d}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x} + \frac{2 \, a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"-a^2*(log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/d^(3/2) - 1/(sqrt(-c^2*d*x^2 + d)*d)) + integrate(b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/((-c^2*d*x^2 + d)^(3/2)*x) + 2*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/((-c^2*d*x^2 + d)^(3/2)*x), x)","F",0
211,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/x^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","a b c {\left(\frac{\sqrt{-d} \log\left(c x + 1\right)}{d^{2}} + \frac{\sqrt{-d} \log\left(c x - 1\right)}{d^{2}} + \frac{2 \, \sqrt{-d} \log\left(x\right)}{d^{2}}\right)} + 2 \, {\left(\frac{2 \, c^{2} x}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{1}{\sqrt{-c^{2} d x^{2} + d} d x}\right)} a b \operatorname{arcosh}\left(c x\right) + {\left(\frac{2 \, c^{2} x}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{1}{\sqrt{-c^{2} d x^{2} + d} d x}\right)} a^{2} + b^{2} \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"a*b*c*(sqrt(-d)*log(c*x + 1)/d^2 + sqrt(-d)*log(c*x - 1)/d^2 + 2*sqrt(-d)*log(x)/d^2) + 2*(2*c^2*x/(sqrt(-c^2*d*x^2 + d)*d) - 1/(sqrt(-c^2*d*x^2 + d)*d*x))*a*b*arccosh(c*x) + (2*c^2*x/(sqrt(-c^2*d*x^2 + d)*d) - 1/(sqrt(-c^2*d*x^2 + d)*d*x))*a^2 + b^2*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/((-c^2*d*x^2 + d)^(3/2)*x^2), x)","F",0
212,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/x^3/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{3 \, c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{3 \, c^{2}}{\sqrt{-c^{2} d x^{2} + d} d} + \frac{1}{\sqrt{-c^{2} d x^{2} + d} d x^{2}}\right)} a^{2} + \int \frac{b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{3}} + \frac{2 \, a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{3}}\,{d x}"," ",0,"-1/2*(3*c^2*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/d^(3/2) - 3*c^2/(sqrt(-c^2*d*x^2 + d)*d) + 1/(sqrt(-c^2*d*x^2 + d)*d*x^2))*a^2 + integrate(b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/((-c^2*d*x^2 + d)^(3/2)*x^3) + 2*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/((-c^2*d*x^2 + d)^(3/2)*x^3), x)","F",0
213,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/x^4/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{8 \, c^{4} x}{\sqrt{-c^{2} d x^{2} + d} d} - \frac{4 \, c^{2}}{\sqrt{-c^{2} d x^{2} + d} d x} - \frac{1}{\sqrt{-c^{2} d x^{2} + d} d x^{3}}\right)} a^{2} + \int \frac{b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{4}} + \frac{2 \, a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{4}}\,{d x}"," ",0,"1/3*(8*c^4*x/(sqrt(-c^2*d*x^2 + d)*d) - 4*c^2/(sqrt(-c^2*d*x^2 + d)*d*x) - 1/(sqrt(-c^2*d*x^2 + d)*d*x^3))*a^2 + integrate(b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/((-c^2*d*x^2 + d)^(3/2)*x^4) + 2*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/((-c^2*d*x^2 + d)^(3/2)*x^4), x)","F",0
214,0,0,0,0.000000," ","integrate(x^5*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} {\left(\frac{3 \, x^{4}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} - \frac{12 \, x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d} + \frac{8}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{6} d}\right)} - \frac{{\left(3 \, b^{2} c^{4} \sqrt{d} x^{4} - 12 \, b^{2} c^{2} \sqrt{d} x^{2} + 8 \, b^{2} \sqrt{d}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{3 \, {\left(c^{10} d^{3} x^{4} - 2 \, c^{8} d^{3} x^{2} + c^{6} d^{3}\right)}} - \int \frac{2 \, {\left({\left(12 \, b^{2} c^{3} x^{3} + 3 \, {\left(a b c^{5} - b^{2} c^{5}\right)} x^{5} - 8 \, b^{2} c x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(15 \, b^{2} c^{4} x^{4} + 3 \, {\left(a b c^{6} - b^{2} c^{6}\right)} x^{6} - 20 \, b^{2} c^{2} x^{2} + 8 \, b^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{3 \, {\left(c^{12} d^{\frac{5}{2}} x^{7} - 3 \, c^{10} d^{\frac{5}{2}} x^{5} + 3 \, c^{8} d^{\frac{5}{2}} x^{3} - c^{6} d^{\frac{5}{2}} x + {\left(c^{11} d^{\frac{5}{2}} x^{6} - 3 \, c^{9} d^{\frac{5}{2}} x^{4} + 3 \, c^{7} d^{\frac{5}{2}} x^{2} - c^{5} d^{\frac{5}{2}}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)}}\,{d x}"," ",0,"-1/3*a^2*(3*x^4/((-c^2*d*x^2 + d)^(3/2)*c^2*d) - 12*x^2/((-c^2*d*x^2 + d)^(3/2)*c^4*d) + 8/((-c^2*d*x^2 + d)^(3/2)*c^6*d)) - 1/3*(3*b^2*c^4*sqrt(d)*x^4 - 12*b^2*c^2*sqrt(d)*x^2 + 8*b^2*sqrt(d))*sqrt(c*x + 1)*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(c^10*d^3*x^4 - 2*c^8*d^3*x^2 + c^6*d^3) - integrate(2/3*((12*b^2*c^3*x^3 + 3*(a*b*c^5 - b^2*c^5)*x^5 - 8*b^2*c*x)*(c*x + 1)*sqrt(c*x - 1) + (15*b^2*c^4*x^4 + 3*(a*b*c^6 - b^2*c^6)*x^6 - 20*b^2*c^2*x^2 + 8*b^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(c^12*d^(5/2)*x^7 - 3*c^10*d^(5/2)*x^5 + 3*c^8*d^(5/2)*x^3 - c^6*d^(5/2)*x + (c^11*d^(5/2)*x^6 - 3*c^9*d^(5/2)*x^4 + 3*c^7*d^(5/2)*x^2 - c^5*d^(5/2))*sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
215,0,0,0,0.000000," ","integrate(x^4*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(x {\left(\frac{3 \, x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} - \frac{2}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)} - \frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{4} d^{2}} + \frac{3 \, \arcsin\left(c x\right)}{c^{5} d^{\frac{5}{2}}}\right)} a^{2} + \int \frac{b^{2} x^{4} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}} + \frac{2 \, a b x^{4} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/3*(x*(3*x^2/((-c^2*d*x^2 + d)^(3/2)*c^2*d) - 2/((-c^2*d*x^2 + d)^(3/2)*c^4*d)) - x/(sqrt(-c^2*d*x^2 + d)*c^4*d^2) + 3*arcsin(c*x)/(c^5*d^(5/2)))*a^2 + integrate(b^2*x^4*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(-c^2*d*x^2 + d)^(5/2) + 2*a*b*x^4*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(-c^2*d*x^2 + d)^(5/2), x)","F",0
216,0,0,0,0.000000," ","integrate(x^3*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, a b c {\left(\frac{2 \, \sqrt{-d} x}{c^{6} d^{3} x^{2} - c^{4} d^{3}} + \frac{5 \, \sqrt{-d} \log\left(c x + 1\right)}{c^{5} d^{3}} - \frac{5 \, \sqrt{-d} \log\left(c x - 1\right)}{c^{5} d^{3}}\right)} + \frac{2}{3} \, a b {\left(\frac{3 \, x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} - \frac{2}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)} \operatorname{arcosh}\left(c x\right) + \frac{1}{3} \, a^{2} {\left(\frac{3 \, x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} - \frac{2}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{4} d}\right)} + b^{2} \int \frac{x^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/6*a*b*c*(2*sqrt(-d)*x/(c^6*d^3*x^2 - c^4*d^3) + 5*sqrt(-d)*log(c*x + 1)/(c^5*d^3) - 5*sqrt(-d)*log(c*x - 1)/(c^5*d^3)) + 2/3*a*b*(3*x^2/((-c^2*d*x^2 + d)^(3/2)*c^2*d) - 2/((-c^2*d*x^2 + d)^(3/2)*c^4*d))*arccosh(c*x) + 1/3*a^2*(3*x^2/((-c^2*d*x^2 + d)^(3/2)*c^2*d) - 2/((-c^2*d*x^2 + d)^(3/2)*c^4*d)) + b^2*integrate(x^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(-c^2*d*x^2 + d)^(5/2), x)","F",0
217,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a b c {\left(\frac{\sqrt{-d}}{c^{6} d^{3} x^{2} - c^{4} d^{3}} - \frac{\sqrt{-d} \log\left(c x + 1\right)}{c^{4} d^{3}} - \frac{\sqrt{-d} \log\left(c x - 1\right)}{c^{4} d^{3}}\right)} - \frac{2}{3} \, a b {\left(\frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{2} d^{2}} - \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}\right)} \operatorname{arcosh}\left(c x\right) - \frac{1}{3} \, a^{2} {\left(\frac{x}{\sqrt{-c^{2} d x^{2} + d} c^{2} d^{2}} - \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d}\right)} + b^{2} \int \frac{x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/3*a*b*c*(sqrt(-d)/(c^6*d^3*x^2 - c^4*d^3) - sqrt(-d)*log(c*x + 1)/(c^4*d^3) - sqrt(-d)*log(c*x - 1)/(c^4*d^3)) - 2/3*a*b*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d^2) - x/((-c^2*d*x^2 + d)^(3/2)*c^2*d))*arccosh(c*x) - 1/3*a^2*(x/(sqrt(-c^2*d*x^2 + d)*c^2*d^2) - x/((-c^2*d*x^2 + d)^(3/2)*c^2*d)) + b^2*integrate(x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(-c^2*d*x^2 + d)^(5/2), x)","F",0
218,0,0,0,0.000000," ","integrate(x*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{a^{2}}{3 \, {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} c^{2} d} + \int \frac{b^{2} x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}} + \frac{2 \, a b x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/3*a^2/((-c^2*d*x^2 + d)^(3/2)*c^2*d) + integrate(b^2*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(-c^2*d*x^2 + d)^(5/2) + 2*a*b*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(-c^2*d*x^2 + d)^(5/2), x)","F",0
219,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a b c {\left(\frac{\sqrt{-d}}{c^{4} d^{3} x^{2} - c^{2} d^{3}} + \frac{2 \, \sqrt{-d} \log\left(c x + 1\right)}{c^{2} d^{3}} + \frac{2 \, \sqrt{-d} \log\left(c x - 1\right)}{c^{2} d^{3}}\right)} + \frac{2}{3} \, a b {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} \operatorname{arcosh}\left(c x\right) + \frac{1}{3} \, a^{2} {\left(\frac{2 \, x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + b^{2} \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/3*a*b*c*(sqrt(-d)/(c^4*d^3*x^2 - c^2*d^3) + 2*sqrt(-d)*log(c*x + 1)/(c^2*d^3) + 2*sqrt(-d)*log(c*x - 1)/(c^2*d^3)) + 2/3*a*b*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d))*arccosh(c*x) + 1/3*a^2*(2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + x/((-c^2*d*x^2 + d)^(3/2)*d)) + b^2*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(-c^2*d*x^2 + d)^(5/2), x)","F",0
220,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/x/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} {\left(\frac{3 \, \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{3}{\sqrt{-c^{2} d x^{2} + d} d^{2}} - \frac{1}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x} + \frac{2 \, a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x}\,{d x}"," ",0,"-1/3*a^2*(3*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/d^(5/2) - 3/(sqrt(-c^2*d*x^2 + d)*d^2) - 1/((-c^2*d*x^2 + d)^(3/2)*d)) + integrate(b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/((-c^2*d*x^2 + d)^(5/2)*x) + 2*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/((-c^2*d*x^2 + d)^(5/2)*x), x)","F",0
221,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/x^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} {\left(\frac{8 \, c^{2} x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{4 \, c^{2} x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} - \frac{3}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}} + \frac{2 \, a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{2}}\,{d x}"," ",0,"1/3*a^2*(8*c^2*x/(sqrt(-c^2*d*x^2 + d)*d^2) + 4*c^2*x/((-c^2*d*x^2 + d)^(3/2)*d) - 3/((-c^2*d*x^2 + d)^(3/2)*d*x)) + integrate(b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/((-c^2*d*x^2 + d)^(5/2)*x^2) + 2*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/((-c^2*d*x^2 + d)^(5/2)*x^2), x)","F",0
222,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/x^3/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{6} \, a^{2} {\left(\frac{15 \, c^{2} \log\left(\frac{2 \, \sqrt{-c^{2} d x^{2} + d} \sqrt{d}}{{\left| x \right|}} + \frac{2 \, d}{{\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{15 \, c^{2}}{\sqrt{-c^{2} d x^{2} + d} d^{2}} - \frac{5 \, c^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} + \frac{3}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{2}}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{3}} + \frac{2 \, a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{3}}\,{d x}"," ",0,"-1/6*a^2*(15*c^2*log(2*sqrt(-c^2*d*x^2 + d)*sqrt(d)/abs(x) + 2*d/abs(x))/d^(5/2) - 15*c^2/(sqrt(-c^2*d*x^2 + d)*d^2) - 5*c^2/((-c^2*d*x^2 + d)^(3/2)*d) + 3/((-c^2*d*x^2 + d)^(3/2)*d*x^2)) + integrate(b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/((-c^2*d*x^2 + d)^(5/2)*x^3) + 2*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/((-c^2*d*x^2 + d)^(5/2)*x^3), x)","F",0
223,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/x^4/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a b c {\left(\frac{8 \, c^{2} \sqrt{-d} \log\left(c x + 1\right)}{d^{3}} + \frac{8 \, c^{2} \sqrt{-d} \log\left(c x - 1\right)}{d^{3}} + \frac{16 \, c^{2} \sqrt{-d} \log\left(x\right)}{d^{3}} + \frac{\sqrt{-d}}{c^{2} d^{3} x^{4} - d^{3} x^{2}}\right)} + \frac{2}{3} \, {\left(\frac{16 \, c^{4} x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{8 \, c^{4} x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} - \frac{6 \, c^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x} - \frac{1}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{3}}\right)} a b \operatorname{arcosh}\left(c x\right) + \frac{1}{3} \, {\left(\frac{16 \, c^{4} x}{\sqrt{-c^{2} d x^{2} + d} d^{2}} + \frac{8 \, c^{4} x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d} - \frac{6 \, c^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x} - \frac{1}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} d x^{3}}\right)} a^{2} + b^{2} \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} x^{4}}\,{d x}"," ",0,"1/3*a*b*c*(8*c^2*sqrt(-d)*log(c*x + 1)/d^3 + 8*c^2*sqrt(-d)*log(c*x - 1)/d^3 + 16*c^2*sqrt(-d)*log(x)/d^3 + sqrt(-d)/(c^2*d^3*x^4 - d^3*x^2)) + 2/3*(16*c^4*x/(sqrt(-c^2*d*x^2 + d)*d^2) + 8*c^4*x/((-c^2*d*x^2 + d)^(3/2)*d) - 6*c^2/((-c^2*d*x^2 + d)^(3/2)*d*x) - 1/((-c^2*d*x^2 + d)^(3/2)*d*x^3))*a*b*arccosh(c*x) + 1/3*(16*c^4*x/(sqrt(-c^2*d*x^2 + d)*d^2) + 8*c^4*x/((-c^2*d*x^2 + d)^(3/2)*d) - 6*c^2/((-c^2*d*x^2 + d)^(3/2)*d*x) - 1/((-c^2*d*x^2 + d)^(3/2)*d*x^3))*a^2 + b^2*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/((-c^2*d*x^2 + d)^(5/2)*x^4), x)","F",0
224,0,0,0,0.000000," ","integrate(arccosh(a*x)^2/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{2}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(arccosh(a*x)^2/(-a^2*c*x^2 + c)^(7/2), x)","F",0
225,-2,0,0,0.000000," ","integrate(x^4*arccosh(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
226,1,105,0,0.469255," ","integrate(x^3*arccosh(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{a^{2}} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{a^{4}}\right)} \operatorname{arcosh}\left(a x\right)^{2} + \frac{2 \, {\left(-i \, \sqrt{a^{2} x^{2} - 1} x^{2} - \frac{20 i \, \sqrt{a^{2} x^{2} - 1}}{a^{2}}\right)}}{27 \, a^{2}} + \frac{2 \, {\left(i \, a^{2} x^{3} + 6 i \, x\right)} \operatorname{arcosh}\left(a x\right)}{9 \, a^{3}}"," ",0,"-1/3*(sqrt(-a^2*x^2 + 1)*x^2/a^2 + 2*sqrt(-a^2*x^2 + 1)/a^4)*arccosh(a*x)^2 + 2/27*(-I*sqrt(a^2*x^2 - 1)*x^2 - 20*I*sqrt(a^2*x^2 - 1)/a^2)/a^2 + 2/9*(I*a^2*x^3 + 6*I*x)*arccosh(a*x)/a^3","C",0
227,-2,0,0,0.000000," ","integrate(x^2*arccosh(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
228,1,50,0,0.376348," ","integrate(x*arccosh(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{2 i \, x \operatorname{arcosh}\left(a x\right)}{a} - \frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{arcosh}\left(a x\right)^{2}}{a^{2}} - \frac{2 i \, \sqrt{a^{2} x^{2} - 1}}{a^{2}}"," ",0,"2*I*x*arccosh(a*x)/a - sqrt(-a^2*x^2 + 1)*arccosh(a*x)^2/a^2 - 2*I*sqrt(a^2*x^2 - 1)/a^2","C",0
229,0,0,0,0.000000," ","integrate(arccosh(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(arccosh(a*x)^2/sqrt(-a^2*x^2 + 1), x)","F",0
230,0,0,0,0.000000," ","integrate(arccosh(a*x)^2/x/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate(arccosh(a*x)^2/(sqrt(-a^2*x^2 + 1)*x), x)","F",0
231,0,0,0,0.000000," ","integrate(arccosh(a*x)^2/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{{\left(a^{2} x^{2} - 1\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{\sqrt{a x + 1} \sqrt{-a x + 1} x} - \int \frac{2 \, {\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{{\left(\sqrt{a x + 1} a x^{2} + {\left(a x + 1\right)} \sqrt{a x - 1} x\right)} \sqrt{-a x + 1}}\,{d x}"," ",0,"(a^2*x^2 - 1)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/(sqrt(a*x + 1)*sqrt(-a*x + 1)*x) - integrate(2*(a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))/((sqrt(a*x + 1)*a*x^2 + (a*x + 1)*sqrt(a*x - 1)*x)*sqrt(-a*x + 1)), x)","F",0
232,0,0,0,0.000000," ","integrate(arccosh(a*x)^2/x^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{2}}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate(arccosh(a*x)^2/(sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
233,0,0,0,0.000000," ","integrate((f*x)^m*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{2} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(5/2)*(b*arccosh(c*x) + a)^2*(f*x)^m, x)","F",0
234,0,0,0,0.000000," ","integrate((f*x)^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{2} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(3/2)*(b*arccosh(c*x) + a)^2*(f*x)^m, x)","F",0
235,0,0,0,0.000000," ","integrate((f*x)^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\int \sqrt{-c^{2} d x^{2} + d} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{2} \left(f x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(-c^2*d*x^2 + d)*(b*arccosh(c*x) + a)^2*(f*x)^m, x)","F",0
236,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{2} \left(f x\right)^{m}}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^2*(f*x)^m/sqrt(-c^2*d*x^2 + d), x)","F",0
237,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{2} \left(f x\right)^{m}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^2*(f*x)^m/(-c^2*d*x^2 + d)^(3/2), x)","F",0
238,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))^2/(-c^2*d*x^2+d)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{2} \left(f x\right)^{m}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^2*(f*x)^m/(-c^2*d*x^2 + d)^(5/2), x)","F",0
239,0,0,0,0.000000," ","integrate((f*x)^m*arccosh(c*x)^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(f x\right)^{m} \operatorname{arcosh}\left(c x\right)^{2}}{\sqrt{-c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((f*x)^m*arccosh(c*x)^2/sqrt(-c^2*x^2 + 1), x)","F",0
240,1,276,0,0.504999," ","integrate((-a^2*c*x^2+c)^3*arccosh(a*x)^3,x, algorithm=""maxima"")","\frac{1}{1225} \, {\left(75 \, \sqrt{a^{2} x^{2} - 1} a^{4} c^{3} x^{6} - 351 \, \sqrt{a^{2} x^{2} - 1} a^{2} c^{3} x^{4} + 757 \, \sqrt{a^{2} x^{2} - 1} c^{3} x^{2} - \frac{2161 \, \sqrt{a^{2} x^{2} - 1} c^{3}}{a^{2}}\right)} a \operatorname{arcosh}\left(a x\right)^{2} - \frac{1}{35} \, {\left(5 \, a^{6} c^{3} x^{7} - 21 \, a^{4} c^{3} x^{5} + 35 \, a^{2} c^{3} x^{3} - 35 \, c^{3} x\right)} \operatorname{arcosh}\left(a x\right)^{3} + \frac{2}{13505625} \, {\left(16875 \, \sqrt{a^{2} x^{2} - 1} a^{4} c^{3} x^{6} - 134541 \, \sqrt{a^{2} x^{2} - 1} a^{2} c^{3} x^{4} + 747937 \, \sqrt{a^{2} x^{2} - 1} c^{3} x^{2} - \frac{22329151 \, \sqrt{a^{2} x^{2} - 1} c^{3}}{a^{2}} - \frac{105 \, {\left(1125 \, a^{6} c^{3} x^{7} - 7371 \, a^{4} c^{3} x^{5} + 26495 \, a^{2} c^{3} x^{3} - 226905 \, c^{3} x\right)} \operatorname{arcosh}\left(a x\right)}{a}\right)} a"," ",0,"1/1225*(75*sqrt(a^2*x^2 - 1)*a^4*c^3*x^6 - 351*sqrt(a^2*x^2 - 1)*a^2*c^3*x^4 + 757*sqrt(a^2*x^2 - 1)*c^3*x^2 - 2161*sqrt(a^2*x^2 - 1)*c^3/a^2)*a*arccosh(a*x)^2 - 1/35*(5*a^6*c^3*x^7 - 21*a^4*c^3*x^5 + 35*a^2*c^3*x^3 - 35*c^3*x)*arccosh(a*x)^3 + 2/13505625*(16875*sqrt(a^2*x^2 - 1)*a^4*c^3*x^6 - 134541*sqrt(a^2*x^2 - 1)*a^2*c^3*x^4 + 747937*sqrt(a^2*x^2 - 1)*c^3*x^2 - 22329151*sqrt(a^2*x^2 - 1)*c^3/a^2 - 105*(1125*a^6*c^3*x^7 - 7371*a^4*c^3*x^5 + 26495*a^2*c^3*x^3 - 226905*c^3*x)*arccosh(a*x)/a)*a","A",0
241,1,210,0,0.418216," ","integrate((-a^2*c*x^2+c)^2*arccosh(a*x)^3,x, algorithm=""maxima"")","-\frac{1}{75} \, {\left(9 \, \sqrt{a^{2} x^{2} - 1} a^{2} c^{2} x^{4} - 38 \, \sqrt{a^{2} x^{2} - 1} c^{2} x^{2} + \frac{149 \, \sqrt{a^{2} x^{2} - 1} c^{2}}{a^{2}}\right)} a \operatorname{arcosh}\left(a x\right)^{2} + \frac{1}{15} \, {\left(3 \, a^{4} c^{2} x^{5} - 10 \, a^{2} c^{2} x^{3} + 15 \, c^{2} x\right)} \operatorname{arcosh}\left(a x\right)^{3} - \frac{2}{16875} \, {\left(81 \, \sqrt{a^{2} x^{2} - 1} a^{2} c^{2} x^{4} - 842 \, \sqrt{a^{2} x^{2} - 1} c^{2} x^{2} - \frac{15 \, {\left(27 \, a^{4} c^{2} x^{5} - 190 \, a^{2} c^{2} x^{3} + 2235 \, c^{2} x\right)} \operatorname{arcosh}\left(a x\right)}{a} + \frac{31841 \, \sqrt{a^{2} x^{2} - 1} c^{2}}{a^{2}}\right)} a"," ",0,"-1/75*(9*sqrt(a^2*x^2 - 1)*a^2*c^2*x^4 - 38*sqrt(a^2*x^2 - 1)*c^2*x^2 + 149*sqrt(a^2*x^2 - 1)*c^2/a^2)*a*arccosh(a*x)^2 + 1/15*(3*a^4*c^2*x^5 - 10*a^2*c^2*x^3 + 15*c^2*x)*arccosh(a*x)^3 - 2/16875*(81*sqrt(a^2*x^2 - 1)*a^2*c^2*x^4 - 842*sqrt(a^2*x^2 - 1)*c^2*x^2 - 15*(27*a^4*c^2*x^5 - 190*a^2*c^2*x^3 + 2235*c^2*x)*arccosh(a*x)/a + 31841*sqrt(a^2*x^2 - 1)*c^2/a^2)*a","A",0
242,1,124,0,0.458575," ","integrate((-a^2*c*x^2+c)*arccosh(a*x)^3,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\sqrt{a^{2} x^{2} - 1} c x^{2} - \frac{7 \, \sqrt{a^{2} x^{2} - 1} c}{a^{2}}\right)} a \operatorname{arcosh}\left(a x\right)^{2} - \frac{1}{3} \, {\left(a^{2} c x^{3} - 3 \, c x\right)} \operatorname{arcosh}\left(a x\right)^{3} + \frac{2}{27} \, {\left(\sqrt{a^{2} x^{2} - 1} c x^{2} - \frac{3 \, {\left(a^{2} c x^{3} - 21 \, c x\right)} \operatorname{arcosh}\left(a x\right)}{a} - \frac{61 \, \sqrt{a^{2} x^{2} - 1} c}{a^{2}}\right)} a"," ",0,"1/3*(sqrt(a^2*x^2 - 1)*c*x^2 - 7*sqrt(a^2*x^2 - 1)*c/a^2)*a*arccosh(a*x)^2 - 1/3*(a^2*c*x^3 - 3*c*x)*arccosh(a*x)^3 + 2/27*(sqrt(a^2*x^2 - 1)*c*x^2 - 3*(a^2*c*x^3 - 21*c*x)*arccosh(a*x)/a - 61*sqrt(a^2*x^2 - 1)*c/a^2)*a","A",0
243,0,0,0,0.000000," ","integrate(arccosh(a*x)^3/(-a^2*c*x^2+c),x, algorithm=""maxima"")","\frac{{\left(\log\left(a x + 1\right) - \log\left(a x - 1\right)\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}}{2 \, a c} - \int \frac{3 \, {\left({\left(a x \log\left(a x + 1\right) - a x \log\left(a x - 1\right)\right)} \sqrt{a x + 1} \sqrt{a x - 1} + {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) - {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{2 \, {\left(a^{3} c x^{3} - a c x + {\left(a^{2} c x^{2} - c\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)}}\,{d x}"," ",0,"1/2*(log(a*x + 1) - log(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3/(a*c) - integrate(3/2*((a*x*log(a*x + 1) - a*x*log(a*x - 1))*sqrt(a*x + 1)*sqrt(a*x - 1) + (a^2*x^2 - 1)*log(a*x + 1) - (a^2*x^2 - 1)*log(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/(a^3*c*x^3 - a*c*x + (a^2*c*x^2 - c)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
244,0,0,0,0.000000," ","integrate(arccosh(a*x)^3/(-a^2*c*x^2+c)^2,x, algorithm=""maxima"")","-\frac{{\left(2 \, a x - {\left(a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}}{4 \, {\left(a^{3} c^{2} x^{2} - a c^{2}\right)}} - \int -\frac{3 \, {\left(2 \, a^{3} x^{3} + {\left(2 \, a^{2} x^{2} - {\left(a^{3} x^{3} - a x\right)} \log\left(a x + 1\right) + {\left(a^{3} x^{3} - a x\right)} \log\left(a x - 1\right)\right)} \sqrt{a x + 1} \sqrt{a x - 1} - 2 \, a x - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{4 \, {\left(a^{5} c^{2} x^{5} - 2 \, a^{3} c^{2} x^{3} + a c^{2} x + {\left(a^{4} c^{2} x^{4} - 2 \, a^{2} c^{2} x^{2} + c^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)}}\,{d x}"," ",0,"-1/4*(2*a*x - (a^2*x^2 - 1)*log(a*x + 1) + (a^2*x^2 - 1)*log(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3/(a^3*c^2*x^2 - a*c^2) - integrate(-3/4*(2*a^3*x^3 + (2*a^2*x^2 - (a^3*x^3 - a*x)*log(a*x + 1) + (a^3*x^3 - a*x)*log(a*x - 1))*sqrt(a*x + 1)*sqrt(a*x - 1) - 2*a*x - (a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1) + (a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/(a^5*c^2*x^5 - 2*a^3*c^2*x^3 + a*c^2*x + (a^4*c^2*x^4 - 2*a^2*c^2*x^2 + c^2)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
245,0,0,0,0.000000," ","integrate(arccosh(a*x)^3/(-a^2*c*x^2+c)^3,x, algorithm=""maxima"")","-\frac{{\left(6 \, a^{3} x^{3} - 10 \, a x - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x + 1\right) + 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}}{16 \, {\left(a^{5} c^{3} x^{4} - 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}} - \int -\frac{3 \, {\left(6 \, a^{5} x^{5} - 16 \, a^{3} x^{3} + {\left(6 \, a^{4} x^{4} - 10 \, a^{2} x^{2} - 3 \, {\left(a^{5} x^{5} - 2 \, a^{3} x^{3} + a x\right)} \log\left(a x + 1\right) + 3 \, {\left(a^{5} x^{5} - 2 \, a^{3} x^{3} + a x\right)} \log\left(a x - 1\right)\right)} \sqrt{a x + 1} \sqrt{a x - 1} + 10 \, a x - 3 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x + 1\right) + 3 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{16 \, {\left(a^{7} c^{3} x^{7} - 3 \, a^{5} c^{3} x^{5} + 3 \, a^{3} c^{3} x^{3} - a c^{3} x + {\left(a^{6} c^{3} x^{6} - 3 \, a^{4} c^{3} x^{4} + 3 \, a^{2} c^{3} x^{2} - c^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)}}\,{d x}"," ",0,"-1/16*(6*a^3*x^3 - 10*a*x - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x + 1) + 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3/(a^5*c^3*x^4 - 2*a^3*c^3*x^2 + a*c^3) - integrate(-3/16*(6*a^5*x^5 - 16*a^3*x^3 + (6*a^4*x^4 - 10*a^2*x^2 - 3*(a^5*x^5 - 2*a^3*x^3 + a*x)*log(a*x + 1) + 3*(a^5*x^5 - 2*a^3*x^3 + a*x)*log(a*x - 1))*sqrt(a*x + 1)*sqrt(a*x - 1) + 10*a*x - 3*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x + 1) + 3*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/(a^7*c^3*x^7 - 3*a^5*c^3*x^5 + 3*a^3*c^3*x^3 - a*c^3*x + (a^6*c^3*x^6 - 3*a^4*c^3*x^4 + 3*a^2*c^3*x^2 - c^3)*sqrt(a*x + 1)*sqrt(a*x - 1)), x)","F",0
246,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(5/2)*arccosh(a*x)^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
247,-2,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)*arccosh(a*x)^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
248,-2,0,0,0.000000," ","integrate(arccosh(a*x)^3*(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
249,0,0,0,0.000000," ","integrate(arccosh(a*x)^3/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{3}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(arccosh(a*x)^3/sqrt(-a^2*c*x^2 + c), x)","F",0
250,0,0,0,0.000000," ","integrate(arccosh(a*x)^3/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{3}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(arccosh(a*x)^3/(-a^2*c*x^2 + c)^(3/2), x)","F",0
251,0,0,0,0.000000," ","integrate(arccosh(a*x)^3/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{3}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(arccosh(a*x)^3/(-a^2*c*x^2 + c)^(5/2), x)","F",0
252,0,0,0,0.000000," ","integrate(arccosh(a*x)^3/(-a^2*c*x^2+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{3}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(arccosh(a*x)^3/(-a^2*c*x^2 + c)^(7/2), x)","F",0
253,-2,0,0,0.000000," ","integrate(x^4*arccosh(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
254,1,131,0,0.707663," ","integrate(x^3*arccosh(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{a^{2}} + \frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{a^{4}}\right)} \operatorname{arcosh}\left(a x\right)^{3} + \frac{2}{27} \, a {\left(\frac{3 \, {\left(-i \, \sqrt{a^{2} x^{2} - 1} x^{2} - \frac{20 i \, \sqrt{a^{2} x^{2} - 1}}{a^{2}}\right)} \operatorname{arcosh}\left(a x\right)}{a^{3}} + \frac{i \, a^{2} x^{3} + 60 i \, x}{a^{4}}\right)} + \frac{{\left(i \, a^{2} x^{3} + 6 i \, x\right)} \operatorname{arcosh}\left(a x\right)^{2}}{3 \, a^{3}}"," ",0,"-1/3*(sqrt(-a^2*x^2 + 1)*x^2/a^2 + 2*sqrt(-a^2*x^2 + 1)/a^4)*arccosh(a*x)^3 + 2/27*a*(3*(-I*sqrt(a^2*x^2 - 1)*x^2 - 20*I*sqrt(a^2*x^2 - 1)/a^2)*arccosh(a*x)/a^3 + (I*a^2*x^3 + 60*I*x)/a^4) + 1/3*(I*a^2*x^3 + 6*I*x)*arccosh(a*x)^2/a^3","C",0
255,-2,0,0,0.000000," ","integrate(x^2*arccosh(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
256,1,65,0,0.327250," ","integrate(x*arccosh(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{3 i \, x \operatorname{arcosh}\left(a x\right)^{2}}{a} - \frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{arcosh}\left(a x\right)^{3}}{a^{2}} - \frac{3 \, {\left(-2 i \, x + \frac{2 i \, \sqrt{a^{2} x^{2} - 1} \operatorname{arcosh}\left(a x\right)}{a}\right)}}{a}"," ",0,"3*I*x*arccosh(a*x)^2/a - sqrt(-a^2*x^2 + 1)*arccosh(a*x)^3/a^2 - 3*(-2*I*x + 2*I*sqrt(a^2*x^2 - 1)*arccosh(a*x)/a)/a","C",0
257,0,0,0,0.000000," ","integrate(arccosh(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(arccosh(a*x)^3/sqrt(-a^2*x^2 + 1), x)","F",0
258,0,0,0,0.000000," ","integrate(arccosh(a*x)^3/x/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate(arccosh(a*x)^3/(sqrt(-a^2*x^2 + 1)*x), x)","F",0
259,0,0,0,0.000000," ","integrate(arccosh(a*x)^3/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{{\left(a^{2} x^{2} - 1\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{3}}{\sqrt{a x + 1} \sqrt{-a x + 1} x} - \int \frac{3 \, {\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}}{{\left(\sqrt{a x + 1} a x^{2} + {\left(a x + 1\right)} \sqrt{a x - 1} x\right)} \sqrt{-a x + 1}}\,{d x}"," ",0,"(a^2*x^2 - 1)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^3/(sqrt(a*x + 1)*sqrt(-a*x + 1)*x) - integrate(3*(a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2/((sqrt(a*x + 1)*a*x^2 + (a*x + 1)*sqrt(a*x - 1)*x)*sqrt(-a*x + 1)), x)","F",0
260,0,0,0,0.000000," ","integrate(arccosh(a*x)^3/x^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{3}}{\sqrt{-a^{2} x^{2} + 1} x^{3}}\,{d x}"," ",0,"integrate(arccosh(a*x)^3/(sqrt(-a^2*x^2 + 1)*x^3), x)","F",0
261,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))^3/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{3} \left(f x\right)^{m}}{\sqrt{-c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^3*(f*x)^m/sqrt(-c^2*x^2 + 1), x)","F",0
262,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^3/arccosh(a*x),x, algorithm=""maxima"")","-\int \frac{{\left(a^{2} c x^{2} - c\right)}^{3}}{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"-integrate((a^2*c*x^2 - c)^3/arccosh(a*x), x)","F",0
263,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^2/arccosh(a*x),x, algorithm=""maxima"")","\int \frac{{\left(a^{2} c x^{2} - c\right)}^{2}}{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate((a^2*c*x^2 - c)^2/arccosh(a*x), x)","F",0
264,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)/arccosh(a*x),x, algorithm=""maxima"")","-\int \frac{a^{2} c x^{2} - c}{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"-integrate((a^2*c*x^2 - c)/arccosh(a*x), x)","F",0
265,0,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)/arccosh(a*x),x, algorithm=""maxima"")","-\int \frac{1}{{\left(a^{2} c x^{2} - c\right)} \operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"-integrate(1/((a^2*c*x^2 - c)*arccosh(a*x)), x)","F",0
266,0,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^2/arccosh(a*x),x, algorithm=""maxima"")","\int \frac{1}{{\left(a^{2} c x^{2} - c\right)}^{2} \operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/((a^2*c*x^2 - c)^2*arccosh(a*x)), x)","F",0
267,0,0,0,0.000000," ","integrate(x^4*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1} x^{4}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)*x^4/(b*arccosh(c*x) + a), x)","F",0
268,0,0,0,0.000000," ","integrate(x^3*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1} x^{3}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)*x^3/(b*arccosh(c*x) + a), x)","F",0
269,0,0,0,0.000000," ","integrate(x^2*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1} x^{2}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)*x^2/(b*arccosh(c*x) + a), x)","F",0
270,0,0,0,0.000000," ","integrate(x*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1} x}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)*x/(b*arccosh(c*x) + a), x)","F",0
271,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)/(b*arccosh(c*x) + a), x)","F",0
272,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/x/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)/((b*arccosh(c*x) + a)*x), x)","F",0
273,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/x^2/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)/((b*arccosh(c*x) + a)*x^2), x)","F",0
274,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/x^3/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} x^{3}}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)/((b*arccosh(c*x) + a)*x^3), x)","F",0
275,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/x^4/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} x^{4}}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)/((b*arccosh(c*x) + a)*x^4), x)","F",0
276,0,0,0,0.000000," ","integrate(x^3*(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{3}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)*x^3/(b*arccosh(c*x) + a), x)","F",0
277,0,0,0,0.000000," ","integrate(x^2*(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{2}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)*x^2/(b*arccosh(c*x) + a), x)","F",0
278,0,0,0,0.000000," ","integrate(x*(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)*x/(b*arccosh(c*x) + a), x)","F",0
279,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)/(b*arccosh(c*x) + a), x)","F",0
280,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/x/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)/((b*arccosh(c*x) + a)*x), x)","F",0
281,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/x^2/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)/((b*arccosh(c*x) + a)*x^2), x)","F",0
282,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/x^3/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} x^{3}}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)/((b*arccosh(c*x) + a)*x^3), x)","F",0
283,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/x^4/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} x^{4}}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)/((b*arccosh(c*x) + a)*x^4), x)","F",0
284,0,0,0,0.000000," ","integrate(x^3*(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}} x^{3}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)*x^3/(b*arccosh(c*x) + a), x)","F",0
285,0,0,0,0.000000," ","integrate(x^2*(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}} x^{2}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)*x^2/(b*arccosh(c*x) + a), x)","F",0
286,0,0,0,0.000000," ","integrate(x*(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}} x}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)*x/(b*arccosh(c*x) + a), x)","F",0
287,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)/(b*arccosh(c*x) + a), x)","F",0
288,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/x/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)/((b*arccosh(c*x) + a)*x), x)","F",0
289,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/x^2/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)/((b*arccosh(c*x) + a)*x^2), x)","F",0
290,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/x^3/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} x^{3}}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)/((b*arccosh(c*x) + a)*x^3), x)","F",0
291,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/x^4/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} x^{4}}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(5/2)/((b*arccosh(c*x) + a)*x^4), x)","F",0
292,0,0,0,0.000000," ","integrate(x^4/arccosh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{4}}{\sqrt{-a^{2} x^{2} + 1} \operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^4/(sqrt(-a^2*x^2 + 1)*arccosh(a*x)), x)","F",0
293,0,0,0,0.000000," ","integrate(x^3/arccosh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\sqrt{-a^{2} x^{2} + 1} \operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^3/(sqrt(-a^2*x^2 + 1)*arccosh(a*x)), x)","F",0
294,0,0,0,0.000000," ","integrate(x^2/arccosh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{-a^{2} x^{2} + 1} \operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(x^2/(sqrt(-a^2*x^2 + 1)*arccosh(a*x)), x)","F",0
295,0,0,0,0.000000," ","integrate(x/arccosh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{-a^{2} x^{2} + 1} \operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(x/(sqrt(-a^2*x^2 + 1)*arccosh(a*x)), x)","F",0
296,0,0,0,0.000000," ","integrate(1/arccosh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a^{2} x^{2} + 1} \operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/(sqrt(-a^2*x^2 + 1)*arccosh(a*x)), x)","F",0
297,0,0,0,0.000000," ","integrate(1/x/arccosh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a^{2} x^{2} + 1} x \operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/(sqrt(-a^2*x^2 + 1)*x*arccosh(a*x)), x)","F",0
298,0,0,0,0.000000," ","integrate(1/x^2/arccosh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a^{2} x^{2} + 1} x^{2} \operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(1/(sqrt(-a^2*x^2 + 1)*x^2*arccosh(a*x)), x)","F",0
299,0,0,0,0.000000," ","integrate(x^3/(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\sqrt{-c^{2} x^{2} + 1} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^3/(sqrt(-c^2*x^2 + 1)*(b*arccosh(c*x) + a)), x)","F",0
300,0,0,0,0.000000," ","integrate(x^2/(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{-c^{2} x^{2} + 1} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^2/(sqrt(-c^2*x^2 + 1)*(b*arccosh(c*x) + a)), x)","F",0
301,0,0,0,0.000000," ","integrate(x/(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{-c^{2} x^{2} + 1} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(-c^2*x^2 + 1)*(b*arccosh(c*x) + a)), x)","F",0
302,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-c^{2} x^{2} + 1} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-c^2*x^2 + 1)*(b*arccosh(c*x) + a)), x)","F",0
303,0,0,0,0.000000," ","integrate(1/x/(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-c^{2} x^{2} + 1} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/(sqrt(-c^2*x^2 + 1)*(b*arccosh(c*x) + a)*x), x)","F",0
304,0,0,0,0.000000," ","integrate(1/x^2/(a+b*arccosh(c*x))/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-c^{2} x^{2} + 1} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(-c^2*x^2 + 1)*(b*arccosh(c*x) + a)*x^2), x)","F",0
305,0,0,0,0.000000," ","integrate(x^2/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^2/((-c^2*x^2 + 1)^(3/2)*(b*arccosh(c*x) + a)), x)","F",0
306,0,0,0,0.000000," ","integrate(x/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{x}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x/((-c^2*x^2 + 1)^(3/2)*(b*arccosh(c*x) + a)), x)","F",0
307,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((-c^2*x^2 + 1)^(3/2)*(b*arccosh(c*x) + a)), x)","F",0
308,0,0,0,0.000000," ","integrate(1/x/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/((-c^2*x^2 + 1)^(3/2)*(b*arccosh(c*x) + a)*x), x)","F",0
309,0,0,0,0.000000," ","integrate(1/x^2/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((-c^2*x^2 + 1)^(3/2)*(b*arccosh(c*x) + a)*x^2), x)","F",0
310,0,0,0,0.000000," ","integrate(x^m*(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} x^{m}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((-c^2*x^2 + 1)^(3/2)*x^m/(b*arccosh(c*x) + a), x)","F",0
311,0,0,0,0.000000," ","integrate(x^m*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} x^{2} + 1} x^{m}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 1)*x^m/(b*arccosh(c*x) + a), x)","F",0
312,0,0,0,0.000000," ","integrate(x^m/(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{x^{m}}{\sqrt{-c^{2} x^{2} + 1} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^m/(sqrt(-c^2*x^2 + 1)*(b*arccosh(c*x) + a)), x)","F",0
313,0,0,0,0.000000," ","integrate(x^m/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^m/((-c^2*x^2 + 1)^(3/2)*(b*arccosh(c*x) + a)), x)","F",0
314,0,0,0,0.000000," ","integrate(x^m/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{x^{m}}{{\left(-c^{2} x^{2} + 1\right)}^{\frac{5}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(x^m/((-c^2*x^2 + 1)^(5/2)*(b*arccosh(c*x) + a)), x)","F",0
315,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^3/arccosh(a*x)^2,x, algorithm=""maxima"")","\frac{a^{9} c^{3} x^{9} - 4 \, a^{7} c^{3} x^{7} + 6 \, a^{5} c^{3} x^{5} - 4 \, a^{3} c^{3} x^{3} + a c^{3} x + {\left(a^{8} c^{3} x^{8} - 4 \, a^{6} c^{3} x^{6} + 6 \, a^{4} c^{3} x^{4} - 4 \, a^{2} c^{3} x^{2} + c^{3}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{{\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)} - \int \frac{7 \, a^{10} c^{3} x^{10} - 29 \, a^{8} c^{3} x^{8} + 46 \, a^{6} c^{3} x^{6} - 34 \, a^{4} c^{3} x^{4} + 11 \, a^{2} c^{3} x^{2} + {\left(7 \, a^{8} c^{3} x^{8} - 20 \, a^{6} c^{3} x^{6} + 18 \, a^{4} c^{3} x^{4} - 4 \, a^{2} c^{3} x^{2} - c^{3}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} - c^{3} + 7 \, {\left(2 \, a^{9} c^{3} x^{9} - 7 \, a^{7} c^{3} x^{7} + 9 \, a^{5} c^{3} x^{5} - 5 \, a^{3} c^{3} x^{3} + a c^{3} x\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{{\left(a^{4} x^{4} + {\left(a x + 1\right)} {\left(a x - 1\right)} a^{2} x^{2} - 2 \, a^{2} x^{2} + 2 \, {\left(a^{3} x^{3} - a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + 1\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"(a^9*c^3*x^9 - 4*a^7*c^3*x^7 + 6*a^5*c^3*x^5 - 4*a^3*c^3*x^3 + a*c^3*x + (a^8*c^3*x^8 - 4*a^6*c^3*x^6 + 6*a^4*c^3*x^4 - 4*a^2*c^3*x^2 + c^3)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))) - integrate((7*a^10*c^3*x^10 - 29*a^8*c^3*x^8 + 46*a^6*c^3*x^6 - 34*a^4*c^3*x^4 + 11*a^2*c^3*x^2 + (7*a^8*c^3*x^8 - 20*a^6*c^3*x^6 + 18*a^4*c^3*x^4 - 4*a^2*c^3*x^2 - c^3)*(a*x + 1)*(a*x - 1) - c^3 + 7*(2*a^9*c^3*x^9 - 7*a^7*c^3*x^7 + 9*a^5*c^3*x^5 - 5*a^3*c^3*x^3 + a*c^3*x)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^4*x^4 + (a*x + 1)*(a*x - 1)*a^2*x^2 - 2*a^2*x^2 + 2*(a^3*x^3 - a*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + 1)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
316,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^2/arccosh(a*x)^2,x, algorithm=""maxima"")","-\frac{a^{7} c^{2} x^{7} - 3 \, a^{5} c^{2} x^{5} + 3 \, a^{3} c^{2} x^{3} - a c^{2} x + {\left(a^{6} c^{2} x^{6} - 3 \, a^{4} c^{2} x^{4} + 3 \, a^{2} c^{2} x^{2} - c^{2}\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{{\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)} + \int \frac{5 \, a^{8} c^{2} x^{8} - 16 \, a^{6} c^{2} x^{6} + 18 \, a^{4} c^{2} x^{4} - 8 \, a^{2} c^{2} x^{2} + {\left(5 \, a^{6} c^{2} x^{6} - 9 \, a^{4} c^{2} x^{4} + 3 \, a^{2} c^{2} x^{2} + c^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 5 \, {\left(2 \, a^{7} c^{2} x^{7} - 5 \, a^{5} c^{2} x^{5} + 4 \, a^{3} c^{2} x^{3} - a c^{2} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + c^{2}}{{\left(a^{4} x^{4} + {\left(a x + 1\right)} {\left(a x - 1\right)} a^{2} x^{2} - 2 \, a^{2} x^{2} + 2 \, {\left(a^{3} x^{3} - a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + 1\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-(a^7*c^2*x^7 - 3*a^5*c^2*x^5 + 3*a^3*c^2*x^3 - a*c^2*x + (a^6*c^2*x^6 - 3*a^4*c^2*x^4 + 3*a^2*c^2*x^2 - c^2)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))) + integrate((5*a^8*c^2*x^8 - 16*a^6*c^2*x^6 + 18*a^4*c^2*x^4 - 8*a^2*c^2*x^2 + (5*a^6*c^2*x^6 - 9*a^4*c^2*x^4 + 3*a^2*c^2*x^2 + c^2)*(a*x + 1)*(a*x - 1) + 5*(2*a^7*c^2*x^7 - 5*a^5*c^2*x^5 + 4*a^3*c^2*x^3 - a*c^2*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + c^2)/((a^4*x^4 + (a*x + 1)*(a*x - 1)*a^2*x^2 - 2*a^2*x^2 + 2*(a^3*x^3 - a*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + 1)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
317,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)/arccosh(a*x)^2,x, algorithm=""maxima"")","\frac{a^{5} c x^{5} - 2 \, a^{3} c x^{3} + a c x + {\left(a^{4} c x^{4} - 2 \, a^{2} c x^{2} + c\right)} \sqrt{a x + 1} \sqrt{a x - 1}}{{\left(a^{3} x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} x - a\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)} - \int \frac{3 \, a^{6} c x^{6} - 7 \, a^{4} c x^{4} + 5 \, a^{2} c x^{2} + {\left(3 \, a^{4} c x^{4} - 2 \, a^{2} c x^{2} - c\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 3 \, {\left(2 \, a^{5} c x^{5} - 3 \, a^{3} c x^{3} + a c x\right)} \sqrt{a x + 1} \sqrt{a x - 1} - c}{{\left(a^{4} x^{4} + {\left(a x + 1\right)} {\left(a x - 1\right)} a^{2} x^{2} - 2 \, a^{2} x^{2} + 2 \, {\left(a^{3} x^{3} - a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + 1\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"(a^5*c*x^5 - 2*a^3*c*x^3 + a*c*x + (a^4*c*x^4 - 2*a^2*c*x^2 + c)*sqrt(a*x + 1)*sqrt(a*x - 1))/((a^3*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*x - a)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))) - integrate((3*a^6*c*x^6 - 7*a^4*c*x^4 + 5*a^2*c*x^2 + (3*a^4*c*x^4 - 2*a^2*c*x^2 - c)*(a*x + 1)*(a*x - 1) + 3*(2*a^5*c*x^5 - 3*a^3*c*x^3 + a*c*x)*sqrt(a*x + 1)*sqrt(a*x - 1) - c)/((a^4*x^4 + (a*x + 1)*(a*x - 1)*a^2*x^2 - 2*a^2*x^2 + 2*(a^3*x^3 - a*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + 1)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
318,0,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)/arccosh(a*x)^2,x, algorithm=""maxima"")","\frac{a x + \sqrt{a x + 1} \sqrt{a x - 1}}{{\left(a^{3} c x^{2} + \sqrt{a x + 1} \sqrt{a x - 1} a^{2} c x - a c\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)} + \int \frac{a^{4} x^{4} + {\left(a^{2} x^{2} - 1\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(2 \, a^{3} x^{3} - a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} - 1}{{\left(a^{6} c x^{6} - 3 \, a^{4} c x^{4} + 3 \, a^{2} c x^{2} + {\left(a^{4} c x^{4} - a^{2} c x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 2 \, {\left(a^{5} c x^{5} - 2 \, a^{3} c x^{3} + a c x\right)} \sqrt{a x + 1} \sqrt{a x - 1} - c\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))/((a^3*c*x^2 + sqrt(a*x + 1)*sqrt(a*x - 1)*a^2*c*x - a*c)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))) + integrate((a^4*x^4 + (a^2*x^2 - 1)*(a*x + 1)*(a*x - 1) + (2*a^3*x^3 - a*x)*sqrt(a*x + 1)*sqrt(a*x - 1) - 1)/((a^6*c*x^6 - 3*a^4*c*x^4 + 3*a^2*c*x^2 + (a^4*c*x^4 - a^2*c*x^2)*(a*x + 1)*(a*x - 1) + 2*(a^5*c*x^5 - 2*a^3*c*x^3 + a*c*x)*sqrt(a*x + 1)*sqrt(a*x - 1) - c)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
319,0,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^2/arccosh(a*x)^2,x, algorithm=""maxima"")","-\frac{a x + \sqrt{a x + 1} \sqrt{a x - 1}}{{\left(a^{5} c^{2} x^{4} - 2 \, a^{3} c^{2} x^{2} + a c^{2} + {\left(a^{4} c^{2} x^{3} - a^{2} c^{2} x\right)} \sqrt{a x + 1} \sqrt{a x - 1}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)} - \int \frac{3 \, a^{4} x^{4} - 2 \, a^{2} x^{2} + {\left(3 \, a^{2} x^{2} - 1\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 3 \, {\left(2 \, a^{3} x^{3} - a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} - 1}{{\left(a^{8} c^{2} x^{8} - 4 \, a^{6} c^{2} x^{6} + 6 \, a^{4} c^{2} x^{4} - 4 \, a^{2} c^{2} x^{2} + {\left(a^{6} c^{2} x^{6} - 2 \, a^{4} c^{2} x^{4} + a^{2} c^{2} x^{2}\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 2 \, {\left(a^{7} c^{2} x^{7} - 3 \, a^{5} c^{2} x^{5} + 3 \, a^{3} c^{2} x^{3} - a c^{2} x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + c^{2}\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))/((a^5*c^2*x^4 - 2*a^3*c^2*x^2 + a*c^2 + (a^4*c^2*x^3 - a^2*c^2*x)*sqrt(a*x + 1)*sqrt(a*x - 1))*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))) - integrate((3*a^4*x^4 - 2*a^2*x^2 + (3*a^2*x^2 - 1)*(a*x + 1)*(a*x - 1) + 3*(2*a^3*x^3 - a*x)*sqrt(a*x + 1)*sqrt(a*x - 1) - 1)/((a^8*c^2*x^8 - 4*a^6*c^2*x^6 + 6*a^4*c^2*x^4 - 4*a^2*c^2*x^2 + (a^6*c^2*x^6 - 2*a^4*c^2*x^4 + a^2*c^2*x^2)*(a*x + 1)*(a*x - 1) + 2*(a^7*c^2*x^7 - 3*a^5*c^2*x^5 + 3*a^3*c^2*x^3 - a*c^2*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + c^2)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
320,0,0,0,0.000000," ","integrate(x^3*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c^{2} x^{5} - x^{3}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{3} x^{6} - c x^{4}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{{\left({\left(5 \, c^{3} x^{5} - 2 \, c x^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + {\left(10 \, c^{4} x^{6} - 11 \, c^{2} x^{4} + 3 \, x^{2}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(5 \, c^{5} x^{7} - 9 \, c^{3} x^{5} + 4 \, c x^{3}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{2} - 2 \, a b c^{3} x^{2} + a b c + 2 \, {\left(a b c^{4} x^{3} - a b c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{2} - 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^2*x^5 - x^3)*(c*x + 1)*sqrt(c*x - 1) + (c^3*x^6 - c*x^4)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate(((5*c^3*x^5 - 2*c*x^3)*(c*x + 1)^(3/2)*(c*x - 1) + (10*c^4*x^6 - 11*c^2*x^4 + 3*x^2)*(c*x + 1)*sqrt(c*x - 1) + (5*c^5*x^7 - 9*c^3*x^5 + 4*c*x^3)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^4 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^2 - 2*a*b*c^3*x^2 + a*b*c + 2*(a*b*c^4*x^3 - a*b*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^2 - 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 - b^2*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
321,0,0,0,0.000000," ","integrate(x^2*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c^{2} x^{4} - x^{2}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{3} x^{5} - c x^{3}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{{\left({\left(4 \, c^{3} x^{4} - c x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(4 \, c^{4} x^{5} - 4 \, c^{2} x^{3} + x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(4 \, c^{5} x^{6} - 7 \, c^{3} x^{4} + 3 \, c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{2} - 2 \, a b c^{3} x^{2} + a b c + 2 \, {\left(a b c^{4} x^{3} - a b c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{2} - 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^2*x^4 - x^2)*(c*x + 1)*sqrt(c*x - 1) + (c^3*x^5 - c*x^3)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate(((4*c^3*x^4 - c*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(4*c^4*x^5 - 4*c^2*x^3 + x)*(c*x + 1)*sqrt(c*x - 1) + (4*c^5*x^6 - 7*c^3*x^4 + 3*c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^4 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^2 - 2*a*b*c^3*x^2 + a*b*c + 2*(a*b*c^4*x^3 - a*b*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^2 - 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 - b^2*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
322,0,0,0,0.000000," ","integrate(x*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c^{2} x^{3} - x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{3} x^{4} - c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{{\left(3 \, {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} c^{3} x^{3} + {\left(6 \, c^{4} x^{4} - 5 \, c^{2} x^{2} + 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(3 \, c^{5} x^{5} - 5 \, c^{3} x^{3} + 2 \, c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{2} - 2 \, a b c^{3} x^{2} + a b c + 2 \, {\left(a b c^{4} x^{3} - a b c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{2} - 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^2*x^3 - x)*(c*x + 1)*sqrt(c*x - 1) + (c^3*x^4 - c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate((3*(c*x + 1)^(3/2)*(c*x - 1)*c^3*x^3 + (6*c^4*x^4 - 5*c^2*x^2 + 1)*(c*x + 1)*sqrt(c*x - 1) + (3*c^5*x^5 - 5*c^3*x^3 + 2*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^4 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^2 - 2*a*b*c^3*x^2 + a*b*c + 2*(a*b*c^4*x^3 - a*b*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^2 - 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 - b^2*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
323,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{3} x^{3} - c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{{\left({\left(2 \, c^{2} x^{2} + 1\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(2 \, c^{3} x^{3} - c x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(2 \, c^{4} x^{4} - 3 \, c^{2} x^{2} + 1\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{4} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{2} x^{2} - 2 \, a b c^{2} x^{2} + 2 \, {\left(a b c^{3} x^{3} - a b c x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + a b + {\left(b^{2} c^{4} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{2} x^{2} - 2 \, b^{2} c^{2} x^{2} + 2 \, {\left(b^{2} c^{3} x^{3} - b^{2} c x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + b^{2}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^2*x^2 - 1)*(c*x + 1)*sqrt(c*x - 1) + (c^3*x^3 - c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate(((2*c^2*x^2 + 1)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(2*c^3*x^3 - c*x)*(c*x + 1)*sqrt(c*x - 1) + (2*c^4*x^4 - 3*c^2*x^2 + 1)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^4*x^4 + (c*x + 1)*(c*x - 1)*a*b*c^2*x^2 - 2*a*b*c^2*x^2 + 2*(a*b*c^3*x^3 - a*b*c*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + a*b + (b^2*c^4*x^4 + (c*x + 1)*(c*x - 1)*b^2*c^2*x^2 - 2*b^2*c^2*x^2 + 2*(b^2*c^3*x^3 - b^2*c*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + b^2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
324,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/x/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{3} x^{3} - c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{3} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x^{2} - a b c x + {\left(b^{2} c^{3} x^{3} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x^{2} - b^{2} c x\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{{\left({\left(c^{3} x^{3} + 2 \, c x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + {\left(2 \, c^{4} x^{4} + c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{5} x^{5} - c^{3} x^{3}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{6} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{4} - 2 \, a b c^{3} x^{4} + a b c x^{2} + 2 \, {\left(a b c^{4} x^{5} - a b c^{2} x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{6} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{4} - 2 \, b^{2} c^{3} x^{4} + b^{2} c x^{2} + 2 \, {\left(b^{2} c^{4} x^{5} - b^{2} c^{2} x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^2*x^2 - 1)*(c*x + 1)*sqrt(c*x - 1) + (c^3*x^3 - c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^3 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x^2 - a*b*c*x + (b^2*c^3*x^3 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x^2 - b^2*c*x)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate(((c^3*x^3 + 2*c*x)*(c*x + 1)^(3/2)*(c*x - 1) + (2*c^4*x^4 + c^2*x^2 - 1)*(c*x + 1)*sqrt(c*x - 1) + (c^5*x^5 - c^3*x^3)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^6 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^4 - 2*a*b*c^3*x^4 + a*b*c*x^2 + 2*(a*b*c^4*x^5 - a*b*c^2*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^6 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^4 - 2*b^2*c^3*x^4 + b^2*c*x^2 + 2*(b^2*c^4*x^5 - b^2*c^2*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
325,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/x^2/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{3} x^{3} - c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{4} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x^{3} - a b c x^{2} + {\left(b^{2} c^{3} x^{4} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x^{3} - b^{2} c x^{2}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{{\left(3 \, {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} c x + 2 \, {\left(2 \, c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{3} x^{3} - c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{7} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{5} - 2 \, a b c^{3} x^{5} + a b c x^{3} + 2 \, {\left(a b c^{4} x^{6} - a b c^{2} x^{4}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{7} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{5} - 2 \, b^{2} c^{3} x^{5} + b^{2} c x^{3} + 2 \, {\left(b^{2} c^{4} x^{6} - b^{2} c^{2} x^{4}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^2*x^2 - 1)*(c*x + 1)*sqrt(c*x - 1) + (c^3*x^3 - c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^4 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x^3 - a*b*c*x^2 + (b^2*c^3*x^4 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x^3 - b^2*c*x^2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate((3*(c*x + 1)^(3/2)*(c*x - 1)*c*x + 2*(2*c^2*x^2 - 1)*(c*x + 1)*sqrt(c*x - 1) + (c^3*x^3 - c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^7 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^5 - 2*a*b*c^3*x^5 + a*b*c*x^3 + 2*(a*b*c^4*x^6 - a*b*c^2*x^4)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^7 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^5 - 2*b^2*c^3*x^5 + b^2*c*x^3 + 2*(b^2*c^4*x^6 - b^2*c^2*x^4)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
326,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/x^3/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{3} x^{3} - c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{5} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x^{4} - a b c x^{3} + {\left(b^{2} c^{3} x^{5} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x^{4} - b^{2} c x^{3}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} - \int \frac{{\left({\left(c^{3} x^{3} - 4 \, c x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + {\left(2 \, c^{4} x^{4} - 7 \, c^{2} x^{2} + 3\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{5} x^{5} - 3 \, c^{3} x^{3} + 2 \, c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{8} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{6} - 2 \, a b c^{3} x^{6} + a b c x^{4} + 2 \, {\left(a b c^{4} x^{7} - a b c^{2} x^{5}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{8} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{6} - 2 \, b^{2} c^{3} x^{6} + b^{2} c x^{4} + 2 \, {\left(b^{2} c^{4} x^{7} - b^{2} c^{2} x^{5}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^2*x^2 - 1)*(c*x + 1)*sqrt(c*x - 1) + (c^3*x^3 - c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^5 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x^4 - a*b*c*x^3 + (b^2*c^3*x^5 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x^4 - b^2*c*x^3)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) - integrate(((c^3*x^3 - 4*c*x)*(c*x + 1)^(3/2)*(c*x - 1) + (2*c^4*x^4 - 7*c^2*x^2 + 3)*(c*x + 1)*sqrt(c*x - 1) + (c^5*x^5 - 3*c^3*x^3 + 2*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^8 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^6 - 2*a*b*c^3*x^6 + a*b*c*x^4 + 2*(a*b*c^4*x^7 - a*b*c^2*x^5)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^8 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^6 - 2*b^2*c^3*x^6 + b^2*c*x^4 + 2*(b^2*c^4*x^7 - b^2*c^2*x^5)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
327,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(1/2)/x^4/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{3} x^{3} - c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{6} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x^{5} - a b c x^{4} + {\left(b^{2} c^{3} x^{6} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x^{5} - b^{2} c x^{4}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} - \int \frac{{\left({\left(2 \, c^{3} x^{3} - 5 \, c x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(2 \, c^{4} x^{4} - 5 \, c^{2} x^{2} + 2\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(2 \, c^{5} x^{5} - 5 \, c^{3} x^{3} + 3 \, c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{9} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{7} - 2 \, a b c^{3} x^{7} + a b c x^{5} + 2 \, {\left(a b c^{4} x^{8} - a b c^{2} x^{6}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{9} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{7} - 2 \, b^{2} c^{3} x^{7} + b^{2} c x^{5} + 2 \, {\left(b^{2} c^{4} x^{8} - b^{2} c^{2} x^{6}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^2*x^2 - 1)*(c*x + 1)*sqrt(c*x - 1) + (c^3*x^3 - c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^6 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x^5 - a*b*c*x^4 + (b^2*c^3*x^6 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x^5 - b^2*c*x^4)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) - integrate(((2*c^3*x^3 - 5*c*x)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(2*c^4*x^4 - 5*c^2*x^2 + 2)*(c*x + 1)*sqrt(c*x - 1) + (2*c^5*x^5 - 5*c^3*x^3 + 3*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^9 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^7 - 2*a*b*c^3*x^7 + a*b*c*x^5 + 2*(a*b*c^4*x^8 - a*b*c^2*x^6)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^9 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^7 - 2*b^2*c^3*x^7 + b^2*c*x^5 + 2*(b^2*c^4*x^8 - b^2*c^2*x^6)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
328,0,0,0,0.000000," ","integrate(x^2*(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{{\left({\left(c^{4} x^{6} - 2 \, c^{2} x^{4} + x^{2}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{5} x^{7} - 2 \, c^{3} x^{5} + c x^{3}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} - \int \frac{{\left({\left(6 \, c^{5} x^{6} - 7 \, c^{3} x^{4} + c x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(6 \, c^{6} x^{7} - 11 \, c^{4} x^{5} + 6 \, c^{2} x^{3} - x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + 3 \, {\left(2 \, c^{7} x^{8} - 5 \, c^{5} x^{6} + 4 \, c^{3} x^{4} - c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{2} - 2 \, a b c^{3} x^{2} + a b c + 2 \, {\left(a b c^{4} x^{3} - a b c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{2} - 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"((c^4*x^6 - 2*c^2*x^4 + x^2)*(c*x + 1)*sqrt(c*x - 1) + (c^5*x^7 - 2*c^3*x^5 + c*x^3)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) - integrate(((6*c^5*x^6 - 7*c^3*x^4 + c*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(6*c^6*x^7 - 11*c^4*x^5 + 6*c^2*x^3 - x)*(c*x + 1)*sqrt(c*x - 1) + 3*(2*c^7*x^8 - 5*c^5*x^6 + 4*c^3*x^4 - c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^4 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^2 - 2*a*b*c^3*x^2 + a*b*c + 2*(a*b*c^4*x^3 - a*b*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^2 - 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 - b^2*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
329,0,0,0,0.000000," ","integrate(x*(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{{\left({\left(c^{4} x^{5} - 2 \, c^{2} x^{3} + x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{5} x^{6} - 2 \, c^{3} x^{4} + c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} - \int \frac{{\left(5 \, {\left(c^{5} x^{5} - c^{3} x^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + {\left(10 \, c^{6} x^{6} - 17 \, c^{4} x^{4} + 8 \, c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(5 \, c^{7} x^{7} - 12 \, c^{5} x^{5} + 9 \, c^{3} x^{3} - 2 \, c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{2} - 2 \, a b c^{3} x^{2} + a b c + 2 \, {\left(a b c^{4} x^{3} - a b c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{2} - 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"((c^4*x^5 - 2*c^2*x^3 + x)*(c*x + 1)*sqrt(c*x - 1) + (c^5*x^6 - 2*c^3*x^4 + c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) - integrate((5*(c^5*x^5 - c^3*x^3)*(c*x + 1)^(3/2)*(c*x - 1) + (10*c^6*x^6 - 17*c^4*x^4 + 8*c^2*x^2 - 1)*(c*x + 1)*sqrt(c*x - 1) + (5*c^7*x^7 - 12*c^5*x^5 + 9*c^3*x^3 - 2*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^4 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^2 - 2*a*b*c^3*x^2 + a*b*c + 2*(a*b*c^4*x^3 - a*b*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^2 - 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 - b^2*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
330,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{{\left({\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{5} x^{5} - 2 \, c^{3} x^{3} + c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} - \int \frac{{\left({\left(4 \, c^{4} x^{4} - 3 \, c^{2} x^{2} - 1\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 4 \, {\left(2 \, c^{5} x^{5} - 3 \, c^{3} x^{3} + c x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(4 \, c^{6} x^{6} - 9 \, c^{4} x^{4} + 6 \, c^{2} x^{2} - 1\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{4} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{2} x^{2} - 2 \, a b c^{2} x^{2} + 2 \, {\left(a b c^{3} x^{3} - a b c x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + a b + {\left(b^{2} c^{4} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{2} x^{2} - 2 \, b^{2} c^{2} x^{2} + 2 \, {\left(b^{2} c^{3} x^{3} - b^{2} c x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + b^{2}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"((c^4*x^4 - 2*c^2*x^2 + 1)*(c*x + 1)*sqrt(c*x - 1) + (c^5*x^5 - 2*c^3*x^3 + c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) - integrate(((4*c^4*x^4 - 3*c^2*x^2 - 1)*(c*x + 1)^(3/2)*(c*x - 1) + 4*(2*c^5*x^5 - 3*c^3*x^3 + c*x)*(c*x + 1)*sqrt(c*x - 1) + (4*c^6*x^6 - 9*c^4*x^4 + 6*c^2*x^2 - 1)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^4*x^4 + (c*x + 1)*(c*x - 1)*a*b*c^2*x^2 - 2*a*b*c^2*x^2 + 2*(a*b*c^3*x^3 - a*b*c*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + a*b + (b^2*c^4*x^4 + (c*x + 1)*(c*x - 1)*b^2*c^2*x^2 - 2*b^2*c^2*x^2 + 2*(b^2*c^3*x^3 - b^2*c*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + b^2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
331,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/x/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{{\left({\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{5} x^{5} - 2 \, c^{3} x^{3} + c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{3} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x^{2} - a b c x + {\left(b^{2} c^{3} x^{3} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x^{2} - b^{2} c x\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} - \int \frac{{\left({\left(3 \, c^{5} x^{5} - c^{3} x^{3} - 2 \, c x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + {\left(6 \, c^{6} x^{6} - 7 \, c^{4} x^{4} + 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + 3 \, {\left(c^{7} x^{7} - 2 \, c^{5} x^{5} + c^{3} x^{3}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{6} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{4} - 2 \, a b c^{3} x^{4} + a b c x^{2} + 2 \, {\left(a b c^{4} x^{5} - a b c^{2} x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{6} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{4} - 2 \, b^{2} c^{3} x^{4} + b^{2} c x^{2} + 2 \, {\left(b^{2} c^{4} x^{5} - b^{2} c^{2} x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"((c^4*x^4 - 2*c^2*x^2 + 1)*(c*x + 1)*sqrt(c*x - 1) + (c^5*x^5 - 2*c^3*x^3 + c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^3 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x^2 - a*b*c*x + (b^2*c^3*x^3 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x^2 - b^2*c*x)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) - integrate(((3*c^5*x^5 - c^3*x^3 - 2*c*x)*(c*x + 1)^(3/2)*(c*x - 1) + (6*c^6*x^6 - 7*c^4*x^4 + 1)*(c*x + 1)*sqrt(c*x - 1) + 3*(c^7*x^7 - 2*c^5*x^5 + c^3*x^3)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^6 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^4 - 2*a*b*c^3*x^4 + a*b*c*x^2 + 2*(a*b*c^4*x^5 - a*b*c^2*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^6 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^4 - 2*b^2*c^3*x^4 + b^2*c*x^2 + 2*(b^2*c^4*x^5 - b^2*c^2*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
332,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/x^2/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{{\left({\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{5} x^{5} - 2 \, c^{3} x^{3} + c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{4} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x^{3} - a b c x^{2} + {\left(b^{2} c^{3} x^{4} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x^{3} - b^{2} c x^{2}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} - \int \frac{{\left({\left(2 \, c^{5} x^{5} + c^{3} x^{3} - 3 \, c x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(2 \, c^{6} x^{6} - c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(2 \, c^{7} x^{7} - 3 \, c^{5} x^{5} + c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{7} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{5} - 2 \, a b c^{3} x^{5} + a b c x^{3} + 2 \, {\left(a b c^{4} x^{6} - a b c^{2} x^{4}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{7} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{5} - 2 \, b^{2} c^{3} x^{5} + b^{2} c x^{3} + 2 \, {\left(b^{2} c^{4} x^{6} - b^{2} c^{2} x^{4}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"((c^4*x^4 - 2*c^2*x^2 + 1)*(c*x + 1)*sqrt(c*x - 1) + (c^5*x^5 - 2*c^3*x^3 + c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^4 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x^3 - a*b*c*x^2 + (b^2*c^3*x^4 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x^3 - b^2*c*x^2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) - integrate(((2*c^5*x^5 + c^3*x^3 - 3*c*x)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(2*c^6*x^6 - c^4*x^4 - 2*c^2*x^2 + 1)*(c*x + 1)*sqrt(c*x - 1) + (2*c^7*x^7 - 3*c^5*x^5 + c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^7 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^5 - 2*a*b*c^3*x^5 + a*b*c*x^3 + 2*(a*b*c^4*x^6 - a*b*c^2*x^4)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^7 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^5 - 2*b^2*c^3*x^5 + b^2*c*x^3 + 2*(b^2*c^4*x^6 - b^2*c^2*x^4)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
333,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/x^3/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{{\left({\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{5} x^{5} - 2 \, c^{3} x^{3} + c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{5} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x^{4} - a b c x^{3} + {\left(b^{2} c^{3} x^{5} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x^{4} - b^{2} c x^{3}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} - \int \frac{{\left({\left(c^{5} x^{5} + 3 \, c^{3} x^{3} - 4 \, c x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + {\left(2 \, c^{6} x^{6} + 3 \, c^{4} x^{4} - 8 \, c^{2} x^{2} + 3\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{7} x^{7} - 3 \, c^{3} x^{3} + 2 \, c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{8} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{6} - 2 \, a b c^{3} x^{6} + a b c x^{4} + 2 \, {\left(a b c^{4} x^{7} - a b c^{2} x^{5}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{8} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{6} - 2 \, b^{2} c^{3} x^{6} + b^{2} c x^{4} + 2 \, {\left(b^{2} c^{4} x^{7} - b^{2} c^{2} x^{5}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"((c^4*x^4 - 2*c^2*x^2 + 1)*(c*x + 1)*sqrt(c*x - 1) + (c^5*x^5 - 2*c^3*x^3 + c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^5 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x^4 - a*b*c*x^3 + (b^2*c^3*x^5 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x^4 - b^2*c*x^3)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) - integrate(((c^5*x^5 + 3*c^3*x^3 - 4*c*x)*(c*x + 1)^(3/2)*(c*x - 1) + (2*c^6*x^6 + 3*c^4*x^4 - 8*c^2*x^2 + 3)*(c*x + 1)*sqrt(c*x - 1) + (c^7*x^7 - 3*c^3*x^3 + 2*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^8 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^6 - 2*a*b*c^3*x^6 + a*b*c*x^4 + 2*(a*b*c^4*x^7 - a*b*c^2*x^5)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^8 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^6 - 2*b^2*c^3*x^6 + b^2*c*x^4 + 2*(b^2*c^4*x^7 - b^2*c^2*x^5)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
334,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(3/2)/x^4/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{{\left({\left(c^{4} x^{4} - 2 \, c^{2} x^{2} + 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{5} x^{5} - 2 \, c^{3} x^{3} + c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{6} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x^{5} - a b c x^{4} + {\left(b^{2} c^{3} x^{6} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x^{5} - b^{2} c x^{4}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} - \int \frac{{\left(5 \, {\left(c^{3} x^{3} - c x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 4 \, {\left(2 \, c^{4} x^{4} - 3 \, c^{2} x^{2} + 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + 3 \, {\left(c^{5} x^{5} - 2 \, c^{3} x^{3} + c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{9} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{7} - 2 \, a b c^{3} x^{7} + a b c x^{5} + 2 \, {\left(a b c^{4} x^{8} - a b c^{2} x^{6}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{9} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{7} - 2 \, b^{2} c^{3} x^{7} + b^{2} c x^{5} + 2 \, {\left(b^{2} c^{4} x^{8} - b^{2} c^{2} x^{6}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"((c^4*x^4 - 2*c^2*x^2 + 1)*(c*x + 1)*sqrt(c*x - 1) + (c^5*x^5 - 2*c^3*x^3 + c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^6 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x^5 - a*b*c*x^4 + (b^2*c^3*x^6 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x^5 - b^2*c*x^4)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) - integrate((5*(c^3*x^3 - c*x)*(c*x + 1)^(3/2)*(c*x - 1) + 4*(2*c^4*x^4 - 3*c^2*x^2 + 1)*(c*x + 1)*sqrt(c*x - 1) + 3*(c^5*x^5 - 2*c^3*x^3 + c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^9 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^7 - 2*a*b*c^3*x^7 + a*b*c*x^5 + 2*(a*b*c^4*x^8 - a*b*c^2*x^6)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^9 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^7 - 2*b^2*c^3*x^7 + b^2*c*x^5 + 2*(b^2*c^4*x^8 - b^2*c^2*x^6)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
335,0,0,0,0.000000," ","integrate(x^2*(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c^{6} x^{8} - 3 \, c^{4} x^{6} + 3 \, c^{2} x^{4} - x^{2}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{7} x^{9} - 3 \, c^{5} x^{7} + 3 \, c^{3} x^{5} - c x^{3}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{{\left({\left(8 \, c^{7} x^{8} - 17 \, c^{5} x^{6} + 10 \, c^{3} x^{4} - c x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(8 \, c^{8} x^{9} - 22 \, c^{6} x^{7} + 21 \, c^{4} x^{5} - 8 \, c^{2} x^{3} + x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(8 \, c^{9} x^{10} - 27 \, c^{7} x^{8} + 33 \, c^{5} x^{6} - 17 \, c^{3} x^{4} + 3 \, c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{2} - 2 \, a b c^{3} x^{2} + a b c + 2 \, {\left(a b c^{4} x^{3} - a b c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{2} - 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^6*x^8 - 3*c^4*x^6 + 3*c^2*x^4 - x^2)*(c*x + 1)*sqrt(c*x - 1) + (c^7*x^9 - 3*c^5*x^7 + 3*c^3*x^5 - c*x^3)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate(((8*c^7*x^8 - 17*c^5*x^6 + 10*c^3*x^4 - c*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(8*c^8*x^9 - 22*c^6*x^7 + 21*c^4*x^5 - 8*c^2*x^3 + x)*(c*x + 1)*sqrt(c*x - 1) + (8*c^9*x^10 - 27*c^7*x^8 + 33*c^5*x^6 - 17*c^3*x^4 + 3*c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^4 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^2 - 2*a*b*c^3*x^2 + a*b*c + 2*(a*b*c^4*x^3 - a*b*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^2 - 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 - b^2*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
336,0,0,0,0.000000," ","integrate(x*(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c^{6} x^{7} - 3 \, c^{4} x^{5} + 3 \, c^{2} x^{3} - x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{7} x^{8} - 3 \, c^{5} x^{6} + 3 \, c^{3} x^{4} - c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{{\left(7 \, {\left(c^{7} x^{7} - 2 \, c^{5} x^{5} + c^{3} x^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + {\left(14 \, c^{8} x^{8} - 37 \, c^{6} x^{6} + 33 \, c^{4} x^{4} - 11 \, c^{2} x^{2} + 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(7 \, c^{9} x^{9} - 23 \, c^{7} x^{7} + 27 \, c^{5} x^{5} - 13 \, c^{3} x^{3} + 2 \, c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{2} - 2 \, a b c^{3} x^{2} + a b c + 2 \, {\left(a b c^{4} x^{3} - a b c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{2} - 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^6*x^7 - 3*c^4*x^5 + 3*c^2*x^3 - x)*(c*x + 1)*sqrt(c*x - 1) + (c^7*x^8 - 3*c^5*x^6 + 3*c^3*x^4 - c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate((7*(c^7*x^7 - 2*c^5*x^5 + c^3*x^3)*(c*x + 1)^(3/2)*(c*x - 1) + (14*c^8*x^8 - 37*c^6*x^6 + 33*c^4*x^4 - 11*c^2*x^2 + 1)*(c*x + 1)*sqrt(c*x - 1) + (7*c^9*x^9 - 23*c^7*x^7 + 27*c^5*x^5 - 13*c^3*x^3 + 2*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^4 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^2 - 2*a*b*c^3*x^2 + a*b*c + 2*(a*b*c^4*x^3 - a*b*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^2 - 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 - b^2*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
337,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{7} x^{7} - 3 \, c^{5} x^{5} + 3 \, c^{3} x^{3} - c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{{\left({\left(6 \, c^{6} x^{6} - 11 \, c^{4} x^{4} + 4 \, c^{2} x^{2} + 1\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 6 \, {\left(2 \, c^{7} x^{7} - 5 \, c^{5} x^{5} + 4 \, c^{3} x^{3} - c x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(6 \, c^{8} x^{8} - 19 \, c^{6} x^{6} + 21 \, c^{4} x^{4} - 9 \, c^{2} x^{2} + 1\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{4} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{2} x^{2} - 2 \, a b c^{2} x^{2} + 2 \, {\left(a b c^{3} x^{3} - a b c x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + a b + {\left(b^{2} c^{4} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{2} x^{2} - 2 \, b^{2} c^{2} x^{2} + 2 \, {\left(b^{2} c^{3} x^{3} - b^{2} c x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + b^{2}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - 1)*(c*x + 1)*sqrt(c*x - 1) + (c^7*x^7 - 3*c^5*x^5 + 3*c^3*x^3 - c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate(((6*c^6*x^6 - 11*c^4*x^4 + 4*c^2*x^2 + 1)*(c*x + 1)^(3/2)*(c*x - 1) + 6*(2*c^7*x^7 - 5*c^5*x^5 + 4*c^3*x^3 - c*x)*(c*x + 1)*sqrt(c*x - 1) + (6*c^8*x^8 - 19*c^6*x^6 + 21*c^4*x^4 - 9*c^2*x^2 + 1)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^4*x^4 + (c*x + 1)*(c*x - 1)*a*b*c^2*x^2 - 2*a*b*c^2*x^2 + 2*(a*b*c^3*x^3 - a*b*c*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + a*b + (b^2*c^4*x^4 + (c*x + 1)*(c*x - 1)*b^2*c^2*x^2 - 2*b^2*c^2*x^2 + 2*(b^2*c^3*x^3 - b^2*c*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + b^2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
338,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/x/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{7} x^{7} - 3 \, c^{5} x^{5} + 3 \, c^{3} x^{3} - c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{3} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x^{2} - a b c x + {\left(b^{2} c^{3} x^{3} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x^{2} - b^{2} c x\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{{\left({\left(5 \, c^{7} x^{7} - 8 \, c^{5} x^{5} + c^{3} x^{3} + 2 \, c x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + {\left(10 \, c^{8} x^{8} - 23 \, c^{6} x^{6} + 15 \, c^{4} x^{4} - c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + 5 \, {\left(c^{9} x^{9} - 3 \, c^{7} x^{7} + 3 \, c^{5} x^{5} - c^{3} x^{3}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{6} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{4} - 2 \, a b c^{3} x^{4} + a b c x^{2} + 2 \, {\left(a b c^{4} x^{5} - a b c^{2} x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{6} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{4} - 2 \, b^{2} c^{3} x^{4} + b^{2} c x^{2} + 2 \, {\left(b^{2} c^{4} x^{5} - b^{2} c^{2} x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - 1)*(c*x + 1)*sqrt(c*x - 1) + (c^7*x^7 - 3*c^5*x^5 + 3*c^3*x^3 - c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^3 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x^2 - a*b*c*x + (b^2*c^3*x^3 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x^2 - b^2*c*x)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate(((5*c^7*x^7 - 8*c^5*x^5 + c^3*x^3 + 2*c*x)*(c*x + 1)^(3/2)*(c*x - 1) + (10*c^8*x^8 - 23*c^6*x^6 + 15*c^4*x^4 - c^2*x^2 - 1)*(c*x + 1)*sqrt(c*x - 1) + 5*(c^9*x^9 - 3*c^7*x^7 + 3*c^5*x^5 - c^3*x^3)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^6 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^4 - 2*a*b*c^3*x^4 + a*b*c*x^2 + 2*(a*b*c^4*x^5 - a*b*c^2*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^6 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^4 - 2*b^2*c^3*x^4 + b^2*c*x^2 + 2*(b^2*c^4*x^5 - b^2*c^2*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
339,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/x^2/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{7} x^{7} - 3 \, c^{5} x^{5} + 3 \, c^{3} x^{3} - c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{4} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x^{3} - a b c x^{2} + {\left(b^{2} c^{3} x^{4} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x^{3} - b^{2} c x^{2}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{{\left({\left(4 \, c^{7} x^{7} - 5 \, c^{5} x^{5} - 2 \, c^{3} x^{3} + 3 \, c x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(4 \, c^{8} x^{8} - 8 \, c^{6} x^{6} + 3 \, c^{4} x^{4} + 2 \, c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(4 \, c^{9} x^{9} - 11 \, c^{7} x^{7} + 9 \, c^{5} x^{5} - c^{3} x^{3} - c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{7} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{5} - 2 \, a b c^{3} x^{5} + a b c x^{3} + 2 \, {\left(a b c^{4} x^{6} - a b c^{2} x^{4}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{7} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{5} - 2 \, b^{2} c^{3} x^{5} + b^{2} c x^{3} + 2 \, {\left(b^{2} c^{4} x^{6} - b^{2} c^{2} x^{4}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - 1)*(c*x + 1)*sqrt(c*x - 1) + (c^7*x^7 - 3*c^5*x^5 + 3*c^3*x^3 - c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^4 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x^3 - a*b*c*x^2 + (b^2*c^3*x^4 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x^3 - b^2*c*x^2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate(((4*c^7*x^7 - 5*c^5*x^5 - 2*c^3*x^3 + 3*c*x)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(4*c^8*x^8 - 8*c^6*x^6 + 3*c^4*x^4 + 2*c^2*x^2 - 1)*(c*x + 1)*sqrt(c*x - 1) + (4*c^9*x^9 - 11*c^7*x^7 + 9*c^5*x^5 - c^3*x^3 - c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^7 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^5 - 2*a*b*c^3*x^5 + a*b*c*x^3 + 2*(a*b*c^4*x^6 - a*b*c^2*x^4)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^7 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^5 - 2*b^2*c^3*x^5 + b^2*c*x^3 + 2*(b^2*c^4*x^6 - b^2*c^2*x^4)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
340,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/x^3/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{7} x^{7} - 3 \, c^{5} x^{5} + 3 \, c^{3} x^{3} - c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{5} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x^{4} - a b c x^{3} + {\left(b^{2} c^{3} x^{5} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x^{4} - b^{2} c x^{3}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{{\left({\left(3 \, c^{7} x^{7} - 2 \, c^{5} x^{5} - 5 \, c^{3} x^{3} + 4 \, c x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 3 \, {\left(2 \, c^{8} x^{8} - 3 \, c^{6} x^{6} - c^{4} x^{4} + 3 \, c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(3 \, c^{9} x^{9} - 7 \, c^{7} x^{7} + 3 \, c^{5} x^{5} + 3 \, c^{3} x^{3} - 2 \, c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{8} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{6} - 2 \, a b c^{3} x^{6} + a b c x^{4} + 2 \, {\left(a b c^{4} x^{7} - a b c^{2} x^{5}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{8} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{6} - 2 \, b^{2} c^{3} x^{6} + b^{2} c x^{4} + 2 \, {\left(b^{2} c^{4} x^{7} - b^{2} c^{2} x^{5}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - 1)*(c*x + 1)*sqrt(c*x - 1) + (c^7*x^7 - 3*c^5*x^5 + 3*c^3*x^3 - c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^5 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x^4 - a*b*c*x^3 + (b^2*c^3*x^5 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x^4 - b^2*c*x^3)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate(((3*c^7*x^7 - 2*c^5*x^5 - 5*c^3*x^3 + 4*c*x)*(c*x + 1)^(3/2)*(c*x - 1) + 3*(2*c^8*x^8 - 3*c^6*x^6 - c^4*x^4 + 3*c^2*x^2 - 1)*(c*x + 1)*sqrt(c*x - 1) + (3*c^9*x^9 - 7*c^7*x^7 + 3*c^5*x^5 + 3*c^3*x^3 - 2*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^8 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^6 - 2*a*b*c^3*x^6 + a*b*c*x^4 + 2*(a*b*c^4*x^7 - a*b*c^2*x^5)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^8 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^6 - 2*b^2*c^3*x^6 + b^2*c*x^4 + 2*(b^2*c^4*x^7 - b^2*c^2*x^5)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
341,0,0,0,0.000000," ","integrate((-c^2*x^2+1)^(5/2)/x^4/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c^{6} x^{6} - 3 \, c^{4} x^{4} + 3 \, c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(c^{7} x^{7} - 3 \, c^{5} x^{5} + 3 \, c^{3} x^{3} - c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{6} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x^{5} - a b c x^{4} + {\left(b^{2} c^{3} x^{6} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x^{5} - b^{2} c x^{4}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{{\left({\left(2 \, c^{7} x^{7} + c^{5} x^{5} - 8 \, c^{3} x^{3} + 5 \, c x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(2 \, c^{8} x^{8} - c^{6} x^{6} - 6 \, c^{4} x^{4} + 7 \, c^{2} x^{2} - 2\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(2 \, c^{9} x^{9} - 3 \, c^{7} x^{7} - 3 \, c^{5} x^{5} + 7 \, c^{3} x^{3} - 3 \, c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{9} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{7} - 2 \, a b c^{3} x^{7} + a b c x^{5} + 2 \, {\left(a b c^{4} x^{8} - a b c^{2} x^{6}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{9} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{7} - 2 \, b^{2} c^{3} x^{7} + b^{2} c x^{5} + 2 \, {\left(b^{2} c^{4} x^{8} - b^{2} c^{2} x^{6}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^6*x^6 - 3*c^4*x^4 + 3*c^2*x^2 - 1)*(c*x + 1)*sqrt(c*x - 1) + (c^7*x^7 - 3*c^5*x^5 + 3*c^3*x^3 - c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^3*x^6 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x^5 - a*b*c*x^4 + (b^2*c^3*x^6 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x^5 - b^2*c*x^4)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate(((2*c^7*x^7 + c^5*x^5 - 8*c^3*x^3 + 5*c*x)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(2*c^8*x^8 - c^6*x^6 - 6*c^4*x^4 + 7*c^2*x^2 - 2)*(c*x + 1)*sqrt(c*x - 1) + (2*c^9*x^9 - 3*c^7*x^7 - 3*c^5*x^5 + 7*c^3*x^3 - 3*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)/(a*b*c^5*x^9 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^7 - 2*a*b*c^3*x^7 + a*b*c*x^5 + 2*(a*b*c^4*x^8 - a*b*c^2*x^6)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^9 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^7 - 2*b^2*c^3*x^7 + b^2*c*x^5 + 2*(b^2*c^4*x^8 - b^2*c^2*x^6)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
342,0,0,0,0.000000," ","integrate(x^5/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{8} - c x^{6} + {\left(c^{2} x^{7} - x^{5}\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(c x + 1\right)} \sqrt{c x - 1} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)} \sqrt{c x - 1} a b c^{2} x + {\left(a b c^{3} x^{2} - a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} + \int \frac{5 \, c^{5} x^{9} - 11 \, c^{3} x^{7} + 6 \, c x^{5} + {\left(5 \, c^{3} x^{7} - 4 \, c x^{5}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 5 \, {\left(2 \, c^{4} x^{8} - 3 \, c^{2} x^{6} + x^{4}\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} b^{2} c^{3} x^{2} + 2 \, {\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} - 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} a b c^{3} x^{2} + 2 \, {\left(a b c^{4} x^{3} - a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{5} x^{4} - 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-(c^3*x^8 - c*x^6 + (c^2*x^7 - x^5)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x + (b^2*c^3*x^2 - b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x + (a*b*c^3*x^2 - a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) + integrate((5*c^5*x^9 - 11*c^3*x^7 + 6*c*x^5 + (5*c^3*x^7 - 4*c*x^5)*(c*x + 1)*(c*x - 1) + 5*(2*c^4*x^8 - 3*c^2*x^6 + x^4)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((c*x + 1)^(3/2)*(c*x - 1)*b^2*c^3*x^2 + 2*(b^2*c^4*x^3 - b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)^(3/2)*(c*x - 1)*a*b*c^3*x^2 + 2*(a*b*c^4*x^3 - a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
343,0,0,0,0.000000," ","integrate(x^4/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{7} - c x^{5} + {\left(c^{2} x^{6} - x^{4}\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(c x + 1\right)} \sqrt{c x - 1} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)} \sqrt{c x - 1} a b c^{2} x + {\left(a b c^{3} x^{2} - a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} + \int \frac{4 \, c^{5} x^{8} - 9 \, c^{3} x^{6} + 5 \, c x^{4} + {\left(4 \, c^{3} x^{6} - 3 \, c x^{4}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 4 \, {\left(2 \, c^{4} x^{7} - 3 \, c^{2} x^{5} + x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} b^{2} c^{3} x^{2} + 2 \, {\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} - 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} a b c^{3} x^{2} + 2 \, {\left(a b c^{4} x^{3} - a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{5} x^{4} - 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-(c^3*x^7 - c*x^5 + (c^2*x^6 - x^4)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x + (b^2*c^3*x^2 - b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x + (a*b*c^3*x^2 - a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) + integrate((4*c^5*x^8 - 9*c^3*x^6 + 5*c*x^4 + (4*c^3*x^6 - 3*c*x^4)*(c*x + 1)*(c*x - 1) + 4*(2*c^4*x^7 - 3*c^2*x^5 + x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((c*x + 1)^(3/2)*(c*x - 1)*b^2*c^3*x^2 + 2*(b^2*c^4*x^3 - b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)^(3/2)*(c*x - 1)*a*b*c^3*x^2 + 2*(a*b*c^4*x^3 - a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
344,0,0,0,0.000000," ","integrate(x^3/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{6} - c x^{4} + {\left(c^{2} x^{5} - x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(c x + 1\right)} \sqrt{c x - 1} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)} \sqrt{c x - 1} a b c^{2} x + {\left(a b c^{3} x^{2} - a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} + \int \frac{3 \, c^{5} x^{7} - 7 \, c^{3} x^{5} + 4 \, c x^{3} + {\left(3 \, c^{3} x^{5} - 2 \, c x^{3}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 3 \, {\left(2 \, c^{4} x^{6} - 3 \, c^{2} x^{4} + x^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} b^{2} c^{3} x^{2} + 2 \, {\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} - 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} a b c^{3} x^{2} + 2 \, {\left(a b c^{4} x^{3} - a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{5} x^{4} - 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-(c^3*x^6 - c*x^4 + (c^2*x^5 - x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x + (b^2*c^3*x^2 - b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x + (a*b*c^3*x^2 - a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) + integrate((3*c^5*x^7 - 7*c^3*x^5 + 4*c*x^3 + (3*c^3*x^5 - 2*c*x^3)*(c*x + 1)*(c*x - 1) + 3*(2*c^4*x^6 - 3*c^2*x^4 + x^2)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((c*x + 1)^(3/2)*(c*x - 1)*b^2*c^3*x^2 + 2*(b^2*c^4*x^3 - b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)^(3/2)*(c*x - 1)*a*b*c^3*x^2 + 2*(a*b*c^4*x^3 - a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
345,0,0,0,0.000000," ","integrate(x^2/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{5} - c x^{3} + {\left(c^{2} x^{4} - x^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(c x + 1\right)} \sqrt{c x - 1} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)} \sqrt{c x - 1} a b c^{2} x + {\left(a b c^{3} x^{2} - a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} + \int \frac{2 \, c^{5} x^{6} - 5 \, c^{3} x^{4} + {\left(2 \, c^{3} x^{4} - c x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 3 \, c x^{2} + 2 \, {\left(2 \, c^{4} x^{5} - 3 \, c^{2} x^{3} + x\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} b^{2} c^{3} x^{2} + 2 \, {\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} - 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} a b c^{3} x^{2} + 2 \, {\left(a b c^{4} x^{3} - a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{5} x^{4} - 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-(c^3*x^5 - c*x^3 + (c^2*x^4 - x^2)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x + (b^2*c^3*x^2 - b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x + (a*b*c^3*x^2 - a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) + integrate((2*c^5*x^6 - 5*c^3*x^4 + (2*c^3*x^4 - c*x^2)*(c*x + 1)*(c*x - 1) + 3*c*x^2 + 2*(2*c^4*x^5 - 3*c^2*x^3 + x)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((c*x + 1)^(3/2)*(c*x - 1)*b^2*c^3*x^2 + 2*(b^2*c^4*x^3 - b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)^(3/2)*(c*x - 1)*a*b*c^3*x^2 + 2*(a*b*c^4*x^3 - a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
346,0,0,0,0.000000," ","integrate(x/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{4} - c x^{2} + {\left(c^{2} x^{3} - x\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(c x + 1\right)} \sqrt{c x - 1} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)} \sqrt{c x - 1} a b c^{2} x + {\left(a b c^{3} x^{2} - a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} + \int \frac{c^{5} x^{5} + {\left(c x + 1\right)} {\left(c x - 1\right)} c^{3} x^{3} - 3 \, c^{3} x^{3} + {\left(2 \, c^{4} x^{4} - 3 \, c^{2} x^{2} + 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} + 2 \, c x}{{\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} b^{2} c^{3} x^{2} + 2 \, {\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} - 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} a b c^{3} x^{2} + 2 \, {\left(a b c^{4} x^{3} - a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{5} x^{4} - 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-(c^3*x^4 - c*x^2 + (c^2*x^3 - x)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x + (b^2*c^3*x^2 - b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x + (a*b*c^3*x^2 - a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) + integrate((c^5*x^5 + (c*x + 1)*(c*x - 1)*c^3*x^3 - 3*c^3*x^3 + (2*c^4*x^4 - 3*c^2*x^2 + 1)*sqrt(c*x + 1)*sqrt(c*x - 1) + 2*c*x)/(((c*x + 1)^(3/2)*(c*x - 1)*b^2*c^3*x^2 + 2*(b^2*c^4*x^3 - b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)^(3/2)*(c*x - 1)*a*b*c^3*x^2 + 2*(a*b*c^4*x^3 - a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
347,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x}{{\left({\left(c x + 1\right)} \sqrt{c x - 1} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)} \sqrt{c x - 1} a b c^{2} x + {\left(a b c^{3} x^{2} - a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} + \int -\frac{c^{2} x^{2} - {\left(c x + 1\right)} {\left(c x - 1\right)} - 1}{{\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} b^{2} c^{2} x^{2} + 2 \, {\left(b^{2} c^{3} x^{3} - b^{2} c x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{4} x^{4} - 2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} a b c^{2} x^{2} + 2 \, {\left(a b c^{3} x^{3} - a b c x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{4} x^{4} - 2 \, a b c^{2} x^{2} + a b\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x)/(((c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x + (b^2*c^3*x^2 - b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x + (a*b*c^3*x^2 - a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) + integrate(-(c^2*x^2 - (c*x + 1)*(c*x - 1) - 1)/(((c*x + 1)^(3/2)*(c*x - 1)*b^2*c^2*x^2 + 2*(b^2*c^3*x^3 - b^2*c*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^4*x^4 - 2*b^2*c^2*x^2 + b^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)^(3/2)*(c*x - 1)*a*b*c^2*x^2 + 2*(a*b*c^3*x^3 - a*b*c*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^4*x^4 - 2*a*b*c^2*x^2 + a*b)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
348,0,0,0,0.000000," ","integrate(1/x/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x}{{\left({\left(c x + 1\right)} \sqrt{c x - 1} b^{2} c^{2} x^{2} + {\left(b^{2} c^{3} x^{3} - b^{2} c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)} \sqrt{c x - 1} a b c^{2} x^{2} + {\left(a b c^{3} x^{3} - a b c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} - \int \frac{c^{5} x^{5} - c^{3} x^{3} + {\left(c^{3} x^{3} - 2 \, c x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(2 \, c^{4} x^{4} - 3 \, c^{2} x^{2} + 1\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} b^{2} c^{3} x^{4} + 2 \, {\left(b^{2} c^{4} x^{5} - b^{2} c^{2} x^{3}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{6} - 2 \, b^{2} c^{3} x^{4} + b^{2} c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} a b c^{3} x^{4} + 2 \, {\left(a b c^{4} x^{5} - a b c^{2} x^{3}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{5} x^{6} - 2 \, a b c^{3} x^{4} + a b c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x)/(((c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x^2 + (b^2*c^3*x^3 - b^2*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x^2 + (a*b*c^3*x^3 - a*b*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)) - integrate((c^5*x^5 - c^3*x^3 + (c^3*x^3 - 2*c*x)*(c*x + 1)*(c*x - 1) + (2*c^4*x^4 - 3*c^2*x^2 + 1)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((c*x + 1)^(3/2)*(c*x - 1)*b^2*c^3*x^4 + 2*(b^2*c^4*x^5 - b^2*c^2*x^3)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^6 - 2*b^2*c^3*x^4 + b^2*c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)^(3/2)*(c*x - 1)*a*b*c^3*x^4 + 2*(a*b*c^4*x^5 - a*b*c^2*x^3)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^5*x^6 - 2*a*b*c^3*x^4 + a*b*c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
349,0,0,0,0.000000," ","integrate(1/x^2/(a+b*arccosh(c*x))^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x}{{\left({\left(c x + 1\right)} \sqrt{c x - 1} b^{2} c^{2} x^{3} + {\left(b^{2} c^{3} x^{4} - b^{2} c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)} \sqrt{c x - 1} a b c^{2} x^{3} + {\left(a b c^{3} x^{4} - a b c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} - \int \frac{2 \, c^{5} x^{5} - 3 \, c^{3} x^{3} + {\left(2 \, c^{3} x^{3} - 3 \, c x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(2 \, c^{4} x^{4} - 3 \, c^{2} x^{2} + 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} + c x}{{\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} b^{2} c^{3} x^{5} + 2 \, {\left(b^{2} c^{4} x^{6} - b^{2} c^{2} x^{4}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{7} - 2 \, b^{2} c^{3} x^{5} + b^{2} c x^{3}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} a b c^{3} x^{5} + 2 \, {\left(a b c^{4} x^{6} - a b c^{2} x^{4}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{5} x^{7} - 2 \, a b c^{3} x^{5} + a b c x^{3}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x)/(((c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x^3 + (b^2*c^3*x^4 - b^2*c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x^3 + (a*b*c^3*x^4 - a*b*c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)) - integrate((2*c^5*x^5 - 3*c^3*x^3 + (2*c^3*x^3 - 3*c*x)*(c*x + 1)*(c*x - 1) + 2*(2*c^4*x^4 - 3*c^2*x^2 + 1)*sqrt(c*x + 1)*sqrt(c*x - 1) + c*x)/(((c*x + 1)^(3/2)*(c*x - 1)*b^2*c^3*x^5 + 2*(b^2*c^4*x^6 - b^2*c^2*x^4)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^7 - 2*b^2*c^3*x^5 + b^2*c*x^3)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)^(3/2)*(c*x - 1)*a*b*c^3*x^5 + 2*(a*b*c^4*x^6 - a*b*c^2*x^4)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^5*x^7 - 2*a*b*c^3*x^5 + a*b*c*x^3)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
350,0,0,0,0.000000," ","integrate(x^3/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{c x^{4} + \sqrt{c x + 1} \sqrt{c x - 1} x^{3}}{{\left({\left(c x + 1\right)} \sqrt{c x - 1} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)} \sqrt{c x - 1} a b c^{2} x + {\left(a b c^{3} x^{2} - a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} - \int \frac{c^{5} x^{7} - 5 \, c^{3} x^{5} + 4 \, c x^{3} + {\left(c^{3} x^{5} - 2 \, c x^{3}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(2 \, c^{4} x^{6} - 7 \, c^{2} x^{4} + 3 \, x^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(b^{2} c^{5} x^{4} - b^{2} c^{3} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{6} x^{5} - 2 \, b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{7} x^{6} - 3 \, b^{2} c^{5} x^{4} + 3 \, b^{2} c^{3} x^{2} - b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{5} x^{4} - a b c^{3} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(a b c^{6} x^{5} - 2 \, a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{7} x^{6} - 3 \, a b c^{5} x^{4} + 3 \, a b c^{3} x^{2} - a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"(c*x^4 + sqrt(c*x + 1)*sqrt(c*x - 1)*x^3)/(((c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x + (b^2*c^3*x^2 - b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x + (a*b*c^3*x^2 - a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) - integrate((c^5*x^7 - 5*c^3*x^5 + 4*c*x^3 + (c^3*x^5 - 2*c*x^3)*(c*x + 1)*(c*x - 1) + (2*c^4*x^6 - 7*c^2*x^4 + 3*x^2)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((b^2*c^5*x^4 - b^2*c^3*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(b^2*c^6*x^5 - 2*b^2*c^4*x^3 + b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^7*x^6 - 3*b^2*c^5*x^4 + 3*b^2*c^3*x^2 - b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^5*x^4 - a*b*c^3*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(a*b*c^6*x^5 - 2*a*b*c^4*x^3 + a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^7*x^6 - 3*a*b*c^5*x^4 + 3*a*b*c^3*x^2 - a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
351,0,0,0,0.000000," ","integrate(x^2/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{c x^{3} + \sqrt{c x + 1} \sqrt{c x - 1} x^{2}}{{\left({\left(c x + 1\right)} \sqrt{c x - 1} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)} \sqrt{c x - 1} a b c^{2} x + {\left(a b c^{3} x^{2} - a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} + \int \frac{3 \, c^{3} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} c x^{2} - 3 \, c x^{2} + 2 \, {\left(2 \, c^{2} x^{3} - x\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(b^{2} c^{5} x^{4} - b^{2} c^{3} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{6} x^{5} - 2 \, b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{7} x^{6} - 3 \, b^{2} c^{5} x^{4} + 3 \, b^{2} c^{3} x^{2} - b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{5} x^{4} - a b c^{3} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(a b c^{6} x^{5} - 2 \, a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{7} x^{6} - 3 \, a b c^{5} x^{4} + 3 \, a b c^{3} x^{2} - a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"(c*x^3 + sqrt(c*x + 1)*sqrt(c*x - 1)*x^2)/(((c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x + (b^2*c^3*x^2 - b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x + (a*b*c^3*x^2 - a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) + integrate((3*c^3*x^4 + (c*x + 1)*(c*x - 1)*c*x^2 - 3*c*x^2 + 2*(2*c^2*x^3 - x)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((b^2*c^5*x^4 - b^2*c^3*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(b^2*c^6*x^5 - 2*b^2*c^4*x^3 + b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^7*x^6 - 3*b^2*c^5*x^4 + 3*b^2*c^3*x^2 - b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^5*x^4 - a*b*c^3*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(a*b*c^6*x^5 - 2*a*b*c^4*x^3 + a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^7*x^6 - 3*a*b*c^5*x^4 + 3*a*b*c^3*x^2 - a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
352,0,0,0,0.000000," ","integrate(x/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{c x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} x}{{\left({\left(c x + 1\right)} \sqrt{c x - 1} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)} \sqrt{c x - 1} a b c^{2} x + {\left(a b c^{3} x^{2} - a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} + \int \frac{c^{5} x^{5} + {\left(c x + 1\right)} {\left(c x - 1\right)} c^{3} x^{3} + c^{3} x^{3} + {\left(2 \, c^{4} x^{4} + c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - 2 \, c x}{{\left({\left(b^{2} c^{5} x^{4} - b^{2} c^{3} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{6} x^{5} - 2 \, b^{2} c^{4} x^{3} + b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{7} x^{6} - 3 \, b^{2} c^{5} x^{4} + 3 \, b^{2} c^{3} x^{2} - b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{5} x^{4} - a b c^{3} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(a b c^{6} x^{5} - 2 \, a b c^{4} x^{3} + a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{7} x^{6} - 3 \, a b c^{5} x^{4} + 3 \, a b c^{3} x^{2} - a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"(c*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*x)/(((c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x + (b^2*c^3*x^2 - b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x + (a*b*c^3*x^2 - a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) + integrate((c^5*x^5 + (c*x + 1)*(c*x - 1)*c^3*x^3 + c^3*x^3 + (2*c^4*x^4 + c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - 2*c*x)/(((b^2*c^5*x^4 - b^2*c^3*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(b^2*c^6*x^5 - 2*b^2*c^4*x^3 + b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^7*x^6 - 3*b^2*c^5*x^4 + 3*b^2*c^3*x^2 - b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^5*x^4 - a*b*c^3*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(a*b*c^6*x^5 - 2*a*b*c^4*x^3 + a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^7*x^6 - 3*a*b*c^5*x^4 + 3*a*b*c^3*x^2 - a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
353,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{c x + \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(c x + 1\right)} \sqrt{c x - 1} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)} \sqrt{c x - 1} a b c^{2} x + {\left(a b c^{3} x^{2} - a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} + \int \frac{2 \, c^{4} x^{4} - c^{2} x^{2} + {\left(2 \, c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(2 \, c^{3} x^{3} - c x\right)} \sqrt{c x + 1} \sqrt{c x - 1} - 1}{{\left({\left(b^{2} c^{4} x^{4} - b^{2} c^{2} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{5} x^{5} - 2 \, b^{2} c^{3} x^{3} + b^{2} c x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{6} x^{6} - 3 \, b^{2} c^{4} x^{4} + 3 \, b^{2} c^{2} x^{2} - b^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{4} x^{4} - a b c^{2} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(a b c^{5} x^{5} - 2 \, a b c^{3} x^{3} + a b c x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{6} x^{6} - 3 \, a b c^{4} x^{4} + 3 \, a b c^{2} x^{2} - a b\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(((c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x + (b^2*c^3*x^2 - b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x + (a*b*c^3*x^2 - a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) + integrate((2*c^4*x^4 - c^2*x^2 + (2*c^2*x^2 - 1)*(c*x + 1)*(c*x - 1) + 2*(2*c^3*x^3 - c*x)*sqrt(c*x + 1)*sqrt(c*x - 1) - 1)/(((b^2*c^4*x^4 - b^2*c^2*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(b^2*c^5*x^5 - 2*b^2*c^3*x^3 + b^2*c*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^6*x^6 - 3*b^2*c^4*x^4 + 3*b^2*c^2*x^2 - b^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^4*x^4 - a*b*c^2*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(a*b*c^5*x^5 - 2*a*b*c^3*x^3 + a*b*c*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^6*x^6 - 3*a*b*c^4*x^4 + 3*a*b*c^2*x^2 - a*b)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
354,0,0,0,0.000000," ","integrate(1/x/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{c x + \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(c x + 1\right)} \sqrt{c x - 1} b^{2} c^{2} x^{2} + {\left(b^{2} c^{3} x^{3} - b^{2} c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)} \sqrt{c x - 1} a b c^{2} x^{2} + {\left(a b c^{3} x^{3} - a b c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} + \int \frac{3 \, c^{5} x^{5} - 3 \, c^{3} x^{3} + {\left(3 \, c^{3} x^{3} - 2 \, c x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(6 \, c^{4} x^{4} - 5 \, c^{2} x^{2} + 1\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(b^{2} c^{5} x^{6} - b^{2} c^{3} x^{4}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{6} x^{7} - 2 \, b^{2} c^{4} x^{5} + b^{2} c^{2} x^{3}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{7} x^{8} - 3 \, b^{2} c^{5} x^{6} + 3 \, b^{2} c^{3} x^{4} - b^{2} c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{5} x^{6} - a b c^{3} x^{4}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(a b c^{6} x^{7} - 2 \, a b c^{4} x^{5} + a b c^{2} x^{3}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{7} x^{8} - 3 \, a b c^{5} x^{6} + 3 \, a b c^{3} x^{4} - a b c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(((c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x^2 + (b^2*c^3*x^3 - b^2*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x^2 + (a*b*c^3*x^3 - a*b*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)) + integrate((3*c^5*x^5 - 3*c^3*x^3 + (3*c^3*x^3 - 2*c*x)*(c*x + 1)*(c*x - 1) + (6*c^4*x^4 - 5*c^2*x^2 + 1)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((b^2*c^5*x^6 - b^2*c^3*x^4)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(b^2*c^6*x^7 - 2*b^2*c^4*x^5 + b^2*c^2*x^3)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^7*x^8 - 3*b^2*c^5*x^6 + 3*b^2*c^3*x^4 - b^2*c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^5*x^6 - a*b*c^3*x^4)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(a*b*c^6*x^7 - 2*a*b*c^4*x^5 + a*b*c^2*x^3)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^7*x^8 - 3*a*b*c^5*x^6 + 3*a*b*c^3*x^4 - a*b*c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
355,0,0,0,0.000000," ","integrate(1/x^2/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{c x + \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(c x + 1\right)} \sqrt{c x - 1} b^{2} c^{2} x^{3} + {\left(b^{2} c^{3} x^{4} - b^{2} c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)} \sqrt{c x - 1} a b c^{2} x^{3} + {\left(a b c^{3} x^{4} - a b c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} + \int \frac{4 \, c^{5} x^{5} - 5 \, c^{3} x^{3} + {\left(4 \, c^{3} x^{3} - 3 \, c x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(4 \, c^{4} x^{4} - 4 \, c^{2} x^{2} + 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} + c x}{{\left({\left(b^{2} c^{5} x^{7} - b^{2} c^{3} x^{5}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{6} x^{8} - 2 \, b^{2} c^{4} x^{6} + b^{2} c^{2} x^{4}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{7} x^{9} - 3 \, b^{2} c^{5} x^{7} + 3 \, b^{2} c^{3} x^{5} - b^{2} c x^{3}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{5} x^{7} - a b c^{3} x^{5}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(a b c^{6} x^{8} - 2 \, a b c^{4} x^{6} + a b c^{2} x^{4}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{7} x^{9} - 3 \, a b c^{5} x^{7} + 3 \, a b c^{3} x^{5} - a b c x^{3}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(((c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x^3 + (b^2*c^3*x^4 - b^2*c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x^3 + (a*b*c^3*x^4 - a*b*c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)) + integrate((4*c^5*x^5 - 5*c^3*x^3 + (4*c^3*x^3 - 3*c*x)*(c*x + 1)*(c*x - 1) + 2*(4*c^4*x^4 - 4*c^2*x^2 + 1)*sqrt(c*x + 1)*sqrt(c*x - 1) + c*x)/(((b^2*c^5*x^7 - b^2*c^3*x^5)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(b^2*c^6*x^8 - 2*b^2*c^4*x^6 + b^2*c^2*x^4)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^7*x^9 - 3*b^2*c^5*x^7 + 3*b^2*c^3*x^5 - b^2*c*x^3)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^5*x^7 - a*b*c^3*x^5)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(a*b*c^6*x^8 - 2*a*b*c^4*x^6 + a*b*c^2*x^4)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^7*x^9 - 3*a*b*c^5*x^7 + 3*a*b*c^3*x^5 - a*b*c*x^3)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
356,0,0,0,0.000000," ","integrate(x^4/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x^{5} + \sqrt{c x + 1} \sqrt{c x - 1} x^{4}}{{\left({\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} - 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{4} x^{3} - a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{5} x^{4} - 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} - \int \frac{5 \, c^{3} x^{6} + 3 \, {\left(c x + 1\right)} {\left(c x - 1\right)} c x^{4} - 5 \, c x^{4} + 4 \, {\left(2 \, c^{2} x^{5} - x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(b^{2} c^{7} x^{6} - 2 \, b^{2} c^{5} x^{4} + b^{2} c^{3} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{8} x^{7} - 3 \, b^{2} c^{6} x^{5} + 3 \, b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{9} x^{8} - 4 \, b^{2} c^{7} x^{6} + 6 \, b^{2} c^{5} x^{4} - 4 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{7} x^{6} - 2 \, a b c^{5} x^{4} + a b c^{3} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(a b c^{8} x^{7} - 3 \, a b c^{6} x^{5} + 3 \, a b c^{4} x^{3} - a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{9} x^{8} - 4 \, a b c^{7} x^{6} + 6 \, a b c^{5} x^{4} - 4 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-(c*x^5 + sqrt(c*x + 1)*sqrt(c*x - 1)*x^4)/(((b^2*c^4*x^3 - b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^4*x^3 - a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) - integrate((5*c^3*x^6 + 3*(c*x + 1)*(c*x - 1)*c*x^4 - 5*c*x^4 + 4*(2*c^2*x^5 - x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((b^2*c^7*x^6 - 2*b^2*c^5*x^4 + b^2*c^3*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(b^2*c^8*x^7 - 3*b^2*c^6*x^5 + 3*b^2*c^4*x^3 - b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^9*x^8 - 4*b^2*c^7*x^6 + 6*b^2*c^5*x^4 - 4*b^2*c^3*x^2 + b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^7*x^6 - 2*a*b*c^5*x^4 + a*b*c^3*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(a*b*c^8*x^7 - 3*a*b*c^6*x^5 + 3*a*b*c^4*x^3 - a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^9*x^8 - 4*a*b*c^7*x^6 + 6*a*b*c^5*x^4 - 4*a*b*c^3*x^2 + a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
357,0,0,0,0.000000," ","integrate(x^3/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x^{4} + \sqrt{c x + 1} \sqrt{c x - 1} x^{3}}{{\left({\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} - 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{4} x^{3} - a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{5} x^{4} - 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} - \int \frac{c^{5} x^{7} + 3 \, c^{3} x^{5} - 4 \, c x^{3} + {\left(c^{3} x^{5} + 2 \, c x^{3}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(2 \, c^{4} x^{6} + 5 \, c^{2} x^{4} - 3 \, x^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(b^{2} c^{7} x^{6} - 2 \, b^{2} c^{5} x^{4} + b^{2} c^{3} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{8} x^{7} - 3 \, b^{2} c^{6} x^{5} + 3 \, b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{9} x^{8} - 4 \, b^{2} c^{7} x^{6} + 6 \, b^{2} c^{5} x^{4} - 4 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{7} x^{6} - 2 \, a b c^{5} x^{4} + a b c^{3} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(a b c^{8} x^{7} - 3 \, a b c^{6} x^{5} + 3 \, a b c^{4} x^{3} - a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{9} x^{8} - 4 \, a b c^{7} x^{6} + 6 \, a b c^{5} x^{4} - 4 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-(c*x^4 + sqrt(c*x + 1)*sqrt(c*x - 1)*x^3)/(((b^2*c^4*x^3 - b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^4*x^3 - a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) - integrate((c^5*x^7 + 3*c^3*x^5 - 4*c*x^3 + (c^3*x^5 + 2*c*x^3)*(c*x + 1)*(c*x - 1) + (2*c^4*x^6 + 5*c^2*x^4 - 3*x^2)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((b^2*c^7*x^6 - 2*b^2*c^5*x^4 + b^2*c^3*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(b^2*c^8*x^7 - 3*b^2*c^6*x^5 + 3*b^2*c^4*x^3 - b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^9*x^8 - 4*b^2*c^7*x^6 + 6*b^2*c^5*x^4 - 4*b^2*c^3*x^2 + b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^7*x^6 - 2*a*b*c^5*x^4 + a*b*c^3*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(a*b*c^8*x^7 - 3*a*b*c^6*x^5 + 3*a*b*c^4*x^3 - a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^9*x^8 - 4*a*b*c^7*x^6 + 6*a*b*c^5*x^4 - 4*a*b*c^3*x^2 + a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
358,0,0,0,0.000000," ","integrate(x^2/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x^{3} + \sqrt{c x + 1} \sqrt{c x - 1} x^{2}}{{\left({\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} - 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{4} x^{3} - a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{5} x^{4} - 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} - \int \frac{2 \, c^{5} x^{6} + c^{3} x^{4} + {\left(2 \, c^{3} x^{4} + c x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - 3 \, c x^{2} + 2 \, {\left(2 \, c^{4} x^{5} + c^{2} x^{3} - x\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(b^{2} c^{7} x^{6} - 2 \, b^{2} c^{5} x^{4} + b^{2} c^{3} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{8} x^{7} - 3 \, b^{2} c^{6} x^{5} + 3 \, b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{9} x^{8} - 4 \, b^{2} c^{7} x^{6} + 6 \, b^{2} c^{5} x^{4} - 4 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{7} x^{6} - 2 \, a b c^{5} x^{4} + a b c^{3} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(a b c^{8} x^{7} - 3 \, a b c^{6} x^{5} + 3 \, a b c^{4} x^{3} - a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{9} x^{8} - 4 \, a b c^{7} x^{6} + 6 \, a b c^{5} x^{4} - 4 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-(c*x^3 + sqrt(c*x + 1)*sqrt(c*x - 1)*x^2)/(((b^2*c^4*x^3 - b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^4*x^3 - a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) - integrate((2*c^5*x^6 + c^3*x^4 + (2*c^3*x^4 + c*x^2)*(c*x + 1)*(c*x - 1) - 3*c*x^2 + 2*(2*c^4*x^5 + c^2*x^3 - x)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((b^2*c^7*x^6 - 2*b^2*c^5*x^4 + b^2*c^3*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(b^2*c^8*x^7 - 3*b^2*c^6*x^5 + 3*b^2*c^4*x^3 - b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^9*x^8 - 4*b^2*c^7*x^6 + 6*b^2*c^5*x^4 - 4*b^2*c^3*x^2 + b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^7*x^6 - 2*a*b*c^5*x^4 + a*b*c^3*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(a*b*c^8*x^7 - 3*a*b*c^6*x^5 + 3*a*b*c^4*x^3 - a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^9*x^8 - 4*a*b*c^7*x^6 + 6*a*b*c^5*x^4 - 4*a*b*c^3*x^2 + a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
359,0,0,0,0.000000," ","integrate(x/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} x}{{\left({\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} - 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{4} x^{3} - a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{5} x^{4} - 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} - \int \frac{3 \, c^{5} x^{5} + 3 \, {\left(c x + 1\right)} {\left(c x - 1\right)} c^{3} x^{3} - c^{3} x^{3} + {\left(6 \, c^{4} x^{4} - c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - 2 \, c x}{{\left({\left(b^{2} c^{7} x^{6} - 2 \, b^{2} c^{5} x^{4} + b^{2} c^{3} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{8} x^{7} - 3 \, b^{2} c^{6} x^{5} + 3 \, b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{9} x^{8} - 4 \, b^{2} c^{7} x^{6} + 6 \, b^{2} c^{5} x^{4} - 4 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{7} x^{6} - 2 \, a b c^{5} x^{4} + a b c^{3} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(a b c^{8} x^{7} - 3 \, a b c^{6} x^{5} + 3 \, a b c^{4} x^{3} - a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{9} x^{8} - 4 \, a b c^{7} x^{6} + 6 \, a b c^{5} x^{4} - 4 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-(c*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*x)/(((b^2*c^4*x^3 - b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^4*x^3 - a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) - integrate((3*c^5*x^5 + 3*(c*x + 1)*(c*x - 1)*c^3*x^3 - c^3*x^3 + (6*c^4*x^4 - c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - 2*c*x)/(((b^2*c^7*x^6 - 2*b^2*c^5*x^4 + b^2*c^3*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(b^2*c^8*x^7 - 3*b^2*c^6*x^5 + 3*b^2*c^4*x^3 - b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^9*x^8 - 4*b^2*c^7*x^6 + 6*b^2*c^5*x^4 - 4*b^2*c^3*x^2 + b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^7*x^6 - 2*a*b*c^5*x^4 + a*b*c^3*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(a*b*c^8*x^7 - 3*a*b*c^6*x^5 + 3*a*b*c^4*x^3 - a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^9*x^8 - 4*a*b*c^7*x^6 + 6*a*b*c^5*x^4 - 4*a*b*c^3*x^2 + a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
360,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x + \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} - 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{4} x^{3} - a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{5} x^{4} - 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} - \int \frac{4 \, c^{4} x^{4} - 3 \, c^{2} x^{2} + {\left(4 \, c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 4 \, {\left(2 \, c^{3} x^{3} - c x\right)} \sqrt{c x + 1} \sqrt{c x - 1} - 1}{{\left({\left(b^{2} c^{6} x^{6} - 2 \, b^{2} c^{4} x^{4} + b^{2} c^{2} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{7} x^{7} - 3 \, b^{2} c^{5} x^{5} + 3 \, b^{2} c^{3} x^{3} - b^{2} c x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{8} x^{8} - 4 \, b^{2} c^{6} x^{6} + 6 \, b^{2} c^{4} x^{4} - 4 \, b^{2} c^{2} x^{2} + b^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{6} x^{6} - 2 \, a b c^{4} x^{4} + a b c^{2} x^{2}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(a b c^{7} x^{7} - 3 \, a b c^{5} x^{5} + 3 \, a b c^{3} x^{3} - a b c x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{8} x^{8} - 4 \, a b c^{6} x^{6} + 6 \, a b c^{4} x^{4} - 4 \, a b c^{2} x^{2} + a b\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(((b^2*c^4*x^3 - b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^4*x^3 - a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) - integrate((4*c^4*x^4 - 3*c^2*x^2 + (4*c^2*x^2 - 1)*(c*x + 1)*(c*x - 1) + 4*(2*c^3*x^3 - c*x)*sqrt(c*x + 1)*sqrt(c*x - 1) - 1)/(((b^2*c^6*x^6 - 2*b^2*c^4*x^4 + b^2*c^2*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(b^2*c^7*x^7 - 3*b^2*c^5*x^5 + 3*b^2*c^3*x^3 - b^2*c*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^8*x^8 - 4*b^2*c^6*x^6 + 6*b^2*c^4*x^4 - 4*b^2*c^2*x^2 + b^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^6*x^6 - 2*a*b*c^4*x^4 + a*b*c^2*x^2)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(a*b*c^7*x^7 - 3*a*b*c^5*x^5 + 3*a*b*c^3*x^3 - a*b*c*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^8*x^8 - 4*a*b*c^6*x^6 + 6*a*b*c^4*x^4 - 4*a*b*c^2*x^2 + a*b)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
361,0,0,0,0.000000," ","integrate(1/x/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x + \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(b^{2} c^{4} x^{4} - b^{2} c^{2} x^{2}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{5} - 2 \, b^{2} c^{3} x^{3} + b^{2} c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{4} x^{4} - a b c^{2} x^{2}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{5} x^{5} - 2 \, a b c^{3} x^{3} + a b c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} - \int \frac{5 \, c^{5} x^{5} - 5 \, c^{3} x^{3} + {\left(5 \, c^{3} x^{3} - 2 \, c x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(10 \, c^{4} x^{4} - 7 \, c^{2} x^{2} + 1\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(b^{2} c^{7} x^{8} - 2 \, b^{2} c^{5} x^{6} + b^{2} c^{3} x^{4}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{8} x^{9} - 3 \, b^{2} c^{6} x^{7} + 3 \, b^{2} c^{4} x^{5} - b^{2} c^{2} x^{3}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{9} x^{10} - 4 \, b^{2} c^{7} x^{8} + 6 \, b^{2} c^{5} x^{6} - 4 \, b^{2} c^{3} x^{4} + b^{2} c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{7} x^{8} - 2 \, a b c^{5} x^{6} + a b c^{3} x^{4}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(a b c^{8} x^{9} - 3 \, a b c^{6} x^{7} + 3 \, a b c^{4} x^{5} - a b c^{2} x^{3}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{9} x^{10} - 4 \, a b c^{7} x^{8} + 6 \, a b c^{5} x^{6} - 4 \, a b c^{3} x^{4} + a b c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(((b^2*c^4*x^4 - b^2*c^2*x^2)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^5 - 2*b^2*c^3*x^3 + b^2*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^4*x^4 - a*b*c^2*x^2)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^5*x^5 - 2*a*b*c^3*x^3 + a*b*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)) - integrate((5*c^5*x^5 - 5*c^3*x^3 + (5*c^3*x^3 - 2*c*x)*(c*x + 1)*(c*x - 1) + (10*c^4*x^4 - 7*c^2*x^2 + 1)*sqrt(c*x + 1)*sqrt(c*x - 1))/(((b^2*c^7*x^8 - 2*b^2*c^5*x^6 + b^2*c^3*x^4)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(b^2*c^8*x^9 - 3*b^2*c^6*x^7 + 3*b^2*c^4*x^5 - b^2*c^2*x^3)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^9*x^10 - 4*b^2*c^7*x^8 + 6*b^2*c^5*x^6 - 4*b^2*c^3*x^4 + b^2*c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^7*x^8 - 2*a*b*c^5*x^6 + a*b*c^3*x^4)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(a*b*c^8*x^9 - 3*a*b*c^6*x^7 + 3*a*b*c^4*x^5 - a*b*c^2*x^3)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^9*x^10 - 4*a*b*c^7*x^8 + 6*a*b*c^5*x^6 - 4*a*b*c^3*x^4 + a*b*c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
362,0,0,0,0.000000," ","integrate(1/x^2/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c x + \sqrt{c x + 1} \sqrt{c x - 1}}{{\left({\left(b^{2} c^{4} x^{5} - b^{2} c^{2} x^{3}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{6} - 2 \, b^{2} c^{3} x^{4} + b^{2} c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{4} x^{5} - a b c^{2} x^{3}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{5} x^{6} - 2 \, a b c^{3} x^{4} + a b c x^{2}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} - \int \frac{6 \, c^{5} x^{5} - 7 \, c^{3} x^{3} + 3 \, {\left(2 \, c^{3} x^{3} - c x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(6 \, c^{4} x^{4} - 5 \, c^{2} x^{2} + 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} + c x}{{\left({\left(b^{2} c^{7} x^{9} - 2 \, b^{2} c^{5} x^{7} + b^{2} c^{3} x^{5}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{8} x^{10} - 3 \, b^{2} c^{6} x^{8} + 3 \, b^{2} c^{4} x^{6} - b^{2} c^{2} x^{4}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{9} x^{11} - 4 \, b^{2} c^{7} x^{9} + 6 \, b^{2} c^{5} x^{7} - 4 \, b^{2} c^{3} x^{5} + b^{2} c x^{3}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{7} x^{9} - 2 \, a b c^{5} x^{7} + a b c^{3} x^{5}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(a b c^{8} x^{10} - 3 \, a b c^{6} x^{8} + 3 \, a b c^{4} x^{6} - a b c^{2} x^{4}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{9} x^{11} - 4 \, a b c^{7} x^{9} + 6 \, a b c^{5} x^{7} - 4 \, a b c^{3} x^{5} + a b c x^{3}\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(((b^2*c^4*x^5 - b^2*c^2*x^3)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^6 - 2*b^2*c^3*x^4 + b^2*c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^4*x^5 - a*b*c^2*x^3)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^5*x^6 - 2*a*b*c^3*x^4 + a*b*c*x^2)*sqrt(c*x + 1))*sqrt(-c*x + 1)) - integrate((6*c^5*x^5 - 7*c^3*x^3 + 3*(2*c^3*x^3 - c*x)*(c*x + 1)*(c*x - 1) + 2*(6*c^4*x^4 - 5*c^2*x^2 + 1)*sqrt(c*x + 1)*sqrt(c*x - 1) + c*x)/(((b^2*c^7*x^9 - 2*b^2*c^5*x^7 + b^2*c^3*x^5)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(b^2*c^8*x^10 - 3*b^2*c^6*x^8 + 3*b^2*c^4*x^6 - b^2*c^2*x^4)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^9*x^11 - 4*b^2*c^7*x^9 + 6*b^2*c^5*x^7 - 4*b^2*c^3*x^5 + b^2*c*x^3)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^7*x^9 - 2*a*b*c^5*x^7 + a*b*c^3*x^5)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(a*b*c^8*x^10 - 3*a*b*c^6*x^8 + 3*a*b*c^4*x^6 - a*b*c^2*x^4)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^9*x^11 - 4*a*b*c^7*x^9 + 6*a*b*c^5*x^7 - 4*a*b*c^3*x^5 + a*b*c*x^3)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
363,0,0,0,0.000000," ","integrate((f*x)^m*(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{{\left({\left(c^{4} f^{m} x^{4} - 2 \, c^{2} f^{m} x^{2} + f^{m}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} x^{m} + {\left(c^{5} f^{m} x^{5} - 2 \, c^{3} f^{m} x^{3} + c f^{m} x\right)} \sqrt{c x + 1} x^{m}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} - \int \frac{{\left({\left(c^{5} f^{m} {\left(m + 4\right)} x^{5} - c^{3} f^{m} {\left(2 \, m + 3\right)} x^{3} + c f^{m} {\left(m - 1\right)} x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} x^{m} + {\left(2 \, c^{6} f^{m} {\left(m + 4\right)} x^{6} - c^{4} f^{m} {\left(5 \, m + 12\right)} x^{4} + 4 \, c^{2} f^{m} {\left(m + 1\right)} x^{2} - f^{m} m\right)} {\left(c x + 1\right)} \sqrt{c x - 1} x^{m} + {\left(c^{7} f^{m} {\left(m + 4\right)} x^{7} - 3 \, c^{5} f^{m} {\left(m + 3\right)} x^{5} + 3 \, c^{3} f^{m} {\left(m + 2\right)} x^{3} - c f^{m} {\left(m + 1\right)} x\right)} \sqrt{c x + 1} x^{m}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{5} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{3} - 2 \, a b c^{3} x^{3} + a b c x + 2 \, {\left(a b c^{4} x^{4} - a b c^{2} x^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{5} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{3} - 2 \, b^{2} c^{3} x^{3} + b^{2} c x + 2 \, {\left(b^{2} c^{4} x^{4} - b^{2} c^{2} x^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"((c^4*f^m*x^4 - 2*c^2*f^m*x^2 + f^m)*(c*x + 1)*sqrt(c*x - 1)*x^m + (c^5*f^m*x^5 - 2*c^3*f^m*x^3 + c*f^m*x)*sqrt(c*x + 1)*x^m)*sqrt(-c*x + 1)/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) - integrate(((c^5*f^m*(m + 4)*x^5 - c^3*f^m*(2*m + 3)*x^3 + c*f^m*(m - 1)*x)*(c*x + 1)^(3/2)*(c*x - 1)*x^m + (2*c^6*f^m*(m + 4)*x^6 - c^4*f^m*(5*m + 12)*x^4 + 4*c^2*f^m*(m + 1)*x^2 - f^m*m)*(c*x + 1)*sqrt(c*x - 1)*x^m + (c^7*f^m*(m + 4)*x^7 - 3*c^5*f^m*(m + 3)*x^5 + 3*c^3*f^m*(m + 2)*x^3 - c*f^m*(m + 1)*x)*sqrt(c*x + 1)*x^m)*sqrt(-c*x + 1)/(a*b*c^5*x^5 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^3 - 2*a*b*c^3*x^3 + a*b*c*x + 2*(a*b*c^4*x^4 - a*b*c^2*x^2)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^5 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^3 - 2*b^2*c^3*x^3 + b^2*c*x + 2*(b^2*c^4*x^4 - b^2*c^2*x^2)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
364,0,0,0,0.000000," ","integrate((f*x)^m*(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(c^{2} f^{m} x^{2} - f^{m}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} x^{m} + {\left(c^{3} f^{m} x^{3} - c f^{m} x\right)} \sqrt{c x + 1} x^{m}\right)} \sqrt{-c x + 1}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{{\left({\left(c^{3} f^{m} {\left(m + 2\right)} x^{3} - c f^{m} {\left(m - 1\right)} x\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} x^{m} + {\left(2 \, c^{4} f^{m} {\left(m + 2\right)} x^{4} - c^{2} f^{m} {\left(3 \, m + 2\right)} x^{2} + f^{m} m\right)} {\left(c x + 1\right)} \sqrt{c x - 1} x^{m} + {\left(c^{5} f^{m} {\left(m + 2\right)} x^{5} - c^{3} f^{m} {\left(2 \, m + 3\right)} x^{3} + c f^{m} {\left(m + 1\right)} x\right)} \sqrt{c x + 1} x^{m}\right)} \sqrt{-c x + 1}}{a b c^{5} x^{5} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{3} - 2 \, a b c^{3} x^{3} + a b c x + 2 \, {\left(a b c^{4} x^{4} - a b c^{2} x^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{5} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{3} - 2 \, b^{2} c^{3} x^{3} + b^{2} c x + 2 \, {\left(b^{2} c^{4} x^{4} - b^{2} c^{2} x^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-((c^2*f^m*x^2 - f^m)*(c*x + 1)*sqrt(c*x - 1)*x^m + (c^3*f^m*x^3 - c*f^m*x)*sqrt(c*x + 1)*x^m)*sqrt(-c*x + 1)/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate(((c^3*f^m*(m + 2)*x^3 - c*f^m*(m - 1)*x)*(c*x + 1)^(3/2)*(c*x - 1)*x^m + (2*c^4*f^m*(m + 2)*x^4 - c^2*f^m*(3*m + 2)*x^2 + f^m*m)*(c*x + 1)*sqrt(c*x - 1)*x^m + (c^5*f^m*(m + 2)*x^5 - c^3*f^m*(2*m + 3)*x^3 + c*f^m*(m + 1)*x)*sqrt(c*x + 1)*x^m)*sqrt(-c*x + 1)/(a*b*c^5*x^5 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^3 - 2*a*b*c^3*x^3 + a*b*c*x + 2*(a*b*c^4*x^4 - a*b*c^2*x^2)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^5 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^3 - 2*b^2*c^3*x^3 + b^2*c*x + 2*(b^2*c^4*x^4 - b^2*c^2*x^2)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
365,0,0,0,0.000000," ","integrate((f*x)^m/(-c^2*x^2+1)^(1/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{2} f^{m} x^{2} - f^{m}\right)} \sqrt{c x + 1} \sqrt{c x - 1} x^{m} + {\left(c^{3} f^{m} x^{3} - c f^{m} x\right)} x^{m}}{{\left({\left(c x + 1\right)} \sqrt{c x - 1} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)} \sqrt{c x - 1} a b c^{2} x + {\left(a b c^{3} x^{2} - a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} + \int \frac{{\left(c^{3} f^{m} m x^{3} - c f^{m} {\left(m - 1\right)} x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} x^{m} + {\left(2 \, c^{4} f^{m} m x^{4} - 3 \, c^{2} f^{m} m x^{2} + f^{m} m\right)} \sqrt{c x + 1} \sqrt{c x - 1} x^{m} + {\left(c^{5} f^{m} m x^{5} - c^{3} f^{m} {\left(2 \, m + 1\right)} x^{3} + c f^{m} {\left(m + 1\right)} x\right)} x^{m}}{{\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} b^{2} c^{3} x^{3} + 2 \, {\left(b^{2} c^{4} x^{4} - b^{2} c^{2} x^{2}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{5} - 2 \, b^{2} c^{3} x^{3} + b^{2} c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} a b c^{3} x^{3} + 2 \, {\left(a b c^{4} x^{4} - a b c^{2} x^{2}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{5} x^{5} - 2 \, a b c^{3} x^{3} + a b c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-((c^2*f^m*x^2 - f^m)*sqrt(c*x + 1)*sqrt(c*x - 1)*x^m + (c^3*f^m*x^3 - c*f^m*x)*x^m)/(((c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x + (b^2*c^3*x^2 - b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x + (a*b*c^3*x^2 - a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) + integrate(((c^3*f^m*m*x^3 - c*f^m*(m - 1)*x)*(c*x + 1)*(c*x - 1)*x^m + (2*c^4*f^m*m*x^4 - 3*c^2*f^m*m*x^2 + f^m*m)*sqrt(c*x + 1)*sqrt(c*x - 1)*x^m + (c^5*f^m*m*x^5 - c^3*f^m*(2*m + 1)*x^3 + c*f^m*(m + 1)*x)*x^m)/(((c*x + 1)^(3/2)*(c*x - 1)*b^2*c^3*x^3 + 2*(b^2*c^4*x^4 - b^2*c^2*x^2)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^5 - 2*b^2*c^3*x^3 + b^2*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)^(3/2)*(c*x - 1)*a*b*c^3*x^3 + 2*(a*b*c^4*x^4 - a*b*c^2*x^2)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^5*x^5 - 2*a*b*c^3*x^3 + a*b*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
366,0,0,0,0.000000," ","integrate((f*x)^m/(-c^2*x^2+1)^(3/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{c f^{m} x x^{m} + \sqrt{c x + 1} \sqrt{c x - 1} f^{m} x^{m}}{{\left({\left(c x + 1\right)} \sqrt{c x - 1} b^{2} c^{2} x + {\left(b^{2} c^{3} x^{2} - b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(c x + 1\right)} \sqrt{c x - 1} a b c^{2} x + {\left(a b c^{3} x^{2} - a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} - \int \frac{{\left(c^{3} f^{m} {\left(m - 2\right)} x^{3} - c f^{m} {\left(m - 1\right)} x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} x^{m} + {\left(2 \, c^{4} f^{m} {\left(m - 2\right)} x^{4} - c^{2} f^{m} {\left(3 \, m - 2\right)} x^{2} + f^{m} m\right)} \sqrt{c x + 1} \sqrt{c x - 1} x^{m} + {\left(c^{5} f^{m} {\left(m - 2\right)} x^{5} - c^{3} f^{m} {\left(2 \, m - 1\right)} x^{3} + c f^{m} {\left(m + 1\right)} x\right)} x^{m}}{{\left({\left(b^{2} c^{5} x^{5} - b^{2} c^{3} x^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{6} x^{6} - 2 \, b^{2} c^{4} x^{4} + b^{2} c^{2} x^{2}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{7} x^{7} - 3 \, b^{2} c^{5} x^{5} + 3 \, b^{2} c^{3} x^{3} - b^{2} c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{5} x^{5} - a b c^{3} x^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(a b c^{6} x^{6} - 2 \, a b c^{4} x^{4} + a b c^{2} x^{2}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{7} x^{7} - 3 \, a b c^{5} x^{5} + 3 \, a b c^{3} x^{3} - a b c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"(c*f^m*x*x^m + sqrt(c*x + 1)*sqrt(c*x - 1)*f^m*x^m)/(((c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x + (b^2*c^3*x^2 - b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x + (a*b*c^3*x^2 - a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) - integrate(((c^3*f^m*(m - 2)*x^3 - c*f^m*(m - 1)*x)*(c*x + 1)*(c*x - 1)*x^m + (2*c^4*f^m*(m - 2)*x^4 - c^2*f^m*(3*m - 2)*x^2 + f^m*m)*sqrt(c*x + 1)*sqrt(c*x - 1)*x^m + (c^5*f^m*(m - 2)*x^5 - c^3*f^m*(2*m - 1)*x^3 + c*f^m*(m + 1)*x)*x^m)/(((b^2*c^5*x^5 - b^2*c^3*x^3)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(b^2*c^6*x^6 - 2*b^2*c^4*x^4 + b^2*c^2*x^2)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^7*x^7 - 3*b^2*c^5*x^5 + 3*b^2*c^3*x^3 - b^2*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^5*x^5 - a*b*c^3*x^3)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(a*b*c^6*x^6 - 2*a*b*c^4*x^4 + a*b*c^2*x^2)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^7*x^7 - 3*a*b*c^5*x^5 + 3*a*b*c^3*x^3 - a*b*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
367,0,0,0,0.000000," ","integrate((f*x)^m/(-c^2*x^2+1)^(5/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c f^{m} x x^{m} + \sqrt{c x + 1} \sqrt{c x - 1} f^{m} x^{m}}{{\left({\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} - 2 \, b^{2} c^{3} x^{2} + b^{2} c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{4} x^{3} - a b c^{2} x\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{5} x^{4} - 2 \, a b c^{3} x^{2} + a b c\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}} + \int \frac{{\left(c^{3} f^{m} {\left(m - 4\right)} x^{3} - c f^{m} {\left(m - 1\right)} x\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} x^{m} + {\left(2 \, c^{4} f^{m} {\left(m - 4\right)} x^{4} - c^{2} f^{m} {\left(3 \, m - 4\right)} x^{2} + f^{m} m\right)} \sqrt{c x + 1} \sqrt{c x - 1} x^{m} + {\left(c^{5} f^{m} {\left(m - 4\right)} x^{5} - c^{3} f^{m} {\left(2 \, m - 3\right)} x^{3} + c f^{m} {\left(m + 1\right)} x\right)} x^{m}}{{\left({\left(b^{2} c^{7} x^{7} - 2 \, b^{2} c^{5} x^{5} + b^{2} c^{3} x^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{8} x^{8} - 3 \, b^{2} c^{6} x^{6} + 3 \, b^{2} c^{4} x^{4} - b^{2} c^{2} x^{2}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(b^{2} c^{9} x^{9} - 4 \, b^{2} c^{7} x^{7} + 6 \, b^{2} c^{5} x^{5} - 4 \, b^{2} c^{3} x^{3} + b^{2} c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left({\left(a b c^{7} x^{7} - 2 \, a b c^{5} x^{5} + a b c^{3} x^{3}\right)} {\left(c x + 1\right)}^{\frac{3}{2}} {\left(c x - 1\right)} + 2 \, {\left(a b c^{8} x^{8} - 3 \, a b c^{6} x^{6} + 3 \, a b c^{4} x^{4} - a b c^{2} x^{2}\right)} {\left(c x + 1\right)} \sqrt{c x - 1} + {\left(a b c^{9} x^{9} - 4 \, a b c^{7} x^{7} + 6 \, a b c^{5} x^{5} - 4 \, a b c^{3} x^{3} + a b c x\right)} \sqrt{c x + 1}\right)} \sqrt{-c x + 1}}\,{d x}"," ",0,"-(c*f^m*x*x^m + sqrt(c*x + 1)*sqrt(c*x - 1)*f^m*x^m)/(((b^2*c^4*x^3 - b^2*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 - 2*b^2*c^3*x^2 + b^2*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^4*x^3 - a*b*c^2*x)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^5*x^4 - 2*a*b*c^3*x^2 + a*b*c)*sqrt(c*x + 1))*sqrt(-c*x + 1)) + integrate(((c^3*f^m*(m - 4)*x^3 - c*f^m*(m - 1)*x)*(c*x + 1)*(c*x - 1)*x^m + (2*c^4*f^m*(m - 4)*x^4 - c^2*f^m*(3*m - 4)*x^2 + f^m*m)*sqrt(c*x + 1)*sqrt(c*x - 1)*x^m + (c^5*f^m*(m - 4)*x^5 - c^3*f^m*(2*m - 3)*x^3 + c*f^m*(m + 1)*x)*x^m)/(((b^2*c^7*x^7 - 2*b^2*c^5*x^5 + b^2*c^3*x^3)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(b^2*c^8*x^8 - 3*b^2*c^6*x^6 + 3*b^2*c^4*x^4 - b^2*c^2*x^2)*(c*x + 1)*sqrt(c*x - 1) + (b^2*c^9*x^9 - 4*b^2*c^7*x^7 + 6*b^2*c^5*x^5 - 4*b^2*c^3*x^3 + b^2*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + ((a*b*c^7*x^7 - 2*a*b*c^5*x^5 + a*b*c^3*x^3)*(c*x + 1)^(3/2)*(c*x - 1) + 2*(a*b*c^8*x^8 - 3*a*b*c^6*x^6 + 3*a*b*c^4*x^4 - a*b*c^2*x^2)*(c*x + 1)*sqrt(c*x - 1) + (a*b*c^9*x^9 - 4*a*b*c^7*x^7 + 6*a*b*c^5*x^5 - 4*a*b*c^3*x^3 + a*b*c*x)*sqrt(c*x + 1))*sqrt(-c*x + 1)), x)","F",0
368,0,0,0,0.000000," ","integrate(1/arccosh(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""maxima"")","-\frac{a^{7} x^{7} - 3 \, a^{5} x^{5} + 3 \, a^{3} x^{3} + {\left(a^{4} x^{4} - a^{2} x^{2}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} + {\left(3 \, a^{5} x^{5} - 5 \, a^{3} x^{3} + 2 \, a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(3 \, a^{6} x^{6} - 7 \, a^{4} x^{4} + 5 \, a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} - a x - {\left(a^{5} x^{5} - 2 \, a^{3} x^{3} - {\left(a^{2} x^{2} - 1\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} - {\left(a^{3} x^{3} - a x\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \sqrt{a x + 1} \sqrt{a x - 1} + a x\right)} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}{2 \, {\left({\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{\frac{3}{2}} a^{4} x^{3} + 3 \, {\left(a^{5} x^{4} - a^{3} x^{2}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)} + 3 \, {\left(a^{6} x^{5} - 2 \, a^{4} x^{3} + a^{2} x\right)} {\left(a x + 1\right)} \sqrt{a x - 1} + {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \sqrt{a x + 1}\right)} \sqrt{-a x + 1} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)^{2}} - \int -\frac{2 \, a^{6} x^{6} - 3 \, a^{4} x^{4} - {\left(2 \, a^{2} x^{2} - 3\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{2} - 4 \, {\left(a^{3} x^{3} - a x\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)}^{\frac{3}{2}} - 4 \, {\left(a^{2} x^{2} - 1\right)} {\left(a x + 1\right)} {\left(a x - 1\right)} + 4 \, {\left(a^{5} x^{5} - 2 \, a^{3} x^{3} + a x\right)} \sqrt{a x + 1} \sqrt{a x - 1} + 1}{2 \, {\left({\left(a x + 1\right)}^{\frac{5}{2}} {\left(a x - 1\right)}^{2} a^{4} x^{4} + 4 \, {\left(a^{5} x^{5} - a^{3} x^{3}\right)} {\left(a x + 1\right)}^{2} {\left(a x - 1\right)}^{\frac{3}{2}} + 6 \, {\left(a^{6} x^{6} - 2 \, a^{4} x^{4} + a^{2} x^{2}\right)} {\left(a x + 1\right)}^{\frac{3}{2}} {\left(a x - 1\right)} + 4 \, {\left(a^{7} x^{7} - 3 \, a^{5} x^{5} + 3 \, a^{3} x^{3} - a x\right)} {\left(a x + 1\right)} \sqrt{a x - 1} + {\left(a^{8} x^{8} - 4 \, a^{6} x^{6} + 6 \, a^{4} x^{4} - 4 \, a^{2} x^{2} + 1\right)} \sqrt{a x + 1}\right)} \sqrt{-a x + 1} \log\left(a x + \sqrt{a x + 1} \sqrt{a x - 1}\right)}\,{d x}"," ",0,"-1/2*(a^7*x^7 - 3*a^5*x^5 + 3*a^3*x^3 + (a^4*x^4 - a^2*x^2)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) + (3*a^5*x^5 - 5*a^3*x^3 + 2*a*x)*(a*x + 1)*(a*x - 1) + (3*a^6*x^6 - 7*a^4*x^4 + 5*a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(a*x - 1) - a*x - (a^5*x^5 - 2*a^3*x^3 - (a^2*x^2 - 1)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) - (a^3*x^3 - a*x)*(a*x + 1)*(a*x - 1) + (a^4*x^4 - 2*a^2*x^2 + 1)*sqrt(a*x + 1)*sqrt(a*x - 1) + a*x)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1)))/(((a*x + 1)^2*(a*x - 1)^(3/2)*a^4*x^3 + 3*(a^5*x^4 - a^3*x^2)*(a*x + 1)^(3/2)*(a*x - 1) + 3*(a^6*x^5 - 2*a^4*x^3 + a^2*x)*(a*x + 1)*sqrt(a*x - 1) + (a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*sqrt(a*x + 1))*sqrt(-a*x + 1)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))^2) - integrate(-1/2*(2*a^6*x^6 - 3*a^4*x^4 - (2*a^2*x^2 - 3)*(a*x + 1)^2*(a*x - 1)^2 - 4*(a^3*x^3 - a*x)*(a*x + 1)^(3/2)*(a*x - 1)^(3/2) - 4*(a^2*x^2 - 1)*(a*x + 1)*(a*x - 1) + 4*(a^5*x^5 - 2*a^3*x^3 + a*x)*sqrt(a*x + 1)*sqrt(a*x - 1) + 1)/(((a*x + 1)^(5/2)*(a*x - 1)^2*a^4*x^4 + 4*(a^5*x^5 - a^3*x^3)*(a*x + 1)^2*(a*x - 1)^(3/2) + 6*(a^6*x^6 - 2*a^4*x^4 + a^2*x^2)*(a*x + 1)^(3/2)*(a*x - 1) + 4*(a^7*x^7 - 3*a^5*x^5 + 3*a^3*x^3 - a*x)*(a*x + 1)*sqrt(a*x - 1) + (a^8*x^8 - 4*a^6*x^6 + 6*a^4*x^4 - 4*a^2*x^2 + 1)*sqrt(a*x + 1))*sqrt(-a*x + 1)*log(a*x + sqrt(a*x + 1)*sqrt(a*x - 1))), x)","F",0
369,0,0,0,0.000000," ","integrate(x^3*(-c^2*d*x^2+d)/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","-\int \frac{{\left(c^{2} d x^{2} - d\right)} x^{3}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((c^2*d*x^2 - d)*x^3/(b*arccosh(c*x) + a)^(3/2), x)","F",0
370,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","-\int \frac{{\left(c^{2} d x^{2} - d\right)} x^{2}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((c^2*d*x^2 - d)*x^2/(b*arccosh(c*x) + a)^(3/2), x)","F",0
371,0,0,0,0.000000," ","integrate(x*(-c^2*d*x^2+d)/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","-\int \frac{{\left(c^{2} d x^{2} - d\right)} x}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((c^2*d*x^2 - d)*x/(b*arccosh(c*x) + a)^(3/2), x)","F",0
372,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","-\int \frac{c^{2} d x^{2} - d}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-integrate((c^2*d*x^2 - d)/(b*arccosh(c*x) + a)^(3/2), x)","F",0
373,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)/x/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","-\int \frac{c^{2} d x^{2} - d}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"-integrate((c^2*d*x^2 - d)/((b*arccosh(c*x) + a)^(3/2)*x), x)","F",0
374,0,0,0,0.000000," ","integrate(x^3*(-c^2*d*x^2+d)^2/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} - d\right)}^{2} x^{3}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c^2*d*x^2 - d)^2*x^3/(b*arccosh(c*x) + a)^(3/2), x)","F",0
375,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^2/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} - d\right)}^{2} x^{2}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c^2*d*x^2 - d)^2*x^2/(b*arccosh(c*x) + a)^(3/2), x)","F",0
376,0,0,0,0.000000," ","integrate(x*(-c^2*d*x^2+d)^2/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} - d\right)}^{2} x}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c^2*d*x^2 - d)^2*x/(b*arccosh(c*x) + a)^(3/2), x)","F",0
377,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^2/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} - d\right)}^{2}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c^2*d*x^2 - d)^2/(b*arccosh(c*x) + a)^(3/2), x)","F",0
378,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^2/x/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(c^{2} d x^{2} - d\right)}^{2}}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate((c^2*d*x^2 - d)^2/((b*arccosh(c*x) + a)^(3/2)*x), x)","F",0
379,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)*arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*sqrt(arccosh(a*x)), x)","F",0
380,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} \sqrt{\operatorname{arcosh}\left(a x\right)}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*sqrt(arccosh(a*x)), x)","F",0
381,0,0,0,0.000000," ","integrate(arccosh(a*x)^(1/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\operatorname{arcosh}\left(a x\right)}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(arccosh(a*x))/sqrt(-a^2*c*x^2 + c), x)","F",0
382,0,0,0,0.000000," ","integrate(arccosh(a*x)^(1/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\operatorname{arcosh}\left(a x\right)}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(arccosh(a*x))/(-a^2*c*x^2 + c)^(3/2), x)","F",0
383,0,0,0,0.000000," ","integrate(arccosh(a*x)^(1/2)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\operatorname{arcosh}\left(a x\right)}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(arccosh(a*x))/(-a^2*c*x^2 + c)^(5/2), x)","F",0
384,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)*arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*arccosh(a*x)^(3/2), x)","F",0
385,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} \operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*arccosh(a*x)^(3/2), x)","F",0
386,0,0,0,0.000000," ","integrate(arccosh(a*x)^(3/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(arccosh(a*x)^(3/2)/sqrt(-a^2*c*x^2 + c), x)","F",0
387,0,0,0,0.000000," ","integrate(arccosh(a*x)^(3/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(arccosh(a*x)^(3/2)/(-a^2*c*x^2 + c)^(3/2), x)","F",0
388,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)*arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int {\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)*arccosh(a*x)^(5/2), x)","F",0
389,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)*arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int \sqrt{-a^{2} c x^{2} + c} \operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)*arccosh(a*x)^(5/2), x)","F",0
390,0,0,0,0.000000," ","integrate(arccosh(a*x)^(5/2)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}}{\sqrt{-a^{2} c x^{2} + c}}\,{d x}"," ",0,"integrate(arccosh(a*x)^(5/2)/sqrt(-a^2*c*x^2 + c), x)","F",0
391,0,0,0,0.000000," ","integrate(arccosh(a*x)^(5/2)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(arccosh(a*x)^(5/2)/(-a^2*c*x^2 + c)^(3/2), x)","F",0
392,0,0,0,0.000000," ","integrate((a^2-x^2)^(3/2)*arccosh(x/a)^(1/2),x, algorithm=""maxima"")","\int {\left(a^{2} - x^{2}\right)}^{\frac{3}{2}} \sqrt{\operatorname{arcosh}\left(\frac{x}{a}\right)}\,{d x}"," ",0,"integrate((a^2 - x^2)^(3/2)*sqrt(arccosh(x/a)), x)","F",0
393,0,0,0,0.000000," ","integrate((a^2-x^2)^(1/2)*arccosh(x/a)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} - x^{2}} \sqrt{\operatorname{arcosh}\left(\frac{x}{a}\right)}\,{d x}"," ",0,"integrate(sqrt(a^2 - x^2)*sqrt(arccosh(x/a)), x)","F",0
394,0,0,0,0.000000," ","integrate(arccosh(x/a)^(1/2)/(a^2-x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\operatorname{arcosh}\left(\frac{x}{a}\right)}}{\sqrt{a^{2} - x^{2}}}\,{d x}"," ",0,"integrate(sqrt(arccosh(x/a))/sqrt(a^2 - x^2), x)","F",0
395,0,0,0,0.000000," ","integrate(arccosh(x/a)^(1/2)/(a^2-x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\operatorname{arcosh}\left(\frac{x}{a}\right)}}{{\left(a^{2} - x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(arccosh(x/a))/(a^2 - x^2)^(3/2), x)","F",0
396,0,0,0,0.000000," ","integrate(arccosh(x/a)^(1/2)/(a^2-x^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\operatorname{arcosh}\left(\frac{x}{a}\right)}}{{\left(a^{2} - x^{2}\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(arccosh(x/a))/(a^2 - x^2)^(5/2), x)","F",0
397,0,0,0,0.000000," ","integrate((a^2-x^2)^(3/2)*arccosh(x/a)^(3/2),x, algorithm=""maxima"")","\int {\left(a^{2} - x^{2}\right)}^{\frac{3}{2}} \operatorname{arcosh}\left(\frac{x}{a}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a^2 - x^2)^(3/2)*arccosh(x/a)^(3/2), x)","F",0
398,0,0,0,0.000000," ","integrate(arccosh(x/a)^(3/2)*(a^2-x^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{a^{2} - x^{2}} \operatorname{arcosh}\left(\frac{x}{a}\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(a^2 - x^2)*arccosh(x/a)^(3/2), x)","F",0
399,0,0,0,0.000000," ","integrate(arccosh(x/a)^(3/2)/(a^2-x^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(\frac{x}{a}\right)^{\frac{3}{2}}}{\sqrt{a^{2} - x^{2}}}\,{d x}"," ",0,"integrate(arccosh(x/a)^(3/2)/sqrt(a^2 - x^2), x)","F",0
400,0,0,0,0.000000," ","integrate(arccosh(x/a)^(3/2)/(a^2-x^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcosh}\left(\frac{x}{a}\right)^{\frac{3}{2}}}{{\left(a^{2} - x^{2}\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(arccosh(x/a)^(3/2)/(a^2 - x^2)^(3/2), x)","F",0
401,0,0,0,0.000000," ","integrate(x/(-x^2+1)^(1/2)/arccosh(x)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{-x^{2} + 1} \sqrt{\operatorname{arcosh}\left(x\right)}}\,{d x}"," ",0,"integrate(x/(sqrt(-x^2 + 1)*sqrt(arccosh(x))), x)","F",0
402,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(5/2)/arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{\sqrt{\operatorname{arcosh}\left(a x\right)}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)/sqrt(arccosh(a*x)), x)","F",0
403,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{\sqrt{\operatorname{arcosh}\left(a x\right)}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)/sqrt(arccosh(a*x)), x)","F",0
404,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{\sqrt{\operatorname{arcosh}\left(a x\right)}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/sqrt(arccosh(a*x)), x)","F",0
405,0,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(1/2)/arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a^{2} c x^{2} + c} \sqrt{\operatorname{arcosh}\left(a x\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-a^2*c*x^2 + c)*sqrt(arccosh(a*x))), x)","F",0
406,0,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \sqrt{\operatorname{arcosh}\left(a x\right)}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(3/2)*sqrt(arccosh(a*x))), x)","F",0
407,0,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(5/2)/arccosh(a*x)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \sqrt{\operatorname{arcosh}\left(a x\right)}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(5/2)*sqrt(arccosh(a*x))), x)","F",0
408,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(5/2)/arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}}}{\operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(5/2)/arccosh(a*x)^(3/2), x)","F",0
409,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{\operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)/arccosh(a*x)^(3/2), x)","F",0
410,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{\operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/arccosh(a*x)^(3/2), x)","F",0
411,0,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(1/2)/arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a^{2} c x^{2} + c} \operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-a^2*c*x^2 + c)*arccosh(a*x)^(3/2)), x)","F",0
412,0,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(3/2)*arccosh(a*x)^(3/2)), x)","F",0
413,0,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(5/2)/arccosh(a*x)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \operatorname{arcosh}\left(a x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(5/2)*arccosh(a*x)^(3/2)), x)","F",0
414,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}}}{\operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-a^2*c*x^2 + c)^(3/2)/arccosh(a*x)^(5/2), x)","F",0
415,0,0,0,0.000000," ","integrate((-a^2*c*x^2+c)^(1/2)/arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-a^{2} c x^{2} + c}}{\operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a^2*c*x^2 + c)/arccosh(a*x)^(5/2), x)","F",0
416,0,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(1/2)/arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a^{2} c x^{2} + c} \operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-a^2*c*x^2 + c)*arccosh(a*x)^(5/2)), x)","F",0
417,0,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(3/2)/arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{3}{2}} \operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(3/2)*arccosh(a*x)^(5/2)), x)","F",0
418,0,0,0,0.000000," ","integrate(1/(-a^2*c*x^2+c)^(5/2)/arccosh(a*x)^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(-a^{2} c x^{2} + c\right)}^{\frac{5}{2}} \operatorname{arcosh}\left(a x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((-a^2*c*x^2 + c)^(5/2)*arccosh(a*x)^(5/2)), x)","F",0
419,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))^n*(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-c^{2} d x^{2} + d} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n} x^{2}\,{d x}"," ",0,"integrate(sqrt(-c^2*d*x^2 + d)*(b*arccosh(c*x) + a)^n*x^2, x)","F",0
420,0,0,0,0.000000," ","integrate(x*(a+b*arccosh(c*x))^n*(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-c^{2} d x^{2} + d} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n} x\,{d x}"," ",0,"integrate(sqrt(-c^2*d*x^2 + d)*(b*arccosh(c*x) + a)^n*x, x)","F",0
421,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^n*(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \sqrt{-c^{2} d x^{2} + d} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}\,{d x}"," ",0,"integrate(sqrt(-c^2*d*x^2 + d)*(b*arccosh(c*x) + a)^n, x)","F",0
422,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^n*(-c^2*d*x^2+d)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{x}\,{d x}"," ",0,"integrate(sqrt(-c^2*d*x^2 + d)*(b*arccosh(c*x) + a)^n/x, x)","F",0
423,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^n*(-c^2*d*x^2+d)^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-c^{2} d x^{2} + d} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(-c^2*d*x^2 + d)*(b*arccosh(c*x) + a)^n/x^2, x)","F",0
424,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n} x^{2}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(3/2)*(b*arccosh(c*x) + a)^n*x^2, x)","F",0
425,0,0,0,0.000000," ","integrate(x*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n} x\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(3/2)*(b*arccosh(c*x) + a)^n*x, x)","F",0
426,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(3/2)*(b*arccosh(c*x) + a)^n, x)","F",0
427,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n/x,x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{x}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(3/2)*(b*arccosh(c*x) + a)^n/x, x)","F",0
428,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n/x^2,x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{x^{2}}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(3/2)*(b*arccosh(c*x) + a)^n/x^2, x)","F",0
429,0,0,0,0.000000," ","integrate(x^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^n,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n} x^{2}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(5/2)*(b*arccosh(c*x) + a)^n*x^2, x)","F",0
430,0,0,0,0.000000," ","integrate(x*(-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^n,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n} x\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(5/2)*(b*arccosh(c*x) + a)^n*x, x)","F",0
431,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^n,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(5/2)*(b*arccosh(c*x) + a)^n, x)","F",0
432,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^n/x,x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{x}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(5/2)*(b*arccosh(c*x) + a)^n/x, x)","F",0
433,0,0,0,0.000000," ","integrate((-c^2*d*x^2+d)^(5/2)*(a+b*arccosh(c*x))^n/x^2,x, algorithm=""maxima"")","\int \frac{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{x^{2}}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(5/2)*(b*arccosh(c*x) + a)^n/x^2, x)","F",0
434,0,0,0,0.000000," ","integrate(x^3*(a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n} x^{3}}{\sqrt{-c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n*x^3/sqrt(-c^2*x^2 + 1), x)","F",0
435,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n} x^{2}}{\sqrt{-c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n*x^2/sqrt(-c^2*x^2 + 1), x)","F",0
436,0,0,0,0.000000," ","integrate(x*(a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n} x}{\sqrt{-c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n*x/sqrt(-c^2*x^2 + 1), x)","F",0
437,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{\sqrt{-c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n/sqrt(-c^2*x^2 + 1), x)","F",0
438,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^n/x/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{\sqrt{-c^{2} x^{2} + 1} x}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n/(sqrt(-c^2*x^2 + 1)*x), x)","F",0
439,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^n/x^2/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{\sqrt{-c^{2} x^{2} + 1} x^{2}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n/(sqrt(-c^2*x^2 + 1)*x^2), x)","F",0
440,0,0,0,0.000000," ","integrate(x^3*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n} x^{3}}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n*x^3/sqrt(-c^2*d*x^2 + d), x)","F",0
441,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n} x^{2}}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n*x^2/sqrt(-c^2*d*x^2 + d), x)","F",0
442,0,0,0,0.000000," ","integrate(x*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n} x}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n*x/sqrt(-c^2*d*x^2 + d), x)","F",0
443,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n/sqrt(-c^2*d*x^2 + d), x)","F",0
444,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^n/x/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{\sqrt{-c^{2} d x^{2} + d} x}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n/(sqrt(-c^2*d*x^2 + d)*x), x)","F",0
445,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^n/x^2/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{\sqrt{-c^{2} d x^{2} + d} x^{2}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n/(sqrt(-c^2*d*x^2 + d)*x^2), x)","F",0
446,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n} x^{2}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n*x^2/(-c^2*d*x^2 + d)^(3/2), x)","F",0
447,0,0,0,0.000000," ","integrate(x*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n} x}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n*x/(-c^2*d*x^2 + d)^(3/2), x)","F",0
448,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n/(-c^2*d*x^2 + d)^(3/2), x)","F",0
449,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^n/x/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n/((-c^2*d*x^2 + d)^(3/2)*x), x)","F",0
450,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^n/x^2/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^n/((-c^2*d*x^2 + d)^(3/2)*x^2), x)","F",0
451,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))^n/(-c^2*x^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(f x\right)^{m} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{\sqrt{-c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate((f*x)^m*(b*arccosh(c*x) + a)^n/sqrt(-c^2*x^2 + 1), x)","F",0
452,0,0,0,0.000000," ","integrate((f*x)^m*(-c^2*d*x^2+d)^2*(a+b*arccosh(c*x))^n,x, algorithm=""maxima"")","\int {\left(c^{2} d x^{2} - d\right)}^{2} \left(f x\right)^{m} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((c^2*d*x^2 - d)^2*(f*x)^m*(b*arccosh(c*x) + a)^n, x)","F",0
453,0,0,0,0.000000," ","integrate((f*x)^m*(-c^2*d*x^2+d)*(a+b*arccosh(c*x))^n,x, algorithm=""maxima"")","-\int {\left(c^{2} d x^{2} - d\right)} \left(f x\right)^{m} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}\,{d x}"," ",0,"-integrate((c^2*d*x^2 - d)*(f*x)^m*(b*arccosh(c*x) + a)^n, x)","F",0
454,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))^n,x, algorithm=""maxima"")","\int \left(f x\right)^{m} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((f*x)^m*(b*arccosh(c*x) + a)^n, x)","F",0
455,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d),x, algorithm=""maxima"")","-\int \frac{\left(f x\right)^{m} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{c^{2} d x^{2} - d}\,{d x}"," ",0,"-integrate((f*x)^m*(b*arccosh(c*x) + a)^n/(c^2*d*x^2 - d), x)","F",0
456,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^2,x, algorithm=""maxima"")","\int \frac{\left(f x\right)^{m} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{{\left(c^{2} d x^{2} - d\right)}^{2}}\,{d x}"," ",0,"integrate((f*x)^m*(b*arccosh(c*x) + a)^n/(c^2*d*x^2 - d)^2, x)","F",0
457,0,0,0,0.000000," ","integrate((f*x)^m*(-c^2*d*x^2+d)^(3/2)*(a+b*arccosh(c*x))^n,x, algorithm=""maxima"")","\int {\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} \left(f x\right)^{m} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((-c^2*d*x^2 + d)^(3/2)*(f*x)^m*(b*arccosh(c*x) + a)^n, x)","F",0
458,0,0,0,0.000000," ","integrate((f*x)^m*(-c^2*d*x^2+d)^(1/2)*(a+b*arccosh(c*x))^n,x, algorithm=""maxima"")","\int \sqrt{-c^{2} d x^{2} + d} \left(f x\right)^{m} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}\,{d x}"," ",0,"integrate(sqrt(-c^2*d*x^2 + d)*(f*x)^m*(b*arccosh(c*x) + a)^n, x)","F",0
459,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{\left(f x\right)^{m} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{\sqrt{-c^{2} d x^{2} + d}}\,{d x}"," ",0,"integrate((f*x)^m*(b*arccosh(c*x) + a)^n/sqrt(-c^2*d*x^2 + d), x)","F",0
460,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))^n/(-c^2*d*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{\left(f x\right)^{m} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{n}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((f*x)^m*(b*arccosh(c*x) + a)^n/(-c^2*d*x^2 + d)^(3/2), x)","F",0
461,1,178,0,0.451483," ","integrate(x^4*(e*x^2+d)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a e x^{7} + \frac{1}{5} \, a d x^{5} + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b d + \frac{1}{245} \, {\left(35 \, x^{7} \operatorname{arcosh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{c^{2} x^{2} - 1}}{c^{8}}\right)} c\right)} b e"," ",0,"1/7*a*e*x^7 + 1/5*a*d*x^5 + 1/75*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*d + 1/245*(35*x^7*arccosh(c*x) - (5*sqrt(c^2*x^2 - 1)*x^6/c^2 + 6*sqrt(c^2*x^2 - 1)*x^4/c^4 + 8*sqrt(c^2*x^2 - 1)*x^2/c^6 + 16*sqrt(c^2*x^2 - 1)/c^8)*c)*b*e","A",0
462,1,196,0,0.362702," ","integrate(x^3*(e*x^2+d)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a e x^{6} + \frac{1}{4} \, a d x^{4} + \frac{1}{32} \, {\left(8 \, x^{4} \operatorname{arcosh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{c^{2} x^{2} - 1} x}{c^{4}} + \frac{3 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{5}}\right)} c\right)} b d + \frac{1}{288} \, {\left(48 \, x^{6} \operatorname{arcosh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} - 1} x}{c^{6}} + \frac{15 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{7}}\right)} c\right)} b e"," ",0,"1/6*a*e*x^6 + 1/4*a*d*x^4 + 1/32*(8*x^4*arccosh(c*x) - (2*sqrt(c^2*x^2 - 1)*x^3/c^2 + 3*sqrt(c^2*x^2 - 1)*x/c^4 + 3*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5)*c)*b*d + 1/288*(48*x^6*arccosh(c*x) - (8*sqrt(c^2*x^2 - 1)*x^5/c^2 + 10*sqrt(c^2*x^2 - 1)*x^3/c^4 + 15*sqrt(c^2*x^2 - 1)*x/c^6 + 15*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^7)*c)*b*e","A",0
463,1,139,0,0.379861," ","integrate(x^2*(e*x^2+d)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e x^{5} + \frac{1}{3} \, a d x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b d + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b e"," ",0,"1/5*a*e*x^5 + 1/3*a*d*x^3 + 1/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*d + 1/75*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*e","A",0
464,1,156,0,0.462891," ","integrate(x*(e*x^2+d)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a e x^{4} + \frac{1}{2} \, a d x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x}{c^{2}} + \frac{\log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{3}}\right)}\right)} b d + \frac{1}{32} \, {\left(8 \, x^{4} \operatorname{arcosh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{c^{2} x^{2} - 1} x}{c^{4}} + \frac{3 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{5}}\right)} c\right)} b e"," ",0,"1/4*a*e*x^4 + 1/2*a*d*x^2 + 1/4*(2*x^2*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x/c^2 + log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3))*b*d + 1/32*(8*x^4*arccosh(c*x) - (2*sqrt(c^2*x^2 - 1)*x^3/c^2 + 3*sqrt(c^2*x^2 - 1)*x/c^4 + 3*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5)*c)*b*e","A",0
465,1,91,0,0.387561," ","integrate((e*x^2+d)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a e x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b e + a d x + \frac{{\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b d}{c}"," ",0,"1/3*a*e*x^3 + 1/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*e + a*d*x + (c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*d/c","A",0
466,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arccosh(c*x))/x,x, algorithm=""maxima"")","\frac{1}{2} \, a e x^{2} + a d \log\left(x\right) + \int b e x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + \frac{b d \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"1/2*a*e*x^2 + a*d*log(x) + integrate(b*e*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + b*d*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
467,1,63,0,0.493468," ","integrate((e*x^2+d)*(a+b*arccosh(c*x))/x^2,x, algorithm=""maxima"")","-{\left(c \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arcosh}\left(c x\right)}{x}\right)} b d + a e x + \frac{{\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b e}{c} - \frac{a d}{x}"," ",0,"-(c*arcsin(1/(c*abs(x))) + arccosh(c*x)/x)*b*d + a*e*x + (c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*e/c - a*d/x","A",0
468,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arccosh(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, b d {\left(\frac{\sqrt{c^{2} x^{2} - 1} c}{x} - \frac{\operatorname{arcosh}\left(c x\right)}{x^{2}}\right)} + b e \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x} + a e \log\left(x\right) - \frac{a d}{2 \, x^{2}}"," ",0,"1/2*b*d*(sqrt(c^2*x^2 - 1)*c/x - arccosh(c*x)/x^2) + b*e*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x) + a*e*log(x) - 1/2*a*d/x^2","F",0
469,1,85,0,0.472572," ","integrate((e*x^2+d)*(a+b*arccosh(c*x))/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(c^{2} \arcsin\left(\frac{1}{c {\left| x \right|}}\right) - \frac{\sqrt{c^{2} x^{2} - 1}}{x^{2}}\right)} c + \frac{2 \, \operatorname{arcosh}\left(c x\right)}{x^{3}}\right)} b d - {\left(c \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arcosh}\left(c x\right)}{x}\right)} b e - \frac{a e}{x} - \frac{a d}{3 \, x^{3}}"," ",0,"-1/6*((c^2*arcsin(1/(c*abs(x))) - sqrt(c^2*x^2 - 1)/x^2)*c + 2*arccosh(c*x)/x^3)*b*d - (c*arcsin(1/(c*abs(x))) + arccosh(c*x)/x)*b*e - a*e/x - 1/3*a*d/x^3","A",0
470,1,305,0,0.342465," ","integrate(x^4*(e*x^2+d)^2*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{9} \, a e^{2} x^{9} + \frac{2}{7} \, a d e x^{7} + \frac{1}{5} \, a d^{2} x^{5} + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b d^{2} + \frac{2}{245} \, {\left(35 \, x^{7} \operatorname{arcosh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{c^{2} x^{2} - 1}}{c^{8}}\right)} c\right)} b d e + \frac{1}{2835} \, {\left(315 \, x^{9} \operatorname{arcosh}\left(c x\right) - {\left(\frac{35 \, \sqrt{c^{2} x^{2} - 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} - 1}}{c^{10}}\right)} c\right)} b e^{2}"," ",0,"1/9*a*e^2*x^9 + 2/7*a*d*e*x^7 + 1/5*a*d^2*x^5 + 1/75*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*d^2 + 2/245*(35*x^7*arccosh(c*x) - (5*sqrt(c^2*x^2 - 1)*x^6/c^2 + 6*sqrt(c^2*x^2 - 1)*x^4/c^4 + 8*sqrt(c^2*x^2 - 1)*x^2/c^6 + 16*sqrt(c^2*x^2 - 1)/c^8)*c)*b*d*e + 1/2835*(315*x^9*arccosh(c*x) - (35*sqrt(c^2*x^2 - 1)*x^8/c^2 + 40*sqrt(c^2*x^2 - 1)*x^6/c^4 + 48*sqrt(c^2*x^2 - 1)*x^4/c^6 + 64*sqrt(c^2*x^2 - 1)*x^2/c^8 + 128*sqrt(c^2*x^2 - 1)/c^10)*c)*b*e^2","A",0
471,1,332,0,0.331784," ","integrate(x^3*(e*x^2+d)^2*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, a e^{2} x^{8} + \frac{1}{3} \, a d e x^{6} + \frac{1}{4} \, a d^{2} x^{4} + \frac{1}{32} \, {\left(8 \, x^{4} \operatorname{arcosh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{c^{2} x^{2} - 1} x}{c^{4}} + \frac{3 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{5}}\right)} c\right)} b d^{2} + \frac{1}{144} \, {\left(48 \, x^{6} \operatorname{arcosh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} - 1} x}{c^{6}} + \frac{15 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{7}}\right)} c\right)} b d e + \frac{1}{3072} \, {\left(384 \, x^{8} \operatorname{arcosh}\left(c x\right) - {\left(\frac{48 \, \sqrt{c^{2} x^{2} - 1} x^{7}}{c^{2}} + \frac{56 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{6}} + \frac{105 \, \sqrt{c^{2} x^{2} - 1} x}{c^{8}} + \frac{105 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{9}}\right)} c\right)} b e^{2}"," ",0,"1/8*a*e^2*x^8 + 1/3*a*d*e*x^6 + 1/4*a*d^2*x^4 + 1/32*(8*x^4*arccosh(c*x) - (2*sqrt(c^2*x^2 - 1)*x^3/c^2 + 3*sqrt(c^2*x^2 - 1)*x/c^4 + 3*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5)*c)*b*d^2 + 1/144*(48*x^6*arccosh(c*x) - (8*sqrt(c^2*x^2 - 1)*x^5/c^2 + 10*sqrt(c^2*x^2 - 1)*x^3/c^4 + 15*sqrt(c^2*x^2 - 1)*x/c^6 + 15*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^7)*c)*b*d*e + 1/3072*(384*x^8*arccosh(c*x) - (48*sqrt(c^2*x^2 - 1)*x^7/c^2 + 56*sqrt(c^2*x^2 - 1)*x^5/c^4 + 70*sqrt(c^2*x^2 - 1)*x^3/c^6 + 105*sqrt(c^2*x^2 - 1)*x/c^8 + 105*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^9)*c)*b*e^2","A",0
472,1,247,0,0.355424," ","integrate(x^2*(e*x^2+d)^2*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a e^{2} x^{7} + \frac{2}{5} \, a d e x^{5} + \frac{1}{3} \, a d^{2} x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b d^{2} + \frac{2}{75} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b d e + \frac{1}{245} \, {\left(35 \, x^{7} \operatorname{arcosh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{c^{2} x^{2} - 1}}{c^{8}}\right)} c\right)} b e^{2}"," ",0,"1/7*a*e^2*x^7 + 2/5*a*d*e*x^5 + 1/3*a*d^2*x^3 + 1/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*d^2 + 2/75*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*d*e + 1/245*(35*x^7*arccosh(c*x) - (5*sqrt(c^2*x^2 - 1)*x^6/c^2 + 6*sqrt(c^2*x^2 - 1)*x^4/c^4 + 8*sqrt(c^2*x^2 - 1)*x^2/c^6 + 16*sqrt(c^2*x^2 - 1)/c^8)*c)*b*e^2","A",0
473,1,273,0,0.983181," ","integrate(x*(e*x^2+d)^2*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a e^{2} x^{6} + \frac{1}{2} \, a d e x^{4} + \frac{1}{2} \, a d^{2} x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x}{c^{2}} + \frac{\log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{3}}\right)}\right)} b d^{2} + \frac{1}{16} \, {\left(8 \, x^{4} \operatorname{arcosh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{c^{2} x^{2} - 1} x}{c^{4}} + \frac{3 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{5}}\right)} c\right)} b d e + \frac{1}{288} \, {\left(48 \, x^{6} \operatorname{arcosh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} - 1} x}{c^{6}} + \frac{15 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{7}}\right)} c\right)} b e^{2}"," ",0,"1/6*a*e^2*x^6 + 1/2*a*d*e*x^4 + 1/2*a*d^2*x^2 + 1/4*(2*x^2*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x/c^2 + log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3))*b*d^2 + 1/16*(8*x^4*arccosh(c*x) - (2*sqrt(c^2*x^2 - 1)*x^3/c^2 + 3*sqrt(c^2*x^2 - 1)*x/c^4 + 3*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5)*c)*b*d*e + 1/288*(48*x^6*arccosh(c*x) - (8*sqrt(c^2*x^2 - 1)*x^5/c^2 + 10*sqrt(c^2*x^2 - 1)*x^3/c^4 + 15*sqrt(c^2*x^2 - 1)*x/c^6 + 15*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^7)*c)*b*e^2","A",0
474,1,180,0,0.465175," ","integrate((e*x^2+d)^2*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e^{2} x^{5} + \frac{2}{3} \, a d e x^{3} + \frac{2}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b d e + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b e^{2} + a d^{2} x + \frac{{\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b d^{2}}{c}"," ",0,"1/5*a*e^2*x^5 + 2/3*a*d*e*x^3 + 2/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*d*e + 1/75*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*e^2 + a*d^2*x + (c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*d^2/c","A",0
475,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arccosh(c*x))/x,x, algorithm=""maxima"")","\frac{1}{4} \, a e^{2} x^{4} + a d e x^{2} + a d^{2} \log\left(x\right) + \int b e^{2} x^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 2 \, b d e x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + \frac{b d^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"1/4*a*e^2*x^4 + a*d*e*x^2 + a*d^2*log(x) + integrate(b*e^2*x^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 2*b*d*e*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + b*d^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
476,1,134,0,0.770458," ","integrate((e*x^2+d)^2*(a+b*arccosh(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{3} \, a e^{2} x^{3} - {\left(c \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arcosh}\left(c x\right)}{x}\right)} b d^{2} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b e^{2} + 2 \, a d e x + \frac{2 \, {\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b d e}{c} - \frac{a d^{2}}{x}"," ",0,"1/3*a*e^2*x^3 - (c*arcsin(1/(c*abs(x))) + arccosh(c*x)/x)*b*d^2 + 1/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*e^2 + 2*a*d*e*x + 2*(c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*d*e/c - a*d^2/x","A",0
477,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arccosh(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, a e^{2} x^{2} + \frac{1}{2} \, b d^{2} {\left(\frac{\sqrt{c^{2} x^{2} - 1} c}{x} - \frac{\operatorname{arcosh}\left(c x\right)}{x^{2}}\right)} + 2 \, a d e \log\left(x\right) - \frac{a d^{2}}{2 \, x^{2}} + \int b e^{2} x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + \frac{2 \, b d e \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"1/2*a*e^2*x^2 + 1/2*b*d^2*(sqrt(c^2*x^2 - 1)*c/x - arccosh(c*x)/x^2) + 2*a*d*e*log(x) - 1/2*a*d^2/x^2 + integrate(b*e^2*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 2*b*d*e*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
478,1,126,0,0.547401," ","integrate((e*x^2+d)^2*(a+b*arccosh(c*x))/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(c^{2} \arcsin\left(\frac{1}{c {\left| x \right|}}\right) - \frac{\sqrt{c^{2} x^{2} - 1}}{x^{2}}\right)} c + \frac{2 \, \operatorname{arcosh}\left(c x\right)}{x^{3}}\right)} b d^{2} - 2 \, {\left(c \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arcosh}\left(c x\right)}{x}\right)} b d e + a e^{2} x + \frac{{\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b e^{2}}{c} - \frac{2 \, a d e}{x} - \frac{a d^{2}}{3 \, x^{3}}"," ",0,"-1/6*((c^2*arcsin(1/(c*abs(x))) - sqrt(c^2*x^2 - 1)/x^2)*c + 2*arccosh(c*x)/x^3)*b*d^2 - 2*(c*arcsin(1/(c*abs(x))) + arccosh(c*x)/x)*b*d*e + a*e^2*x + (c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*e^2/c - 2*a*d*e/x - 1/3*a*d^2/x^3","A",0
479,1,451,0,0.530871," ","integrate(x^4*(e*x^2+d)^3*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{11} \, a e^{3} x^{11} + \frac{1}{3} \, a d e^{2} x^{9} + \frac{3}{7} \, a d^{2} e x^{7} + \frac{1}{5} \, a d^{3} x^{5} + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b d^{3} + \frac{3}{245} \, {\left(35 \, x^{7} \operatorname{arcosh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{c^{2} x^{2} - 1}}{c^{8}}\right)} c\right)} b d^{2} e + \frac{1}{945} \, {\left(315 \, x^{9} \operatorname{arcosh}\left(c x\right) - {\left(\frac{35 \, \sqrt{c^{2} x^{2} - 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} - 1}}{c^{10}}\right)} c\right)} b d e^{2} + \frac{1}{7623} \, {\left(693 \, x^{11} \operatorname{arcosh}\left(c x\right) - {\left(\frac{63 \, \sqrt{c^{2} x^{2} - 1} x^{10}}{c^{2}} + \frac{70 \, \sqrt{c^{2} x^{2} - 1} x^{8}}{c^{4}} + \frac{80 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{6}} + \frac{96 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{10}} + \frac{256 \, \sqrt{c^{2} x^{2} - 1}}{c^{12}}\right)} c\right)} b e^{3}"," ",0,"1/11*a*e^3*x^11 + 1/3*a*d*e^2*x^9 + 3/7*a*d^2*e*x^7 + 1/5*a*d^3*x^5 + 1/75*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*d^3 + 3/245*(35*x^7*arccosh(c*x) - (5*sqrt(c^2*x^2 - 1)*x^6/c^2 + 6*sqrt(c^2*x^2 - 1)*x^4/c^4 + 8*sqrt(c^2*x^2 - 1)*x^2/c^6 + 16*sqrt(c^2*x^2 - 1)/c^8)*c)*b*d^2*e + 1/945*(315*x^9*arccosh(c*x) - (35*sqrt(c^2*x^2 - 1)*x^8/c^2 + 40*sqrt(c^2*x^2 - 1)*x^6/c^4 + 48*sqrt(c^2*x^2 - 1)*x^4/c^6 + 64*sqrt(c^2*x^2 - 1)*x^2/c^8 + 128*sqrt(c^2*x^2 - 1)/c^10)*c)*b*d*e^2 + 1/7623*(693*x^11*arccosh(c*x) - (63*sqrt(c^2*x^2 - 1)*x^10/c^2 + 70*sqrt(c^2*x^2 - 1)*x^8/c^4 + 80*sqrt(c^2*x^2 - 1)*x^6/c^6 + 96*sqrt(c^2*x^2 - 1)*x^4/c^8 + 128*sqrt(c^2*x^2 - 1)*x^2/c^10 + 256*sqrt(c^2*x^2 - 1)/c^12)*c)*b*e^3","A",0
480,1,487,0,0.402448," ","integrate(x^3*(e*x^2+d)^3*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{10} \, a e^{3} x^{10} + \frac{3}{8} \, a d e^{2} x^{8} + \frac{1}{2} \, a d^{2} e x^{6} + \frac{1}{4} \, a d^{3} x^{4} + \frac{1}{32} \, {\left(8 \, x^{4} \operatorname{arcosh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{c^{2} x^{2} - 1} x}{c^{4}} + \frac{3 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{5}}\right)} c\right)} b d^{3} + \frac{1}{96} \, {\left(48 \, x^{6} \operatorname{arcosh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} - 1} x}{c^{6}} + \frac{15 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{7}}\right)} c\right)} b d^{2} e + \frac{1}{1024} \, {\left(384 \, x^{8} \operatorname{arcosh}\left(c x\right) - {\left(\frac{48 \, \sqrt{c^{2} x^{2} - 1} x^{7}}{c^{2}} + \frac{56 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{6}} + \frac{105 \, \sqrt{c^{2} x^{2} - 1} x}{c^{8}} + \frac{105 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{9}}\right)} c\right)} b d e^{2} + \frac{1}{12800} \, {\left(1280 \, x^{10} \operatorname{arcosh}\left(c x\right) - {\left(\frac{128 \, \sqrt{c^{2} x^{2} - 1} x^{9}}{c^{2}} + \frac{144 \, \sqrt{c^{2} x^{2} - 1} x^{7}}{c^{4}} + \frac{168 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{6}} + \frac{210 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{8}} + \frac{315 \, \sqrt{c^{2} x^{2} - 1} x}{c^{10}} + \frac{315 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{11}}\right)} c\right)} b e^{3}"," ",0,"1/10*a*e^3*x^10 + 3/8*a*d*e^2*x^8 + 1/2*a*d^2*e*x^6 + 1/4*a*d^3*x^4 + 1/32*(8*x^4*arccosh(c*x) - (2*sqrt(c^2*x^2 - 1)*x^3/c^2 + 3*sqrt(c^2*x^2 - 1)*x/c^4 + 3*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5)*c)*b*d^3 + 1/96*(48*x^6*arccosh(c*x) - (8*sqrt(c^2*x^2 - 1)*x^5/c^2 + 10*sqrt(c^2*x^2 - 1)*x^3/c^4 + 15*sqrt(c^2*x^2 - 1)*x/c^6 + 15*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^7)*c)*b*d^2*e + 1/1024*(384*x^8*arccosh(c*x) - (48*sqrt(c^2*x^2 - 1)*x^7/c^2 + 56*sqrt(c^2*x^2 - 1)*x^5/c^4 + 70*sqrt(c^2*x^2 - 1)*x^3/c^6 + 105*sqrt(c^2*x^2 - 1)*x/c^8 + 105*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^9)*c)*b*d*e^2 + 1/12800*(1280*x^10*arccosh(c*x) - (128*sqrt(c^2*x^2 - 1)*x^9/c^2 + 144*sqrt(c^2*x^2 - 1)*x^7/c^4 + 168*sqrt(c^2*x^2 - 1)*x^5/c^6 + 210*sqrt(c^2*x^2 - 1)*x^3/c^8 + 315*sqrt(c^2*x^2 - 1)*x/c^10 + 315*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^11)*c)*b*e^3","A",0
481,1,374,0,0.369663," ","integrate(x^2*(e*x^2+d)^3*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{9} \, a e^{3} x^{9} + \frac{3}{7} \, a d e^{2} x^{7} + \frac{3}{5} \, a d^{2} e x^{5} + \frac{1}{3} \, a d^{3} x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b d^{3} + \frac{1}{25} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b d^{2} e + \frac{3}{245} \, {\left(35 \, x^{7} \operatorname{arcosh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{c^{2} x^{2} - 1}}{c^{8}}\right)} c\right)} b d e^{2} + \frac{1}{2835} \, {\left(315 \, x^{9} \operatorname{arcosh}\left(c x\right) - {\left(\frac{35 \, \sqrt{c^{2} x^{2} - 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} - 1}}{c^{10}}\right)} c\right)} b e^{3}"," ",0,"1/9*a*e^3*x^9 + 3/7*a*d*e^2*x^7 + 3/5*a*d^2*e*x^5 + 1/3*a*d^3*x^3 + 1/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*d^3 + 1/25*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*d^2*e + 3/245*(35*x^7*arccosh(c*x) - (5*sqrt(c^2*x^2 - 1)*x^6/c^2 + 6*sqrt(c^2*x^2 - 1)*x^4/c^4 + 8*sqrt(c^2*x^2 - 1)*x^2/c^6 + 16*sqrt(c^2*x^2 - 1)/c^8)*c)*b*d*e^2 + 1/2835*(315*x^9*arccosh(c*x) - (35*sqrt(c^2*x^2 - 1)*x^8/c^2 + 40*sqrt(c^2*x^2 - 1)*x^6/c^4 + 48*sqrt(c^2*x^2 - 1)*x^4/c^6 + 64*sqrt(c^2*x^2 - 1)*x^2/c^8 + 128*sqrt(c^2*x^2 - 1)/c^10)*c)*b*e^3","A",0
482,1,409,0,0.460631," ","integrate(x*(e*x^2+d)^3*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, a e^{3} x^{8} + \frac{1}{2} \, a d e^{2} x^{6} + \frac{3}{4} \, a d^{2} e x^{4} + \frac{1}{2} \, a d^{3} x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x}{c^{2}} + \frac{\log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{3}}\right)}\right)} b d^{3} + \frac{3}{32} \, {\left(8 \, x^{4} \operatorname{arcosh}\left(c x\right) - {\left(\frac{2 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{2}} + \frac{3 \, \sqrt{c^{2} x^{2} - 1} x}{c^{4}} + \frac{3 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{5}}\right)} c\right)} b d^{2} e + \frac{1}{96} \, {\left(48 \, x^{6} \operatorname{arcosh}\left(c x\right) - {\left(\frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{2}} + \frac{10 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{4}} + \frac{15 \, \sqrt{c^{2} x^{2} - 1} x}{c^{6}} + \frac{15 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{7}}\right)} c\right)} b d e^{2} + \frac{1}{3072} \, {\left(384 \, x^{8} \operatorname{arcosh}\left(c x\right) - {\left(\frac{48 \, \sqrt{c^{2} x^{2} - 1} x^{7}}{c^{2}} + \frac{56 \, \sqrt{c^{2} x^{2} - 1} x^{5}}{c^{4}} + \frac{70 \, \sqrt{c^{2} x^{2} - 1} x^{3}}{c^{6}} + \frac{105 \, \sqrt{c^{2} x^{2} - 1} x}{c^{8}} + \frac{105 \, \log\left(2 \, c^{2} x + 2 \, \sqrt{c^{2} x^{2} - 1} c\right)}{c^{9}}\right)} c\right)} b e^{3}"," ",0,"1/8*a*e^3*x^8 + 1/2*a*d*e^2*x^6 + 3/4*a*d^2*e*x^4 + 1/2*a*d^3*x^2 + 1/4*(2*x^2*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x/c^2 + log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^3))*b*d^3 + 3/32*(8*x^4*arccosh(c*x) - (2*sqrt(c^2*x^2 - 1)*x^3/c^2 + 3*sqrt(c^2*x^2 - 1)*x/c^4 + 3*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^5)*c)*b*d^2*e + 1/96*(48*x^6*arccosh(c*x) - (8*sqrt(c^2*x^2 - 1)*x^5/c^2 + 10*sqrt(c^2*x^2 - 1)*x^3/c^4 + 15*sqrt(c^2*x^2 - 1)*x/c^6 + 15*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^7)*c)*b*d*e^2 + 1/3072*(384*x^8*arccosh(c*x) - (48*sqrt(c^2*x^2 - 1)*x^7/c^2 + 56*sqrt(c^2*x^2 - 1)*x^5/c^4 + 70*sqrt(c^2*x^2 - 1)*x^3/c^6 + 105*sqrt(c^2*x^2 - 1)*x/c^8 + 105*log(2*c^2*x + 2*sqrt(c^2*x^2 - 1)*c)/c^9)*c)*b*e^3","A",0
483,1,287,0,0.429077," ","integrate((e*x^2+d)^3*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a e^{3} x^{7} + \frac{3}{5} \, a d e^{2} x^{5} + a d^{2} e x^{3} + \frac{1}{3} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b d^{2} e + \frac{1}{25} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b d e^{2} + \frac{1}{245} \, {\left(35 \, x^{7} \operatorname{arcosh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{c^{2} x^{2} - 1}}{c^{8}}\right)} c\right)} b e^{3} + a d^{3} x + \frac{{\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b d^{3}}{c}"," ",0,"1/7*a*e^3*x^7 + 3/5*a*d*e^2*x^5 + a*d^2*e*x^3 + 1/3*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*d^2*e + 1/25*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*d*e^2 + 1/245*(35*x^7*arccosh(c*x) - (5*sqrt(c^2*x^2 - 1)*x^6/c^2 + 6*sqrt(c^2*x^2 - 1)*x^4/c^4 + 8*sqrt(c^2*x^2 - 1)*x^2/c^6 + 16*sqrt(c^2*x^2 - 1)/c^8)*c)*b*e^3 + a*d^3*x + (c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*d^3/c","A",0
484,0,0,0,0.000000," ","integrate((e*x^2+d)^3*(a+b*arccosh(c*x))/x,x, algorithm=""maxima"")","\frac{1}{6} \, a e^{3} x^{6} + \frac{3}{4} \, a d e^{2} x^{4} + \frac{3}{2} \, a d^{2} e x^{2} + a d^{3} \log\left(x\right) + \int b e^{3} x^{5} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 3 \, b d e^{2} x^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 3 \, b d^{2} e x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + \frac{b d^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"1/6*a*e^3*x^6 + 3/4*a*d*e^2*x^4 + 3/2*a*d^2*e*x^2 + a*d^3*log(x) + integrate(b*e^3*x^5*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 3*b*d*e^2*x^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 3*b*d^2*e*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + b*d^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
485,1,222,0,0.405858," ","integrate((e*x^2+d)^3*(a+b*arccosh(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{5} \, a e^{3} x^{5} + a d e^{2} x^{3} - {\left(c \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arcosh}\left(c x\right)}{x}\right)} b d^{3} + \frac{1}{3} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b d e^{2} + \frac{1}{75} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b e^{3} + 3 \, a d^{2} e x + \frac{3 \, {\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b d^{2} e}{c} - \frac{a d^{3}}{x}"," ",0,"1/5*a*e^3*x^5 + a*d*e^2*x^3 - (c*arcsin(1/(c*abs(x))) + arccosh(c*x)/x)*b*d^3 + 1/3*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*d*e^2 + 1/75*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*e^3 + 3*a*d^2*e*x + 3*(c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*d^2*e/c - a*d^3/x","A",0
486,0,0,0,0.000000," ","integrate((e*x^2+d)^3*(a+b*arccosh(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, a e^{3} x^{4} + \frac{3}{2} \, a d e^{2} x^{2} + \frac{1}{2} \, b d^{3} {\left(\frac{\sqrt{c^{2} x^{2} - 1} c}{x} - \frac{\operatorname{arcosh}\left(c x\right)}{x^{2}}\right)} + 3 \, a d^{2} e \log\left(x\right) - \frac{a d^{3}}{2 \, x^{2}} + \int b e^{3} x^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + 3 \, b d e^{2} x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + \frac{3 \, b d^{2} e \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"1/4*a*e^3*x^4 + 3/2*a*d*e^2*x^2 + 1/2*b*d^3*(sqrt(c^2*x^2 - 1)*c/x - arccosh(c*x)/x^2) + 3*a*d^2*e*log(x) - 1/2*a*d^3/x^2 + integrate(b*e^3*x^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 3*b*d*e^2*x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + 3*b*d^2*e*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
487,1,197,0,0.574187," ","integrate((e*x^2+d)^3*(a+b*arccosh(c*x))/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, a e^{3} x^{3} - \frac{1}{6} \, {\left({\left(c^{2} \arcsin\left(\frac{1}{c {\left| x \right|}}\right) - \frac{\sqrt{c^{2} x^{2} - 1}}{x^{2}}\right)} c + \frac{2 \, \operatorname{arcosh}\left(c x\right)}{x^{3}}\right)} b d^{3} - 3 \, {\left(c \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{\operatorname{arcosh}\left(c x\right)}{x}\right)} b d^{2} e + \frac{1}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b e^{3} + 3 \, a d e^{2} x + \frac{3 \, {\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b d e^{2}}{c} - \frac{3 \, a d^{2} e}{x} - \frac{a d^{3}}{3 \, x^{3}}"," ",0,"1/3*a*e^3*x^3 - 1/6*((c^2*arcsin(1/(c*abs(x))) - sqrt(c^2*x^2 - 1)/x^2)*c + 2*arccosh(c*x)/x^3)*b*d^3 - 3*(c*arcsin(1/(c*abs(x))) + arccosh(c*x)/x)*b*d^2*e + 1/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*e^3 + 3*a*d*e^2*x + 3*(c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*d*e^2/c - 3*a*d^2*e/x - 1/3*a*d^3/x^3","A",0
488,1,415,0,0.358891," ","integrate((e*x^2+d)^4*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{1}{9} \, a e^{4} x^{9} + \frac{4}{7} \, a d e^{3} x^{7} + \frac{6}{5} \, a d^{2} e^{2} x^{5} + \frac{4}{3} \, a d^{3} e x^{3} + \frac{4}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} b d^{3} e + \frac{2}{25} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} b d^{2} e^{2} + \frac{4}{245} \, {\left(35 \, x^{7} \operatorname{arcosh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{c^{2} x^{2} - 1}}{c^{8}}\right)} c\right)} b d e^{3} + \frac{1}{2835} \, {\left(315 \, x^{9} \operatorname{arcosh}\left(c x\right) - {\left(\frac{35 \, \sqrt{c^{2} x^{2} - 1} x^{8}}{c^{2}} + \frac{40 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{4}} + \frac{48 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{6}} + \frac{64 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{8}} + \frac{128 \, \sqrt{c^{2} x^{2} - 1}}{c^{10}}\right)} c\right)} b e^{4} + a d^{4} x + \frac{{\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} b d^{4}}{c}"," ",0,"1/9*a*e^4*x^9 + 4/7*a*d*e^3*x^7 + 6/5*a*d^2*e^2*x^5 + 4/3*a*d^3*e*x^3 + 4/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*b*d^3*e + 2/25*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*b*d^2*e^2 + 4/245*(35*x^7*arccosh(c*x) - (5*sqrt(c^2*x^2 - 1)*x^6/c^2 + 6*sqrt(c^2*x^2 - 1)*x^4/c^4 + 8*sqrt(c^2*x^2 - 1)*x^2/c^6 + 16*sqrt(c^2*x^2 - 1)/c^8)*c)*b*d*e^3 + 1/2835*(315*x^9*arccosh(c*x) - (35*sqrt(c^2*x^2 - 1)*x^8/c^2 + 40*sqrt(c^2*x^2 - 1)*x^6/c^4 + 48*sqrt(c^2*x^2 - 1)*x^4/c^6 + 64*sqrt(c^2*x^2 - 1)*x^2/c^8 + 128*sqrt(c^2*x^2 - 1)/c^10)*c)*b*e^4 + a*d^4*x + (c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*b*d^4/c","A",0
489,0,0,0,0.000000," ","integrate(x^4*(a+b*arccosh(c*x))/(e*x^2+d),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{3 \, d^{2} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{2}} + \frac{e x^{3} - 3 \, d x}{e^{2}}\right)} + b \int \frac{x^{4} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x^{2} + d}\,{d x}"," ",0,"1/3*a*(3*d^2*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^2) + (e*x^3 - 3*d*x)/e^2) + b*integrate(x^4*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^2 + d), x)","F",0
490,0,0,0,0.000000," ","integrate(x^3*(a+b*arccosh(c*x))/(e*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{x^{2}}{e} - \frac{d \log\left(e x^{2} + d\right)}{e^{2}}\right)} + b \int \frac{x^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x^{2} + d}\,{d x}"," ",0,"1/2*a*(x^2/e - d*log(e*x^2 + d)/e^2) + b*integrate(x^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^2 + d), x)","F",0
491,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))/(e*x^2+d),x, algorithm=""maxima"")","-a {\left(\frac{d \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e} - \frac{x}{e}\right)} + b \int \frac{x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x^{2} + d}\,{d x}"," ",0,"-a*(d*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e) - x/e) + b*integrate(x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^2 + d), x)","F",0
492,0,0,0,0.000000," ","integrate(x*(a+b*arccosh(c*x))/(e*x^2+d),x, algorithm=""maxima"")","b \int \frac{x \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x^{2} + d}\,{d x} + \frac{a \log\left(e x^{2} + d\right)}{2 \, e}"," ",0,"b*integrate(x*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^2 + d), x) + 1/2*a*log(e*x^2 + d)/e","F",0
493,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(e*x^2+d),x, algorithm=""maxima"")","b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x^{2} + d}\,{d x} + \frac{a \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}"," ",0,"b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^2 + d), x) + a*arctan(e*x/sqrt(d*e))/sqrt(d*e)","F",0
494,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x/(e*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\log\left(e x^{2} + d\right)}{d} - \frac{2 \, \log\left(x\right)}{d}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x^{3} + d x}\,{d x}"," ",0,"-1/2*a*(log(e*x^2 + d)/d - 2*log(x)/d) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^3 + d*x), x)","F",0
495,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^2/(e*x^2+d),x, algorithm=""maxima"")","-a {\left(\frac{e \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d} + \frac{1}{d x}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x^{4} + d x^{2}}\,{d x}"," ",0,"-a*(e*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d) + 1/(d*x)) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^4 + d*x^2), x)","F",0
496,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^3/(e*x^2+d),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{e \log\left(e x^{2} + d\right)}{d^{2}} - \frac{2 \, e \log\left(x\right)}{d^{2}} - \frac{1}{d x^{2}}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x^{5} + d x^{3}}\,{d x}"," ",0,"1/2*a*(e*log(e*x^2 + d)/d^2 - 2*e*log(x)/d^2 - 1/(d*x^2)) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^5 + d*x^3), x)","F",0
497,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^4/(e*x^2+d),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{3 \, e^{2} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d^{2}} + \frac{3 \, e x^{2} - d}{d^{2} x^{3}}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x^{6} + d x^{4}}\,{d x}"," ",0,"1/3*a*(3*e^2*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d^2) + (3*e*x^2 - d)/(d^2*x^3)) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^6 + d*x^4), x)","F",0
498,0,0,0,0.000000," ","integrate(x^3*(a+b*arccosh(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{d}{e^{3} x^{2} + d e^{2}} + \frac{\log\left(e x^{2} + d\right)}{e^{2}}\right)} + b \int \frac{x^{3} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}"," ",0,"1/2*a*(d/(e^3*x^2 + d*e^2) + log(e*x^2 + d)/e^2) + b*integrate(x^3*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
499,0,0,0,0.000000," ","integrate(x*(a+b*arccosh(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(4 \, c \int \frac{1}{2 \, {\left(c^{3} e^{2} x^{5} - c d e x + {\left(c^{3} d e - c e^{2}\right)} x^{3} + {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)}\right)}}\,{d x} + \frac{c^{2} \log\left(e x^{2} + d\right)}{c^{2} d e + e^{2}} + \frac{2 \, {\left(c^{2} d + e\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) - {\left(c^{2} e x^{2} + c^{2} d\right)} \log\left(c x + 1\right) - {\left(c^{2} e x^{2} + c^{2} d\right)} \log\left(c x - 1\right)}{c^{2} d^{2} e + d e^{2} + {\left(c^{2} d e^{2} + e^{3}\right)} x^{2}}\right)} b - \frac{a}{2 \, {\left(e^{2} x^{2} + d e\right)}}"," ",0,"-1/4*(4*c*integrate(1/2/(c^3*e^2*x^5 - c*d*e*x + (c^3*d*e - c*e^2)*x^3 + (c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1))), x) + c^2*log(e*x^2 + d)/(c^2*d*e + e^2) + (2*(c^2*d + e)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) - (c^2*e*x^2 + c^2*d)*log(c*x + 1) - (c^2*e*x^2 + c^2*d)*log(c*x - 1))/(c^2*d^2*e + d*e^2 + (c^2*d*e^2 + e^3)*x^2))*b - 1/2*a/(e^2*x^2 + d*e)","F",0
500,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{1}{d e x^{2} + d^{2}} - \frac{\log\left(e x^{2} + d\right)}{d^{2}} + \frac{2 \, \log\left(x\right)}{d^{2}}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{2} x^{5} + 2 \, d e x^{3} + d^{2} x}\,{d x}"," ",0,"1/2*a*(1/(d*e*x^2 + d^2) - log(e*x^2 + d)/d^2 + 2*log(x)/d^2) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e^2*x^5 + 2*d*e*x^3 + d^2*x), x)","F",0
501,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^3/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{2 \, e x^{2} + d}{d^{2} e x^{4} + d^{3} x^{2}} - \frac{2 \, e \log\left(e x^{2} + d\right)}{d^{3}} + \frac{4 \, e \log\left(x\right)}{d^{3}}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{2} x^{7} + 2 \, d e x^{5} + d^{2} x^{3}}\,{d x}"," ",0,"-1/2*a*((2*e*x^2 + d)/(d^2*e*x^4 + d^3*x^2) - 2*e*log(e*x^2 + d)/d^3 + 4*e*log(x)/d^3) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e^2*x^7 + 2*d*e*x^5 + d^2*x^3), x)","F",0
502,0,0,0,0.000000," ","integrate(x^4*(a+b*arccosh(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{d x}{e^{3} x^{2} + d e^{2}} - \frac{3 \, d \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{2}} + \frac{2 \, x}{e^{2}}\right)} + b \int \frac{x^{4} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}"," ",0,"1/2*a*(d*x/(e^3*x^2 + d*e^2) - 3*d*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^2) + 2*x/e^2) + b*integrate(x^4*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
503,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{x}{e^{2} x^{2} + d e} - \frac{\arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e}\right)} + b \int \frac{x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}"," ",0,"-1/2*a*(x/(e^2*x^2 + d*e) - arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e)) + b*integrate(x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
504,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{x}{d e x^{2} + d^{2}} + \frac{\arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}"," ",0,"1/2*a*(x/(d*e*x^2 + d^2) + arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d)) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
505,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^2/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{3 \, e x^{2} + 2 \, d}{d^{2} e x^{3} + d^{3} x} + \frac{3 \, e \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d^{2}}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{2} x^{6} + 2 \, d e x^{4} + d^{2} x^{2}}\,{d x}"," ",0,"-1/2*a*((3*e*x^2 + 2*d)/(d^2*e*x^3 + d^3*x) + 3*e*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d^2)) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e^2*x^6 + 2*d*e*x^4 + d^2*x^2), x)","F",0
506,0,0,0,0.000000," ","integrate(x^5*(a+b*arccosh(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{4} \, a {\left(\frac{4 \, d e x^{2} + 3 \, d^{2}}{e^{5} x^{4} + 2 \, d e^{4} x^{2} + d^{2} e^{3}} + \frac{2 \, \log\left(e x^{2} + d\right)}{e^{3}}\right)} + b \int \frac{x^{5} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}\,{d x}"," ",0,"1/4*a*((4*d*e*x^2 + 3*d^2)/(e^5*x^4 + 2*d*e^4*x^2 + d^2*e^3) + 2*log(e*x^2 + d)/e^3) + b*integrate(x^5*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
507,0,0,0,0.000000," ","integrate(x^3*(a+b*arccosh(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{8} \, b {\left(\frac{{\left(c^{4} d + 2 \, c^{2} e\right)} \log\left(e x^{2} + d\right)}{c^{4} d^{2} e^{2} + 2 \, c^{2} d e^{3} + e^{4}} + \frac{c^{4} d^{3} + c^{2} d^{2} e + {\left(c^{4} d^{2} e + c^{2} d e^{2}\right)} x^{2} + 2 \, {\left(c^{4} d^{3} + 2 \, c^{2} d^{2} e + d e^{2} + 2 \, {\left(c^{4} d^{2} e + 2 \, c^{2} d e^{2} + e^{3}\right)} x^{2}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) - {\left(c^{4} d^{3} + 2 \, c^{2} d^{2} e + {\left(c^{4} d e^{2} + 2 \, c^{2} e^{3}\right)} x^{4} + 2 \, {\left(c^{4} d^{2} e + 2 \, c^{2} d e^{2}\right)} x^{2}\right)} \log\left(c x + 1\right) - {\left(c^{4} d^{3} + 2 \, c^{2} d^{2} e + {\left(c^{4} d e^{2} + 2 \, c^{2} e^{3}\right)} x^{4} + 2 \, {\left(c^{4} d^{2} e + 2 \, c^{2} d e^{2}\right)} x^{2}\right)} \log\left(c x - 1\right)}{c^{4} d^{4} e^{2} + 2 \, c^{2} d^{3} e^{3} + d^{2} e^{4} + {\left(c^{4} d^{2} e^{4} + 2 \, c^{2} d e^{5} + e^{6}\right)} x^{4} + 2 \, {\left(c^{4} d^{3} e^{3} + 2 \, c^{2} d^{2} e^{4} + d e^{5}\right)} x^{2}} + 8 \, \int \frac{2 \, c e x^{2} + c d}{4 \, {\left(c^{3} e^{4} x^{7} - c d^{2} e^{2} x + {\left(2 \, c^{3} d e^{3} - c e^{4}\right)} x^{5} + {\left(c^{3} d^{2} e^{2} - 2 \, c d e^{3}\right)} x^{3} + {\left(c^{2} e^{4} x^{6} + {\left(2 \, c^{2} d e^{3} - e^{4}\right)} x^{4} - d^{2} e^{2} + {\left(c^{2} d^{2} e^{2} - 2 \, d e^{3}\right)} x^{2}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)}\right)}}\,{d x}\right)} - \frac{{\left(2 \, e x^{2} + d\right)} a}{4 \, {\left(e^{4} x^{4} + 2 \, d e^{3} x^{2} + d^{2} e^{2}\right)}}"," ",0,"-1/8*b*((c^4*d + 2*c^2*e)*log(e*x^2 + d)/(c^4*d^2*e^2 + 2*c^2*d*e^3 + e^4) + (c^4*d^3 + c^2*d^2*e + (c^4*d^2*e + c^2*d*e^2)*x^2 + 2*(c^4*d^3 + 2*c^2*d^2*e + d*e^2 + 2*(c^4*d^2*e + 2*c^2*d*e^2 + e^3)*x^2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) - (c^4*d^3 + 2*c^2*d^2*e + (c^4*d*e^2 + 2*c^2*e^3)*x^4 + 2*(c^4*d^2*e + 2*c^2*d*e^2)*x^2)*log(c*x + 1) - (c^4*d^3 + 2*c^2*d^2*e + (c^4*d*e^2 + 2*c^2*e^3)*x^4 + 2*(c^4*d^2*e + 2*c^2*d*e^2)*x^2)*log(c*x - 1))/(c^4*d^4*e^2 + 2*c^2*d^3*e^3 + d^2*e^4 + (c^4*d^2*e^4 + 2*c^2*d*e^5 + e^6)*x^4 + 2*(c^4*d^3*e^3 + 2*c^2*d^2*e^4 + d*e^5)*x^2) + 8*integrate(1/4*(2*c*e*x^2 + c*d)/(c^3*e^4*x^7 - c*d^2*e^2*x + (2*c^3*d*e^3 - c*e^4)*x^5 + (c^3*d^2*e^2 - 2*c*d*e^3)*x^3 + (c^2*e^4*x^6 + (2*c^2*d*e^3 - e^4)*x^4 - d^2*e^2 + (c^2*d^2*e^2 - 2*d*e^3)*x^2)*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1))), x)) - 1/4*(2*e*x^2 + d)*a/(e^4*x^4 + 2*d*e^3*x^2 + d^2*e^2)","F",0
508,0,0,0,0.000000," ","integrate(x*(a+b*arccosh(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(\frac{c^{4} \log\left(e x^{2} + d\right)}{c^{4} d^{2} e + 2 \, c^{2} d e^{2} + e^{3}} + 8 \, c \int \frac{1}{4 \, {\left(c^{3} e^{3} x^{7} + {\left(2 \, c^{3} d e^{2} - c e^{3}\right)} x^{5} - c d^{2} e x + {\left(c^{3} d^{2} e - 2 \, c d e^{2}\right)} x^{3} + {\left(c^{2} e^{3} x^{6} + {\left(2 \, c^{2} d e^{2} - e^{3}\right)} x^{4} - d^{2} e + {\left(c^{2} d^{2} e - 2 \, d e^{2}\right)} x^{2}\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)}\right)}}\,{d x} - \frac{c^{4} d^{2} + c^{2} d e + {\left(c^{4} d e + c^{2} e^{2}\right)} x^{2} - 2 \, {\left(c^{4} d^{2} + 2 \, c^{2} d e + e^{2}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(c^{4} e^{2} x^{4} + 2 \, c^{4} d e x^{2} + c^{4} d^{2}\right)} \log\left(c x + 1\right) + {\left(c^{4} e^{2} x^{4} + 2 \, c^{4} d e x^{2} + c^{4} d^{2}\right)} \log\left(c x - 1\right)}{c^{4} d^{4} e + 2 \, c^{2} d^{3} e^{2} + d^{2} e^{3} + {\left(c^{4} d^{2} e^{3} + 2 \, c^{2} d e^{4} + e^{5}\right)} x^{4} + 2 \, {\left(c^{4} d^{3} e^{2} + 2 \, c^{2} d^{2} e^{3} + d e^{4}\right)} x^{2}}\right)} b - \frac{a}{4 \, {\left(e^{3} x^{4} + 2 \, d e^{2} x^{2} + d^{2} e\right)}}"," ",0,"-1/8*(c^4*log(e*x^2 + d)/(c^4*d^2*e + 2*c^2*d*e^2 + e^3) + 8*c*integrate(1/4/(c^3*e^3*x^7 + (2*c^3*d*e^2 - c*e^3)*x^5 - c*d^2*e*x + (c^3*d^2*e - 2*c*d*e^2)*x^3 + (c^2*e^3*x^6 + (2*c^2*d*e^2 - e^3)*x^4 - d^2*e + (c^2*d^2*e - 2*d*e^2)*x^2)*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1))), x) - (c^4*d^2 + c^2*d*e + (c^4*d*e + c^2*e^2)*x^2 - 2*(c^4*d^2 + 2*c^2*d*e + e^2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + (c^4*e^2*x^4 + 2*c^4*d*e*x^2 + c^4*d^2)*log(c*x + 1) + (c^4*e^2*x^4 + 2*c^4*d*e*x^2 + c^4*d^2)*log(c*x - 1))/(c^4*d^4*e + 2*c^2*d^3*e^2 + d^2*e^3 + (c^4*d^2*e^3 + 2*c^2*d*e^4 + e^5)*x^4 + 2*(c^4*d^3*e^2 + 2*c^2*d^2*e^3 + d*e^4)*x^2))*b - 1/4*a/(e^3*x^4 + 2*d*e^2*x^2 + d^2*e)","F",0
509,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{4} \, a {\left(\frac{2 \, e x^{2} + 3 \, d}{d^{2} e^{2} x^{4} + 2 \, d^{3} e x^{2} + d^{4}} - \frac{2 \, \log\left(e x^{2} + d\right)}{d^{3}} + \frac{4 \, \log\left(x\right)}{d^{3}}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{3} x^{7} + 3 \, d e^{2} x^{5} + 3 \, d^{2} e x^{3} + d^{3} x}\,{d x}"," ",0,"1/4*a*((2*e*x^2 + 3*d)/(d^2*e^2*x^4 + 2*d^3*e*x^2 + d^4) - 2*log(e*x^2 + d)/d^3 + 4*log(x)/d^3) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e^3*x^7 + 3*d*e^2*x^5 + 3*d^2*e*x^3 + d^3*x), x)","F",0
510,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/x^3/(e*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{6 \, e^{2} x^{4} + 9 \, d e x^{2} + 2 \, d^{2}}{d^{3} e^{2} x^{6} + 2 \, d^{4} e x^{4} + d^{5} x^{2}} - \frac{6 \, e \log\left(e x^{2} + d\right)}{d^{4}} + \frac{12 \, e \log\left(x\right)}{d^{4}}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{3} x^{9} + 3 \, d e^{2} x^{7} + 3 \, d^{2} e x^{5} + d^{3} x^{3}}\,{d x}"," ",0,"-1/4*a*((6*e^2*x^4 + 9*d*e*x^2 + 2*d^2)/(d^3*e^2*x^6 + 2*d^4*e*x^4 + d^5*x^2) - 6*e*log(e*x^2 + d)/d^4 + 12*e*log(x)/d^4) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e^3*x^9 + 3*d*e^2*x^7 + 3*d^2*e*x^5 + d^3*x^3), x)","F",0
511,0,0,0,0.000000," ","integrate(x^4*(a+b*arccosh(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(\frac{5 \, e x^{3} + 3 \, d x}{e^{4} x^{4} + 2 \, d e^{3} x^{2} + d^{2} e^{2}} - \frac{3 \, \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{2}}\right)} + b \int \frac{x^{4} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}\,{d x}"," ",0,"-1/8*a*((5*e*x^3 + 3*d*x)/(e^4*x^4 + 2*d*e^3*x^2 + d^2*e^2) - 3*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^2)) + b*integrate(x^4*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
512,0,0,0,0.000000," ","integrate(x^2*(a+b*arccosh(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{e x^{3} - d x}{d e^{3} x^{4} + 2 \, d^{2} e^{2} x^{2} + d^{3} e} + \frac{\arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d e}\right)} + b \int \frac{x^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}\,{d x}"," ",0,"1/8*a*((e*x^3 - d*x)/(d*e^3*x^4 + 2*d^2*e^2*x^2 + d^3*e) + arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d*e)) + b*integrate(x^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
513,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{3 \, e x^{3} + 5 \, d x}{d^{2} e^{2} x^{4} + 2 \, d^{3} e x^{2} + d^{4}} + \frac{3 \, \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d^{2}}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}\,{d x}"," ",0,"1/8*a*((3*e*x^3 + 5*d*x)/(d^2*e^2*x^4 + 2*d^3*e*x^2 + d^4) + 3*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d^2)) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
514,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))*(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\sqrt{e x^{2} + d} x + \frac{d \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}}\right)} a + b \int \sqrt{e x^{2} + d} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/2*(sqrt(e*x^2 + d)*x + d*arcsinh(e*x/sqrt(d*e))/sqrt(e))*a + b*integrate(sqrt(e*x^2 + d)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
515,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{e x^{2} + d}}\,{d x} + \frac{a \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}}"," ",0,"b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(e*x^2 + d), x) + a*arcsinh(e*x/sqrt(d*e))/sqrt(e)","F",0
516,-2,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d zero or nonzero?","F(-2)",0
517,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{2 \, x}{\sqrt{e x^{2} + d} d^{2}} + \frac{x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/3*a*(2*x/(sqrt(e*x^2 + d)*d^2) + x/((e*x^2 + d)^(3/2)*d)) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^2 + d)^(5/2), x)","F",0
518,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))/(e*x^2+d)^(7/2),x, algorithm=""maxima"")","\frac{1}{15} \, a {\left(\frac{8 \, x}{\sqrt{e x^{2} + d} d^{3}} + \frac{4 \, x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d^{2}} + \frac{3 \, x}{{\left(e x^{2} + d\right)}^{\frac{5}{2}} d}\right)} + b \int \frac{\log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(e x^{2} + d\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"1/15*a*(8*x/(sqrt(e*x^2 + d)*d^3) + 4*x/((e*x^2 + d)^(3/2)*d^2) + 3*x/((e*x^2 + d)^(5/2)*d)) + b*integrate(log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^2 + d)^(7/2), x)","F",0
519,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^3*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{a e^{3} f^{m} x^{7} x^{m}}{m + 7} + \frac{3 \, a d e^{2} f^{m} x^{5} x^{m}}{m + 5} + \frac{3 \, a d^{2} e f^{m} x^{3} x^{m}}{m + 3} + \frac{\left(f x\right)^{m + 1} a d^{3}}{f {\left(m + 1\right)}} + \frac{{\left({\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} b e^{3} f^{m} x^{7} + 3 \, {\left(m^{3} + 11 \, m^{2} + 31 \, m + 21\right)} b d e^{2} f^{m} x^{5} + 3 \, {\left(m^{3} + 13 \, m^{2} + 47 \, m + 35\right)} b d^{2} e f^{m} x^{3} + {\left(m^{3} + 15 \, m^{2} + 71 \, m + 105\right)} b d^{3} f^{m} x\right)} x^{m} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105} + \int \frac{{\left({\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} b c e^{3} f^{m} x^{7} + 3 \, {\left(m^{3} + 11 \, m^{2} + 31 \, m + 21\right)} b c d e^{2} f^{m} x^{5} + 3 \, {\left(m^{3} + 13 \, m^{2} + 47 \, m + 35\right)} b c d^{2} e f^{m} x^{3} + {\left(m^{3} + 15 \, m^{2} + 71 \, m + 105\right)} b c d^{3} f^{m} x\right)} x^{m}}{{\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} c^{3} x^{3} - {\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} c x + {\left({\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} c^{2} x^{2} - m^{4} - 16 \, m^{3} - 86 \, m^{2} - 176 \, m - 105\right)} \sqrt{c x + 1} \sqrt{c x - 1}}\,{d x} - \int \frac{{\left({\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} b c^{2} e^{3} f^{m} x^{8} + 3 \, {\left(m^{3} + 11 \, m^{2} + 31 \, m + 21\right)} b c^{2} d e^{2} f^{m} x^{6} + 3 \, {\left(m^{3} + 13 \, m^{2} + 47 \, m + 35\right)} b c^{2} d^{2} e f^{m} x^{4} + {\left(m^{3} + 15 \, m^{2} + 71 \, m + 105\right)} b c^{2} d^{3} f^{m} x^{2}\right)} x^{m}}{{\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} c^{2} x^{2} - m^{4} - 16 \, m^{3} - 86 \, m^{2} - 176 \, m - 105}\,{d x}"," ",0,"a*e^3*f^m*x^7*x^m/(m + 7) + 3*a*d*e^2*f^m*x^5*x^m/(m + 5) + 3*a*d^2*e*f^m*x^3*x^m/(m + 3) + (f*x)^(m + 1)*a*d^3/(f*(m + 1)) + ((m^3 + 9*m^2 + 23*m + 15)*b*e^3*f^m*x^7 + 3*(m^3 + 11*m^2 + 31*m + 21)*b*d*e^2*f^m*x^5 + 3*(m^3 + 13*m^2 + 47*m + 35)*b*d^2*e*f^m*x^3 + (m^3 + 15*m^2 + 71*m + 105)*b*d^3*f^m*x)*x^m*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105) + integrate(((m^3 + 9*m^2 + 23*m + 15)*b*c*e^3*f^m*x^7 + 3*(m^3 + 11*m^2 + 31*m + 21)*b*c*d*e^2*f^m*x^5 + 3*(m^3 + 13*m^2 + 47*m + 35)*b*c*d^2*e*f^m*x^3 + (m^3 + 15*m^2 + 71*m + 105)*b*c*d^3*f^m*x)*x^m/((m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*c^3*x^3 - (m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*c*x + ((m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*c^2*x^2 - m^4 - 16*m^3 - 86*m^2 - 176*m - 105)*sqrt(c*x + 1)*sqrt(c*x - 1)), x) - integrate(((m^3 + 9*m^2 + 23*m + 15)*b*c^2*e^3*f^m*x^8 + 3*(m^3 + 11*m^2 + 31*m + 21)*b*c^2*d*e^2*f^m*x^6 + 3*(m^3 + 13*m^2 + 47*m + 35)*b*c^2*d^2*e*f^m*x^4 + (m^3 + 15*m^2 + 71*m + 105)*b*c^2*d^3*f^m*x^2)*x^m/((m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*c^2*x^2 - m^4 - 16*m^3 - 86*m^2 - 176*m - 105), x)","F",0
520,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^2*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{a e^{2} f^{m} x^{5} x^{m}}{m + 5} + \frac{2 \, a d e f^{m} x^{3} x^{m}}{m + 3} + \frac{\left(f x\right)^{m + 1} a d^{2}}{f {\left(m + 1\right)}} + \frac{{\left({\left(m^{2} + 4 \, m + 3\right)} b e^{2} f^{m} x^{5} + 2 \, {\left(m^{2} + 6 \, m + 5\right)} b d e f^{m} x^{3} + {\left(m^{2} + 8 \, m + 15\right)} b d^{2} f^{m} x\right)} x^{m} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{m^{3} + 9 \, m^{2} + 23 \, m + 15} + \int \frac{{\left({\left(m^{2} + 4 \, m + 3\right)} b c e^{2} f^{m} x^{5} + 2 \, {\left(m^{2} + 6 \, m + 5\right)} b c d e f^{m} x^{3} + {\left(m^{2} + 8 \, m + 15\right)} b c d^{2} f^{m} x\right)} x^{m}}{{\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} c^{3} x^{3} - {\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} c x + {\left({\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} c^{2} x^{2} - m^{3} - 9 \, m^{2} - 23 \, m - 15\right)} \sqrt{c x + 1} \sqrt{c x - 1}}\,{d x} - \int \frac{{\left({\left(m^{2} + 4 \, m + 3\right)} b c^{2} e^{2} f^{m} x^{6} + 2 \, {\left(m^{2} + 6 \, m + 5\right)} b c^{2} d e f^{m} x^{4} + {\left(m^{2} + 8 \, m + 15\right)} b c^{2} d^{2} f^{m} x^{2}\right)} x^{m}}{{\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} c^{2} x^{2} - m^{3} - 9 \, m^{2} - 23 \, m - 15}\,{d x}"," ",0,"a*e^2*f^m*x^5*x^m/(m + 5) + 2*a*d*e*f^m*x^3*x^m/(m + 3) + (f*x)^(m + 1)*a*d^2/(f*(m + 1)) + ((m^2 + 4*m + 3)*b*e^2*f^m*x^5 + 2*(m^2 + 6*m + 5)*b*d*e*f^m*x^3 + (m^2 + 8*m + 15)*b*d^2*f^m*x)*x^m*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(m^3 + 9*m^2 + 23*m + 15) + integrate(((m^2 + 4*m + 3)*b*c*e^2*f^m*x^5 + 2*(m^2 + 6*m + 5)*b*c*d*e*f^m*x^3 + (m^2 + 8*m + 15)*b*c*d^2*f^m*x)*x^m/((m^3 + 9*m^2 + 23*m + 15)*c^3*x^3 - (m^3 + 9*m^2 + 23*m + 15)*c*x + ((m^3 + 9*m^2 + 23*m + 15)*c^2*x^2 - m^3 - 9*m^2 - 23*m - 15)*sqrt(c*x + 1)*sqrt(c*x - 1)), x) - integrate(((m^2 + 4*m + 3)*b*c^2*e^2*f^m*x^6 + 2*(m^2 + 6*m + 5)*b*c^2*d*e*f^m*x^4 + (m^2 + 8*m + 15)*b*c^2*d^2*f^m*x^2)*x^m/((m^3 + 9*m^2 + 23*m + 15)*c^2*x^2 - m^3 - 9*m^2 - 23*m - 15), x)","F",0
521,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)*(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\frac{a e f^{m} x^{3} x^{m}}{m + 3} + \frac{{\left(b e f^{m} {\left(m + 1\right)} x^{3} + b d f^{m} {\left(m + 3\right)} x\right)} x^{m} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{m^{2} + 4 \, m + 3} + \frac{\left(f x\right)^{m + 1} a d}{f {\left(m + 1\right)}} + \int \frac{{\left(b c e f^{m} {\left(m + 1\right)} x^{3} + b c d f^{m} {\left(m + 3\right)} x\right)} x^{m}}{{\left(m^{2} + 4 \, m + 3\right)} c^{3} x^{3} - {\left(m^{2} + 4 \, m + 3\right)} c x + {\left({\left(m^{2} + 4 \, m + 3\right)} c^{2} x^{2} - m^{2} - 4 \, m - 3\right)} \sqrt{c x + 1} \sqrt{c x - 1}}\,{d x} - \int \frac{{\left(b c^{2} e f^{m} {\left(m + 1\right)} x^{4} + b c^{2} d f^{m} {\left(m + 3\right)} x^{2}\right)} x^{m}}{{\left(m^{2} + 4 \, m + 3\right)} c^{2} x^{2} - m^{2} - 4 \, m - 3}\,{d x}"," ",0,"a*e*f^m*x^3*x^m/(m + 3) + (b*e*f^m*(m + 1)*x^3 + b*d*f^m*(m + 3)*x)*x^m*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(m^2 + 4*m + 3) + (f*x)^(m + 1)*a*d/(f*(m + 1)) + integrate((b*c*e*f^m*(m + 1)*x^3 + b*c*d*f^m*(m + 3)*x)*x^m/((m^2 + 4*m + 3)*c^3*x^3 - (m^2 + 4*m + 3)*c*x + ((m^2 + 4*m + 3)*c^2*x^2 - m^2 - 4*m - 3)*sqrt(c*x + 1)*sqrt(c*x - 1)), x) - integrate((b*c^2*e*f^m*(m + 1)*x^4 + b*c^2*d*f^m*(m + 3)*x^2)*x^m/((m^2 + 4*m + 3)*c^2*x^2 - m^2 - 4*m - 3), x)","F",0
522,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))/(e*x^2+d),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}}{e x^{2} + d}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)*(f*x)^m/(e*x^2 + d), x)","F",0
523,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)*(f*x)^m/(e*x^2 + d)^2, x)","F",0
524,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arccosh(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(e x^{2} + d\right)}^{3}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)*(f*x)^m/(e*x^2 + d)^3, x)","F",0
525,1,684,0,0.492518," ","integrate((e*x^2+d)^3*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{7} \, b^{2} e^{3} x^{7} \operatorname{arcosh}\left(c x\right)^{2} + \frac{1}{7} \, a^{2} e^{3} x^{7} + \frac{3}{5} \, b^{2} d e^{2} x^{5} \operatorname{arcosh}\left(c x\right)^{2} + \frac{3}{5} \, a^{2} d e^{2} x^{5} + b^{2} d^{2} e x^{3} \operatorname{arcosh}\left(c x\right)^{2} + a^{2} d^{2} e x^{3} + b^{2} d^{3} x \operatorname{arcosh}\left(c x\right)^{2} + \frac{2}{3} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} a b d^{2} e - \frac{2}{9} \, {\left(3 \, c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)} \operatorname{arcosh}\left(c x\right) - \frac{c^{2} x^{3} + 6 \, x}{c^{2}}\right)} b^{2} d^{2} e + \frac{2}{25} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} a b d e^{2} - \frac{2}{375} \, {\left(15 \, {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c \operatorname{arcosh}\left(c x\right) - \frac{9 \, c^{4} x^{5} + 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} d e^{2} + \frac{2}{245} \, {\left(35 \, x^{7} \operatorname{arcosh}\left(c x\right) - {\left(\frac{5 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{c^{2} x^{2} - 1}}{c^{8}}\right)} c\right)} a b e^{3} - \frac{2}{25725} \, {\left(105 \, {\left(\frac{5 \, \sqrt{c^{2} x^{2} - 1} x^{6}}{c^{2}} + \frac{6 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{6}} + \frac{16 \, \sqrt{c^{2} x^{2} - 1}}{c^{8}}\right)} c \operatorname{arcosh}\left(c x\right) - \frac{75 \, c^{6} x^{7} + 126 \, c^{4} x^{5} + 280 \, c^{2} x^{3} + 1680 \, x}{c^{6}}\right)} b^{2} e^{3} + 2 \, b^{2} d^{3} {\left(x - \frac{\sqrt{c^{2} x^{2} - 1} \operatorname{arcosh}\left(c x\right)}{c}\right)} + a^{2} d^{3} x + \frac{2 \, {\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} a b d^{3}}{c}"," ",0,"1/7*b^2*e^3*x^7*arccosh(c*x)^2 + 1/7*a^2*e^3*x^7 + 3/5*b^2*d*e^2*x^5*arccosh(c*x)^2 + 3/5*a^2*d*e^2*x^5 + b^2*d^2*e*x^3*arccosh(c*x)^2 + a^2*d^2*e*x^3 + b^2*d^3*x*arccosh(c*x)^2 + 2/3*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*a*b*d^2*e - 2/9*(3*c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4)*arccosh(c*x) - (c^2*x^3 + 6*x)/c^2)*b^2*d^2*e + 2/25*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*a*b*d*e^2 - 2/375*(15*(3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c*arccosh(c*x) - (9*c^4*x^5 + 20*c^2*x^3 + 120*x)/c^4)*b^2*d*e^2 + 2/245*(35*x^7*arccosh(c*x) - (5*sqrt(c^2*x^2 - 1)*x^6/c^2 + 6*sqrt(c^2*x^2 - 1)*x^4/c^4 + 8*sqrt(c^2*x^2 - 1)*x^2/c^6 + 16*sqrt(c^2*x^2 - 1)/c^8)*c)*a*b*e^3 - 2/25725*(105*(5*sqrt(c^2*x^2 - 1)*x^6/c^2 + 6*sqrt(c^2*x^2 - 1)*x^4/c^4 + 8*sqrt(c^2*x^2 - 1)*x^2/c^6 + 16*sqrt(c^2*x^2 - 1)/c^8)*c*arccosh(c*x) - (75*c^6*x^7 + 126*c^4*x^5 + 280*c^2*x^3 + 1680*x)/c^6)*b^2*e^3 + 2*b^2*d^3*(x - sqrt(c^2*x^2 - 1)*arccosh(c*x)/c) + a^2*d^3*x + 2*(c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*a*b*d^3/c","A",0
526,1,429,0,0.425056," ","integrate((e*x^2+d)^2*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{5} \, b^{2} e^{2} x^{5} \operatorname{arcosh}\left(c x\right)^{2} + \frac{1}{5} \, a^{2} e^{2} x^{5} + \frac{2}{3} \, b^{2} d e x^{3} \operatorname{arcosh}\left(c x\right)^{2} + \frac{2}{3} \, a^{2} d e x^{3} + b^{2} d^{2} x \operatorname{arcosh}\left(c x\right)^{2} + \frac{4}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} a b d e - \frac{4}{27} \, {\left(3 \, c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)} \operatorname{arcosh}\left(c x\right) - \frac{c^{2} x^{3} + 6 \, x}{c^{2}}\right)} b^{2} d e + \frac{2}{75} \, {\left(15 \, x^{5} \operatorname{arcosh}\left(c x\right) - {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c\right)} a b e^{2} - \frac{2}{1125} \, {\left(15 \, {\left(\frac{3 \, \sqrt{c^{2} x^{2} - 1} x^{4}}{c^{2}} + \frac{4 \, \sqrt{c^{2} x^{2} - 1} x^{2}}{c^{4}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1}}{c^{6}}\right)} c \operatorname{arcosh}\left(c x\right) - \frac{9 \, c^{4} x^{5} + 20 \, c^{2} x^{3} + 120 \, x}{c^{4}}\right)} b^{2} e^{2} + 2 \, b^{2} d^{2} {\left(x - \frac{\sqrt{c^{2} x^{2} - 1} \operatorname{arcosh}\left(c x\right)}{c}\right)} + a^{2} d^{2} x + \frac{2 \, {\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} a b d^{2}}{c}"," ",0,"1/5*b^2*e^2*x^5*arccosh(c*x)^2 + 1/5*a^2*e^2*x^5 + 2/3*b^2*d*e*x^3*arccosh(c*x)^2 + 2/3*a^2*d*e*x^3 + b^2*d^2*x*arccosh(c*x)^2 + 4/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*a*b*d*e - 4/27*(3*c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4)*arccosh(c*x) - (c^2*x^3 + 6*x)/c^2)*b^2*d*e + 2/75*(15*x^5*arccosh(c*x) - (3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c)*a*b*e^2 - 2/1125*(15*(3*sqrt(c^2*x^2 - 1)*x^4/c^2 + 4*sqrt(c^2*x^2 - 1)*x^2/c^4 + 8*sqrt(c^2*x^2 - 1)/c^6)*c*arccosh(c*x) - (9*c^4*x^5 + 20*c^2*x^3 + 120*x)/c^4)*b^2*e^2 + 2*b^2*d^2*(x - sqrt(c^2*x^2 - 1)*arccosh(c*x)/c) + a^2*d^2*x + 2*(c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*a*b*d^2/c","A",0
527,1,218,0,0.514029," ","integrate((e*x^2+d)*(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} e x^{3} \operatorname{arcosh}\left(c x\right)^{2} + \frac{1}{3} \, a^{2} e x^{3} + b^{2} d x \operatorname{arcosh}\left(c x\right)^{2} + \frac{2}{9} \, {\left(3 \, x^{3} \operatorname{arcosh}\left(c x\right) - c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)}\right)} a b e - \frac{2}{27} \, {\left(3 \, c {\left(\frac{\sqrt{c^{2} x^{2} - 1} x^{2}}{c^{2}} + \frac{2 \, \sqrt{c^{2} x^{2} - 1}}{c^{4}}\right)} \operatorname{arcosh}\left(c x\right) - \frac{c^{2} x^{3} + 6 \, x}{c^{2}}\right)} b^{2} e + 2 \, b^{2} d {\left(x - \frac{\sqrt{c^{2} x^{2} - 1} \operatorname{arcosh}\left(c x\right)}{c}\right)} + a^{2} d x + \frac{2 \, {\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} a b d}{c}"," ",0,"1/3*b^2*e*x^3*arccosh(c*x)^2 + 1/3*a^2*e*x^3 + b^2*d*x*arccosh(c*x)^2 + 2/9*(3*x^3*arccosh(c*x) - c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4))*a*b*e - 2/27*(3*c*(sqrt(c^2*x^2 - 1)*x^2/c^2 + 2*sqrt(c^2*x^2 - 1)/c^4)*arccosh(c*x) - (c^2*x^3 + 6*x)/c^2)*b^2*e + 2*b^2*d*(x - sqrt(c^2*x^2 - 1)*arccosh(c*x)/c) + a^2*d*x + 2*(c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*a*b*d/c","A",0
528,1,72,0,0.308890," ","integrate((a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","b^{2} x \operatorname{arcosh}\left(c x\right)^{2} + 2 \, b^{2} {\left(x - \frac{\sqrt{c^{2} x^{2} - 1} \operatorname{arcosh}\left(c x\right)}{c}\right)} + a^{2} x + \frac{2 \, {\left(c x \operatorname{arcosh}\left(c x\right) - \sqrt{c^{2} x^{2} - 1}\right)} a b}{c}"," ",0,"b^2*x*arccosh(c*x)^2 + 2*b^2*(x - sqrt(c^2*x^2 - 1)*arccosh(c*x)/c) + a^2*x + 2*(c*x*arccosh(c*x) - sqrt(c^2*x^2 - 1))*a*b/c","A",0
529,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/(e*x^2+d),x, algorithm=""maxima"")","\frac{a^{2} \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}} + \int \frac{b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{e x^{2} + d} + \frac{2 \, a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x^{2} + d}\,{d x}"," ",0,"a^2*arctan(e*x/sqrt(d*e))/sqrt(d*e) + integrate(b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(e*x^2 + d) + 2*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^2 + d), x)","F",0
530,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2*(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\sqrt{e x^{2} + d} x + \frac{d \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}}\right)} a^{2} + \int \sqrt{e x^{2} + d} b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 2 \, \sqrt{e x^{2} + d} a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/2*(sqrt(e*x^2 + d)*x + d*arcsinh(e*x/sqrt(d*e))/sqrt(e))*a^2 + integrate(sqrt(e*x^2 + d)*b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 2*sqrt(e*x^2 + d)*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
531,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{a^{2} \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}} + \int \frac{b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{\sqrt{e x^{2} + d}} + \frac{2 \, a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"a^2*arcsinh(e*x/sqrt(d*e))/sqrt(e) + integrate(b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/sqrt(e*x^2 + d) + 2*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(e*x^2 + d), x)","F",0
532,-2,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(e-c^2*d>0)', see `assume?` for more details)Is e-c^2*d zero or nonzero?","F(-2)",0
533,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^2/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} {\left(\frac{2 \, x}{\sqrt{e x^{2} + d} d^{2}} + \frac{x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + \int \frac{b^{2} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}} + \frac{2 \, a b \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"1/3*a^2*(2*x/(sqrt(e*x^2 + d)*d^2) + x/((e*x^2 + d)^(3/2)*d)) + integrate(b^2*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))^2/(e*x^2 + d)^(5/2) + 2*a*b*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^2 + d)^(5/2), x)","F",0
534,0,0,0,0.000000," ","integrate((e*x^2+d)^2/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{{\left(e x^{2} + d\right)}^{2}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x^2 + d)^2/(b*arccosh(c*x) + a), x)","F",0
535,0,0,0,0.000000," ","integrate((e*x^2+d)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{e x^{2} + d}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x^2 + d)/(b*arccosh(c*x) + a), x)","F",0
536,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(1/(b*arccosh(c*x) + a), x)","F",0
537,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)*(b*arccosh(c*x) + a)), x)","F",0
538,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)}^{2} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)^2*(b*arccosh(c*x) + a)), x)","F",0
539,0,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{\sqrt{e x^{2} + d}}{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)/(b*arccosh(c*x) + a), x)","F",0
540,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{e x^{2} + d} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(e*x^2 + d)*(b*arccosh(c*x) + a)), x)","F",0
541,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^(3/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)^(3/2)*(b*arccosh(c*x) + a)), x)","F",0
542,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^(5/2)/(a+b*arccosh(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)}^{\frac{5}{2}} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)^(5/2)*(b*arccosh(c*x) + a)), x)","F",0
543,0,0,0,0.000000," ","integrate((e*x^2+d)^2/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} e^{2} x^{7} + {\left(2 \, c^{3} d e - c e^{2}\right)} x^{5} - c d^{2} x + {\left(c^{3} d^{2} - 2 \, c d e\right)} x^{3} + {\left(c^{2} e^{2} x^{6} + {\left(2 \, c^{2} d e - e^{2}\right)} x^{4} + {\left(c^{2} d^{2} - 2 \, d e\right)} x^{2} - d^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{5 \, c^{5} e^{2} x^{8} + 2 \, {\left(3 \, c^{5} d e - 5 \, c^{3} e^{2}\right)} x^{6} + {\left(c^{5} d^{2} - 12 \, c^{3} d e + 5 \, c e^{2}\right)} x^{4} + {\left(5 \, c^{3} e^{2} x^{6} + 3 \, {\left(2 \, c^{3} d e - c e^{2}\right)} x^{4} + c d^{2} + {\left(c^{3} d^{2} - 2 \, c d e\right)} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + c d^{2} - 2 \, {\left(c^{3} d^{2} - 3 \, c d e\right)} x^{2} + {\left(10 \, c^{4} e^{2} x^{7} + {\left(12 \, c^{4} d e - 13 \, c^{2} e^{2}\right)} x^{5} + 2 \, {\left(c^{4} d^{2} - 7 \, c^{2} d e + 2 \, e^{2}\right)} x^{3} - {\left(c^{2} d^{2} - 4 \, d e\right)} x\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{a b c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{2} - 2 \, a b c^{3} x^{2} + a b c + 2 \, {\left(a b c^{4} x^{3} - a b c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{2} - 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-(c^3*e^2*x^7 + (2*c^3*d*e - c*e^2)*x^5 - c*d^2*x + (c^3*d^2 - 2*c*d*e)*x^3 + (c^2*e^2*x^6 + (2*c^2*d*e - e^2)*x^4 + (c^2*d^2 - 2*d*e)*x^2 - d^2)*sqrt(c*x + 1)*sqrt(c*x - 1))/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate((5*c^5*e^2*x^8 + 2*(3*c^5*d*e - 5*c^3*e^2)*x^6 + (c^5*d^2 - 12*c^3*d*e + 5*c*e^2)*x^4 + (5*c^3*e^2*x^6 + 3*(2*c^3*d*e - c*e^2)*x^4 + c*d^2 + (c^3*d^2 - 2*c*d*e)*x^2)*(c*x + 1)*(c*x - 1) + c*d^2 - 2*(c^3*d^2 - 3*c*d*e)*x^2 + (10*c^4*e^2*x^7 + (12*c^4*d*e - 13*c^2*e^2)*x^5 + 2*(c^4*d^2 - 7*c^2*d*e + 2*e^2)*x^3 - (c^2*d^2 - 4*d*e)*x)*sqrt(c*x + 1)*sqrt(c*x - 1))/(a*b*c^5*x^4 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^2 - 2*a*b*c^3*x^2 + a*b*c + 2*(a*b*c^4*x^3 - a*b*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^2 - 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 - b^2*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
544,0,0,0,0.000000," ","integrate((e*x^2+d)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} e x^{5} + {\left(c^{3} d - c e\right)} x^{3} - c d x + {\left(c^{2} e x^{4} + {\left(c^{2} d - e\right)} x^{2} - d\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{3 \, c^{5} e x^{6} + {\left(c^{5} d - 6 \, c^{3} e\right)} x^{4} + {\left(3 \, c^{3} e x^{4} + {\left(c^{3} d - c e\right)} x^{2} + c d\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - {\left(2 \, c^{3} d - 3 \, c e\right)} x^{2} + {\left(6 \, c^{4} e x^{5} + {\left(2 \, c^{4} d - 7 \, c^{2} e\right)} x^{3} - {\left(c^{2} d - 2 \, e\right)} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + c d}{a b c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{3} x^{2} - 2 \, a b c^{3} x^{2} + a b c + 2 \, {\left(a b c^{4} x^{3} - a b c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{3} x^{2} - 2 \, b^{2} c^{3} x^{2} + b^{2} c + 2 \, {\left(b^{2} c^{4} x^{3} - b^{2} c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-(c^3*e*x^5 + (c^3*d - c*e)*x^3 - c*d*x + (c^2*e*x^4 + (c^2*d - e)*x^2 - d)*sqrt(c*x + 1)*sqrt(c*x - 1))/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate((3*c^5*e*x^6 + (c^5*d - 6*c^3*e)*x^4 + (3*c^3*e*x^4 + (c^3*d - c*e)*x^2 + c*d)*(c*x + 1)*(c*x - 1) - (2*c^3*d - 3*c*e)*x^2 + (6*c^4*e*x^5 + (2*c^4*d - 7*c^2*e)*x^3 - (c^2*d - 2*e)*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + c*d)/(a*b*c^5*x^4 + (c*x + 1)*(c*x - 1)*a*b*c^3*x^2 - 2*a*b*c^3*x^2 + a*b*c + 2*(a*b*c^4*x^3 - a*b*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*x^4 + (c*x + 1)*(c*x - 1)*b^2*c^3*x^2 - 2*b^2*c^3*x^2 + b^2*c + 2*(b^2*c^4*x^3 - b^2*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
545,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{c^{4} x^{4} - 2 \, c^{2} x^{2} + {\left(c^{2} x^{2} + 1\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(2 \, c^{3} x^{3} - c x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + 1}{a b c^{4} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} a b c^{2} x^{2} - 2 \, a b c^{2} x^{2} + 2 \, {\left(a b c^{3} x^{3} - a b c x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + a b + {\left(b^{2} c^{4} x^{4} + {\left(c x + 1\right)} {\left(c x - 1\right)} b^{2} c^{2} x^{2} - 2 \, b^{2} c^{2} x^{2} + 2 \, {\left(b^{2} c^{3} x^{3} - b^{2} c x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + b^{2}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x)/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate((c^4*x^4 - 2*c^2*x^2 + (c^2*x^2 + 1)*(c*x + 1)*(c*x - 1) + (2*c^3*x^3 - c*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + 1)/(a*b*c^4*x^4 + (c*x + 1)*(c*x - 1)*a*b*c^2*x^2 - 2*a*b*c^2*x^2 + 2*(a*b*c^3*x^3 - a*b*c*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + a*b + (b^2*c^4*x^4 + (c*x + 1)*(c*x - 1)*b^2*c^2*x^2 - 2*b^2*c^2*x^2 + 2*(b^2*c^3*x^3 - b^2*c*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + b^2)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
546,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x}{a b c^{3} e x^{4} + {\left(c^{3} d - c e\right)} a b x^{2} - a b c d + {\left(a b c^{2} e x^{3} + a b c^{2} d x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{3} e x^{4} + {\left(c^{3} d - c e\right)} b^{2} x^{2} - b^{2} c d + {\left(b^{2} c^{2} e x^{3} + b^{2} c^{2} d x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} - \int \frac{c^{5} e x^{6} - {\left(c^{5} d + 2 \, c^{3} e\right)} x^{4} + {\left(c^{3} e x^{4} - {\left(c^{3} d + 3 \, c e\right)} x^{2} - c d\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(2 \, c^{3} d + c e\right)} x^{2} + {\left(2 \, c^{4} e x^{5} - {\left(2 \, c^{4} d + 5 \, c^{2} e\right)} x^{3} + {\left(c^{2} d + 2 \, e\right)} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c d}{a b c^{5} e^{2} x^{8} + 2 \, {\left(c^{5} d e - c^{3} e^{2}\right)} a b x^{6} + {\left(c^{5} d^{2} - 4 \, c^{3} d e + c e^{2}\right)} a b x^{4} + a b c d^{2} - 2 \, {\left(c^{3} d^{2} - c d e\right)} a b x^{2} + {\left(a b c^{3} e^{2} x^{6} + 2 \, a b c^{3} d e x^{4} + a b c^{3} d^{2} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(a b c^{4} e^{2} x^{7} + {\left(2 \, c^{4} d e - c^{2} e^{2}\right)} a b x^{5} - a b c^{2} d^{2} x + {\left(c^{4} d^{2} - 2 \, c^{2} d e\right)} a b x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} e^{2} x^{8} + 2 \, {\left(c^{5} d e - c^{3} e^{2}\right)} b^{2} x^{6} + {\left(c^{5} d^{2} - 4 \, c^{3} d e + c e^{2}\right)} b^{2} x^{4} + b^{2} c d^{2} - 2 \, {\left(c^{3} d^{2} - c d e\right)} b^{2} x^{2} + {\left(b^{2} c^{3} e^{2} x^{6} + 2 \, b^{2} c^{3} d e x^{4} + b^{2} c^{3} d^{2} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{4} e^{2} x^{7} + {\left(2 \, c^{4} d e - c^{2} e^{2}\right)} b^{2} x^{5} - b^{2} c^{2} d^{2} x + {\left(c^{4} d^{2} - 2 \, c^{2} d e\right)} b^{2} x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x)/(a*b*c^3*e*x^4 + (c^3*d - c*e)*a*b*x^2 - a*b*c*d + (a*b*c^2*e*x^3 + a*b*c^2*d*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^3*e*x^4 + (c^3*d - c*e)*b^2*x^2 - b^2*c*d + (b^2*c^2*e*x^3 + b^2*c^2*d*x)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) - integrate((c^5*e*x^6 - (c^5*d + 2*c^3*e)*x^4 + (c^3*e*x^4 - (c^3*d + 3*c*e)*x^2 - c*d)*(c*x + 1)*(c*x - 1) + (2*c^3*d + c*e)*x^2 + (2*c^4*e*x^5 - (2*c^4*d + 5*c^2*e)*x^3 + (c^2*d + 2*e)*x)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*d)/(a*b*c^5*e^2*x^8 + 2*(c^5*d*e - c^3*e^2)*a*b*x^6 + (c^5*d^2 - 4*c^3*d*e + c*e^2)*a*b*x^4 + a*b*c*d^2 - 2*(c^3*d^2 - c*d*e)*a*b*x^2 + (a*b*c^3*e^2*x^6 + 2*a*b*c^3*d*e*x^4 + a*b*c^3*d^2*x^2)*(c*x + 1)*(c*x - 1) + 2*(a*b*c^4*e^2*x^7 + (2*c^4*d*e - c^2*e^2)*a*b*x^5 - a*b*c^2*d^2*x + (c^4*d^2 - 2*c^2*d*e)*a*b*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*e^2*x^8 + 2*(c^5*d*e - c^3*e^2)*b^2*x^6 + (c^5*d^2 - 4*c^3*d*e + c*e^2)*b^2*x^4 + b^2*c*d^2 - 2*(c^3*d^2 - c*d*e)*b^2*x^2 + (b^2*c^3*e^2*x^6 + 2*b^2*c^3*d*e*x^4 + b^2*c^3*d^2*x^2)*(c*x + 1)*(c*x - 1) + 2*(b^2*c^4*e^2*x^7 + (2*c^4*d*e - c^2*e^2)*b^2*x^5 - b^2*c^2*d^2*x + (c^4*d^2 - 2*c^2*d*e)*b^2*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
547,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x}{a b c^{3} e^{2} x^{6} + {\left(2 \, c^{3} d e - c e^{2}\right)} a b x^{4} - a b c d^{2} + {\left(c^{3} d^{2} - 2 \, c d e\right)} a b x^{2} + {\left(a b c^{2} e^{2} x^{5} + 2 \, a b c^{2} d e x^{3} + a b c^{2} d^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{3} e^{2} x^{6} + {\left(2 \, c^{3} d e - c e^{2}\right)} b^{2} x^{4} - b^{2} c d^{2} + {\left(c^{3} d^{2} - 2 \, c d e\right)} b^{2} x^{2} + {\left(b^{2} c^{2} e^{2} x^{5} + 2 \, b^{2} c^{2} d e x^{3} + b^{2} c^{2} d^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} - \int \frac{3 \, c^{5} e x^{6} - {\left(c^{5} d + 6 \, c^{3} e\right)} x^{4} + {\left(3 \, c^{3} e x^{4} - {\left(c^{3} d + 5 \, c e\right)} x^{2} - c d\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(2 \, c^{3} d + 3 \, c e\right)} x^{2} + {\left(6 \, c^{4} e x^{5} - {\left(2 \, c^{4} d + 11 \, c^{2} e\right)} x^{3} + {\left(c^{2} d + 4 \, e\right)} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c d}{a b c^{5} e^{3} x^{10} + {\left(3 \, c^{5} d e^{2} - 2 \, c^{3} e^{3}\right)} a b x^{8} + {\left(3 \, c^{5} d^{2} e - 6 \, c^{3} d e^{2} + c e^{3}\right)} a b x^{6} + {\left(c^{5} d^{3} - 6 \, c^{3} d^{2} e + 3 \, c d e^{2}\right)} a b x^{4} + a b c d^{3} - {\left(2 \, c^{3} d^{3} - 3 \, c d^{2} e\right)} a b x^{2} + {\left(a b c^{3} e^{3} x^{8} + 3 \, a b c^{3} d e^{2} x^{6} + 3 \, a b c^{3} d^{2} e x^{4} + a b c^{3} d^{3} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(a b c^{4} e^{3} x^{9} + {\left(3 \, c^{4} d e^{2} - c^{2} e^{3}\right)} a b x^{7} - a b c^{2} d^{3} x + 3 \, {\left(c^{4} d^{2} e - c^{2} d e^{2}\right)} a b x^{5} + {\left(c^{4} d^{3} - 3 \, c^{2} d^{2} e\right)} a b x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} e^{3} x^{10} + {\left(3 \, c^{5} d e^{2} - 2 \, c^{3} e^{3}\right)} b^{2} x^{8} + {\left(3 \, c^{5} d^{2} e - 6 \, c^{3} d e^{2} + c e^{3}\right)} b^{2} x^{6} + {\left(c^{5} d^{3} - 6 \, c^{3} d^{2} e + 3 \, c d e^{2}\right)} b^{2} x^{4} + b^{2} c d^{3} - {\left(2 \, c^{3} d^{3} - 3 \, c d^{2} e\right)} b^{2} x^{2} + {\left(b^{2} c^{3} e^{3} x^{8} + 3 \, b^{2} c^{3} d e^{2} x^{6} + 3 \, b^{2} c^{3} d^{2} e x^{4} + b^{2} c^{3} d^{3} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{4} e^{3} x^{9} + {\left(3 \, c^{4} d e^{2} - c^{2} e^{3}\right)} b^{2} x^{7} - b^{2} c^{2} d^{3} x + 3 \, {\left(c^{4} d^{2} e - c^{2} d e^{2}\right)} b^{2} x^{5} + {\left(c^{4} d^{3} - 3 \, c^{2} d^{2} e\right)} b^{2} x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x)/(a*b*c^3*e^2*x^6 + (2*c^3*d*e - c*e^2)*a*b*x^4 - a*b*c*d^2 + (c^3*d^2 - 2*c*d*e)*a*b*x^2 + (a*b*c^2*e^2*x^5 + 2*a*b*c^2*d*e*x^3 + a*b*c^2*d^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^3*e^2*x^6 + (2*c^3*d*e - c*e^2)*b^2*x^4 - b^2*c*d^2 + (c^3*d^2 - 2*c*d*e)*b^2*x^2 + (b^2*c^2*e^2*x^5 + 2*b^2*c^2*d*e*x^3 + b^2*c^2*d^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) - integrate((3*c^5*e*x^6 - (c^5*d + 6*c^3*e)*x^4 + (3*c^3*e*x^4 - (c^3*d + 5*c*e)*x^2 - c*d)*(c*x + 1)*(c*x - 1) + (2*c^3*d + 3*c*e)*x^2 + (6*c^4*e*x^5 - (2*c^4*d + 11*c^2*e)*x^3 + (c^2*d + 4*e)*x)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*d)/(a*b*c^5*e^3*x^10 + (3*c^5*d*e^2 - 2*c^3*e^3)*a*b*x^8 + (3*c^5*d^2*e - 6*c^3*d*e^2 + c*e^3)*a*b*x^6 + (c^5*d^3 - 6*c^3*d^2*e + 3*c*d*e^2)*a*b*x^4 + a*b*c*d^3 - (2*c^3*d^3 - 3*c*d^2*e)*a*b*x^2 + (a*b*c^3*e^3*x^8 + 3*a*b*c^3*d*e^2*x^6 + 3*a*b*c^3*d^2*e*x^4 + a*b*c^3*d^3*x^2)*(c*x + 1)*(c*x - 1) + 2*(a*b*c^4*e^3*x^9 + (3*c^4*d*e^2 - c^2*e^3)*a*b*x^7 - a*b*c^2*d^3*x + 3*(c^4*d^2*e - c^2*d*e^2)*a*b*x^5 + (c^4*d^3 - 3*c^2*d^2*e)*a*b*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*e^3*x^10 + (3*c^5*d*e^2 - 2*c^3*e^3)*b^2*x^8 + (3*c^5*d^2*e - 6*c^3*d*e^2 + c*e^3)*b^2*x^6 + (c^5*d^3 - 6*c^3*d^2*e + 3*c*d*e^2)*b^2*x^4 + b^2*c*d^3 - (2*c^3*d^3 - 3*c*d^2*e)*b^2*x^2 + (b^2*c^3*e^3*x^8 + 3*b^2*c^3*d*e^2*x^6 + 3*b^2*c^3*d^2*e*x^4 + b^2*c^3*d^3*x^2)*(c*x + 1)*(c*x - 1) + 2*(b^2*c^4*e^3*x^9 + (3*c^4*d*e^2 - c^2*e^3)*b^2*x^7 - b^2*c^2*d^3*x + 3*(c^4*d^2*e - c^2*d*e^2)*b^2*x^5 + (c^4*d^3 - 3*c^2*d^2*e)*b^2*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
548,0,0,0,0.000000," ","integrate((e*x^2+d)^(1/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{{\left(c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x\right)} \sqrt{e x^{2} + d}}{a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c + {\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)} + \int \frac{{\left(2 \, c^{5} e x^{6} + {\left(c^{5} d - 4 \, c^{3} e\right)} x^{4} + {\left(2 \, c^{3} e x^{4} + c^{3} d x^{2} + c d\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - 2 \, {\left(c^{3} d - c e\right)} x^{2} + {\left(4 \, c^{4} e x^{5} + 2 \, {\left(c^{4} d - 2 \, c^{2} e\right)} x^{3} - {\left(c^{2} d - e\right)} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + c d\right)} \sqrt{e x^{2} + d}}{a b c^{5} e x^{6} + {\left(c^{5} d - 2 \, c^{3} e\right)} a b x^{4} - {\left(2 \, c^{3} d - c e\right)} a b x^{2} + a b c d + {\left(a b c^{3} e x^{4} + a b c^{3} d x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(a b c^{4} e x^{5} - a b c^{2} d x + {\left(c^{4} d - c^{2} e\right)} a b x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + {\left(b^{2} c^{5} e x^{6} + {\left(c^{5} d - 2 \, c^{3} e\right)} b^{2} x^{4} - {\left(2 \, c^{3} d - c e\right)} b^{2} x^{2} + b^{2} c d + {\left(b^{2} c^{3} e x^{4} + b^{2} c^{3} d x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{4} e x^{5} - b^{2} c^{2} d x + {\left(c^{4} d - c^{2} e\right)} b^{2} x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right)}\,{d x}"," ",0,"-(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x)*sqrt(e*x^2 + d)/(a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c + (b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))) + integrate((2*c^5*e*x^6 + (c^5*d - 4*c^3*e)*x^4 + (2*c^3*e*x^4 + c^3*d*x^2 + c*d)*(c*x + 1)*(c*x - 1) - 2*(c^3*d - c*e)*x^2 + (4*c^4*e*x^5 + 2*(c^4*d - 2*c^2*e)*x^3 - (c^2*d - e)*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + c*d)*sqrt(e*x^2 + d)/(a*b*c^5*e*x^6 + (c^5*d - 2*c^3*e)*a*b*x^4 - (2*c^3*d - c*e)*a*b*x^2 + a*b*c*d + (a*b*c^3*e*x^4 + a*b*c^3*d*x^2)*(c*x + 1)*(c*x - 1) + 2*(a*b*c^4*e*x^5 - a*b*c^2*d*x + (c^4*d - c^2*e)*a*b*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1) + (b^2*c^5*e*x^6 + (c^5*d - 2*c^3*e)*b^2*x^4 - (2*c^3*d - c*e)*b^2*x^2 + b^2*c*d + (b^2*c^3*e*x^4 + b^2*c^3*d*x^2)*(c*x + 1)*(c*x - 1) + 2*(b^2*c^4*e*x^5 - b^2*c^2*d*x + (c^4*d - c^2*e)*b^2*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1))), x)","F",0
549,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(c*x))^2/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x}{{\left(b^{2} c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} b^{2} c^{2} x - b^{2} c\right)} \sqrt{e x^{2} + d} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(a b c^{3} x^{2} + \sqrt{c x + 1} \sqrt{c x - 1} a b c^{2} x - a b c\right)} \sqrt{e x^{2} + d}} + \int \frac{c^{5} d x^{4} - 2 \, c^{3} d x^{2} + {\left({\left(c^{3} d + 2 \, c e\right)} x^{2} + c d\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(2 \, {\left(c^{4} d + c^{2} e\right)} x^{3} - {\left(c^{2} d + e\right)} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + c d}{{\left(b^{2} c^{5} e x^{6} + {\left(c^{5} d - 2 \, c^{3} e\right)} b^{2} x^{4} - {\left(2 \, c^{3} d - c e\right)} b^{2} x^{2} + b^{2} c d + {\left(b^{2} c^{3} e x^{4} + b^{2} c^{3} d x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{4} e x^{5} - b^{2} c^{2} d x + {\left(c^{4} d - c^{2} e\right)} b^{2} x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \sqrt{e x^{2} + d} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(a b c^{5} e x^{6} + {\left(c^{5} d - 2 \, c^{3} e\right)} a b x^{4} - {\left(2 \, c^{3} d - c e\right)} a b x^{2} + a b c d + {\left(a b c^{3} e x^{4} + a b c^{3} d x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(a b c^{4} e x^{5} - a b c^{2} d x + {\left(c^{4} d - c^{2} e\right)} a b x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"-(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x)/((b^2*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*b^2*c^2*x - b^2*c)*sqrt(e*x^2 + d)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + (a*b*c^3*x^2 + sqrt(c*x + 1)*sqrt(c*x - 1)*a*b*c^2*x - a*b*c)*sqrt(e*x^2 + d)) + integrate((c^5*d*x^4 - 2*c^3*d*x^2 + ((c^3*d + 2*c*e)*x^2 + c*d)*(c*x + 1)*(c*x - 1) + (2*(c^4*d + c^2*e)*x^3 - (c^2*d + e)*x)*sqrt(c*x + 1)*sqrt(c*x - 1) + c*d)/((b^2*c^5*e*x^6 + (c^5*d - 2*c^3*e)*b^2*x^4 - (2*c^3*d - c*e)*b^2*x^2 + b^2*c*d + (b^2*c^3*e*x^4 + b^2*c^3*d*x^2)*(c*x + 1)*(c*x - 1) + 2*(b^2*c^4*e*x^5 - b^2*c^2*d*x + (c^4*d - c^2*e)*b^2*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))*sqrt(e*x^2 + d)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + (a*b*c^5*e*x^6 + (c^5*d - 2*c^3*e)*a*b*x^4 - (2*c^3*d - c*e)*a*b*x^2 + a*b*c*d + (a*b*c^3*e*x^4 + a*b*c^3*d*x^2)*(c*x + 1)*(c*x - 1) + 2*(a*b*c^4*e*x^5 - a*b*c^2*d*x + (c^4*d - c^2*e)*a*b*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))*sqrt(e*x^2 + d)), x)","F",0
550,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^(3/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x}{{\left(b^{2} c^{3} e x^{4} + {\left(c^{3} d - c e\right)} b^{2} x^{2} - b^{2} c d + {\left(b^{2} c^{2} e x^{3} + b^{2} c^{2} d x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \sqrt{e x^{2} + d} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(a b c^{3} e x^{4} + {\left(c^{3} d - c e\right)} a b x^{2} - a b c d + {\left(a b c^{2} e x^{3} + a b c^{2} d x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \sqrt{e x^{2} + d}} - \int \frac{2 \, c^{5} e x^{6} - {\left(c^{5} d + 4 \, c^{3} e\right)} x^{4} + {\left(2 \, c^{3} e x^{4} - {\left(c^{3} d + 4 \, c e\right)} x^{2} - c d\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(c^{3} d + c e\right)} x^{2} + {\left(4 \, c^{4} e x^{5} - 2 \, {\left(c^{4} d + 4 \, c^{2} e\right)} x^{3} + {\left(c^{2} d + 3 \, e\right)} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c d}{{\left(b^{2} c^{5} e^{2} x^{8} + 2 \, {\left(c^{5} d e - c^{3} e^{2}\right)} b^{2} x^{6} + {\left(c^{5} d^{2} - 4 \, c^{3} d e + c e^{2}\right)} b^{2} x^{4} + b^{2} c d^{2} - 2 \, {\left(c^{3} d^{2} - c d e\right)} b^{2} x^{2} + {\left(b^{2} c^{3} e^{2} x^{6} + 2 \, b^{2} c^{3} d e x^{4} + b^{2} c^{3} d^{2} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{4} e^{2} x^{7} + {\left(2 \, c^{4} d e - c^{2} e^{2}\right)} b^{2} x^{5} - b^{2} c^{2} d^{2} x + {\left(c^{4} d^{2} - 2 \, c^{2} d e\right)} b^{2} x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \sqrt{e x^{2} + d} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(a b c^{5} e^{2} x^{8} + 2 \, {\left(c^{5} d e - c^{3} e^{2}\right)} a b x^{6} + {\left(c^{5} d^{2} - 4 \, c^{3} d e + c e^{2}\right)} a b x^{4} + a b c d^{2} - 2 \, {\left(c^{3} d^{2} - c d e\right)} a b x^{2} + {\left(a b c^{3} e^{2} x^{6} + 2 \, a b c^{3} d e x^{4} + a b c^{3} d^{2} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(a b c^{4} e^{2} x^{7} + {\left(2 \, c^{4} d e - c^{2} e^{2}\right)} a b x^{5} - a b c^{2} d^{2} x + {\left(c^{4} d^{2} - 2 \, c^{2} d e\right)} a b x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"-(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x)/((b^2*c^3*e*x^4 + (c^3*d - c*e)*b^2*x^2 - b^2*c*d + (b^2*c^2*e*x^3 + b^2*c^2*d*x)*sqrt(c*x + 1)*sqrt(c*x - 1))*sqrt(e*x^2 + d)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + (a*b*c^3*e*x^4 + (c^3*d - c*e)*a*b*x^2 - a*b*c*d + (a*b*c^2*e*x^3 + a*b*c^2*d*x)*sqrt(c*x + 1)*sqrt(c*x - 1))*sqrt(e*x^2 + d)) - integrate((2*c^5*e*x^6 - (c^5*d + 4*c^3*e)*x^4 + (2*c^3*e*x^4 - (c^3*d + 4*c*e)*x^2 - c*d)*(c*x + 1)*(c*x - 1) + 2*(c^3*d + c*e)*x^2 + (4*c^4*e*x^5 - 2*(c^4*d + 4*c^2*e)*x^3 + (c^2*d + 3*e)*x)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*d)/((b^2*c^5*e^2*x^8 + 2*(c^5*d*e - c^3*e^2)*b^2*x^6 + (c^5*d^2 - 4*c^3*d*e + c*e^2)*b^2*x^4 + b^2*c*d^2 - 2*(c^3*d^2 - c*d*e)*b^2*x^2 + (b^2*c^3*e^2*x^6 + 2*b^2*c^3*d*e*x^4 + b^2*c^3*d^2*x^2)*(c*x + 1)*(c*x - 1) + 2*(b^2*c^4*e^2*x^7 + (2*c^4*d*e - c^2*e^2)*b^2*x^5 - b^2*c^2*d^2*x + (c^4*d^2 - 2*c^2*d*e)*b^2*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))*sqrt(e*x^2 + d)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + (a*b*c^5*e^2*x^8 + 2*(c^5*d*e - c^3*e^2)*a*b*x^6 + (c^5*d^2 - 4*c^3*d*e + c*e^2)*a*b*x^4 + a*b*c*d^2 - 2*(c^3*d^2 - c*d*e)*a*b*x^2 + (a*b*c^3*e^2*x^6 + 2*a*b*c^3*d*e*x^4 + a*b*c^3*d^2*x^2)*(c*x + 1)*(c*x - 1) + 2*(a*b*c^4*e^2*x^7 + (2*c^4*d*e - c^2*e^2)*a*b*x^5 - a*b*c^2*d^2*x + (c^4*d^2 - 2*c^2*d*e)*a*b*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))*sqrt(e*x^2 + d)), x)","F",0
551,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^(5/2)/(a+b*arccosh(c*x))^2,x, algorithm=""maxima"")","-\frac{c^{3} x^{3} + {\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c x}{{\left(b^{2} c^{3} e^{2} x^{6} + {\left(2 \, c^{3} d e - c e^{2}\right)} b^{2} x^{4} - b^{2} c d^{2} + {\left(c^{3} d^{2} - 2 \, c d e\right)} b^{2} x^{2} + {\left(b^{2} c^{2} e^{2} x^{5} + 2 \, b^{2} c^{2} d e x^{3} + b^{2} c^{2} d^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \sqrt{e x^{2} + d} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(a b c^{3} e^{2} x^{6} + {\left(2 \, c^{3} d e - c e^{2}\right)} a b x^{4} - a b c d^{2} + {\left(c^{3} d^{2} - 2 \, c d e\right)} a b x^{2} + {\left(a b c^{2} e^{2} x^{5} + 2 \, a b c^{2} d e x^{3} + a b c^{2} d^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \sqrt{e x^{2} + d}} - \int \frac{4 \, c^{5} e x^{6} - {\left(c^{5} d + 8 \, c^{3} e\right)} x^{4} + {\left(4 \, c^{3} e x^{4} - {\left(c^{3} d + 6 \, c e\right)} x^{2} - c d\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(c^{3} d + 2 \, c e\right)} x^{2} + {\left(8 \, c^{4} e x^{5} - 2 \, {\left(c^{4} d + 7 \, c^{2} e\right)} x^{3} + {\left(c^{2} d + 5 \, e\right)} x\right)} \sqrt{c x + 1} \sqrt{c x - 1} - c d}{{\left(b^{2} c^{5} e^{3} x^{10} + {\left(3 \, c^{5} d e^{2} - 2 \, c^{3} e^{3}\right)} b^{2} x^{8} + {\left(3 \, c^{5} d^{2} e - 6 \, c^{3} d e^{2} + c e^{3}\right)} b^{2} x^{6} + {\left(c^{5} d^{3} - 6 \, c^{3} d^{2} e + 3 \, c d e^{2}\right)} b^{2} x^{4} + b^{2} c d^{3} - {\left(2 \, c^{3} d^{3} - 3 \, c d^{2} e\right)} b^{2} x^{2} + {\left(b^{2} c^{3} e^{3} x^{8} + 3 \, b^{2} c^{3} d e^{2} x^{6} + 3 \, b^{2} c^{3} d^{2} e x^{4} + b^{2} c^{3} d^{3} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(b^{2} c^{4} e^{3} x^{9} + {\left(3 \, c^{4} d e^{2} - c^{2} e^{3}\right)} b^{2} x^{7} - b^{2} c^{2} d^{3} x + 3 \, {\left(c^{4} d^{2} e - c^{2} d e^{2}\right)} b^{2} x^{5} + {\left(c^{4} d^{3} - 3 \, c^{2} d^{2} e\right)} b^{2} x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \sqrt{e x^{2} + d} \log\left(c x + \sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(a b c^{5} e^{3} x^{10} + {\left(3 \, c^{5} d e^{2} - 2 \, c^{3} e^{3}\right)} a b x^{8} + {\left(3 \, c^{5} d^{2} e - 6 \, c^{3} d e^{2} + c e^{3}\right)} a b x^{6} + {\left(c^{5} d^{3} - 6 \, c^{3} d^{2} e + 3 \, c d e^{2}\right)} a b x^{4} + a b c d^{3} - {\left(2 \, c^{3} d^{3} - 3 \, c d^{2} e\right)} a b x^{2} + {\left(a b c^{3} e^{3} x^{8} + 3 \, a b c^{3} d e^{2} x^{6} + 3 \, a b c^{3} d^{2} e x^{4} + a b c^{3} d^{3} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + 2 \, {\left(a b c^{4} e^{3} x^{9} + {\left(3 \, c^{4} d e^{2} - c^{2} e^{3}\right)} a b x^{7} - a b c^{2} d^{3} x + 3 \, {\left(c^{4} d^{2} e - c^{2} d e^{2}\right)} a b x^{5} + {\left(c^{4} d^{3} - 3 \, c^{2} d^{2} e\right)} a b x^{3}\right)} \sqrt{c x + 1} \sqrt{c x - 1}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"-(c^3*x^3 + (c^2*x^2 - 1)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*x)/((b^2*c^3*e^2*x^6 + (2*c^3*d*e - c*e^2)*b^2*x^4 - b^2*c*d^2 + (c^3*d^2 - 2*c*d*e)*b^2*x^2 + (b^2*c^2*e^2*x^5 + 2*b^2*c^2*d*e*x^3 + b^2*c^2*d^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1))*sqrt(e*x^2 + d)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + (a*b*c^3*e^2*x^6 + (2*c^3*d*e - c*e^2)*a*b*x^4 - a*b*c*d^2 + (c^3*d^2 - 2*c*d*e)*a*b*x^2 + (a*b*c^2*e^2*x^5 + 2*a*b*c^2*d*e*x^3 + a*b*c^2*d^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1))*sqrt(e*x^2 + d)) - integrate((4*c^5*e*x^6 - (c^5*d + 8*c^3*e)*x^4 + (4*c^3*e*x^4 - (c^3*d + 6*c*e)*x^2 - c*d)*(c*x + 1)*(c*x - 1) + 2*(c^3*d + 2*c*e)*x^2 + (8*c^4*e*x^5 - 2*(c^4*d + 7*c^2*e)*x^3 + (c^2*d + 5*e)*x)*sqrt(c*x + 1)*sqrt(c*x - 1) - c*d)/((b^2*c^5*e^3*x^10 + (3*c^5*d*e^2 - 2*c^3*e^3)*b^2*x^8 + (3*c^5*d^2*e - 6*c^3*d*e^2 + c*e^3)*b^2*x^6 + (c^5*d^3 - 6*c^3*d^2*e + 3*c*d*e^2)*b^2*x^4 + b^2*c*d^3 - (2*c^3*d^3 - 3*c*d^2*e)*b^2*x^2 + (b^2*c^3*e^3*x^8 + 3*b^2*c^3*d*e^2*x^6 + 3*b^2*c^3*d^2*e*x^4 + b^2*c^3*d^3*x^2)*(c*x + 1)*(c*x - 1) + 2*(b^2*c^4*e^3*x^9 + (3*c^4*d*e^2 - c^2*e^3)*b^2*x^7 - b^2*c^2*d^3*x + 3*(c^4*d^2*e - c^2*d*e^2)*b^2*x^5 + (c^4*d^3 - 3*c^2*d^2*e)*b^2*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))*sqrt(e*x^2 + d)*log(c*x + sqrt(c*x + 1)*sqrt(c*x - 1)) + (a*b*c^5*e^3*x^10 + (3*c^5*d*e^2 - 2*c^3*e^3)*a*b*x^8 + (3*c^5*d^2*e - 6*c^3*d*e^2 + c*e^3)*a*b*x^6 + (c^5*d^3 - 6*c^3*d^2*e + 3*c*d*e^2)*a*b*x^4 + a*b*c*d^3 - (2*c^3*d^3 - 3*c*d^2*e)*a*b*x^2 + (a*b*c^3*e^3*x^8 + 3*a*b*c^3*d*e^2*x^6 + 3*a*b*c^3*d^2*e*x^4 + a*b*c^3*d^3*x^2)*(c*x + 1)*(c*x - 1) + 2*(a*b*c^4*e^3*x^9 + (3*c^4*d*e^2 - c^2*e^3)*a*b*x^7 - a*b*c^2*d^3*x + 3*(c^4*d^2*e - c^2*d*e^2)*a*b*x^5 + (c^4*d^3 - 3*c^2*d^2*e)*a*b*x^3)*sqrt(c*x + 1)*sqrt(c*x - 1))*sqrt(e*x^2 + d)), x)","F",0
552,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arccosh(c*x))^(1/2),x, algorithm=""maxima"")","\int {\left(e x^{2} + d\right)}^{2} \sqrt{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x^2 + d)^2*sqrt(b*arccosh(c*x) + a), x)","F",0
553,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arccosh(c*x))^(1/2),x, algorithm=""maxima"")","\int {\left(e x^{2} + d\right)} \sqrt{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((e*x^2 + d)*sqrt(b*arccosh(c*x) + a), x)","F",0
554,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \operatorname{arcosh}\left(c x\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*arccosh(c*x) + a), x)","F",0
555,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^(1/2)/(e*x^2+d),x, algorithm=""maxima"")","\int \frac{\sqrt{b \operatorname{arcosh}\left(c x\right) + a}}{e x^{2} + d}\,{d x}"," ",0,"integrate(sqrt(b*arccosh(c*x) + a)/(e*x^2 + d), x)","F",0
556,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^(1/2)/(e*x^2+d)^2,x, algorithm=""maxima"")","\int \frac{\sqrt{b \operatorname{arcosh}\left(c x\right) + a}}{{\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(b*arccosh(c*x) + a)/(e*x^2 + d)^2, x)","F",0
557,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int {\left(e x^{2} + d\right)} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((e*x^2 + d)*(b*arccosh(c*x) + a)^(3/2), x)","F",0
558,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^(3/2), x)","F",0
559,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^(3/2)/(e*x^2+d),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}{e x^{2} + d}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^(3/2)/(e*x^2 + d), x)","F",0
560,0,0,0,0.000000," ","integrate((a+b*arccosh(c*x))^(3/2)/(e*x^2+d)^2,x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}{{\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^(3/2)/(e*x^2 + d)^2, x)","F",0
561,0,0,0,0.000000," ","integrate((e*x^2+d)^2/(a+b*arccosh(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(e x^{2} + d\right)}^{2}}{\sqrt{b \operatorname{arcosh}\left(c x\right) + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)^2/sqrt(b*arccosh(c*x) + a), x)","F",0
562,0,0,0,0.000000," ","integrate((e*x^2+d)/(a+b*arccosh(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{e x^{2} + d}{\sqrt{b \operatorname{arcosh}\left(c x\right) + a}}\,{d x}"," ",0,"integrate((e*x^2 + d)/sqrt(b*arccosh(c*x) + a), x)","F",0
563,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \operatorname{arcosh}\left(c x\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*arccosh(c*x) + a), x)","F",0
564,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(a+b*arccosh(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)} \sqrt{b \operatorname{arcosh}\left(c x\right) + a}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)*sqrt(b*arccosh(c*x) + a)), x)","F",0
565,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(a+b*arccosh(c*x))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)}^{2} \sqrt{b \operatorname{arcosh}\left(c x\right) + a}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)^2*sqrt(b*arccosh(c*x) + a)), x)","F",0
566,0,0,0,0.000000," ","integrate((e*x^2+d)/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{e x^{2} + d}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((e*x^2 + d)/(b*arccosh(c*x) + a)^(3/2), x)","F",0
567,0,0,0,0.000000," ","integrate(1/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arccosh(c*x) + a)^(-3/2), x)","F",0
568,0,0,0,0.000000," ","integrate(1/(e*x^2+d)/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)*(b*arccosh(c*x) + a)^(3/2)), x)","F",0
569,0,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(a+b*arccosh(c*x))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(e x^{2} + d\right)}^{2} {\left(b \operatorname{arcosh}\left(c x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((e*x^2 + d)^2*(b*arccosh(c*x) + a)^(3/2)), x)","F",0
