1,0,0,0,0.582895," ","integrate(x^4*arcsech(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{4} \operatorname{arsech}\left(a x\right)^{2}, x\right)"," ",0,"integral(x^4*arcsech(a*x)^2, x)","F",0
2,1,125,0,0.607666," ","integrate(x^3*arcsech(a*x)^2,x, algorithm=""fricas"")","\frac{3 \, a^{4} x^{4} \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right)^{2} - a^{2} x^{2} - 2 \, {\left(a^{3} x^{3} + 2 \, a x\right)} \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right) - 4 \, \log\left(x\right)}{12 \, a^{4}}"," ",0,"1/12*(3*a^4*x^4*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x))^2 - a^2*x^2 - 2*(a^3*x^3 + 2*a*x)*sqrt(-(a^2*x^2 - 1)/(a^2*x^2))*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x)) - 4*log(x))/a^4","A",0
3,0,0,0,0.688853," ","integrate(x^2*arcsech(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \operatorname{arsech}\left(a x\right)^{2}, x\right)"," ",0,"integral(x^2*arcsech(a*x)^2, x)","F",0
4,1,106,0,0.625484," ","integrate(x*arcsech(a*x)^2,x, algorithm=""fricas"")","\frac{a^{2} x^{2} \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right)^{2} - 2 \, a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right) - 2 \, \log\left(x\right)}{2 \, a^{2}}"," ",0,"1/2*(a^2*x^2*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x))^2 - 2*a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2))*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x)) - 2*log(x))/a^2","B",0
5,0,0,0,0.527345," ","integrate(arcsech(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{arsech}\left(a x\right)^{2}, x\right)"," ",0,"integral(arcsech(a*x)^2, x)","F",0
6,0,0,0,0.678381," ","integrate(arcsech(a*x)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arsech}\left(a x\right)^{2}}{x}, x\right)"," ",0,"integral(arcsech(a*x)^2/x, x)","F",0
7,1,97,0,0.474397," ","integrate(arcsech(a*x)^2/x^2,x, algorithm=""fricas"")","\frac{2 \, a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right) - \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right)^{2} - 2}{x}"," ",0,"(2*a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2))*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x)) - log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x))^2 - 2)/x","B",0
8,1,106,0,0.562351," ","integrate(arcsech(a*x)^2/x^3,x, algorithm=""fricas"")","\frac{2 \, a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right) + {\left(a^{2} x^{2} - 2\right)} \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right)^{2} - 1}{4 \, x^{2}}"," ",0,"1/4*(2*a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2))*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x)) + (a^2*x^2 - 2)*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x))^2 - 1)/x^2","A",0
9,1,116,0,0.952910," ","integrate(arcsech(a*x)^2/x^4,x, algorithm=""fricas"")","-\frac{12 \, a^{2} x^{2} - 6 \, {\left(2 \, a^{3} x^{3} + a x\right)} \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right) + 9 \, \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right)^{2} + 2}{27 \, x^{3}}"," ",0,"-1/27*(12*a^2*x^2 - 6*(2*a^3*x^3 + a*x)*sqrt(-(a^2*x^2 - 1)/(a^2*x^2))*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x)) + 9*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x))^2 + 2)/x^3","A",0
10,0,0,0,0.635741," ","integrate(x^4*arcsech(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(x^{4} \operatorname{arsech}\left(a x\right)^{3}, x\right)"," ",0,"integral(x^4*arcsech(a*x)^3, x)","F",0
11,0,0,0,0.709395," ","integrate(x^3*arcsech(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(x^{3} \operatorname{arsech}\left(a x\right)^{3}, x\right)"," ",0,"integral(x^3*arcsech(a*x)^3, x)","F",0
12,0,0,0,0.671677," ","integrate(x^2*arcsech(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \operatorname{arsech}\left(a x\right)^{3}, x\right)"," ",0,"integral(x^2*arcsech(a*x)^3, x)","F",0
13,0,0,0,0.695812," ","integrate(x*arcsech(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(x \operatorname{arsech}\left(a x\right)^{3}, x\right)"," ",0,"integral(x*arcsech(a*x)^3, x)","F",0
14,0,0,0,0.567850," ","integrate(arcsech(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{arsech}\left(a x\right)^{3}, x\right)"," ",0,"integral(arcsech(a*x)^3, x)","F",0
15,0,0,0,0.627322," ","integrate(arcsech(a*x)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arsech}\left(a x\right)^{3}}{x}, x\right)"," ",0,"integral(arcsech(a*x)^3/x, x)","F",0
16,1,155,0,0.710289," ","integrate(arcsech(a*x)^3/x^2,x, algorithm=""fricas"")","\frac{3 \, a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right)^{2} - \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right)^{3} + 6 \, a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} - 6 \, \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right)}{x}"," ",0,"(3*a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2))*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x))^2 - log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x))^3 + 6*a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) - 6*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x)))/x","A",0
17,1,174,0,0.628509," ","integrate(arcsech(a*x)^3/x^3,x, algorithm=""fricas"")","\frac{6 \, a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right)^{2} + 2 \, {\left(a^{2} x^{2} - 2\right)} \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right)^{3} + 3 \, a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 3 \, {\left(a^{2} x^{2} - 2\right)} \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right)}{8 \, x^{2}}"," ",0,"1/8*(6*a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2))*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x))^2 + 2*(a^2*x^2 - 2)*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x))^3 + 3*a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 3*(a^2*x^2 - 2)*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x)))/x^2","A",0
18,1,186,0,0.677797," ","integrate(arcsech(a*x)^3/x^4,x, algorithm=""fricas"")","\frac{9 \, {\left(2 \, a^{3} x^{3} + a x\right)} \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right)^{2} - 9 \, \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right)^{3} - 6 \, {\left(6 \, a^{2} x^{2} + 1\right)} \log\left(\frac{a x \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}} + 1}{a x}\right) + 2 \, {\left(20 \, a^{3} x^{3} + a x\right)} \sqrt{-\frac{a^{2} x^{2} - 1}{a^{2} x^{2}}}}{27 \, x^{3}}"," ",0,"1/27*(9*(2*a^3*x^3 + a*x)*sqrt(-(a^2*x^2 - 1)/(a^2*x^2))*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x))^2 - 9*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x))^3 - 6*(6*a^2*x^2 + 1)*log((a*x*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)) + 1)/(a*x)) + 2*(20*a^3*x^3 + a*x)*sqrt(-(a^2*x^2 - 1)/(a^2*x^2)))/x^3","A",0
19,1,183,0,0.587022," ","integrate(x^6*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{48 \, a c^{7} x^{7} - 48 \, b c^{7} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) - 30 \, b \arctan\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c x}\right) + 48 \, {\left(b c^{7} x^{7} - b c^{7}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(8 \, b c^{6} x^{6} + 10 \, b c^{4} x^{4} + 15 \, b c^{2} x^{2}\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{336 \, c^{7}}"," ",0,"1/336*(48*a*c^7*x^7 - 48*b*c^7*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) - 30*b*arctan((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c*x)) + 48*(b*c^7*x^7 - b*c^7)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (8*b*c^6*x^6 + 10*b*c^4*x^4 + 15*b*c^2*x^2)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c^7","A",0
20,1,100,0,0.510436," ","integrate(x^5*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{15 \, b c^{5} x^{6} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 15 \, a c^{5} x^{6} - {\left(3 \, b c^{4} x^{5} + 4 \, b c^{2} x^{3} + 8 \, b x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{90 \, c^{5}}"," ",0,"1/90*(15*b*c^5*x^6*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 15*a*c^5*x^6 - (3*b*c^4*x^5 + 4*b*c^2*x^3 + 8*b*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c^5","A",0
21,1,174,0,0.552860," ","integrate(x^4*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{8 \, a c^{5} x^{5} - 8 \, b c^{5} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) - 6 \, b \arctan\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c x}\right) + 8 \, {\left(b c^{5} x^{5} - b c^{5}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(2 \, b c^{4} x^{4} + 3 \, b c^{2} x^{2}\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{40 \, c^{5}}"," ",0,"1/40*(8*a*c^5*x^5 - 8*b*c^5*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) - 6*b*arctan((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c*x)) + 8*(b*c^5*x^5 - b*c^5)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (2*b*c^4*x^4 + 3*b*c^2*x^2)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c^5","B",0
22,1,90,0,0.469939," ","integrate(x^3*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{3 \, b c^{3} x^{4} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 3 \, a c^{3} x^{4} - {\left(b c^{2} x^{3} + 2 \, b x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{12 \, c^{3}}"," ",0,"1/12*(3*b*c^3*x^4*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 3*a*c^3*x^4 - (b*c^2*x^3 + 2*b*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c^3","A",0
23,1,162,0,0.639797," ","integrate(x^2*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{2 \, a c^{3} x^{3} - b c^{2} x^{2} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 2 \, b c^{3} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) - 2 \, b \arctan\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c x}\right) + 2 \, {\left(b c^{3} x^{3} - b c^{3}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)}{6 \, c^{3}}"," ",0,"1/6*(2*a*c^3*x^3 - b*c^2*x^2*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 2*b*c^3*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) - 2*b*arctan((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c*x)) + 2*(b*c^3*x^3 - b*c^3)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)))/c^3","B",0
24,1,73,0,0.583042," ","integrate(x*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{b c x^{2} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + a c x^{2} - b x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, c}"," ",0,"1/2*(b*c*x^2*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + a*c*x^2 - b*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c","B",0
25,1,119,0,0.542742," ","integrate(a+b*arcsech(c*x),x, algorithm=""fricas"")","\frac{a c x - b c \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) - 2 \, b \arctan\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c x}\right) + {\left(b c x - b c\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)}{c}"," ",0,"(a*c*x - b*c*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) - 2*b*arctan((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c*x)) + (b*c*x - b*c)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)))/c","B",0
26,0,0,0,0.543363," ","integrate((a+b*arcsech(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arsech}\left(c x\right) + a}{x}, x\right)"," ",0,"integral((b*arcsech(c*x) + a)/x, x)","F",0
27,1,66,0,0.485878," ","integrate((a+b*arcsech(c*x))/x^2,x, algorithm=""fricas"")","\frac{b c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - b \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - a}{x}"," ",0,"(b*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - b*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - a)/x","A",0
28,1,77,0,0.431039," ","integrate((a+b*arcsech(c*x))/x^3,x, algorithm=""fricas"")","\frac{b c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + {\left(b c^{2} x^{2} - 2 \, b\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 2 \, a}{4 \, x^{2}}"," ",0,"1/4*(b*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + (b*c^2*x^2 - 2*b)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 2*a)/x^2","A",0
29,1,79,0,0.579291," ","integrate((a+b*arcsech(c*x))/x^4,x, algorithm=""fricas"")","-\frac{3 \, b \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(2 \, b c^{3} x^{3} + b c x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 3 \, a}{9 \, x^{3}}"," ",0,"-1/9*(3*b*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (2*b*c^3*x^3 + b*c*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 3*a)/x^3","A",0
30,1,90,0,0.599206," ","integrate((a+b*arcsech(c*x))/x^5,x, algorithm=""fricas"")","\frac{{\left(3 \, b c^{4} x^{4} - 8 \, b\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + {\left(3 \, b c^{3} x^{3} + 2 \, b c x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 8 \, a}{32 \, x^{4}}"," ",0,"1/32*((3*b*c^4*x^4 - 8*b)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + (3*b*c^3*x^3 + 2*b*c*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 8*a)/x^4","A",0
31,1,89,0,0.633751," ","integrate((a+b*arcsech(c*x))/x^6,x, algorithm=""fricas"")","-\frac{15 \, b \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(8 \, b c^{5} x^{5} + 4 \, b c^{3} x^{3} + 3 \, b c x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 15 \, a}{75 \, x^{5}}"," ",0,"-1/75*(15*b*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (8*b*c^5*x^5 + 4*b*c^3*x^3 + 3*b*c*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 15*a)/x^5","A",0
32,1,100,0,0.591110," ","integrate((a+b*arcsech(c*x))/x^7,x, algorithm=""fricas"")","\frac{3 \, {\left(5 \, b c^{6} x^{6} - 16 \, b\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + {\left(15 \, b c^{5} x^{5} + 10 \, b c^{3} x^{3} + 8 \, b c x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 48 \, a}{288 \, x^{6}}"," ",0,"1/288*(3*(5*b*c^6*x^6 - 16*b)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + (15*b*c^5*x^5 + 10*b*c^3*x^3 + 8*b*c*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 48*a)/x^6","A",0
33,1,244,0,0.534869," ","integrate(x^3*(a+b*arcsech(c*x))^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} c^{4} x^{4} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)^{2} + 3 \, a^{2} c^{4} x^{4} - 6 \, a b c^{4} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) - b^{2} c^{2} x^{2} - 4 \, b^{2} \log\left(x\right) + 2 \, {\left(3 \, a b c^{4} x^{4} - 3 \, a b c^{4} - {\left(b^{2} c^{3} x^{3} + 2 \, b^{2} c x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 2 \, {\left(a b c^{3} x^{3} + 2 \, a b c x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{12 \, c^{4}}"," ",0,"1/12*(3*b^2*c^4*x^4*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x))^2 + 3*a^2*c^4*x^4 - 6*a*b*c^4*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) - b^2*c^2*x^2 - 4*b^2*log(x) + 2*(3*a*b*c^4*x^4 - 3*a*b*c^4 - (b^2*c^3*x^3 + 2*b^2*c*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 2*(a*b*c^3*x^3 + 2*a*b*c*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c^4","B",0
34,0,0,0,0.495521," ","integrate(x^2*(a+b*arcsech(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \operatorname{arsech}\left(c x\right)^{2} + 2 \, a b x^{2} \operatorname{arsech}\left(c x\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*arcsech(c*x)^2 + 2*a*b*x^2*arcsech(c*x) + a^2*x^2, x)","F",0
35,1,205,0,0.702339," ","integrate(x*(a+b*arcsech(c*x))^2,x, algorithm=""fricas"")","\frac{b^{2} c^{2} x^{2} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)^{2} + a^{2} c^{2} x^{2} - 2 \, a b c^{2} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) - 2 \, a b c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 2 \, b^{2} \log\left(x\right) + 2 \, {\left(a b c^{2} x^{2} - b^{2} c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - a b c^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)}{2 \, c^{2}}"," ",0,"1/2*(b^2*c^2*x^2*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x))^2 + a^2*c^2*x^2 - 2*a*b*c^2*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) - 2*a*b*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 2*b^2*log(x) + 2*(a*b*c^2*x^2 - b^2*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - a*b*c^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)))/c^2","B",0
36,0,0,0,0.699305," ","integrate((a+b*arcsech(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \operatorname{arsech}\left(c x\right)^{2} + 2 \, a b \operatorname{arsech}\left(c x\right) + a^{2}, x\right)"," ",0,"integral(b^2*arcsech(c*x)^2 + 2*a*b*arcsech(c*x) + a^2, x)","F",0
37,0,0,0,0.620261," ","integrate((a+b*arcsech(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{arsech}\left(c x\right)^{2} + 2 \, a b \operatorname{arsech}\left(c x\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*arcsech(c*x)^2 + 2*a*b*arcsech(c*x) + a^2)/x, x)","F",0
38,1,143,0,0.586808," ","integrate((a+b*arcsech(c*x))^2/x^2,x, algorithm=""fricas"")","\frac{2 \, a b c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - b^{2} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)^{2} - a^{2} - 2 \, b^{2} + 2 \, {\left(b^{2} c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - a b\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)}{x}"," ",0,"(2*a*b*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - b^2*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x))^2 - a^2 - 2*b^2 + 2*(b^2*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - a*b)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)))/x","B",0
39,1,165,0,0.580281," ","integrate((a+b*arcsech(c*x))^2/x^3,x, algorithm=""fricas"")","\frac{2 \, a b c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + {\left(b^{2} c^{2} x^{2} - 2 \, b^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)^{2} - 2 \, a^{2} - b^{2} + 2 \, {\left(a b c^{2} x^{2} + b^{2} c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 2 \, a b\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)}{4 \, x^{2}}"," ",0,"1/4*(2*a*b*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + (b^2*c^2*x^2 - 2*b^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x))^2 - 2*a^2 - b^2 + 2*(a*b*c^2*x^2 + b^2*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 2*a*b)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)))/x^2","A",0
40,1,181,0,0.523904," ","integrate((a+b*arcsech(c*x))^2/x^4,x, algorithm=""fricas"")","-\frac{12 \, b^{2} c^{2} x^{2} + 9 \, b^{2} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)^{2} + 9 \, a^{2} + 2 \, b^{2} + 6 \, {\left(3 \, a b - {\left(2 \, b^{2} c^{3} x^{3} + b^{2} c x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 6 \, {\left(2 \, a b c^{3} x^{3} + a b c x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{27 \, x^{3}}"," ",0,"-1/27*(12*b^2*c^2*x^2 + 9*b^2*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x))^2 + 9*a^2 + 2*b^2 + 6*(3*a*b - (2*b^2*c^3*x^3 + b^2*c*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 6*(2*a*b*c^3*x^3 + a*b*c*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/x^3","A",0
41,1,204,0,0.616119," ","integrate((a+b*arcsech(c*x))^2/x^5,x, algorithm=""fricas"")","-\frac{3 \, b^{2} c^{2} x^{2} - {\left(3 \, b^{2} c^{4} x^{4} - 8 \, b^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)^{2} + 8 \, a^{2} + b^{2} - 2 \, {\left(3 \, a b c^{4} x^{4} - 8 \, a b + {\left(3 \, b^{2} c^{3} x^{3} + 2 \, b^{2} c x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 2 \, {\left(3 \, a b c^{3} x^{3} + 2 \, a b c x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{32 \, x^{4}}"," ",0,"-1/32*(3*b^2*c^2*x^2 - (3*b^2*c^4*x^4 - 8*b^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x))^2 + 8*a^2 + b^2 - 2*(3*a*b*c^4*x^4 - 8*a*b + (3*b^2*c^3*x^3 + 2*b^2*c*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 2*(3*a*b*c^3*x^3 + 2*a*b*c*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/x^4","A",0
42,0,0,0,0.615386," ","integrate(x^3*(a+b*arcsech(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{3} \operatorname{arsech}\left(c x\right)^{3} + 3 \, a b^{2} x^{3} \operatorname{arsech}\left(c x\right)^{2} + 3 \, a^{2} b x^{3} \operatorname{arsech}\left(c x\right) + a^{3} x^{3}, x\right)"," ",0,"integral(b^3*x^3*arcsech(c*x)^3 + 3*a*b^2*x^3*arcsech(c*x)^2 + 3*a^2*b*x^3*arcsech(c*x) + a^3*x^3, x)","F",0
43,0,0,0,0.538759," ","integrate(x^2*(a+b*arcsech(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{2} \operatorname{arsech}\left(c x\right)^{3} + 3 \, a b^{2} x^{2} \operatorname{arsech}\left(c x\right)^{2} + 3 \, a^{2} b x^{2} \operatorname{arsech}\left(c x\right) + a^{3} x^{2}, x\right)"," ",0,"integral(b^3*x^2*arcsech(c*x)^3 + 3*a*b^2*x^2*arcsech(c*x)^2 + 3*a^2*b*x^2*arcsech(c*x) + a^3*x^2, x)","F",0
44,0,0,0,0.606365," ","integrate(x*(a+b*arcsech(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x \operatorname{arsech}\left(c x\right)^{3} + 3 \, a b^{2} x \operatorname{arsech}\left(c x\right)^{2} + 3 \, a^{2} b x \operatorname{arsech}\left(c x\right) + a^{3} x, x\right)"," ",0,"integral(b^3*x*arcsech(c*x)^3 + 3*a*b^2*x*arcsech(c*x)^2 + 3*a^2*b*x*arcsech(c*x) + a^3*x, x)","F",0
45,0,0,0,0.521450," ","integrate((a+b*arcsech(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} \operatorname{arsech}\left(c x\right)^{3} + 3 \, a b^{2} \operatorname{arsech}\left(c x\right)^{2} + 3 \, a^{2} b \operatorname{arsech}\left(c x\right) + a^{3}, x\right)"," ",0,"integral(b^3*arcsech(c*x)^3 + 3*a*b^2*arcsech(c*x)^2 + 3*a^2*b*arcsech(c*x) + a^3, x)","F",0
46,0,0,0,0.474514," ","integrate((a+b*arcsech(c*x))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{arsech}\left(c x\right)^{3} + 3 \, a b^{2} \operatorname{arsech}\left(c x\right)^{2} + 3 \, a^{2} b \operatorname{arsech}\left(c x\right) + a^{3}}{x}, x\right)"," ",0,"integral((b^3*arcsech(c*x)^3 + 3*a*b^2*arcsech(c*x)^2 + 3*a^2*b*arcsech(c*x) + a^3)/x, x)","F",0
47,1,228,0,0.541538," ","integrate((a+b*arcsech(c*x))^3/x^2,x, algorithm=""fricas"")","-\frac{b^{3} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)^{3} - 3 \, {\left(a^{2} b + 2 \, b^{3}\right)} c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + a^{3} + 6 \, a b^{2} - 3 \, {\left(b^{3} c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - a b^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)^{2} - 3 \, {\left(2 \, a b^{2} c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - a^{2} b - 2 \, b^{3}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)}{x}"," ",0,"-(b^3*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x))^3 - 3*(a^2*b + 2*b^3)*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + a^3 + 6*a*b^2 - 3*(b^3*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - a*b^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x))^2 - 3*(2*a*b^2*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - a^2*b - 2*b^3)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)))/x","B",0
48,1,271,0,0.479816," ","integrate((a+b*arcsech(c*x))^3/x^3,x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} c^{2} x^{2} - 2 \, b^{3}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)^{3} + 3 \, {\left(2 \, a^{2} b + b^{3}\right)} c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 4 \, a^{3} - 6 \, a b^{2} + 6 \, {\left(a b^{2} c^{2} x^{2} + b^{3} c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 2 \, a b^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)^{2} + 3 \, {\left(4 \, a b^{2} c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + {\left(2 \, a^{2} b + b^{3}\right)} c^{2} x^{2} - 4 \, a^{2} b - 2 \, b^{3}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)}{8 \, x^{2}}"," ",0,"1/8*(2*(b^3*c^2*x^2 - 2*b^3)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x))^3 + 3*(2*a^2*b + b^3)*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 4*a^3 - 6*a*b^2 + 6*(a*b^2*c^2*x^2 + b^3*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 2*a*b^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x))^2 + 3*(4*a*b^2*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + (2*a^2*b + b^3)*c^2*x^2 - 4*a^2*b - 2*b^3)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)))/x^2","A",0
49,1,305,0,0.718914," ","integrate((a+b*arcsech(c*x))^3/x^4,x, algorithm=""fricas"")","-\frac{36 \, a b^{2} c^{2} x^{2} + 9 \, b^{3} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)^{3} + 9 \, a^{3} + 6 \, a b^{2} + 9 \, {\left(3 \, a b^{2} - {\left(2 \, b^{3} c^{3} x^{3} + b^{3} c x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)^{2} + 3 \, {\left(12 \, b^{3} c^{2} x^{2} + 9 \, a^{2} b + 2 \, b^{3} - 6 \, {\left(2 \, a b^{2} c^{3} x^{3} + a b^{2} c x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(2 \, {\left(9 \, a^{2} b + 20 \, b^{3}\right)} c^{3} x^{3} + {\left(9 \, a^{2} b + 2 \, b^{3}\right)} c x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{27 \, x^{3}}"," ",0,"-1/27*(36*a*b^2*c^2*x^2 + 9*b^3*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x))^3 + 9*a^3 + 6*a*b^2 + 9*(3*a*b^2 - (2*b^3*c^3*x^3 + b^3*c*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x))^2 + 3*(12*b^3*c^2*x^2 + 9*a^2*b + 2*b^3 - 6*(2*a*b^2*c^3*x^3 + a*b^2*c*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (2*(9*a^2*b + 20*b^3)*c^3*x^3 + (9*a^2*b + 2*b^3)*c*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/x^3","A",0
50,1,351,0,0.604748," ","integrate((a+b*arcsech(c*x))^3/x^5,x, algorithm=""fricas"")","-\frac{72 \, a b^{2} c^{2} x^{2} - 8 \, {\left(3 \, b^{3} c^{4} x^{4} - 8 \, b^{3}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)^{3} + 64 \, a^{3} + 24 \, a b^{2} - 24 \, {\left(3 \, a b^{2} c^{4} x^{4} - 8 \, a b^{2} + {\left(3 \, b^{3} c^{3} x^{3} + 2 \, b^{3} c x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)^{2} - 3 \, {\left(3 \, {\left(8 \, a^{2} b + 5 \, b^{3}\right)} c^{4} x^{4} - 24 \, b^{3} c^{2} x^{2} - 64 \, a^{2} b - 8 \, b^{3} + 16 \, {\left(3 \, a b^{2} c^{3} x^{3} + 2 \, a b^{2} c x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 3 \, {\left(3 \, {\left(8 \, a^{2} b + 5 \, b^{3}\right)} c^{3} x^{3} + 2 \, {\left(8 \, a^{2} b + b^{3}\right)} c x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{256 \, x^{4}}"," ",0,"-1/256*(72*a*b^2*c^2*x^2 - 8*(3*b^3*c^4*x^4 - 8*b^3)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x))^3 + 64*a^3 + 24*a*b^2 - 24*(3*a*b^2*c^4*x^4 - 8*a*b^2 + (3*b^3*c^3*x^3 + 2*b^3*c*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x))^2 - 3*(3*(8*a^2*b + 5*b^3)*c^4*x^4 - 24*b^3*c^2*x^2 - 64*a^2*b - 8*b^3 + 16*(3*a*b^2*c^3*x^3 + 2*a*b^2*c*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 3*(3*(8*a^2*b + 5*b^3)*c^3*x^3 + 2*(8*a^2*b + b^3)*c*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/x^4","A",0
51,0,0,0,0.573011," ","integrate(x/(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b \operatorname{arsech}\left(c x\right) + a}, x\right)"," ",0,"integral(x/(b*arcsech(c*x) + a), x)","F",0
52,0,0,0,0.440866," ","integrate(1/(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b \operatorname{arsech}\left(c x\right) + a}, x\right)"," ",0,"integral(1/(b*arcsech(c*x) + a), x)","F",0
53,0,0,0,0.559325," ","integrate(1/x/(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x \operatorname{arsech}\left(c x\right) + a x}, x\right)"," ",0,"integral(1/(b*x*arcsech(c*x) + a*x), x)","F",0
54,0,0,0,0.541786," ","integrate(1/x^2/(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x^{2} \operatorname{arsech}\left(c x\right) + a x^{2}}, x\right)"," ",0,"integral(1/(b*x^2*arcsech(c*x) + a*x^2), x)","F",0
55,0,0,0,0.525574," ","integrate(1/x^3/(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x^{3} \operatorname{arsech}\left(c x\right) + a x^{3}}, x\right)"," ",0,"integral(1/(b*x^3*arcsech(c*x) + a*x^3), x)","F",0
56,0,0,0,0.507200," ","integrate(1/x^4/(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x^{4} \operatorname{arsech}\left(c x\right) + a x^{4}}, x\right)"," ",0,"integral(1/(b*x^4*arcsech(c*x) + a*x^4), x)","F",0
57,0,0,0,0.509785," ","integrate(x/(a+b*arcsech(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b^{2} \operatorname{arsech}\left(c x\right)^{2} + 2 \, a b \operatorname{arsech}\left(c x\right) + a^{2}}, x\right)"," ",0,"integral(x/(b^2*arcsech(c*x)^2 + 2*a*b*arcsech(c*x) + a^2), x)","F",0
58,0,0,0,0.609074," ","integrate(1/(a+b*arcsech(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} \operatorname{arsech}\left(c x\right)^{2} + 2 \, a b \operatorname{arsech}\left(c x\right) + a^{2}}, x\right)"," ",0,"integral(1/(b^2*arcsech(c*x)^2 + 2*a*b*arcsech(c*x) + a^2), x)","F",0
59,0,0,0,0.678304," ","integrate(1/x/(a+b*arcsech(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x \operatorname{arsech}\left(c x\right)^{2} + 2 \, a b x \operatorname{arsech}\left(c x\right) + a^{2} x}, x\right)"," ",0,"integral(1/(b^2*x*arcsech(c*x)^2 + 2*a*b*x*arcsech(c*x) + a^2*x), x)","F",0
60,0,0,0,0.499747," ","integrate(1/x^2/(a+b*arcsech(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{2} \operatorname{arsech}\left(c x\right)^{2} + 2 \, a b x^{2} \operatorname{arsech}\left(c x\right) + a^{2} x^{2}}, x\right)"," ",0,"integral(1/(b^2*x^2*arcsech(c*x)^2 + 2*a*b*x^2*arcsech(c*x) + a^2*x^2), x)","F",0
61,0,0,0,0.639736," ","integrate(1/x^3/(a+b*arcsech(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{3} \operatorname{arsech}\left(c x\right)^{2} + 2 \, a b x^{3} \operatorname{arsech}\left(c x\right) + a^{2} x^{3}}, x\right)"," ",0,"integral(1/(b^2*x^3*arcsech(c*x)^2 + 2*a*b*x^3*arcsech(c*x) + a^2*x^3), x)","F",0
62,0,0,0,0.841804," ","integrate(1/x^4/(a+b*arcsech(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{4} \operatorname{arsech}\left(c x\right)^{2} + 2 \, a b x^{4} \operatorname{arsech}\left(c x\right) + a^{2} x^{4}}, x\right)"," ",0,"integral(1/(b^2*x^4*arcsech(c*x)^2 + 2*a*b*x^4*arcsech(c*x) + a^2*x^4), x)","F",0
63,0,0,0,1.046401," ","integrate(x/(a+b*arcsech(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b^{3} \operatorname{arsech}\left(c x\right)^{3} + 3 \, a b^{2} \operatorname{arsech}\left(c x\right)^{2} + 3 \, a^{2} b \operatorname{arsech}\left(c x\right) + a^{3}}, x\right)"," ",0,"integral(x/(b^3*arcsech(c*x)^3 + 3*a*b^2*arcsech(c*x)^2 + 3*a^2*b*arcsech(c*x) + a^3), x)","F",0
64,0,0,0,0.613698," ","integrate(1/(a+b*arcsech(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} \operatorname{arsech}\left(c x\right)^{3} + 3 \, a b^{2} \operatorname{arsech}\left(c x\right)^{2} + 3 \, a^{2} b \operatorname{arsech}\left(c x\right) + a^{3}}, x\right)"," ",0,"integral(1/(b^3*arcsech(c*x)^3 + 3*a*b^2*arcsech(c*x)^2 + 3*a^2*b*arcsech(c*x) + a^3), x)","F",0
65,0,0,0,0.645537," ","integrate(1/x/(a+b*arcsech(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} x \operatorname{arsech}\left(c x\right)^{3} + 3 \, a b^{2} x \operatorname{arsech}\left(c x\right)^{2} + 3 \, a^{2} b x \operatorname{arsech}\left(c x\right) + a^{3} x}, x\right)"," ",0,"integral(1/(b^3*x*arcsech(c*x)^3 + 3*a*b^2*x*arcsech(c*x)^2 + 3*a^2*b*x*arcsech(c*x) + a^3*x), x)","F",0
66,0,0,0,0.546979," ","integrate(1/x^2/(a+b*arcsech(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} x^{2} \operatorname{arsech}\left(c x\right)^{3} + 3 \, a b^{2} x^{2} \operatorname{arsech}\left(c x\right)^{2} + 3 \, a^{2} b x^{2} \operatorname{arsech}\left(c x\right) + a^{3} x^{2}}, x\right)"," ",0,"integral(1/(b^3*x^2*arcsech(c*x)^3 + 3*a*b^2*x^2*arcsech(c*x)^2 + 3*a^2*b*x^2*arcsech(c*x) + a^3*x^2), x)","F",0
67,0,0,0,0.959358," ","integrate(1/x^3/(a+b*arcsech(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} x^{3} \operatorname{arsech}\left(c x\right)^{3} + 3 \, a b^{2} x^{3} \operatorname{arsech}\left(c x\right)^{2} + 3 \, a^{2} b x^{3} \operatorname{arsech}\left(c x\right) + a^{3} x^{3}}, x\right)"," ",0,"integral(1/(b^3*x^3*arcsech(c*x)^3 + 3*a*b^2*x^3*arcsech(c*x)^2 + 3*a^2*b*x^3*arcsech(c*x) + a^3*x^3), x)","F",0
68,0,0,0,0.613284," ","integrate(1/x^4/(a+b*arcsech(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} x^{4} \operatorname{arsech}\left(c x\right)^{3} + 3 \, a b^{2} x^{4} \operatorname{arsech}\left(c x\right)^{2} + 3 \, a^{2} b x^{4} \operatorname{arsech}\left(c x\right) + a^{3} x^{4}}, x\right)"," ",0,"integral(1/(b^3*x^4*arcsech(c*x)^3 + 3*a*b^2*x^4*arcsech(c*x)^2 + 3*a^2*b*x^4*arcsech(c*x) + a^3*x^4), x)","F",0
69,0,0,0,0.697450," ","integrate((d*x)^m*(a+b*arcsech(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \operatorname{arsech}\left(c x\right)^{3} + 3 \, a b^{2} \operatorname{arsech}\left(c x\right)^{2} + 3 \, a^{2} b \operatorname{arsech}\left(c x\right) + a^{3}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^3*arcsech(c*x)^3 + 3*a*b^2*arcsech(c*x)^2 + 3*a^2*b*arcsech(c*x) + a^3)*(d*x)^m, x)","F",0
70,0,0,0,0.720520," ","integrate((d*x)^m*(a+b*arcsech(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \operatorname{arsech}\left(c x\right)^{2} + 2 \, a b \operatorname{arsech}\left(c x\right) + a^{2}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^2*arcsech(c*x)^2 + 2*a*b*arcsech(c*x) + a^2)*(d*x)^m, x)","F",0
71,0,0,0,1.231830," ","integrate((d*x)^m*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \operatorname{arsech}\left(c x\right) + a\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b*arcsech(c*x) + a)*(d*x)^m, x)","F",0
72,0,0,0,0.644934," ","integrate((d*x)^m/(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b \operatorname{arsech}\left(c x\right) + a}, x\right)"," ",0,"integral((d*x)^m/(b*arcsech(c*x) + a), x)","F",0
73,0,0,0,0.558110," ","integrate((d*x)^m/(a+b*arcsech(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b^{2} \operatorname{arsech}\left(c x\right)^{2} + 2 \, a b \operatorname{arsech}\left(c x\right) + a^{2}}, x\right)"," ",0,"integral((d*x)^m/(b^2*arcsech(c*x)^2 + 2*a*b*arcsech(c*x) + a^2), x)","F",0
74,1,358,0,0.762126," ","integrate((e*x+d)^3*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{3 \, a c^{3} e^{3} x^{4} + 12 \, a c^{3} d e^{2} x^{3} + 18 \, a c^{3} d^{2} e x^{2} + 12 \, a c^{3} d^{3} x - 12 \, {\left(2 \, b c^{2} d^{3} + b d e^{2}\right)} \arctan\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c x}\right) - 3 \, {\left(4 \, b c^{3} d^{3} + 6 \, b c^{3} d^{2} e + 4 \, b c^{3} d e^{2} + b c^{3} e^{3}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + 3 \, {\left(b c^{3} e^{3} x^{4} + 4 \, b c^{3} d e^{2} x^{3} + 6 \, b c^{3} d^{2} e x^{2} + 4 \, b c^{3} d^{3} x - 4 \, b c^{3} d^{3} - 6 \, b c^{3} d^{2} e - 4 \, b c^{3} d e^{2} - b c^{3} e^{3}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(b c^{2} e^{3} x^{3} + 6 \, b c^{2} d e^{2} x^{2} + 2 \, {\left(9 \, b c^{2} d^{2} e + b e^{3}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{12 \, c^{3}}"," ",0,"1/12*(3*a*c^3*e^3*x^4 + 12*a*c^3*d*e^2*x^3 + 18*a*c^3*d^2*e*x^2 + 12*a*c^3*d^3*x - 12*(2*b*c^2*d^3 + b*d*e^2)*arctan((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c*x)) - 3*(4*b*c^3*d^3 + 6*b*c^3*d^2*e + 4*b*c^3*d*e^2 + b*c^3*e^3)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + 3*(b*c^3*e^3*x^4 + 4*b*c^3*d*e^2*x^3 + 6*b*c^3*d^2*e*x^2 + 4*b*c^3*d^3*x - 4*b*c^3*d^3 - 6*b*c^3*d^2*e - 4*b*c^3*d*e^2 - b*c^3*e^3)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (b*c^2*e^3*x^3 + 6*b*c^2*d*e^2*x^2 + 2*(9*b*c^2*d^2*e + b*e^3)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c^3","B",0
75,1,280,0,0.695254," ","integrate((e*x+d)^2*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{2 \, a c^{3} e^{2} x^{3} + 6 \, a c^{3} d e x^{2} + 6 \, a c^{3} d^{2} x - 2 \, {\left(6 \, b c^{2} d^{2} + b e^{2}\right)} \arctan\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c x}\right) - 2 \, {\left(3 \, b c^{3} d^{2} + 3 \, b c^{3} d e + b c^{3} e^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + 2 \, {\left(b c^{3} e^{2} x^{3} + 3 \, b c^{3} d e x^{2} + 3 \, b c^{3} d^{2} x - 3 \, b c^{3} d^{2} - 3 \, b c^{3} d e - b c^{3} e^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(b c^{2} e^{2} x^{2} + 6 \, b c^{2} d e x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{6 \, c^{3}}"," ",0,"1/6*(2*a*c^3*e^2*x^3 + 6*a*c^3*d*e*x^2 + 6*a*c^3*d^2*x - 2*(6*b*c^2*d^2 + b*e^2)*arctan((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c*x)) - 2*(3*b*c^3*d^2 + 3*b*c^3*d*e + b*c^3*e^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + 2*(b*c^3*e^2*x^3 + 3*b*c^3*d*e*x^2 + 3*b*c^3*d^2*x - 3*b*c^3*d^2 - 3*b*c^3*d*e - b*c^3*e^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (b*c^2*e^2*x^2 + 6*b*c^2*d*e*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c^3","B",0
76,1,177,0,0.679157," ","integrate((e*x+d)*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{a c e x^{2} + 2 \, a c d x - b e x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 4 \, b d \arctan\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c x}\right) - {\left(2 \, b c d + b c e\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + {\left(b c e x^{2} + 2 \, b c d x - 2 \, b c d - b c e\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)}{2 \, c}"," ",0,"1/2*(a*c*e*x^2 + 2*a*c*d*x - b*e*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 4*b*d*arctan((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c*x)) - (2*b*c*d + b*c*e)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + (b*c*e*x^2 + 2*b*c*d*x - 2*b*c*d - b*c*e)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)))/c","B",0
77,1,119,0,0.681581," ","integrate(a+b*arcsech(c*x),x, algorithm=""fricas"")","\frac{a c x - b c \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) - 2 \, b \arctan\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c x}\right) + {\left(b c x - b c\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)}{c}"," ",0,"(a*c*x - b*c*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) - 2*b*arctan((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c*x)) + (b*c*x - b*c)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)))/c","B",0
78,0,0,0,0.690268," ","integrate((a+b*arcsech(c*x))/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arsech}\left(c x\right) + a}{e x + d}, x\right)"," ",0,"integral((b*arcsech(c*x) + a)/(e*x + d), x)","F",0
79,1,578,0,1.080967," ","integrate((a+b*arcsech(c*x))/(e*x+d)^2,x, algorithm=""fricas"")","\left[-\frac{a c^{2} d^{3} - a d e^{2} + \sqrt{-c^{2} d^{2} + e^{2}} {\left(b e^{2} x + b d e\right)} \log\left(\frac{c^{2} d e x - {\left(c^{3} d^{2} - c e^{2}\right)} x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2} - \sqrt{-c^{2} d^{2} + e^{2}} {\left(c^{2} d x + c e x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e\right)}}{e x + d}\right) + {\left(b c^{2} d^{3} - b d e^{2} + {\left(b c^{2} d^{2} e - b e^{3}\right)} x\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + {\left(b c^{2} d^{3} - b d e^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)}{c^{2} d^{4} e - d^{2} e^{3} + {\left(c^{2} d^{3} e^{2} - d e^{4}\right)} x}, -\frac{a c^{2} d^{3} - a d e^{2} - 2 \, \sqrt{c^{2} d^{2} - e^{2}} {\left(b e^{2} x + b d e\right)} \arctan\left(-\frac{\sqrt{c^{2} d^{2} - e^{2}} c d x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - \sqrt{c^{2} d^{2} - e^{2}} {\left(e x + d\right)}}{{\left(c^{2} d^{2} - e^{2}\right)} x}\right) + {\left(b c^{2} d^{3} - b d e^{2} + {\left(b c^{2} d^{2} e - b e^{3}\right)} x\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + {\left(b c^{2} d^{3} - b d e^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)}{c^{2} d^{4} e - d^{2} e^{3} + {\left(c^{2} d^{3} e^{2} - d e^{4}\right)} x}\right]"," ",0,"[-(a*c^2*d^3 - a*d*e^2 + sqrt(-c^2*d^2 + e^2)*(b*e^2*x + b*d*e)*log((c^2*d*e*x - (c^3*d^2 - c*e^2)*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2 - sqrt(-c^2*d^2 + e^2)*(c^2*d*x + c*e*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e))/(e*x + d)) + (b*c^2*d^3 - b*d*e^2 + (b*c^2*d^2*e - b*e^3)*x)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + (b*c^2*d^3 - b*d*e^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)))/(c^2*d^4*e - d^2*e^3 + (c^2*d^3*e^2 - d*e^4)*x), -(a*c^2*d^3 - a*d*e^2 - 2*sqrt(c^2*d^2 - e^2)*(b*e^2*x + b*d*e)*arctan(-(sqrt(c^2*d^2 - e^2)*c*d*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - sqrt(c^2*d^2 - e^2)*(e*x + d))/((c^2*d^2 - e^2)*x)) + (b*c^2*d^3 - b*d*e^2 + (b*c^2*d^2*e - b*e^3)*x)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + (b*c^2*d^3 - b*d*e^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)))/(c^2*d^4*e - d^2*e^3 + (c^2*d^3*e^2 - d*e^4)*x)]","B",0
80,1,1212,0,0.878068," ","integrate((a+b*arcsech(c*x))/(e*x+d)^3,x, algorithm=""fricas"")","\left[-\frac{a c^{4} d^{6} - {\left(2 \, a + b\right)} c^{2} d^{4} e^{2} + {\left(a + b\right)} d^{2} e^{4} - {\left(b c^{2} d^{2} e^{4} - b e^{6}\right)} x^{2} + {\left(2 \, b c^{2} d^{4} e - b d^{2} e^{3} + {\left(2 \, b c^{2} d^{2} e^{3} - b e^{5}\right)} x^{2} + 2 \, {\left(2 \, b c^{2} d^{3} e^{2} - b d e^{4}\right)} x\right)} \sqrt{-c^{2} d^{2} + e^{2}} \log\left(\frac{c^{2} d e x - {\left(c^{3} d^{2} - c e^{2}\right)} x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2} - \sqrt{-c^{2} d^{2} + e^{2}} {\left(c^{2} d x + c e x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e\right)}}{e x + d}\right) - 2 \, {\left(b c^{2} d^{3} e^{3} - b d e^{5}\right)} x + {\left(b c^{4} d^{6} - 2 \, b c^{2} d^{4} e^{2} + b d^{2} e^{4} + {\left(b c^{4} d^{4} e^{2} - 2 \, b c^{2} d^{2} e^{4} + b e^{6}\right)} x^{2} + 2 \, {\left(b c^{4} d^{5} e - 2 \, b c^{2} d^{3} e^{3} + b d e^{5}\right)} x\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + {\left(b c^{4} d^{6} - 2 \, b c^{2} d^{4} e^{2} + b d^{2} e^{4}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left({\left(b c^{3} d^{3} e^{3} - b c d e^{5}\right)} x^{2} + {\left(b c^{3} d^{4} e^{2} - b c d^{2} e^{4}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{4} d^{8} e - 2 \, c^{2} d^{6} e^{3} + d^{4} e^{5} + {\left(c^{4} d^{6} e^{3} - 2 \, c^{2} d^{4} e^{5} + d^{2} e^{7}\right)} x^{2} + 2 \, {\left(c^{4} d^{7} e^{2} - 2 \, c^{2} d^{5} e^{4} + d^{3} e^{6}\right)} x\right)}}, -\frac{a c^{4} d^{6} - {\left(2 \, a + b\right)} c^{2} d^{4} e^{2} + {\left(a + b\right)} d^{2} e^{4} - {\left(b c^{2} d^{2} e^{4} - b e^{6}\right)} x^{2} - 2 \, {\left(2 \, b c^{2} d^{4} e - b d^{2} e^{3} + {\left(2 \, b c^{2} d^{2} e^{3} - b e^{5}\right)} x^{2} + 2 \, {\left(2 \, b c^{2} d^{3} e^{2} - b d e^{4}\right)} x\right)} \sqrt{c^{2} d^{2} - e^{2}} \arctan\left(-\frac{\sqrt{c^{2} d^{2} - e^{2}} c d x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - \sqrt{c^{2} d^{2} - e^{2}} {\left(e x + d\right)}}{{\left(c^{2} d^{2} - e^{2}\right)} x}\right) - 2 \, {\left(b c^{2} d^{3} e^{3} - b d e^{5}\right)} x + {\left(b c^{4} d^{6} - 2 \, b c^{2} d^{4} e^{2} + b d^{2} e^{4} + {\left(b c^{4} d^{4} e^{2} - 2 \, b c^{2} d^{2} e^{4} + b e^{6}\right)} x^{2} + 2 \, {\left(b c^{4} d^{5} e - 2 \, b c^{2} d^{3} e^{3} + b d e^{5}\right)} x\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + {\left(b c^{4} d^{6} - 2 \, b c^{2} d^{4} e^{2} + b d^{2} e^{4}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left({\left(b c^{3} d^{3} e^{3} - b c d e^{5}\right)} x^{2} + {\left(b c^{3} d^{4} e^{2} - b c d^{2} e^{4}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{4} d^{8} e - 2 \, c^{2} d^{6} e^{3} + d^{4} e^{5} + {\left(c^{4} d^{6} e^{3} - 2 \, c^{2} d^{4} e^{5} + d^{2} e^{7}\right)} x^{2} + 2 \, {\left(c^{4} d^{7} e^{2} - 2 \, c^{2} d^{5} e^{4} + d^{3} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/2*(a*c^4*d^6 - (2*a + b)*c^2*d^4*e^2 + (a + b)*d^2*e^4 - (b*c^2*d^2*e^4 - b*e^6)*x^2 + (2*b*c^2*d^4*e - b*d^2*e^3 + (2*b*c^2*d^2*e^3 - b*e^5)*x^2 + 2*(2*b*c^2*d^3*e^2 - b*d*e^4)*x)*sqrt(-c^2*d^2 + e^2)*log((c^2*d*e*x - (c^3*d^2 - c*e^2)*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2 - sqrt(-c^2*d^2 + e^2)*(c^2*d*x + c*e*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e))/(e*x + d)) - 2*(b*c^2*d^3*e^3 - b*d*e^5)*x + (b*c^4*d^6 - 2*b*c^2*d^4*e^2 + b*d^2*e^4 + (b*c^4*d^4*e^2 - 2*b*c^2*d^2*e^4 + b*e^6)*x^2 + 2*(b*c^4*d^5*e - 2*b*c^2*d^3*e^3 + b*d*e^5)*x)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + (b*c^4*d^6 - 2*b*c^2*d^4*e^2 + b*d^2*e^4)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - ((b*c^3*d^3*e^3 - b*c*d*e^5)*x^2 + (b*c^3*d^4*e^2 - b*c*d^2*e^4)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/(c^4*d^8*e - 2*c^2*d^6*e^3 + d^4*e^5 + (c^4*d^6*e^3 - 2*c^2*d^4*e^5 + d^2*e^7)*x^2 + 2*(c^4*d^7*e^2 - 2*c^2*d^5*e^4 + d^3*e^6)*x), -1/2*(a*c^4*d^6 - (2*a + b)*c^2*d^4*e^2 + (a + b)*d^2*e^4 - (b*c^2*d^2*e^4 - b*e^6)*x^2 - 2*(2*b*c^2*d^4*e - b*d^2*e^3 + (2*b*c^2*d^2*e^3 - b*e^5)*x^2 + 2*(2*b*c^2*d^3*e^2 - b*d*e^4)*x)*sqrt(c^2*d^2 - e^2)*arctan(-(sqrt(c^2*d^2 - e^2)*c*d*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - sqrt(c^2*d^2 - e^2)*(e*x + d))/((c^2*d^2 - e^2)*x)) - 2*(b*c^2*d^3*e^3 - b*d*e^5)*x + (b*c^4*d^6 - 2*b*c^2*d^4*e^2 + b*d^2*e^4 + (b*c^4*d^4*e^2 - 2*b*c^2*d^2*e^4 + b*e^6)*x^2 + 2*(b*c^4*d^5*e - 2*b*c^2*d^3*e^3 + b*d*e^5)*x)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + (b*c^4*d^6 - 2*b*c^2*d^4*e^2 + b*d^2*e^4)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - ((b*c^3*d^3*e^3 - b*c*d*e^5)*x^2 + (b*c^3*d^4*e^2 - b*c*d^2*e^4)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/(c^4*d^8*e - 2*c^2*d^6*e^3 + d^4*e^5 + (c^4*d^6*e^3 - 2*c^2*d^4*e^5 + d^2*e^7)*x^2 + 2*(c^4*d^7*e^2 - 2*c^2*d^5*e^4 + d^3*e^6)*x)]","B",0
81,0,0,0,173.839944," ","integrate((e*x+d)^(3/2)*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e x + a d + {\left(b e x + b d\right)} \operatorname{arsech}\left(c x\right)\right)} \sqrt{e x + d}, x\right)"," ",0,"integral((a*e*x + a*d + (b*e*x + b*d)*arcsech(c*x))*sqrt(e*x + d), x)","F",0
82,0,0,0,9.079471," ","integrate((e*x+d)^(1/2)*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}, x\right)"," ",0,"integral(sqrt(e*x + d)*(b*arcsech(c*x) + a), x)","F",0
83,-1,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/(e*x+d)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,0,0,0,7.574110," ","integrate((a+b*arcsech(c*x))/(e*x+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{e^{2} x^{2} + 2 \, d e x + d^{2}}, x\right)"," ",0,"integral(sqrt(e*x + d)*(b*arcsech(c*x) + a)/(e^2*x^2 + 2*d*e*x + d^2), x)","F",0
85,0,0,0,5.006825," ","integrate((a+b*arcsech(c*x))/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{e^{3} x^{3} + 3 \, d e^{2} x^{2} + 3 \, d^{2} e x + d^{3}}, x\right)"," ",0,"integral(sqrt(e*x + d)*(b*arcsech(c*x) + a)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
86,-1,0,0,0.000000," ","integrate((a+b*arcsech(c*x))/(e*x+d)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,0,0,0,1.189828," ","integrate((e*x+d)^m*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \operatorname{arsech}\left(c x\right) + a\right)} {\left(e x + d\right)}^{m}, x\right)"," ",0,"integral((b*arcsech(c*x) + a)*(e*x + d)^m, x)","F",0
88,1,259,0,1.007439," ","integrate(x^4*(e*x^2+d)*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{240 \, a c^{7} e x^{7} + 336 \, a c^{7} d x^{5} - 6 \, {\left(42 \, b c^{2} d + 25 \, b e\right)} \arctan\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c x}\right) - 48 \, {\left(7 \, b c^{7} d + 5 \, b c^{7} e\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + 48 \, {\left(5 \, b c^{7} e x^{7} + 7 \, b c^{7} d x^{5} - 7 \, b c^{7} d - 5 \, b c^{7} e\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(40 \, b c^{6} e x^{6} + 2 \, {\left(42 \, b c^{6} d + 25 \, b c^{4} e\right)} x^{4} + 3 \, {\left(42 \, b c^{4} d + 25 \, b c^{2} e\right)} x^{2}\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{1680 \, c^{7}}"," ",0,"1/1680*(240*a*c^7*e*x^7 + 336*a*c^7*d*x^5 - 6*(42*b*c^2*d + 25*b*e)*arctan((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c*x)) - 48*(7*b*c^7*d + 5*b*c^7*e)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + 48*(5*b*c^7*e*x^7 + 7*b*c^7*d*x^5 - 7*b*c^7*d - 5*b*c^7*e)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (40*b*c^6*e*x^6 + 2*(42*b*c^6*d + 25*b*c^4*e)*x^4 + 3*(42*b*c^4*d + 25*b*c^2*e)*x^2)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c^7","A",0
89,1,238,0,1.019963," ","integrate(x^2*(e*x^2+d)*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{24 \, a c^{5} e x^{5} + 40 \, a c^{5} d x^{3} - 2 \, {\left(20 \, b c^{2} d + 9 \, b e\right)} \arctan\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c x}\right) - 8 \, {\left(5 \, b c^{5} d + 3 \, b c^{5} e\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + 8 \, {\left(3 \, b c^{5} e x^{5} + 5 \, b c^{5} d x^{3} - 5 \, b c^{5} d - 3 \, b c^{5} e\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(6 \, b c^{4} e x^{4} + {\left(20 \, b c^{4} d + 9 \, b c^{2} e\right)} x^{2}\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{120 \, c^{5}}"," ",0,"1/120*(24*a*c^5*e*x^5 + 40*a*c^5*d*x^3 - 2*(20*b*c^2*d + 9*b*e)*arctan((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c*x)) - 8*(5*b*c^5*d + 3*b*c^5*e)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + 8*(3*b*c^5*e*x^5 + 5*b*c^5*d*x^3 - 5*b*c^5*d - 3*b*c^5*e)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (6*b*c^4*e*x^4 + (20*b*c^4*d + 9*b*c^2*e)*x^2)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c^5","B",0
90,1,209,0,0.980570," ","integrate((e*x^2+d)*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{2 \, a c^{3} e x^{3} - b c^{2} e x^{2} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 6 \, a c^{3} d x - 2 \, {\left(6 \, b c^{2} d + b e\right)} \arctan\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c x}\right) - 2 \, {\left(3 \, b c^{3} d + b c^{3} e\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + 2 \, {\left(b c^{3} e x^{3} + 3 \, b c^{3} d x - 3 \, b c^{3} d - b c^{3} e\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)}{6 \, c^{3}}"," ",0,"1/6*(2*a*c^3*e*x^3 - b*c^2*e*x^2*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 6*a*c^3*d*x - 2*(6*b*c^2*d + b*e)*arctan((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c*x)) - 2*(3*b*c^3*d + b*c^3*e)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + 2*(b*c^3*e*x^3 + 3*b*c^3*d*x - 3*b*c^3*d - b*c^3*e)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)))/c^3","B",0
91,1,182,0,0.530846," ","integrate((e*x^2+d)*(a+b*arcsech(c*x))/x^2,x, algorithm=""fricas"")","\frac{b c^{2} d x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + a c e x^{2} - 2 \, b e x \arctan\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c x}\right) - a c d + {\left(b c d - b c e\right)} x \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + {\left(b c e x^{2} - b c d + {\left(b c d - b c e\right)} x\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)}{c x}"," ",0,"(b*c^2*d*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + a*c*e*x^2 - 2*b*e*x*arctan((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c*x)) - a*c*d + (b*c*d - b*c*e)*x*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + (b*c*e*x^2 - b*c*d + (b*c*d - b*c*e)*x)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)))/(c*x)","B",0
92,1,106,0,0.612279," ","integrate((e*x^2+d)*(a+b*arcsech(c*x))/x^4,x, algorithm=""fricas"")","-\frac{9 \, a e x^{2} + 3 \, a d + 3 \, {\left(3 \, b e x^{2} + b d\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(b c d x + {\left(2 \, b c^{3} d + 9 \, b c e\right)} x^{3}\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{9 \, x^{3}}"," ",0,"-1/9*(9*a*e*x^2 + 3*a*d + 3*(3*b*e*x^2 + b*d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (b*c*d*x + (2*b*c^3*d + 9*b*c*e)*x^3)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/x^3","A",0
93,1,128,0,0.630316," ","integrate((e*x^2+d)*(a+b*arcsech(c*x))/x^6,x, algorithm=""fricas"")","-\frac{75 \, a e x^{2} + 45 \, a d + 15 \, {\left(5 \, b e x^{2} + 3 \, b d\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(2 \, {\left(12 \, b c^{5} d + 25 \, b c^{3} e\right)} x^{5} + 9 \, b c d x + {\left(12 \, b c^{3} d + 25 \, b c e\right)} x^{3}\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{225 \, x^{5}}"," ",0,"-1/225*(75*a*e*x^2 + 45*a*d + 15*(5*b*e*x^2 + 3*b*d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (2*(12*b*c^5*d + 25*b*c^3*e)*x^5 + 9*b*c*d*x + (12*b*c^3*d + 25*b*c*e)*x^3)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/x^5","A",0
94,1,149,0,0.579531," ","integrate((e*x^2+d)*(a+b*arcsech(c*x))/x^8,x, algorithm=""fricas"")","-\frac{735 \, a e x^{2} + 525 \, a d + 105 \, {\left(7 \, b e x^{2} + 5 \, b d\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(8 \, {\left(30 \, b c^{7} d + 49 \, b c^{5} e\right)} x^{7} + 4 \, {\left(30 \, b c^{5} d + 49 \, b c^{3} e\right)} x^{5} + 75 \, b c d x + 3 \, {\left(30 \, b c^{3} d + 49 \, b c e\right)} x^{3}\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{3675 \, x^{7}}"," ",0,"-1/3675*(735*a*e*x^2 + 525*a*d + 105*(7*b*e*x^2 + 5*b*d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (8*(30*b*c^7*d + 49*b*c^5*e)*x^7 + 4*(30*b*c^5*d + 49*b*c^3*e)*x^5 + 75*b*c*d*x + 3*(30*b*c^3*d + 49*b*c*e)*x^3)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/x^7","A",0
95,1,168,0,0.662580," ","integrate(x^5*(e*x^2+d)*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{315 \, a c^{7} e x^{8} + 420 \, a c^{7} d x^{6} + 105 \, {\left(3 \, b c^{7} e x^{8} + 4 \, b c^{7} d x^{6}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(45 \, b c^{6} e x^{7} + 6 \, {\left(14 \, b c^{6} d + 9 \, b c^{4} e\right)} x^{5} + 8 \, {\left(14 \, b c^{4} d + 9 \, b c^{2} e\right)} x^{3} + 16 \, {\left(14 \, b c^{2} d + 9 \, b e\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2520 \, c^{7}}"," ",0,"1/2520*(315*a*c^7*e*x^8 + 420*a*c^7*d*x^6 + 105*(3*b*c^7*e*x^8 + 4*b*c^7*d*x^6)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (45*b*c^6*e*x^7 + 6*(14*b*c^6*d + 9*b*c^4*e)*x^5 + 8*(14*b*c^4*d + 9*b*c^2*e)*x^3 + 16*(14*b*c^2*d + 9*b*e)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c^7","A",0
96,1,147,0,0.498372," ","integrate(x^3*(e*x^2+d)*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{30 \, a c^{5} e x^{6} + 45 \, a c^{5} d x^{4} + 15 \, {\left(2 \, b c^{5} e x^{6} + 3 \, b c^{5} d x^{4}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(6 \, b c^{4} e x^{5} + {\left(15 \, b c^{4} d + 8 \, b c^{2} e\right)} x^{3} + 2 \, {\left(15 \, b c^{2} d + 8 \, b e\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{180 \, c^{5}}"," ",0,"1/180*(30*a*c^5*e*x^6 + 45*a*c^5*d*x^4 + 15*(2*b*c^5*e*x^6 + 3*b*c^5*d*x^4)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (6*b*c^4*e*x^5 + (15*b*c^4*d + 8*b*c^2*e)*x^3 + 2*(15*b*c^2*d + 8*b*e)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c^5","A",0
97,1,125,0,0.689428," ","integrate(x*(e*x^2+d)*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{3 \, a c^{3} e x^{4} + 6 \, a c^{3} d x^{2} + 3 \, {\left(b c^{3} e x^{4} + 2 \, b c^{3} d x^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(b c^{2} e x^{3} + 2 \, {\left(3 \, b c^{2} d + b e\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{12 \, c^{3}}"," ",0,"1/12*(3*a*c^3*e*x^4 + 6*a*c^3*d*x^2 + 3*(b*c^3*e*x^4 + 2*b*c^3*d*x^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (b*c^2*e*x^3 + 2*(3*b*c^2*d + b*e)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c^3","A",0
98,0,0,0,0.521328," ","integrate((e*x^2+d)*(a+b*arcsech(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \operatorname{arsech}\left(c x\right)}{x}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsech(c*x))/x, x)","F",0
99,0,0,0,0.703801," ","integrate((e*x^2+d)*(a+b*arcsech(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \operatorname{arsech}\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsech(c*x))/x^3, x)","F",0
100,1,341,0,1.823122," ","integrate(x^2*(e*x^2+d)^2*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{240 \, a c^{7} e^{2} x^{7} + 672 \, a c^{7} d e x^{5} + 560 \, a c^{7} d^{2} x^{3} - 2 \, {\left(280 \, b c^{4} d^{2} + 252 \, b c^{2} d e + 75 \, b e^{2}\right)} \arctan\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c x}\right) - 16 \, {\left(35 \, b c^{7} d^{2} + 42 \, b c^{7} d e + 15 \, b c^{7} e^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + 16 \, {\left(15 \, b c^{7} e^{2} x^{7} + 42 \, b c^{7} d e x^{5} + 35 \, b c^{7} d^{2} x^{3} - 35 \, b c^{7} d^{2} - 42 \, b c^{7} d e - 15 \, b c^{7} e^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(40 \, b c^{6} e^{2} x^{6} + 2 \, {\left(84 \, b c^{6} d e + 25 \, b c^{4} e^{2}\right)} x^{4} + {\left(280 \, b c^{6} d^{2} + 252 \, b c^{4} d e + 75 \, b c^{2} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{1680 \, c^{7}}"," ",0,"1/1680*(240*a*c^7*e^2*x^7 + 672*a*c^7*d*e*x^5 + 560*a*c^7*d^2*x^3 - 2*(280*b*c^4*d^2 + 252*b*c^2*d*e + 75*b*e^2)*arctan((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c*x)) - 16*(35*b*c^7*d^2 + 42*b*c^7*d*e + 15*b*c^7*e^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + 16*(15*b*c^7*e^2*x^7 + 42*b*c^7*d*e*x^5 + 35*b*c^7*d^2*x^3 - 35*b*c^7*d^2 - 42*b*c^7*d*e - 15*b*c^7*e^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (40*b*c^6*e^2*x^6 + 2*(84*b*c^6*d*e + 25*b*c^4*e^2)*x^4 + (280*b*c^6*d^2 + 252*b*c^4*d*e + 75*b*c^2*e^2)*x^2)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c^7","A",0
101,1,305,0,0.809391," ","integrate((e*x^2+d)^2*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{24 \, a c^{5} e^{2} x^{5} + 80 \, a c^{5} d e x^{3} + 120 \, a c^{5} d^{2} x - 2 \, {\left(120 \, b c^{4} d^{2} + 40 \, b c^{2} d e + 9 \, b e^{2}\right)} \arctan\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c x}\right) - 8 \, {\left(15 \, b c^{5} d^{2} + 10 \, b c^{5} d e + 3 \, b c^{5} e^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + 8 \, {\left(3 \, b c^{5} e^{2} x^{5} + 10 \, b c^{5} d e x^{3} + 15 \, b c^{5} d^{2} x - 15 \, b c^{5} d^{2} - 10 \, b c^{5} d e - 3 \, b c^{5} e^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(6 \, b c^{4} e^{2} x^{4} + {\left(40 \, b c^{4} d e + 9 \, b c^{2} e^{2}\right)} x^{2}\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{120 \, c^{5}}"," ",0,"1/120*(24*a*c^5*e^2*x^5 + 80*a*c^5*d*e*x^3 + 120*a*c^5*d^2*x - 2*(120*b*c^4*d^2 + 40*b*c^2*d*e + 9*b*e^2)*arctan((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c*x)) - 8*(15*b*c^5*d^2 + 10*b*c^5*d*e + 3*b*c^5*e^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + 8*(3*b*c^5*e^2*x^5 + 10*b*c^5*d*e*x^3 + 15*b*c^5*d^2*x - 15*b*c^5*d^2 - 10*b*c^5*d*e - 3*b*c^5*e^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (6*b*c^4*e^2*x^4 + (40*b*c^4*d*e + 9*b*c^2*e^2)*x^2)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c^5","B",0
102,1,287,0,1.839532," ","integrate((e*x^2+d)^2*(a+b*arcsech(c*x))/x^2,x, algorithm=""fricas"")","\frac{2 \, a c^{3} e^{2} x^{4} + 12 \, a c^{3} d e x^{2} - 6 \, a c^{3} d^{2} - 2 \, {\left(12 \, b c^{2} d e + b e^{2}\right)} x \arctan\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c x}\right) + 2 \, {\left(3 \, b c^{3} d^{2} - 6 \, b c^{3} d e - b c^{3} e^{2}\right)} x \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + 2 \, {\left(b c^{3} e^{2} x^{4} + 6 \, b c^{3} d e x^{2} - 3 \, b c^{3} d^{2} + {\left(3 \, b c^{3} d^{2} - 6 \, b c^{3} d e - b c^{3} e^{2}\right)} x\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + {\left(6 \, b c^{4} d^{2} x - b c^{2} e^{2} x^{3}\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{6 \, c^{3} x}"," ",0,"1/6*(2*a*c^3*e^2*x^4 + 12*a*c^3*d*e*x^2 - 6*a*c^3*d^2 - 2*(12*b*c^2*d*e + b*e^2)*x*arctan((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c*x)) + 2*(3*b*c^3*d^2 - 6*b*c^3*d*e - b*c^3*e^2)*x*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + 2*(b*c^3*e^2*x^4 + 6*b*c^3*d*e*x^2 - 3*b*c^3*d^2 + (3*b*c^3*d^2 - 6*b*c^3*d*e - b*c^3*e^2)*x)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + (6*b*c^4*d^2*x - b*c^2*e^2*x^3)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/(c^3*x)","B",0
103,1,267,0,0.700635," ","integrate((e*x^2+d)^2*(a+b*arcsech(c*x))/x^4,x, algorithm=""fricas"")","\frac{9 \, a c e^{2} x^{4} - 18 \, b e^{2} x^{3} \arctan\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c x}\right) - 18 \, a c d e x^{2} + 3 \, {\left(b c d^{2} + 6 \, b c d e - 3 \, b c e^{2}\right)} x^{3} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) - 3 \, a c d^{2} + 3 \, {\left(3 \, b c e^{2} x^{4} - 6 \, b c d e x^{2} - b c d^{2} + {\left(b c d^{2} + 6 \, b c d e - 3 \, b c e^{2}\right)} x^{3}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + {\left(b c^{2} d^{2} x + 2 \, {\left(b c^{4} d^{2} + 9 \, b c^{2} d e\right)} x^{3}\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{9 \, c x^{3}}"," ",0,"1/9*(9*a*c*e^2*x^4 - 18*b*e^2*x^3*arctan((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c*x)) - 18*a*c*d*e*x^2 + 3*(b*c*d^2 + 6*b*c*d*e - 3*b*c*e^2)*x^3*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) - 3*a*c*d^2 + 3*(3*b*c*e^2*x^4 - 6*b*c*d*e*x^2 - b*c*d^2 + (b*c*d^2 + 6*b*c*d*e - 3*b*c*e^2)*x^3)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + (b*c^2*d^2*x + 2*(b*c^4*d^2 + 9*b*c^2*d*e)*x^3)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/(c*x^3)","B",0
104,1,167,0,1.074997," ","integrate((e*x^2+d)^2*(a+b*arcsech(c*x))/x^6,x, algorithm=""fricas"")","-\frac{225 \, a e^{2} x^{4} + 150 \, a d e x^{2} + 45 \, a d^{2} + 15 \, {\left(15 \, b e^{2} x^{4} + 10 \, b d e x^{2} + 3 \, b d^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left({\left(24 \, b c^{5} d^{2} + 100 \, b c^{3} d e + 225 \, b c e^{2}\right)} x^{5} + 9 \, b c d^{2} x + 2 \, {\left(6 \, b c^{3} d^{2} + 25 \, b c d e\right)} x^{3}\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{225 \, x^{5}}"," ",0,"-1/225*(225*a*e^2*x^4 + 150*a*d*e*x^2 + 45*a*d^2 + 15*(15*b*e^2*x^4 + 10*b*d*e*x^2 + 3*b*d^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - ((24*b*c^5*d^2 + 100*b*c^3*d*e + 225*b*c*e^2)*x^5 + 9*b*c*d^2*x + 2*(6*b*c^3*d^2 + 25*b*c*d*e)*x^3)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/x^5","A",0
105,1,199,0,0.546641," ","integrate((e*x^2+d)^2*(a+b*arcsech(c*x))/x^8,x, algorithm=""fricas"")","-\frac{3675 \, a e^{2} x^{4} + 4410 \, a d e x^{2} + 1575 \, a d^{2} + 105 \, {\left(35 \, b e^{2} x^{4} + 42 \, b d e x^{2} + 15 \, b d^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(2 \, {\left(360 \, b c^{7} d^{2} + 1176 \, b c^{5} d e + 1225 \, b c^{3} e^{2}\right)} x^{7} + {\left(360 \, b c^{5} d^{2} + 1176 \, b c^{3} d e + 1225 \, b c e^{2}\right)} x^{5} + 225 \, b c d^{2} x + 18 \, {\left(15 \, b c^{3} d^{2} + 49 \, b c d e\right)} x^{3}\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{11025 \, x^{7}}"," ",0,"-1/11025*(3675*a*e^2*x^4 + 4410*a*d*e*x^2 + 1575*a*d^2 + 105*(35*b*e^2*x^4 + 42*b*d*e*x^2 + 15*b*d^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (2*(360*b*c^7*d^2 + 1176*b*c^5*d*e + 1225*b*c^3*e^2)*x^7 + (360*b*c^5*d^2 + 1176*b*c^3*d*e + 1225*b*c*e^2)*x^5 + 225*b*c*d^2*x + 18*(15*b*c^3*d^2 + 49*b*c*d*e)*x^3)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/x^7","A",0
106,1,227,0,1.084268," ","integrate(x^3*(e*x^2+d)^2*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{315 \, a c^{7} e^{2} x^{8} + 840 \, a c^{7} d e x^{6} + 630 \, a c^{7} d^{2} x^{4} + 105 \, {\left(3 \, b c^{7} e^{2} x^{8} + 8 \, b c^{7} d e x^{6} + 6 \, b c^{7} d^{2} x^{4}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(45 \, b c^{6} e^{2} x^{7} + 6 \, {\left(28 \, b c^{6} d e + 9 \, b c^{4} e^{2}\right)} x^{5} + 2 \, {\left(105 \, b c^{6} d^{2} + 112 \, b c^{4} d e + 36 \, b c^{2} e^{2}\right)} x^{3} + 4 \, {\left(105 \, b c^{4} d^{2} + 112 \, b c^{2} d e + 36 \, b e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2520 \, c^{7}}"," ",0,"1/2520*(315*a*c^7*e^2*x^8 + 840*a*c^7*d*e*x^6 + 630*a*c^7*d^2*x^4 + 105*(3*b*c^7*e^2*x^8 + 8*b*c^7*d*e*x^6 + 6*b*c^7*d^2*x^4)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (45*b*c^6*e^2*x^7 + 6*(28*b*c^6*d*e + 9*b*c^4*e^2)*x^5 + 2*(105*b*c^6*d^2 + 112*b*c^4*d*e + 36*b*c^2*e^2)*x^3 + 4*(105*b*c^4*d^2 + 112*b*c^2*d*e + 36*b*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c^7","A",0
107,1,192,0,0.998712," ","integrate(x*(e*x^2+d)^2*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\frac{15 \, a c^{5} e^{2} x^{6} + 45 \, a c^{5} d e x^{4} + 45 \, a c^{5} d^{2} x^{2} + 15 \, {\left(b c^{5} e^{2} x^{6} + 3 \, b c^{5} d e x^{4} + 3 \, b c^{5} d^{2} x^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(3 \, b c^{4} e^{2} x^{5} + {\left(15 \, b c^{4} d e + 4 \, b c^{2} e^{2}\right)} x^{3} + {\left(45 \, b c^{4} d^{2} + 30 \, b c^{2} d e + 8 \, b e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{90 \, c^{5}}"," ",0,"1/90*(15*a*c^5*e^2*x^6 + 45*a*c^5*d*e*x^4 + 45*a*c^5*d^2*x^2 + 15*(b*c^5*e^2*x^6 + 3*b*c^5*d*e*x^4 + 3*b*c^5*d^2*x^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (3*b*c^4*e^2*x^5 + (15*b*c^4*d*e + 4*b*c^2*e^2)*x^3 + (45*b*c^4*d^2 + 30*b*c^2*d*e + 8*b*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/c^5","A",0
108,0,0,0,1.904355," ","integrate((e*x^2+d)^2*(a+b*arcsech(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \operatorname{arsech}\left(c x\right)}{x}, x\right)"," ",0,"integral((a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arcsech(c*x))/x, x)","F",0
109,0,0,0,0.508704," ","integrate((e*x^2+d)^2*(a+b*arcsech(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \operatorname{arsech}\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arcsech(c*x))/x^3, x)","F",0
110,0,0,0,1.580285," ","integrate(x^2*(a+b*arcsech(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \operatorname{arsech}\left(c x\right) + a x^{2}}{e x^{2} + d}, x\right)"," ",0,"integral((b*x^2*arcsech(c*x) + a*x^2)/(e*x^2 + d), x)","F",0
111,0,0,0,0.716526," ","integrate(x*(a+b*arcsech(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x \operatorname{arsech}\left(c x\right) + a x}{e x^{2} + d}, x\right)"," ",0,"integral((b*x*arcsech(c*x) + a*x)/(e*x^2 + d), x)","F",0
112,0,0,0,0.666969," ","integrate((a+b*arcsech(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arsech}\left(c x\right) + a}{e x^{2} + d}, x\right)"," ",0,"integral((b*arcsech(c*x) + a)/(e*x^2 + d), x)","F",0
113,0,0,0,0.640824," ","integrate((a+b*arcsech(c*x))/x/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arsech}\left(c x\right) + a}{e x^{3} + d x}, x\right)"," ",0,"integral((b*arcsech(c*x) + a)/(e*x^3 + d*x), x)","F",0
114,0,0,0,0.715008," ","integrate((a+b*arcsech(c*x))/x^2/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arsech}\left(c x\right) + a}{e x^{4} + d x^{2}}, x\right)"," ",0,"integral((b*arcsech(c*x) + a)/(e*x^4 + d*x^2), x)","F",0
115,0,0,0,0.788635," ","integrate(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{5} \operatorname{arsech}\left(c x\right) + a x^{5}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*x^5*arcsech(c*x) + a*x^5)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
116,0,0,0,0.854547," ","integrate(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{3} \operatorname{arsech}\left(c x\right) + a x^{3}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*x^3*arcsech(c*x) + a*x^3)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
117,1,602,0,0.663007," ","integrate(x*(a+b*arcsech(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a c^{2} d^{2} + 2 \, a d e - \sqrt{c^{2} d e + e^{2}} {\left(b e x^{2} + b d\right)} \log\left(\frac{c^{4} d^{2} + 4 \, c^{2} d e - {\left(c^{4} d e + 2 \, c^{2} e^{2}\right)} x^{2} + 4 \, {\left(c^{3} d e + c e^{2}\right)} x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 4 \, e^{2} + 2 \, {\left(c^{2} e x^{2} - c^{2} d - {\left(c^{3} d + 2 \, c e\right)} x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 2 \, e\right)} \sqrt{c^{2} d e + e^{2}}}{e x^{2} + d}\right) + 2 \, {\left(b c^{2} d^{2} + b d e + {\left(b c^{2} d e + b e^{2}\right)} x^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + 2 \, {\left(b c^{2} d^{2} + b d e\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)}{4 \, {\left(c^{2} d^{3} e + d^{2} e^{2} + {\left(c^{2} d^{2} e^{2} + d e^{3}\right)} x^{2}\right)}}, -\frac{a c^{2} d^{2} + a d e + \sqrt{-c^{2} d e - e^{2}} {\left(b e x^{2} + b d\right)} \arctan\left(\frac{\sqrt{-c^{2} d e - e^{2}} c d x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - \sqrt{-c^{2} d e - e^{2}} {\left(e x^{2} + d\right)}}{{\left(c^{2} d e + e^{2}\right)} x^{2}}\right) + {\left(b c^{2} d^{2} + b d e + {\left(b c^{2} d e + b e^{2}\right)} x^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + {\left(b c^{2} d^{2} + b d e\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right)}{2 \, {\left(c^{2} d^{3} e + d^{2} e^{2} + {\left(c^{2} d^{2} e^{2} + d e^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(2*a*c^2*d^2 + 2*a*d*e - sqrt(c^2*d*e + e^2)*(b*e*x^2 + b*d)*log((c^4*d^2 + 4*c^2*d*e - (c^4*d*e + 2*c^2*e^2)*x^2 + 4*(c^3*d*e + c*e^2)*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 4*e^2 + 2*(c^2*e*x^2 - c^2*d - (c^3*d + 2*c*e)*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 2*e)*sqrt(c^2*d*e + e^2))/(e*x^2 + d)) + 2*(b*c^2*d^2 + b*d*e + (b*c^2*d*e + b*e^2)*x^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + 2*(b*c^2*d^2 + b*d*e)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)))/(c^2*d^3*e + d^2*e^2 + (c^2*d^2*e^2 + d*e^3)*x^2), -1/2*(a*c^2*d^2 + a*d*e + sqrt(-c^2*d*e - e^2)*(b*e*x^2 + b*d)*arctan((sqrt(-c^2*d*e - e^2)*c*d*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - sqrt(-c^2*d*e - e^2)*(e*x^2 + d))/((c^2*d*e + e^2)*x^2)) + (b*c^2*d^2 + b*d*e + (b*c^2*d*e + b*e^2)*x^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + (b*c^2*d^2 + b*d*e)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)))/(c^2*d^3*e + d^2*e^2 + (c^2*d^2*e^2 + d*e^3)*x^2)]","B",0
118,0,0,0,1.180158," ","integrate((a+b*arcsech(c*x))/x/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arsech}\left(c x\right) + a}{e^{2} x^{5} + 2 \, d e x^{3} + d^{2} x}, x\right)"," ",0,"integral((b*arcsech(c*x) + a)/(e^2*x^5 + 2*d*e*x^3 + d^2*x), x)","F",0
119,0,0,0,0.464628," ","integrate(x^4*(a+b*arcsech(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{4} \operatorname{arsech}\left(c x\right) + a x^{4}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*x^4*arcsech(c*x) + a*x^4)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
120,0,0,0,0.659478," ","integrate(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \operatorname{arsech}\left(c x\right) + a x^{2}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*x^2*arcsech(c*x) + a*x^2)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
121,0,0,0,1.303978," ","integrate((a+b*arcsech(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arsech}\left(c x\right) + a}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*arcsech(c*x) + a)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
122,0,0,0,1.068704," ","integrate((a+b*arcsech(c*x))/x^2/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arsech}\left(c x\right) + a}{e^{2} x^{6} + 2 \, d e x^{4} + d^{2} x^{2}}, x\right)"," ",0,"integral((b*arcsech(c*x) + a)/(e^2*x^6 + 2*d*e*x^4 + d^2*x^2), x)","F",0
123,0,0,0,0.653221," ","integrate(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{5} \operatorname{arsech}\left(c x\right) + a x^{5}}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral((b*x^5*arcsech(c*x) + a*x^5)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
124,1,1346,0,0.900020," ","integrate(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, a c^{4} d^{4} + 2 \, {\left(4 \, a - b\right)} c^{2} d^{3} e + 2 \, {\left(2 \, a - b\right)} d^{2} e^{2} - 2 \, {\left(b c^{2} d e^{3} + b e^{4}\right)} x^{4} + 4 \, {\left(2 \, a c^{4} d^{3} e + {\left(4 \, a - b\right)} c^{2} d^{2} e^{2} + {\left(2 \, a - b\right)} d e^{3}\right)} x^{2} - {\left(b c^{2} d^{3} + {\left(b c^{2} d e^{2} + 2 \, b e^{3}\right)} x^{4} + 2 \, b d^{2} e + 2 \, {\left(b c^{2} d^{2} e + 2 \, b d e^{2}\right)} x^{2}\right)} \sqrt{c^{2} d e + e^{2}} \log\left(\frac{c^{4} d^{2} + 4 \, c^{2} d e - {\left(c^{4} d e + 2 \, c^{2} e^{2}\right)} x^{2} + 4 \, {\left(c^{3} d e + c e^{2}\right)} x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 4 \, e^{2} + 2 \, {\left(c^{2} e x^{2} - c^{2} d - {\left(c^{3} d + 2 \, c e\right)} x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 2 \, e\right)} \sqrt{c^{2} d e + e^{2}}}{e x^{2} + d}\right) + 4 \, {\left(b c^{4} d^{4} + 2 \, b c^{2} d^{3} e + b d^{2} e^{2} + {\left(b c^{4} d^{2} e^{2} + 2 \, b c^{2} d e^{3} + b e^{4}\right)} x^{4} + 2 \, {\left(b c^{4} d^{3} e + 2 \, b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + 4 \, {\left(b c^{4} d^{4} + 2 \, b c^{2} d^{3} e + b d^{2} e^{2} + 2 \, {\left(b c^{4} d^{3} e + 2 \, b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 2 \, {\left({\left(b c^{3} d^{2} e^{2} + b c d e^{3}\right)} x^{3} + {\left(b c^{3} d^{3} e + b c d^{2} e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{16 \, {\left(c^{4} d^{5} e^{2} + 2 \, c^{2} d^{4} e^{3} + d^{3} e^{4} + {\left(c^{4} d^{3} e^{4} + 2 \, c^{2} d^{2} e^{5} + d e^{6}\right)} x^{4} + 2 \, {\left(c^{4} d^{4} e^{3} + 2 \, c^{2} d^{3} e^{4} + d^{2} e^{5}\right)} x^{2}\right)}}, -\frac{2 \, a c^{4} d^{4} + {\left(4 \, a - b\right)} c^{2} d^{3} e + {\left(2 \, a - b\right)} d^{2} e^{2} - {\left(b c^{2} d e^{3} + b e^{4}\right)} x^{4} + 2 \, {\left(2 \, a c^{4} d^{3} e + {\left(4 \, a - b\right)} c^{2} d^{2} e^{2} + {\left(2 \, a - b\right)} d e^{3}\right)} x^{2} + {\left(b c^{2} d^{3} + {\left(b c^{2} d e^{2} + 2 \, b e^{3}\right)} x^{4} + 2 \, b d^{2} e + 2 \, {\left(b c^{2} d^{2} e + 2 \, b d e^{2}\right)} x^{2}\right)} \sqrt{-c^{2} d e - e^{2}} \arctan\left(\frac{\sqrt{-c^{2} d e - e^{2}} c d x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - \sqrt{-c^{2} d e - e^{2}} {\left(e x^{2} + d\right)}}{{\left(c^{2} d e + e^{2}\right)} x^{2}}\right) + 2 \, {\left(b c^{4} d^{4} + 2 \, b c^{2} d^{3} e + b d^{2} e^{2} + {\left(b c^{4} d^{2} e^{2} + 2 \, b c^{2} d e^{3} + b e^{4}\right)} x^{4} + 2 \, {\left(b c^{4} d^{3} e + 2 \, b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + 2 \, {\left(b c^{4} d^{4} + 2 \, b c^{2} d^{3} e + b d^{2} e^{2} + 2 \, {\left(b c^{4} d^{3} e + 2 \, b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left({\left(b c^{3} d^{2} e^{2} + b c d e^{3}\right)} x^{3} + {\left(b c^{3} d^{3} e + b c d^{2} e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{8 \, {\left(c^{4} d^{5} e^{2} + 2 \, c^{2} d^{4} e^{3} + d^{3} e^{4} + {\left(c^{4} d^{3} e^{4} + 2 \, c^{2} d^{2} e^{5} + d e^{6}\right)} x^{4} + 2 \, {\left(c^{4} d^{4} e^{3} + 2 \, c^{2} d^{3} e^{4} + d^{2} e^{5}\right)} x^{2}\right)}}\right]"," ",0,"[-1/16*(4*a*c^4*d^4 + 2*(4*a - b)*c^2*d^3*e + 2*(2*a - b)*d^2*e^2 - 2*(b*c^2*d*e^3 + b*e^4)*x^4 + 4*(2*a*c^4*d^3*e + (4*a - b)*c^2*d^2*e^2 + (2*a - b)*d*e^3)*x^2 - (b*c^2*d^3 + (b*c^2*d*e^2 + 2*b*e^3)*x^4 + 2*b*d^2*e + 2*(b*c^2*d^2*e + 2*b*d*e^2)*x^2)*sqrt(c^2*d*e + e^2)*log((c^4*d^2 + 4*c^2*d*e - (c^4*d*e + 2*c^2*e^2)*x^2 + 4*(c^3*d*e + c*e^2)*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 4*e^2 + 2*(c^2*e*x^2 - c^2*d - (c^3*d + 2*c*e)*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 2*e)*sqrt(c^2*d*e + e^2))/(e*x^2 + d)) + 4*(b*c^4*d^4 + 2*b*c^2*d^3*e + b*d^2*e^2 + (b*c^4*d^2*e^2 + 2*b*c^2*d*e^3 + b*e^4)*x^4 + 2*(b*c^4*d^3*e + 2*b*c^2*d^2*e^2 + b*d*e^3)*x^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + 4*(b*c^4*d^4 + 2*b*c^2*d^3*e + b*d^2*e^2 + 2*(b*c^4*d^3*e + 2*b*c^2*d^2*e^2 + b*d*e^3)*x^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 2*((b*c^3*d^2*e^2 + b*c*d*e^3)*x^3 + (b*c^3*d^3*e + b*c*d^2*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/(c^4*d^5*e^2 + 2*c^2*d^4*e^3 + d^3*e^4 + (c^4*d^3*e^4 + 2*c^2*d^2*e^5 + d*e^6)*x^4 + 2*(c^4*d^4*e^3 + 2*c^2*d^3*e^4 + d^2*e^5)*x^2), -1/8*(2*a*c^4*d^4 + (4*a - b)*c^2*d^3*e + (2*a - b)*d^2*e^2 - (b*c^2*d*e^3 + b*e^4)*x^4 + 2*(2*a*c^4*d^3*e + (4*a - b)*c^2*d^2*e^2 + (2*a - b)*d*e^3)*x^2 + (b*c^2*d^3 + (b*c^2*d*e^2 + 2*b*e^3)*x^4 + 2*b*d^2*e + 2*(b*c^2*d^2*e + 2*b*d*e^2)*x^2)*sqrt(-c^2*d*e - e^2)*arctan((sqrt(-c^2*d*e - e^2)*c*d*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - sqrt(-c^2*d*e - e^2)*(e*x^2 + d))/((c^2*d*e + e^2)*x^2)) + 2*(b*c^4*d^4 + 2*b*c^2*d^3*e + b*d^2*e^2 + (b*c^4*d^2*e^2 + 2*b*c^2*d*e^3 + b*e^4)*x^4 + 2*(b*c^4*d^3*e + 2*b*c^2*d^2*e^2 + b*d*e^3)*x^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + 2*(b*c^4*d^4 + 2*b*c^2*d^3*e + b*d^2*e^2 + 2*(b*c^4*d^3*e + 2*b*c^2*d^2*e^2 + b*d*e^3)*x^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - ((b*c^3*d^2*e^2 + b*c*d*e^3)*x^3 + (b*c^3*d^3*e + b*c*d^2*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/(c^4*d^5*e^2 + 2*c^2*d^4*e^3 + d^3*e^4 + (c^4*d^3*e^4 + 2*c^2*d^2*e^5 + d*e^6)*x^4 + 2*(c^4*d^4*e^3 + 2*c^2*d^3*e^4 + d^2*e^5)*x^2)]","B",0
125,1,1232,0,0.715214," ","integrate(x*(a+b*arcsech(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, a c^{4} d^{4} + 2 \, {\left(4 \, a + b\right)} c^{2} d^{3} e + 2 \, {\left(2 \, a + b\right)} d^{2} e^{2} + 2 \, {\left(b c^{2} d e^{3} + b e^{4}\right)} x^{4} + 4 \, {\left(b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2} - {\left(3 \, b c^{2} d^{3} + {\left(3 \, b c^{2} d e^{2} + 2 \, b e^{3}\right)} x^{4} + 2 \, b d^{2} e + 2 \, {\left(3 \, b c^{2} d^{2} e + 2 \, b d e^{2}\right)} x^{2}\right)} \sqrt{c^{2} d e + e^{2}} \log\left(\frac{c^{4} d^{2} + 4 \, c^{2} d e - {\left(c^{4} d e + 2 \, c^{2} e^{2}\right)} x^{2} + 4 \, {\left(c^{3} d e + c e^{2}\right)} x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 4 \, e^{2} + 2 \, {\left(c^{2} e x^{2} - c^{2} d - {\left(c^{3} d + 2 \, c e\right)} x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 2 \, e\right)} \sqrt{c^{2} d e + e^{2}}}{e x^{2} + d}\right) + 4 \, {\left(b c^{4} d^{4} + 2 \, b c^{2} d^{3} e + b d^{2} e^{2} + {\left(b c^{4} d^{2} e^{2} + 2 \, b c^{2} d e^{3} + b e^{4}\right)} x^{4} + 2 \, {\left(b c^{4} d^{3} e + 2 \, b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + 4 \, {\left(b c^{4} d^{4} + 2 \, b c^{2} d^{3} e + b d^{2} e^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 2 \, {\left({\left(b c^{3} d^{2} e^{2} + b c d e^{3}\right)} x^{3} + {\left(b c^{3} d^{3} e + b c d^{2} e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{16 \, {\left(c^{4} d^{6} e + 2 \, c^{2} d^{5} e^{2} + d^{4} e^{3} + {\left(c^{4} d^{4} e^{3} + 2 \, c^{2} d^{3} e^{4} + d^{2} e^{5}\right)} x^{4} + 2 \, {\left(c^{4} d^{5} e^{2} + 2 \, c^{2} d^{4} e^{3} + d^{3} e^{4}\right)} x^{2}\right)}}, -\frac{2 \, a c^{4} d^{4} + {\left(4 \, a + b\right)} c^{2} d^{3} e + {\left(2 \, a + b\right)} d^{2} e^{2} + {\left(b c^{2} d e^{3} + b e^{4}\right)} x^{4} + 2 \, {\left(b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2} + {\left(3 \, b c^{2} d^{3} + {\left(3 \, b c^{2} d e^{2} + 2 \, b e^{3}\right)} x^{4} + 2 \, b d^{2} e + 2 \, {\left(3 \, b c^{2} d^{2} e + 2 \, b d e^{2}\right)} x^{2}\right)} \sqrt{-c^{2} d e - e^{2}} \arctan\left(\frac{\sqrt{-c^{2} d e - e^{2}} c d x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - \sqrt{-c^{2} d e - e^{2}} {\left(e x^{2} + d\right)}}{{\left(c^{2} d e + e^{2}\right)} x^{2}}\right) + 2 \, {\left(b c^{4} d^{4} + 2 \, b c^{2} d^{3} e + b d^{2} e^{2} + {\left(b c^{4} d^{2} e^{2} + 2 \, b c^{2} d e^{3} + b e^{4}\right)} x^{4} + 2 \, {\left(b c^{4} d^{3} e + 2 \, b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{x}\right) + 2 \, {\left(b c^{4} d^{4} + 2 \, b c^{2} d^{3} e + b d^{2} e^{2}\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + {\left({\left(b c^{3} d^{2} e^{2} + b c d e^{3}\right)} x^{3} + {\left(b c^{3} d^{3} e + b c d^{2} e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{8 \, {\left(c^{4} d^{6} e + 2 \, c^{2} d^{5} e^{2} + d^{4} e^{3} + {\left(c^{4} d^{4} e^{3} + 2 \, c^{2} d^{3} e^{4} + d^{2} e^{5}\right)} x^{4} + 2 \, {\left(c^{4} d^{5} e^{2} + 2 \, c^{2} d^{4} e^{3} + d^{3} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/16*(4*a*c^4*d^4 + 2*(4*a + b)*c^2*d^3*e + 2*(2*a + b)*d^2*e^2 + 2*(b*c^2*d*e^3 + b*e^4)*x^4 + 4*(b*c^2*d^2*e^2 + b*d*e^3)*x^2 - (3*b*c^2*d^3 + (3*b*c^2*d*e^2 + 2*b*e^3)*x^4 + 2*b*d^2*e + 2*(3*b*c^2*d^2*e + 2*b*d*e^2)*x^2)*sqrt(c^2*d*e + e^2)*log((c^4*d^2 + 4*c^2*d*e - (c^4*d*e + 2*c^2*e^2)*x^2 + 4*(c^3*d*e + c*e^2)*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 4*e^2 + 2*(c^2*e*x^2 - c^2*d - (c^3*d + 2*c*e)*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 2*e)*sqrt(c^2*d*e + e^2))/(e*x^2 + d)) + 4*(b*c^4*d^4 + 2*b*c^2*d^3*e + b*d^2*e^2 + (b*c^4*d^2*e^2 + 2*b*c^2*d*e^3 + b*e^4)*x^4 + 2*(b*c^4*d^3*e + 2*b*c^2*d^2*e^2 + b*d*e^3)*x^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + 4*(b*c^4*d^4 + 2*b*c^2*d^3*e + b*d^2*e^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 2*((b*c^3*d^2*e^2 + b*c*d*e^3)*x^3 + (b*c^3*d^3*e + b*c*d^2*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/(c^4*d^6*e + 2*c^2*d^5*e^2 + d^4*e^3 + (c^4*d^4*e^3 + 2*c^2*d^3*e^4 + d^2*e^5)*x^4 + 2*(c^4*d^5*e^2 + 2*c^2*d^4*e^3 + d^3*e^4)*x^2), -1/8*(2*a*c^4*d^4 + (4*a + b)*c^2*d^3*e + (2*a + b)*d^2*e^2 + (b*c^2*d*e^3 + b*e^4)*x^4 + 2*(b*c^2*d^2*e^2 + b*d*e^3)*x^2 + (3*b*c^2*d^3 + (3*b*c^2*d*e^2 + 2*b*e^3)*x^4 + 2*b*d^2*e + 2*(3*b*c^2*d^2*e + 2*b*d*e^2)*x^2)*sqrt(-c^2*d*e - e^2)*arctan((sqrt(-c^2*d*e - e^2)*c*d*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - sqrt(-c^2*d*e - e^2)*(e*x^2 + d))/((c^2*d*e + e^2)*x^2)) + 2*(b*c^4*d^4 + 2*b*c^2*d^3*e + b*d^2*e^2 + (b*c^4*d^2*e^2 + 2*b*c^2*d*e^3 + b*e^4)*x^4 + 2*(b*c^4*d^3*e + 2*b*c^2*d^2*e^2 + b*d*e^3)*x^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/x) + 2*(b*c^4*d^4 + 2*b*c^2*d^3*e + b*d^2*e^2)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + ((b*c^3*d^2*e^2 + b*c*d*e^3)*x^3 + (b*c^3*d^3*e + b*c*d^2*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))/(c^4*d^6*e + 2*c^2*d^5*e^2 + d^4*e^3 + (c^4*d^4*e^3 + 2*c^2*d^3*e^4 + d^2*e^5)*x^4 + 2*(c^4*d^5*e^2 + 2*c^2*d^4*e^3 + d^3*e^4)*x^2)]","B",0
126,0,0,0,0.574040," ","integrate((a+b*arcsech(c*x))/x/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arsech}\left(c x\right) + a}{e^{3} x^{7} + 3 \, d e^{2} x^{5} + 3 \, d^{2} e x^{3} + d^{3} x}, x\right)"," ",0,"integral((b*arcsech(c*x) + a)/(e^3*x^7 + 3*d*e^2*x^5 + 3*d^2*e*x^3 + d^3*x), x)","F",0
127,0,0,0,0.730528," ","integrate(x^4*(a+b*arcsech(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{4} \operatorname{arsech}\left(c x\right) + a x^{4}}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral((b*x^4*arcsech(c*x) + a*x^4)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
128,0,0,0,1.122957," ","integrate(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \operatorname{arsech}\left(c x\right) + a x^{2}}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral((b*x^2*arcsech(c*x) + a*x^2)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
129,0,0,0,0.507477," ","integrate((a+b*arcsech(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arsech}\left(c x\right) + a}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral((b*arcsech(c*x) + a)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
130,1,1995,0,3.530860," ","integrate(x^5*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{128 \, b c^{7} d^{\frac{7}{2}} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} + 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) - {\left(105 \, b c^{6} d^{3} - 35 \, b c^{4} d^{2} e + 63 \, b c^{2} d e^{2} + 75 \, b e^{3}\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) + 64 \, {\left(15 \, b c^{7} e^{3} x^{6} + 3 \, b c^{7} d e^{2} x^{4} - 4 \, b c^{7} d^{2} e x^{2} + 8 \, b c^{7} d^{3}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 4 \, {\left(240 \, a c^{7} e^{3} x^{6} + 48 \, a c^{7} d e^{2} x^{4} - 64 \, a c^{7} d^{2} e x^{2} + 128 \, a c^{7} d^{3} - {\left(40 \, b c^{6} e^{3} x^{5} + 2 \, {\left(11 \, b c^{6} d e^{2} + 25 \, b c^{4} e^{3}\right)} x^{3} - {\left(41 \, b c^{6} d^{2} e - 38 \, b c^{4} d e^{2} - 75 \, b c^{2} e^{3}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{6720 \, c^{7} e^{3}}, \frac{64 \, b c^{7} d^{\frac{7}{2}} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} + 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) - {\left(105 \, b c^{6} d^{3} - 35 \, b c^{4} d^{2} e + 63 \, b c^{2} d e^{2} + 75 \, b e^{3}\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) + 32 \, {\left(15 \, b c^{7} e^{3} x^{6} + 3 \, b c^{7} d e^{2} x^{4} - 4 \, b c^{7} d^{2} e x^{2} + 8 \, b c^{7} d^{3}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 2 \, {\left(240 \, a c^{7} e^{3} x^{6} + 48 \, a c^{7} d e^{2} x^{4} - 64 \, a c^{7} d^{2} e x^{2} + 128 \, a c^{7} d^{3} - {\left(40 \, b c^{6} e^{3} x^{5} + 2 \, {\left(11 \, b c^{6} d e^{2} + 25 \, b c^{4} e^{3}\right)} x^{3} - {\left(41 \, b c^{6} d^{2} e - 38 \, b c^{4} d e^{2} - 75 \, b c^{2} e^{3}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{3360 \, c^{7} e^{3}}, -\frac{256 \, b c^{7} \sqrt{-d} d^{3} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + {\left(105 \, b c^{6} d^{3} - 35 \, b c^{4} d^{2} e + 63 \, b c^{2} d e^{2} + 75 \, b e^{3}\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) - 64 \, {\left(15 \, b c^{7} e^{3} x^{6} + 3 \, b c^{7} d e^{2} x^{4} - 4 \, b c^{7} d^{2} e x^{2} + 8 \, b c^{7} d^{3}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 4 \, {\left(240 \, a c^{7} e^{3} x^{6} + 48 \, a c^{7} d e^{2} x^{4} - 64 \, a c^{7} d^{2} e x^{2} + 128 \, a c^{7} d^{3} - {\left(40 \, b c^{6} e^{3} x^{5} + 2 \, {\left(11 \, b c^{6} d e^{2} + 25 \, b c^{4} e^{3}\right)} x^{3} - {\left(41 \, b c^{6} d^{2} e - 38 \, b c^{4} d e^{2} - 75 \, b c^{2} e^{3}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{6720 \, c^{7} e^{3}}, -\frac{128 \, b c^{7} \sqrt{-d} d^{3} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + {\left(105 \, b c^{6} d^{3} - 35 \, b c^{4} d^{2} e + 63 \, b c^{2} d e^{2} + 75 \, b e^{3}\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) - 32 \, {\left(15 \, b c^{7} e^{3} x^{6} + 3 \, b c^{7} d e^{2} x^{4} - 4 \, b c^{7} d^{2} e x^{2} + 8 \, b c^{7} d^{3}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 2 \, {\left(240 \, a c^{7} e^{3} x^{6} + 48 \, a c^{7} d e^{2} x^{4} - 64 \, a c^{7} d^{2} e x^{2} + 128 \, a c^{7} d^{3} - {\left(40 \, b c^{6} e^{3} x^{5} + 2 \, {\left(11 \, b c^{6} d e^{2} + 25 \, b c^{4} e^{3}\right)} x^{3} - {\left(41 \, b c^{6} d^{2} e - 38 \, b c^{4} d e^{2} - 75 \, b c^{2} e^{3}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{3360 \, c^{7} e^{3}}\right]"," ",0,"[1/6720*(128*b*c^7*d^(7/2)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 + 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) - (105*b*c^6*d^3 - 35*b*c^4*d^2*e + 63*b*c^2*d*e^2 + 75*b*e^3)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) + 64*(15*b*c^7*e^3*x^6 + 3*b*c^7*d*e^2*x^4 - 4*b*c^7*d^2*e*x^2 + 8*b*c^7*d^3)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 4*(240*a*c^7*e^3*x^6 + 48*a*c^7*d*e^2*x^4 - 64*a*c^7*d^2*e*x^2 + 128*a*c^7*d^3 - (40*b*c^6*e^3*x^5 + 2*(11*b*c^6*d*e^2 + 25*b*c^4*e^3)*x^3 - (41*b*c^6*d^2*e - 38*b*c^4*d*e^2 - 75*b*c^2*e^3)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^7*e^3), 1/3360*(64*b*c^7*d^(7/2)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 + 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) - (105*b*c^6*d^3 - 35*b*c^4*d^2*e + 63*b*c^2*d*e^2 + 75*b*e^3)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) + 32*(15*b*c^7*e^3*x^6 + 3*b*c^7*d*e^2*x^4 - 4*b*c^7*d^2*e*x^2 + 8*b*c^7*d^3)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 2*(240*a*c^7*e^3*x^6 + 48*a*c^7*d*e^2*x^4 - 64*a*c^7*d^2*e*x^2 + 128*a*c^7*d^3 - (40*b*c^6*e^3*x^5 + 2*(11*b*c^6*d*e^2 + 25*b*c^4*e^3)*x^3 - (41*b*c^6*d^2*e - 38*b*c^4*d*e^2 - 75*b*c^2*e^3)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^7*e^3), -1/6720*(256*b*c^7*sqrt(-d)*d^3*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + (105*b*c^6*d^3 - 35*b*c^4*d^2*e + 63*b*c^2*d*e^2 + 75*b*e^3)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) - 64*(15*b*c^7*e^3*x^6 + 3*b*c^7*d*e^2*x^4 - 4*b*c^7*d^2*e*x^2 + 8*b*c^7*d^3)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 4*(240*a*c^7*e^3*x^6 + 48*a*c^7*d*e^2*x^4 - 64*a*c^7*d^2*e*x^2 + 128*a*c^7*d^3 - (40*b*c^6*e^3*x^5 + 2*(11*b*c^6*d*e^2 + 25*b*c^4*e^3)*x^3 - (41*b*c^6*d^2*e - 38*b*c^4*d*e^2 - 75*b*c^2*e^3)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^7*e^3), -1/3360*(128*b*c^7*sqrt(-d)*d^3*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + (105*b*c^6*d^3 - 35*b*c^4*d^2*e + 63*b*c^2*d*e^2 + 75*b*e^3)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) - 32*(15*b*c^7*e^3*x^6 + 3*b*c^7*d*e^2*x^4 - 4*b*c^7*d^2*e*x^2 + 8*b*c^7*d^3)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 2*(240*a*c^7*e^3*x^6 + 48*a*c^7*d*e^2*x^4 - 64*a*c^7*d^2*e*x^2 + 128*a*c^7*d^3 - (40*b*c^6*e^3*x^5 + 2*(11*b*c^6*d*e^2 + 25*b*c^4*e^3)*x^3 - (41*b*c^6*d^2*e - 38*b*c^4*d*e^2 - 75*b*c^2*e^3)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^7*e^3)]","A",0
131,1,1669,0,1.993010," ","integrate(x^3*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{16 \, b c^{5} d^{\frac{5}{2}} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} - 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) + {\left(15 \, b c^{4} d^{2} - 10 \, b c^{2} d e - 9 \, b e^{2}\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) + 32 \, {\left(3 \, b c^{5} e^{2} x^{4} + b c^{5} d e x^{2} - 2 \, b c^{5} d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 4 \, {\left(24 \, a c^{5} e^{2} x^{4} + 8 \, a c^{5} d e x^{2} - 16 \, a c^{5} d^{2} - {\left(6 \, b c^{4} e^{2} x^{3} + {\left(7 \, b c^{4} d e + 9 \, b c^{2} e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{480 \, c^{5} e^{2}}, \frac{8 \, b c^{5} d^{\frac{5}{2}} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} - 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) + {\left(15 \, b c^{4} d^{2} - 10 \, b c^{2} d e - 9 \, b e^{2}\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) + 16 \, {\left(3 \, b c^{5} e^{2} x^{4} + b c^{5} d e x^{2} - 2 \, b c^{5} d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 2 \, {\left(24 \, a c^{5} e^{2} x^{4} + 8 \, a c^{5} d e x^{2} - 16 \, a c^{5} d^{2} - {\left(6 \, b c^{4} e^{2} x^{3} + {\left(7 \, b c^{4} d e + 9 \, b c^{2} e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{240 \, c^{5} e^{2}}, \frac{32 \, b c^{5} \sqrt{-d} d^{2} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + {\left(15 \, b c^{4} d^{2} - 10 \, b c^{2} d e - 9 \, b e^{2}\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) + 32 \, {\left(3 \, b c^{5} e^{2} x^{4} + b c^{5} d e x^{2} - 2 \, b c^{5} d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 4 \, {\left(24 \, a c^{5} e^{2} x^{4} + 8 \, a c^{5} d e x^{2} - 16 \, a c^{5} d^{2} - {\left(6 \, b c^{4} e^{2} x^{3} + {\left(7 \, b c^{4} d e + 9 \, b c^{2} e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{480 \, c^{5} e^{2}}, \frac{16 \, b c^{5} \sqrt{-d} d^{2} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + {\left(15 \, b c^{4} d^{2} - 10 \, b c^{2} d e - 9 \, b e^{2}\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) + 16 \, {\left(3 \, b c^{5} e^{2} x^{4} + b c^{5} d e x^{2} - 2 \, b c^{5} d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 2 \, {\left(24 \, a c^{5} e^{2} x^{4} + 8 \, a c^{5} d e x^{2} - 16 \, a c^{5} d^{2} - {\left(6 \, b c^{4} e^{2} x^{3} + {\left(7 \, b c^{4} d e + 9 \, b c^{2} e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{240 \, c^{5} e^{2}}\right]"," ",0,"[1/480*(16*b*c^5*d^(5/2)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 - 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) + (15*b*c^4*d^2 - 10*b*c^2*d*e - 9*b*e^2)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) + 32*(3*b*c^5*e^2*x^4 + b*c^5*d*e*x^2 - 2*b*c^5*d^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 4*(24*a*c^5*e^2*x^4 + 8*a*c^5*d*e*x^2 - 16*a*c^5*d^2 - (6*b*c^4*e^2*x^3 + (7*b*c^4*d*e + 9*b*c^2*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^5*e^2), 1/240*(8*b*c^5*d^(5/2)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 - 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) + (15*b*c^4*d^2 - 10*b*c^2*d*e - 9*b*e^2)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) + 16*(3*b*c^5*e^2*x^4 + b*c^5*d*e*x^2 - 2*b*c^5*d^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 2*(24*a*c^5*e^2*x^4 + 8*a*c^5*d*e*x^2 - 16*a*c^5*d^2 - (6*b*c^4*e^2*x^3 + (7*b*c^4*d*e + 9*b*c^2*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^5*e^2), 1/480*(32*b*c^5*sqrt(-d)*d^2*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + (15*b*c^4*d^2 - 10*b*c^2*d*e - 9*b*e^2)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) + 32*(3*b*c^5*e^2*x^4 + b*c^5*d*e*x^2 - 2*b*c^5*d^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 4*(24*a*c^5*e^2*x^4 + 8*a*c^5*d*e*x^2 - 16*a*c^5*d^2 - (6*b*c^4*e^2*x^3 + (7*b*c^4*d*e + 9*b*c^2*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^5*e^2), 1/240*(16*b*c^5*sqrt(-d)*d^2*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + (15*b*c^4*d^2 - 10*b*c^2*d*e - 9*b*e^2)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) + 16*(3*b*c^5*e^2*x^4 + b*c^5*d*e*x^2 - 2*b*c^5*d^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 2*(24*a*c^5*e^2*x^4 + 8*a*c^5*d*e*x^2 - 16*a*c^5*d^2 - (6*b*c^4*e^2*x^3 + (7*b*c^4*d*e + 9*b*c^2*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^5*e^2)]","A",0
132,1,1382,0,2.022633," ","integrate(x*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, b c^{3} d^{\frac{3}{2}} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} + 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) - {\left(3 \, b c^{2} d + b e\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) + 8 \, {\left(b c^{3} e x^{2} + b c^{3} d\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 4 \, {\left(2 \, a c^{3} e x^{2} - b c^{2} e x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 2 \, a c^{3} d\right)} \sqrt{e x^{2} + d}}{24 \, c^{3} e}, \frac{b c^{3} d^{\frac{3}{2}} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} + 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) - {\left(3 \, b c^{2} d + b e\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) + 4 \, {\left(b c^{3} e x^{2} + b c^{3} d\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 2 \, {\left(2 \, a c^{3} e x^{2} - b c^{2} e x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 2 \, a c^{3} d\right)} \sqrt{e x^{2} + d}}{12 \, c^{3} e}, -\frac{4 \, b c^{3} \sqrt{-d} d \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + {\left(3 \, b c^{2} d + b e\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) - 8 \, {\left(b c^{3} e x^{2} + b c^{3} d\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 4 \, {\left(2 \, a c^{3} e x^{2} - b c^{2} e x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 2 \, a c^{3} d\right)} \sqrt{e x^{2} + d}}{24 \, c^{3} e}, -\frac{2 \, b c^{3} \sqrt{-d} d \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + {\left(3 \, b c^{2} d + b e\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) - 4 \, {\left(b c^{3} e x^{2} + b c^{3} d\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 2 \, {\left(2 \, a c^{3} e x^{2} - b c^{2} e x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 2 \, a c^{3} d\right)} \sqrt{e x^{2} + d}}{12 \, c^{3} e}\right]"," ",0,"[1/24*(2*b*c^3*d^(3/2)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 + 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) - (3*b*c^2*d + b*e)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) + 8*(b*c^3*e*x^2 + b*c^3*d)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 4*(2*a*c^3*e*x^2 - b*c^2*e*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 2*a*c^3*d)*sqrt(e*x^2 + d))/(c^3*e), 1/12*(b*c^3*d^(3/2)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 + 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) - (3*b*c^2*d + b*e)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) + 4*(b*c^3*e*x^2 + b*c^3*d)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 2*(2*a*c^3*e*x^2 - b*c^2*e*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 2*a*c^3*d)*sqrt(e*x^2 + d))/(c^3*e), -1/24*(4*b*c^3*sqrt(-d)*d*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + (3*b*c^2*d + b*e)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) - 8*(b*c^3*e*x^2 + b*c^3*d)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 4*(2*a*c^3*e*x^2 - b*c^2*e*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 2*a*c^3*d)*sqrt(e*x^2 + d))/(c^3*e), -1/12*(2*b*c^3*sqrt(-d)*d*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + (3*b*c^2*d + b*e)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) - 4*(b*c^3*e*x^2 + b*c^3*d)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 2*(2*a*c^3*e*x^2 - b*c^2*e*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 2*a*c^3*d)*sqrt(e*x^2 + d))/(c^3*e)]","B",0
133,0,0,0,0.564408," ","integrate((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{x}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)/x, x)","F",0
134,0,0,0,0.611516," ","integrate((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{x^{3}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)/x^3, x)","F",0
135,0,0,0,0.638160," ","integrate(x^2*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{2} \operatorname{arsech}\left(c x\right) + a x^{2}\right)} \sqrt{e x^{2} + d}, x\right)"," ",0,"integral((b*x^2*arcsech(c*x) + a*x^2)*sqrt(e*x^2 + d), x)","F",0
136,0,0,0,0.686957," ","integrate((a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a), x)","F",0
137,0,0,0,0.625180," ","integrate((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{x^{2}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)/x^2, x)","F",0
138,0,0,0,0.646299," ","integrate((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{x^{4}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)/x^4, x)","F",0
139,0,0,0,0.752746," ","integrate((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{x^{6}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)/x^6, x)","F",0
140,1,1989,0,3.980217," ","integrate(x^3*(e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\left[\frac{96 \, b c^{7} d^{\frac{7}{2}} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} - 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) + 3 \, {\left(35 \, b c^{6} d^{3} - 35 \, b c^{4} d^{2} e - 63 \, b c^{2} d e^{2} - 25 \, b e^{3}\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) + 192 \, {\left(5 \, b c^{7} e^{3} x^{6} + 8 \, b c^{7} d e^{2} x^{4} + b c^{7} d^{2} e x^{2} - 2 \, b c^{7} d^{3}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 4 \, {\left(240 \, a c^{7} e^{3} x^{6} + 384 \, a c^{7} d e^{2} x^{4} + 48 \, a c^{7} d^{2} e x^{2} - 96 \, a c^{7} d^{3} - {\left(40 \, b c^{6} e^{3} x^{5} + 2 \, {\left(53 \, b c^{6} d e^{2} + 25 \, b c^{4} e^{3}\right)} x^{3} + {\left(57 \, b c^{6} d^{2} e + 164 \, b c^{4} d e^{2} + 75 \, b c^{2} e^{3}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{6720 \, c^{7} e^{2}}, \frac{48 \, b c^{7} d^{\frac{7}{2}} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} - 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) + 3 \, {\left(35 \, b c^{6} d^{3} - 35 \, b c^{4} d^{2} e - 63 \, b c^{2} d e^{2} - 25 \, b e^{3}\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) + 96 \, {\left(5 \, b c^{7} e^{3} x^{6} + 8 \, b c^{7} d e^{2} x^{4} + b c^{7} d^{2} e x^{2} - 2 \, b c^{7} d^{3}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 2 \, {\left(240 \, a c^{7} e^{3} x^{6} + 384 \, a c^{7} d e^{2} x^{4} + 48 \, a c^{7} d^{2} e x^{2} - 96 \, a c^{7} d^{3} - {\left(40 \, b c^{6} e^{3} x^{5} + 2 \, {\left(53 \, b c^{6} d e^{2} + 25 \, b c^{4} e^{3}\right)} x^{3} + {\left(57 \, b c^{6} d^{2} e + 164 \, b c^{4} d e^{2} + 75 \, b c^{2} e^{3}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{3360 \, c^{7} e^{2}}, \frac{192 \, b c^{7} \sqrt{-d} d^{3} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + 3 \, {\left(35 \, b c^{6} d^{3} - 35 \, b c^{4} d^{2} e - 63 \, b c^{2} d e^{2} - 25 \, b e^{3}\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) + 192 \, {\left(5 \, b c^{7} e^{3} x^{6} + 8 \, b c^{7} d e^{2} x^{4} + b c^{7} d^{2} e x^{2} - 2 \, b c^{7} d^{3}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 4 \, {\left(240 \, a c^{7} e^{3} x^{6} + 384 \, a c^{7} d e^{2} x^{4} + 48 \, a c^{7} d^{2} e x^{2} - 96 \, a c^{7} d^{3} - {\left(40 \, b c^{6} e^{3} x^{5} + 2 \, {\left(53 \, b c^{6} d e^{2} + 25 \, b c^{4} e^{3}\right)} x^{3} + {\left(57 \, b c^{6} d^{2} e + 164 \, b c^{4} d e^{2} + 75 \, b c^{2} e^{3}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{6720 \, c^{7} e^{2}}, \frac{96 \, b c^{7} \sqrt{-d} d^{3} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + 3 \, {\left(35 \, b c^{6} d^{3} - 35 \, b c^{4} d^{2} e - 63 \, b c^{2} d e^{2} - 25 \, b e^{3}\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) + 96 \, {\left(5 \, b c^{7} e^{3} x^{6} + 8 \, b c^{7} d e^{2} x^{4} + b c^{7} d^{2} e x^{2} - 2 \, b c^{7} d^{3}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 2 \, {\left(240 \, a c^{7} e^{3} x^{6} + 384 \, a c^{7} d e^{2} x^{4} + 48 \, a c^{7} d^{2} e x^{2} - 96 \, a c^{7} d^{3} - {\left(40 \, b c^{6} e^{3} x^{5} + 2 \, {\left(53 \, b c^{6} d e^{2} + 25 \, b c^{4} e^{3}\right)} x^{3} + {\left(57 \, b c^{6} d^{2} e + 164 \, b c^{4} d e^{2} + 75 \, b c^{2} e^{3}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{3360 \, c^{7} e^{2}}\right]"," ",0,"[1/6720*(96*b*c^7*d^(7/2)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 - 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) + 3*(35*b*c^6*d^3 - 35*b*c^4*d^2*e - 63*b*c^2*d*e^2 - 25*b*e^3)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) + 192*(5*b*c^7*e^3*x^6 + 8*b*c^7*d*e^2*x^4 + b*c^7*d^2*e*x^2 - 2*b*c^7*d^3)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 4*(240*a*c^7*e^3*x^6 + 384*a*c^7*d*e^2*x^4 + 48*a*c^7*d^2*e*x^2 - 96*a*c^7*d^3 - (40*b*c^6*e^3*x^5 + 2*(53*b*c^6*d*e^2 + 25*b*c^4*e^3)*x^3 + (57*b*c^6*d^2*e + 164*b*c^4*d*e^2 + 75*b*c^2*e^3)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^7*e^2), 1/3360*(48*b*c^7*d^(7/2)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 - 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) + 3*(35*b*c^6*d^3 - 35*b*c^4*d^2*e - 63*b*c^2*d*e^2 - 25*b*e^3)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) + 96*(5*b*c^7*e^3*x^6 + 8*b*c^7*d*e^2*x^4 + b*c^7*d^2*e*x^2 - 2*b*c^7*d^3)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 2*(240*a*c^7*e^3*x^6 + 384*a*c^7*d*e^2*x^4 + 48*a*c^7*d^2*e*x^2 - 96*a*c^7*d^3 - (40*b*c^6*e^3*x^5 + 2*(53*b*c^6*d*e^2 + 25*b*c^4*e^3)*x^3 + (57*b*c^6*d^2*e + 164*b*c^4*d*e^2 + 75*b*c^2*e^3)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^7*e^2), 1/6720*(192*b*c^7*sqrt(-d)*d^3*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + 3*(35*b*c^6*d^3 - 35*b*c^4*d^2*e - 63*b*c^2*d*e^2 - 25*b*e^3)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) + 192*(5*b*c^7*e^3*x^6 + 8*b*c^7*d*e^2*x^4 + b*c^7*d^2*e*x^2 - 2*b*c^7*d^3)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 4*(240*a*c^7*e^3*x^6 + 384*a*c^7*d*e^2*x^4 + 48*a*c^7*d^2*e*x^2 - 96*a*c^7*d^3 - (40*b*c^6*e^3*x^5 + 2*(53*b*c^6*d*e^2 + 25*b*c^4*e^3)*x^3 + (57*b*c^6*d^2*e + 164*b*c^4*d*e^2 + 75*b*c^2*e^3)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^7*e^2), 1/3360*(96*b*c^7*sqrt(-d)*d^3*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + 3*(35*b*c^6*d^3 - 35*b*c^4*d^2*e - 63*b*c^2*d*e^2 - 25*b*e^3)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) + 96*(5*b*c^7*e^3*x^6 + 8*b*c^7*d*e^2*x^4 + b*c^7*d^2*e*x^2 - 2*b*c^7*d^3)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 2*(240*a*c^7*e^3*x^6 + 384*a*c^7*d*e^2*x^4 + 48*a*c^7*d^2*e*x^2 - 96*a*c^7*d^3 - (40*b*c^6*e^3*x^5 + 2*(53*b*c^6*d*e^2 + 25*b*c^4*e^3)*x^3 + (57*b*c^6*d^2*e + 164*b*c^4*d*e^2 + 75*b*c^2*e^3)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^7*e^2)]","A",0
141,1,1667,0,1.567905," ","integrate(x*(e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","\left[\frac{8 \, b c^{5} d^{\frac{5}{2}} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} + 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) - {\left(15 \, b c^{4} d^{2} + 10 \, b c^{2} d e + 3 \, b e^{2}\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) + 32 \, {\left(b c^{5} e^{2} x^{4} + 2 \, b c^{5} d e x^{2} + b c^{5} d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 4 \, {\left(8 \, a c^{5} e^{2} x^{4} + 16 \, a c^{5} d e x^{2} + 8 \, a c^{5} d^{2} - {\left(2 \, b c^{4} e^{2} x^{3} + 3 \, {\left(3 \, b c^{4} d e + b c^{2} e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{160 \, c^{5} e}, \frac{4 \, b c^{5} d^{\frac{5}{2}} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} + 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) - {\left(15 \, b c^{4} d^{2} + 10 \, b c^{2} d e + 3 \, b e^{2}\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) + 16 \, {\left(b c^{5} e^{2} x^{4} + 2 \, b c^{5} d e x^{2} + b c^{5} d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 2 \, {\left(8 \, a c^{5} e^{2} x^{4} + 16 \, a c^{5} d e x^{2} + 8 \, a c^{5} d^{2} - {\left(2 \, b c^{4} e^{2} x^{3} + 3 \, {\left(3 \, b c^{4} d e + b c^{2} e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{80 \, c^{5} e}, -\frac{16 \, b c^{5} \sqrt{-d} d^{2} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + {\left(15 \, b c^{4} d^{2} + 10 \, b c^{2} d e + 3 \, b e^{2}\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) - 32 \, {\left(b c^{5} e^{2} x^{4} + 2 \, b c^{5} d e x^{2} + b c^{5} d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 4 \, {\left(8 \, a c^{5} e^{2} x^{4} + 16 \, a c^{5} d e x^{2} + 8 \, a c^{5} d^{2} - {\left(2 \, b c^{4} e^{2} x^{3} + 3 \, {\left(3 \, b c^{4} d e + b c^{2} e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{160 \, c^{5} e}, -\frac{8 \, b c^{5} \sqrt{-d} d^{2} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + {\left(15 \, b c^{4} d^{2} + 10 \, b c^{2} d e + 3 \, b e^{2}\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) - 16 \, {\left(b c^{5} e^{2} x^{4} + 2 \, b c^{5} d e x^{2} + b c^{5} d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 2 \, {\left(8 \, a c^{5} e^{2} x^{4} + 16 \, a c^{5} d e x^{2} + 8 \, a c^{5} d^{2} - {\left(2 \, b c^{4} e^{2} x^{3} + 3 \, {\left(3 \, b c^{4} d e + b c^{2} e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{80 \, c^{5} e}\right]"," ",0,"[1/160*(8*b*c^5*d^(5/2)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 + 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) - (15*b*c^4*d^2 + 10*b*c^2*d*e + 3*b*e^2)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) + 32*(b*c^5*e^2*x^4 + 2*b*c^5*d*e*x^2 + b*c^5*d^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 4*(8*a*c^5*e^2*x^4 + 16*a*c^5*d*e*x^2 + 8*a*c^5*d^2 - (2*b*c^4*e^2*x^3 + 3*(3*b*c^4*d*e + b*c^2*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^5*e), 1/80*(4*b*c^5*d^(5/2)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 + 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) - (15*b*c^4*d^2 + 10*b*c^2*d*e + 3*b*e^2)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) + 16*(b*c^5*e^2*x^4 + 2*b*c^5*d*e*x^2 + b*c^5*d^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 2*(8*a*c^5*e^2*x^4 + 16*a*c^5*d*e*x^2 + 8*a*c^5*d^2 - (2*b*c^4*e^2*x^3 + 3*(3*b*c^4*d*e + b*c^2*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^5*e), -1/160*(16*b*c^5*sqrt(-d)*d^2*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + (15*b*c^4*d^2 + 10*b*c^2*d*e + 3*b*e^2)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) - 32*(b*c^5*e^2*x^4 + 2*b*c^5*d*e*x^2 + b*c^5*d^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 4*(8*a*c^5*e^2*x^4 + 16*a*c^5*d*e*x^2 + 8*a*c^5*d^2 - (2*b*c^4*e^2*x^3 + 3*(3*b*c^4*d*e + b*c^2*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^5*e), -1/80*(8*b*c^5*sqrt(-d)*d^2*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + (15*b*c^4*d^2 + 10*b*c^2*d*e + 3*b*e^2)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) - 16*(b*c^5*e^2*x^4 + 2*b*c^5*d*e*x^2 + b*c^5*d^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 2*(8*a*c^5*e^2*x^4 + 16*a*c^5*d*e*x^2 + 8*a*c^5*d^2 - (2*b*c^4*e^2*x^3 + 3*(3*b*c^4*d*e + b*c^2*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^5*e)]","B",0
142,0,0,0,0.662217," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \operatorname{arsech}\left(c x\right)\right)} \sqrt{e x^{2} + d}}{x}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsech(c*x))*sqrt(e*x^2 + d)/x, x)","F",0
143,0,0,0,0.794819," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \operatorname{arsech}\left(c x\right)\right)} \sqrt{e x^{2} + d}}{x^{3}}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsech(c*x))*sqrt(e*x^2 + d)/x^3, x)","F",0
144,0,0,0,0.600230," ","integrate(x^2*(e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e x^{4} + a d x^{2} + {\left(b e x^{4} + b d x^{2}\right)} \operatorname{arsech}\left(c x\right)\right)} \sqrt{e x^{2} + d}, x\right)"," ",0,"integral((a*e*x^4 + a*d*x^2 + (b*e*x^4 + b*d*x^2)*arcsech(c*x))*sqrt(e*x^2 + d), x)","F",0
145,0,0,0,0.592315," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \operatorname{arsech}\left(c x\right)\right)} \sqrt{e x^{2} + d}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsech(c*x))*sqrt(e*x^2 + d), x)","F",0
146,0,0,0,0.562074," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \operatorname{arsech}\left(c x\right)\right)} \sqrt{e x^{2} + d}}{x^{2}}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsech(c*x))*sqrt(e*x^2 + d)/x^2, x)","F",0
147,0,0,0,0.527767," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \operatorname{arsech}\left(c x\right)\right)} \sqrt{e x^{2} + d}}{x^{4}}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsech(c*x))*sqrt(e*x^2 + d)/x^4, x)","F",0
148,0,0,0,0.598948," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \operatorname{arsech}\left(c x\right)\right)} \sqrt{e x^{2} + d}}{x^{6}}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsech(c*x))*sqrt(e*x^2 + d)/x^6, x)","F",0
149,0,0,0,0.664486," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^8,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \operatorname{arsech}\left(c x\right)\right)} \sqrt{e x^{2} + d}}{x^{8}}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsech(c*x))*sqrt(e*x^2 + d)/x^8, x)","F",0
150,1,1679,0,1.847245," ","integrate(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{64 \, b c^{5} d^{\frac{5}{2}} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} + 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) - {\left(45 \, b c^{4} d^{2} - 10 \, b c^{2} d e + 9 \, b e^{2}\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) + 32 \, {\left(3 \, b c^{5} e^{2} x^{4} - 4 \, b c^{5} d e x^{2} + 8 \, b c^{5} d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 4 \, {\left(24 \, a c^{5} e^{2} x^{4} - 32 \, a c^{5} d e x^{2} + 64 \, a c^{5} d^{2} - {\left(6 \, b c^{4} e^{2} x^{3} - {\left(13 \, b c^{4} d e - 9 \, b c^{2} e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{480 \, c^{5} e^{3}}, \frac{32 \, b c^{5} d^{\frac{5}{2}} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} + 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) - {\left(45 \, b c^{4} d^{2} - 10 \, b c^{2} d e + 9 \, b e^{2}\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) + 16 \, {\left(3 \, b c^{5} e^{2} x^{4} - 4 \, b c^{5} d e x^{2} + 8 \, b c^{5} d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 2 \, {\left(24 \, a c^{5} e^{2} x^{4} - 32 \, a c^{5} d e x^{2} + 64 \, a c^{5} d^{2} - {\left(6 \, b c^{4} e^{2} x^{3} - {\left(13 \, b c^{4} d e - 9 \, b c^{2} e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{240 \, c^{5} e^{3}}, -\frac{128 \, b c^{5} \sqrt{-d} d^{2} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + {\left(45 \, b c^{4} d^{2} - 10 \, b c^{2} d e + 9 \, b e^{2}\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) - 32 \, {\left(3 \, b c^{5} e^{2} x^{4} - 4 \, b c^{5} d e x^{2} + 8 \, b c^{5} d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 4 \, {\left(24 \, a c^{5} e^{2} x^{4} - 32 \, a c^{5} d e x^{2} + 64 \, a c^{5} d^{2} - {\left(6 \, b c^{4} e^{2} x^{3} - {\left(13 \, b c^{4} d e - 9 \, b c^{2} e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{480 \, c^{5} e^{3}}, -\frac{64 \, b c^{5} \sqrt{-d} d^{2} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + {\left(45 \, b c^{4} d^{2} - 10 \, b c^{2} d e + 9 \, b e^{2}\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) - 16 \, {\left(3 \, b c^{5} e^{2} x^{4} - 4 \, b c^{5} d e x^{2} + 8 \, b c^{5} d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 2 \, {\left(24 \, a c^{5} e^{2} x^{4} - 32 \, a c^{5} d e x^{2} + 64 \, a c^{5} d^{2} - {\left(6 \, b c^{4} e^{2} x^{3} - {\left(13 \, b c^{4} d e - 9 \, b c^{2} e^{2}\right)} x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{240 \, c^{5} e^{3}}\right]"," ",0,"[1/480*(64*b*c^5*d^(5/2)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 + 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) - (45*b*c^4*d^2 - 10*b*c^2*d*e + 9*b*e^2)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) + 32*(3*b*c^5*e^2*x^4 - 4*b*c^5*d*e*x^2 + 8*b*c^5*d^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 4*(24*a*c^5*e^2*x^4 - 32*a*c^5*d*e*x^2 + 64*a*c^5*d^2 - (6*b*c^4*e^2*x^3 - (13*b*c^4*d*e - 9*b*c^2*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^5*e^3), 1/240*(32*b*c^5*d^(5/2)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 + 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) - (45*b*c^4*d^2 - 10*b*c^2*d*e + 9*b*e^2)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) + 16*(3*b*c^5*e^2*x^4 - 4*b*c^5*d*e*x^2 + 8*b*c^5*d^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 2*(24*a*c^5*e^2*x^4 - 32*a*c^5*d*e*x^2 + 64*a*c^5*d^2 - (6*b*c^4*e^2*x^3 - (13*b*c^4*d*e - 9*b*c^2*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^5*e^3), -1/480*(128*b*c^5*sqrt(-d)*d^2*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + (45*b*c^4*d^2 - 10*b*c^2*d*e + 9*b*e^2)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) - 32*(3*b*c^5*e^2*x^4 - 4*b*c^5*d*e*x^2 + 8*b*c^5*d^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 4*(24*a*c^5*e^2*x^4 - 32*a*c^5*d*e*x^2 + 64*a*c^5*d^2 - (6*b*c^4*e^2*x^3 - (13*b*c^4*d*e - 9*b*c^2*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^5*e^3), -1/240*(64*b*c^5*sqrt(-d)*d^2*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + (45*b*c^4*d^2 - 10*b*c^2*d*e + 9*b*e^2)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) - 16*(3*b*c^5*e^2*x^4 - 4*b*c^5*d*e*x^2 + 8*b*c^5*d^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 2*(24*a*c^5*e^2*x^4 - 32*a*c^5*d*e*x^2 + 64*a*c^5*d^2 - (6*b*c^4*e^2*x^3 - (13*b*c^4*d*e - 9*b*c^2*e^2)*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^5*e^3)]","A",0
151,1,1389,0,1.005168," ","integrate(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, b c^{3} d^{\frac{3}{2}} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} - 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) + {\left(3 \, b c^{2} d - b e\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) + 8 \, {\left(b c^{3} e x^{2} - 2 \, b c^{3} d\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 4 \, {\left(2 \, a c^{3} e x^{2} - b c^{2} e x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 4 \, a c^{3} d\right)} \sqrt{e x^{2} + d}}{24 \, c^{3} e^{2}}, \frac{2 \, b c^{3} d^{\frac{3}{2}} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} - 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) + {\left(3 \, b c^{2} d - b e\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) + 4 \, {\left(b c^{3} e x^{2} - 2 \, b c^{3} d\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 2 \, {\left(2 \, a c^{3} e x^{2} - b c^{2} e x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 4 \, a c^{3} d\right)} \sqrt{e x^{2} + d}}{12 \, c^{3} e^{2}}, \frac{8 \, b c^{3} \sqrt{-d} d \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + {\left(3 \, b c^{2} d - b e\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) + 8 \, {\left(b c^{3} e x^{2} - 2 \, b c^{3} d\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 4 \, {\left(2 \, a c^{3} e x^{2} - b c^{2} e x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 4 \, a c^{3} d\right)} \sqrt{e x^{2} + d}}{24 \, c^{3} e^{2}}, \frac{4 \, b c^{3} \sqrt{-d} d \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + {\left(3 \, b c^{2} d - b e\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) + 4 \, {\left(b c^{3} e x^{2} - 2 \, b c^{3} d\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 2 \, {\left(2 \, a c^{3} e x^{2} - b c^{2} e x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 4 \, a c^{3} d\right)} \sqrt{e x^{2} + d}}{12 \, c^{3} e^{2}}\right]"," ",0,"[1/24*(4*b*c^3*d^(3/2)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 - 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) + (3*b*c^2*d - b*e)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) + 8*(b*c^3*e*x^2 - 2*b*c^3*d)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 4*(2*a*c^3*e*x^2 - b*c^2*e*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 4*a*c^3*d)*sqrt(e*x^2 + d))/(c^3*e^2), 1/12*(2*b*c^3*d^(3/2)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 - 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) + (3*b*c^2*d - b*e)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) + 4*(b*c^3*e*x^2 - 2*b*c^3*d)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 2*(2*a*c^3*e*x^2 - b*c^2*e*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 4*a*c^3*d)*sqrt(e*x^2 + d))/(c^3*e^2), 1/24*(8*b*c^3*sqrt(-d)*d*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + (3*b*c^2*d - b*e)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) + 8*(b*c^3*e*x^2 - 2*b*c^3*d)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 4*(2*a*c^3*e*x^2 - b*c^2*e*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 4*a*c^3*d)*sqrt(e*x^2 + d))/(c^3*e^2), 1/12*(4*b*c^3*sqrt(-d)*d*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + (3*b*c^2*d - b*e)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) + 4*(b*c^3*e*x^2 - 2*b*c^3*d)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 2*(2*a*c^3*e*x^2 - b*c^2*e*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 4*a*c^3*d)*sqrt(e*x^2 + d))/(c^3*e^2)]","B",0
152,1,1102,0,0.820783," ","integrate(x*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{e x^{2} + d} b c \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + b c \sqrt{d} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} + 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) + 4 \, \sqrt{e x^{2} + d} a c - b \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right)}{4 \, c e}, \frac{4 \, \sqrt{e x^{2} + d} b c \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + b c \sqrt{d} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} + 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) + 4 \, \sqrt{e x^{2} + d} a c - 2 \, b \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right)}{4 \, c e}, -\frac{2 \, b c \sqrt{-d} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) - 4 \, \sqrt{e x^{2} + d} b c \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 4 \, \sqrt{e x^{2} + d} a c + b \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right)}{4 \, c e}, -\frac{b c \sqrt{-d} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) - 2 \, \sqrt{e x^{2} + d} b c \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 2 \, \sqrt{e x^{2} + d} a c + b \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right)}{2 \, c e}\right]"," ",0,"[1/4*(4*sqrt(e*x^2 + d)*b*c*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + b*c*sqrt(d)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 + 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) + 4*sqrt(e*x^2 + d)*a*c - b*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2))/(c*e), 1/4*(4*sqrt(e*x^2 + d)*b*c*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + b*c*sqrt(d)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 + 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) + 4*sqrt(e*x^2 + d)*a*c - 2*b*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)))/(c*e), -1/4*(2*b*c*sqrt(-d)*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) - 4*sqrt(e*x^2 + d)*b*c*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 4*sqrt(e*x^2 + d)*a*c + b*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2))/(c*e), -1/2*(b*c*sqrt(-d)*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) - 2*sqrt(e*x^2 + d)*b*c*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 2*sqrt(e*x^2 + d)*a*c + b*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)))/(c*e)]","B",0
153,0,0,0,0.785727," ","integrate((a+b*arcsech(c*x))/x/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{e x^{3} + d x}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)/(e*x^3 + d*x), x)","F",0
154,0,0,0,0.532059," ","integrate((a+b*arcsech(c*x))/x^3/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{e x^{5} + d x^{3}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)/(e*x^5 + d*x^3), x)","F",0
155,0,0,0,0.667224," ","integrate(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \operatorname{arsech}\left(c x\right) + a x^{2}}{\sqrt{e x^{2} + d}}, x\right)"," ",0,"integral((b*x^2*arcsech(c*x) + a*x^2)/sqrt(e*x^2 + d), x)","F",0
156,0,0,0,0.688775," ","integrate((a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arsech}\left(c x\right) + a}{\sqrt{e x^{2} + d}}, x\right)"," ",0,"integral((b*arcsech(c*x) + a)/sqrt(e*x^2 + d), x)","F",0
157,0,0,0,0.575501," ","integrate((a+b*arcsech(c*x))/x^2/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{e x^{4} + d x^{2}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)/(e*x^4 + d*x^2), x)","F",0
158,0,0,0,0.653535," ","integrate((a+b*arcsech(c*x))/x^4/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{e x^{6} + d x^{4}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)/(e*x^6 + d*x^4), x)","F",0
159,1,1771,0,2.588138," ","integrate(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(9 \, b c^{2} d^{2} - b d e + {\left(9 \, b c^{2} d e - b e^{2}\right)} x^{2}\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) + 8 \, {\left(b c^{3} e^{2} x^{4} - 4 \, b c^{3} d e x^{2} - 8 \, b c^{3} d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 16 \, {\left(b c^{3} d e x^{2} + b c^{3} d^{2}\right)} \sqrt{d} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} - 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) + 4 \, {\left(2 \, a c^{3} e^{2} x^{4} - 8 \, a c^{3} d e x^{2} - 16 \, a c^{3} d^{2} - {\left(b c^{2} e^{2} x^{3} + b c^{2} d e x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{24 \, {\left(c^{3} e^{4} x^{2} + c^{3} d e^{3}\right)}}, \frac{{\left(9 \, b c^{2} d^{2} - b d e + {\left(9 \, b c^{2} d e - b e^{2}\right)} x^{2}\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) + 4 \, {\left(b c^{3} e^{2} x^{4} - 4 \, b c^{3} d e x^{2} - 8 \, b c^{3} d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 8 \, {\left(b c^{3} d e x^{2} + b c^{3} d^{2}\right)} \sqrt{d} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} - 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) + 2 \, {\left(2 \, a c^{3} e^{2} x^{4} - 8 \, a c^{3} d e x^{2} - 16 \, a c^{3} d^{2} - {\left(b c^{2} e^{2} x^{3} + b c^{2} d e x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{12 \, {\left(c^{3} e^{4} x^{2} + c^{3} d e^{3}\right)}}, \frac{32 \, {\left(b c^{3} d e x^{2} + b c^{3} d^{2}\right)} \sqrt{-d} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + {\left(9 \, b c^{2} d^{2} - b d e + {\left(9 \, b c^{2} d e - b e^{2}\right)} x^{2}\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) + 8 \, {\left(b c^{3} e^{2} x^{4} - 4 \, b c^{3} d e x^{2} - 8 \, b c^{3} d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 4 \, {\left(2 \, a c^{3} e^{2} x^{4} - 8 \, a c^{3} d e x^{2} - 16 \, a c^{3} d^{2} - {\left(b c^{2} e^{2} x^{3} + b c^{2} d e x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{24 \, {\left(c^{3} e^{4} x^{2} + c^{3} d e^{3}\right)}}, \frac{16 \, {\left(b c^{3} d e x^{2} + b c^{3} d^{2}\right)} \sqrt{-d} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + {\left(9 \, b c^{2} d^{2} - b d e + {\left(9 \, b c^{2} d e - b e^{2}\right)} x^{2}\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) + 4 \, {\left(b c^{3} e^{2} x^{4} - 4 \, b c^{3} d e x^{2} - 8 \, b c^{3} d^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 2 \, {\left(2 \, a c^{3} e^{2} x^{4} - 8 \, a c^{3} d e x^{2} - 16 \, a c^{3} d^{2} - {\left(b c^{2} e^{2} x^{3} + b c^{2} d e x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{12 \, {\left(c^{3} e^{4} x^{2} + c^{3} d e^{3}\right)}}\right]"," ",0,"[1/24*((9*b*c^2*d^2 - b*d*e + (9*b*c^2*d*e - b*e^2)*x^2)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) + 8*(b*c^3*e^2*x^4 - 4*b*c^3*d*e*x^2 - 8*b*c^3*d^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 16*(b*c^3*d*e*x^2 + b*c^3*d^2)*sqrt(d)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 - 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) + 4*(2*a*c^3*e^2*x^4 - 8*a*c^3*d*e*x^2 - 16*a*c^3*d^2 - (b*c^2*e^2*x^3 + b*c^2*d*e*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^3*e^4*x^2 + c^3*d*e^3), 1/12*((9*b*c^2*d^2 - b*d*e + (9*b*c^2*d*e - b*e^2)*x^2)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) + 4*(b*c^3*e^2*x^4 - 4*b*c^3*d*e*x^2 - 8*b*c^3*d^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 8*(b*c^3*d*e*x^2 + b*c^3*d^2)*sqrt(d)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 - 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) + 2*(2*a*c^3*e^2*x^4 - 8*a*c^3*d*e*x^2 - 16*a*c^3*d^2 - (b*c^2*e^2*x^3 + b*c^2*d*e*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^3*e^4*x^2 + c^3*d*e^3), 1/24*(32*(b*c^3*d*e*x^2 + b*c^3*d^2)*sqrt(-d)*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + (9*b*c^2*d^2 - b*d*e + (9*b*c^2*d*e - b*e^2)*x^2)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) + 8*(b*c^3*e^2*x^4 - 4*b*c^3*d*e*x^2 - 8*b*c^3*d^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 4*(2*a*c^3*e^2*x^4 - 8*a*c^3*d*e*x^2 - 16*a*c^3*d^2 - (b*c^2*e^2*x^3 + b*c^2*d*e*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^3*e^4*x^2 + c^3*d*e^3), 1/12*(16*(b*c^3*d*e*x^2 + b*c^3*d^2)*sqrt(-d)*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + (9*b*c^2*d^2 - b*d*e + (9*b*c^2*d*e - b*e^2)*x^2)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) + 4*(b*c^3*e^2*x^4 - 4*b*c^3*d*e*x^2 - 8*b*c^3*d^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 2*(2*a*c^3*e^2*x^4 - 8*a*c^3*d*e*x^2 - 16*a*c^3*d^2 - (b*c^2*e^2*x^3 + b*c^2*d*e*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^3*e^4*x^2 + c^3*d*e^3)]","B",0
160,1,1311,0,1.801072," ","integrate(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b e x^{2} + b d\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) - 4 \, {\left(b c e x^{2} + 2 \, b c d\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 2 \, {\left(b c e x^{2} + b c d\right)} \sqrt{d} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} + 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) - 4 \, {\left(a c e x^{2} + 2 \, a c d\right)} \sqrt{e x^{2} + d}}{4 \, {\left(c e^{3} x^{2} + c d e^{2}\right)}}, -\frac{{\left(b e x^{2} + b d\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) - 2 \, {\left(b c e x^{2} + 2 \, b c d\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(b c e x^{2} + b c d\right)} \sqrt{d} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} + 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) - 2 \, {\left(a c e x^{2} + 2 \, a c d\right)} \sqrt{e x^{2} + d}}{2 \, {\left(c e^{3} x^{2} + c d e^{2}\right)}}, -\frac{4 \, {\left(b c e x^{2} + b c d\right)} \sqrt{-d} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + {\left(b e x^{2} + b d\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) - 4 \, {\left(b c e x^{2} + 2 \, b c d\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 4 \, {\left(a c e x^{2} + 2 \, a c d\right)} \sqrt{e x^{2} + d}}{4 \, {\left(c e^{3} x^{2} + c d e^{2}\right)}}, -\frac{2 \, {\left(b c e x^{2} + b c d\right)} \sqrt{-d} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + {\left(b e x^{2} + b d\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) - 2 \, {\left(b c e x^{2} + 2 \, b c d\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 2 \, {\left(a c e x^{2} + 2 \, a c d\right)} \sqrt{e x^{2} + d}}{2 \, {\left(c e^{3} x^{2} + c d e^{2}\right)}}\right]"," ",0,"[-1/4*((b*e*x^2 + b*d)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) - 4*(b*c*e*x^2 + 2*b*c*d)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 2*(b*c*e*x^2 + b*c*d)*sqrt(d)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 + 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) - 4*(a*c*e*x^2 + 2*a*c*d)*sqrt(e*x^2 + d))/(c*e^3*x^2 + c*d*e^2), -1/2*((b*e*x^2 + b*d)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) - 2*(b*c*e*x^2 + 2*b*c*d)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (b*c*e*x^2 + b*c*d)*sqrt(d)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 + 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) - 2*(a*c*e*x^2 + 2*a*c*d)*sqrt(e*x^2 + d))/(c*e^3*x^2 + c*d*e^2), -1/4*(4*(b*c*e*x^2 + b*c*d)*sqrt(-d)*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + (b*e*x^2 + b*d)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) - 4*(b*c*e*x^2 + 2*b*c*d)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 4*(a*c*e*x^2 + 2*a*c*d)*sqrt(e*x^2 + d))/(c*e^3*x^2 + c*d*e^2), -1/2*(2*(b*c*e*x^2 + b*c*d)*sqrt(-d)*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + (b*e*x^2 + b*d)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) - 2*(b*c*e*x^2 + 2*b*c*d)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 2*(a*c*e*x^2 + 2*a*c*d)*sqrt(e*x^2 + d))/(c*e^3*x^2 + c*d*e^2)]","B",0
161,1,379,0,0.608752," ","integrate(x*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, \sqrt{e x^{2} + d} b d \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 4 \, \sqrt{e x^{2} + d} a d - {\left(b e x^{2} + b d\right)} \sqrt{d} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} - 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right)}{4 \, {\left(d e^{2} x^{2} + d^{2} e\right)}}, -\frac{2 \, \sqrt{e x^{2} + d} b d \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) + 2 \, \sqrt{e x^{2} + d} a d - {\left(b e x^{2} + b d\right)} \sqrt{-d} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right)}{2 \, {\left(d e^{2} x^{2} + d^{2} e\right)}}\right]"," ",0,"[-1/4*(4*sqrt(e*x^2 + d)*b*d*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 4*sqrt(e*x^2 + d)*a*d - (b*e*x^2 + b*d)*sqrt(d)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 - 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4))/(d*e^2*x^2 + d^2*e), -1/2*(2*sqrt(e*x^2 + d)*b*d*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) + 2*sqrt(e*x^2 + d)*a*d - (b*e*x^2 + b*d)*sqrt(-d)*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)))/(d*e^2*x^2 + d^2*e)]","B",0
162,0,0,0,1.038566," ","integrate((a+b*arcsech(c*x))/x/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{e^{2} x^{5} + 2 \, d e x^{3} + d^{2} x}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)/(e^2*x^5 + 2*d*e*x^3 + d^2*x), x)","F",0
163,0,0,0,0.667306," ","integrate((a+b*arcsech(c*x))/x^3/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{e^{2} x^{7} + 2 \, d e x^{5} + d^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)/(e^2*x^7 + 2*d*e*x^5 + d^2*x^3), x)","F",0
164,0,0,0,0.563162," ","integrate(x^4*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} \operatorname{arsech}\left(c x\right) + a x^{4}\right)} \sqrt{e x^{2} + d}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*x^4*arcsech(c*x) + a*x^4)*sqrt(e*x^2 + d)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
165,0,0,0,0.506103," ","integrate(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} \operatorname{arsech}\left(c x\right) + a x^{2}\right)} \sqrt{e x^{2} + d}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*x^2*arcsech(c*x) + a*x^2)*sqrt(e*x^2 + d)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
166,0,0,0,0.716425," ","integrate((a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
167,0,0,0,0.518940," ","integrate((a+b*arcsech(c*x))/x^2/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{e^{2} x^{6} + 2 \, d e x^{4} + d^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)/(e^2*x^6 + 2*d*e*x^4 + d^2*x^2), x)","F",0
168,1,2415,0,1.185527," ","integrate(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b c^{2} d^{3} + {\left(b c^{2} d e^{2} + b e^{3}\right)} x^{4} + b d^{2} e + 2 \, {\left(b c^{2} d^{2} e + b d e^{2}\right)} x^{2}\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) - 4 \, {\left(8 \, b c^{3} d^{3} + 8 \, b c d^{2} e + 3 \, {\left(b c^{3} d e^{2} + b c e^{3}\right)} x^{4} + 12 \, {\left(b c^{3} d^{2} e + b c d e^{2}\right)} x^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 8 \, {\left(b c^{3} d^{3} + b c d^{2} e + {\left(b c^{3} d e^{2} + b c e^{3}\right)} x^{4} + 2 \, {\left(b c^{3} d^{2} e + b c d e^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} + 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) - 4 \, {\left(8 \, a c^{3} d^{3} + 8 \, a c d^{2} e + 3 \, {\left(a c^{3} d e^{2} + a c e^{3}\right)} x^{4} + 12 \, {\left(a c^{3} d^{2} e + a c d e^{2}\right)} x^{2} - {\left(b c^{2} d e^{2} x^{3} + b c^{2} d^{2} e x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{12 \, {\left(c^{3} d^{3} e^{3} + c d^{2} e^{4} + {\left(c^{3} d e^{5} + c e^{6}\right)} x^{4} + 2 \, {\left(c^{3} d^{2} e^{4} + c d e^{5}\right)} x^{2}\right)}}, -\frac{3 \, {\left(b c^{2} d^{3} + {\left(b c^{2} d e^{2} + b e^{3}\right)} x^{4} + b d^{2} e + 2 \, {\left(b c^{2} d^{2} e + b d e^{2}\right)} x^{2}\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) - 2 \, {\left(8 \, b c^{3} d^{3} + 8 \, b c d^{2} e + 3 \, {\left(b c^{3} d e^{2} + b c e^{3}\right)} x^{4} + 12 \, {\left(b c^{3} d^{2} e + b c d e^{2}\right)} x^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 4 \, {\left(b c^{3} d^{3} + b c d^{2} e + {\left(b c^{3} d e^{2} + b c e^{3}\right)} x^{4} + 2 \, {\left(b c^{3} d^{2} e + b c d e^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} + 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) - 2 \, {\left(8 \, a c^{3} d^{3} + 8 \, a c d^{2} e + 3 \, {\left(a c^{3} d e^{2} + a c e^{3}\right)} x^{4} + 12 \, {\left(a c^{3} d^{2} e + a c d e^{2}\right)} x^{2} - {\left(b c^{2} d e^{2} x^{3} + b c^{2} d^{2} e x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{6 \, {\left(c^{3} d^{3} e^{3} + c d^{2} e^{4} + {\left(c^{3} d e^{5} + c e^{6}\right)} x^{4} + 2 \, {\left(c^{3} d^{2} e^{4} + c d e^{5}\right)} x^{2}\right)}}, -\frac{16 \, {\left(b c^{3} d^{3} + b c d^{2} e + {\left(b c^{3} d e^{2} + b c e^{3}\right)} x^{4} + 2 \, {\left(b c^{3} d^{2} e + b c d e^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + 3 \, {\left(b c^{2} d^{3} + {\left(b c^{2} d e^{2} + b e^{3}\right)} x^{4} + b d^{2} e + 2 \, {\left(b c^{2} d^{2} e + b d e^{2}\right)} x^{2}\right)} \sqrt{-e} \log\left(8 \, c^{4} e^{2} x^{4} + c^{4} d^{2} - 6 \, c^{2} d e + 8 \, {\left(c^{4} d e - c^{2} e^{2}\right)} x^{2} - 4 \, {\left(2 \, c^{4} e x^{3} + {\left(c^{4} d - c^{2} e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{-e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + e^{2}\right) - 4 \, {\left(8 \, b c^{3} d^{3} + 8 \, b c d^{2} e + 3 \, {\left(b c^{3} d e^{2} + b c e^{3}\right)} x^{4} + 12 \, {\left(b c^{3} d^{2} e + b c d e^{2}\right)} x^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 4 \, {\left(8 \, a c^{3} d^{3} + 8 \, a c d^{2} e + 3 \, {\left(a c^{3} d e^{2} + a c e^{3}\right)} x^{4} + 12 \, {\left(a c^{3} d^{2} e + a c d e^{2}\right)} x^{2} - {\left(b c^{2} d e^{2} x^{3} + b c^{2} d^{2} e x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{12 \, {\left(c^{3} d^{3} e^{3} + c d^{2} e^{4} + {\left(c^{3} d e^{5} + c e^{6}\right)} x^{4} + 2 \, {\left(c^{3} d^{2} e^{4} + c d e^{5}\right)} x^{2}\right)}}, -\frac{8 \, {\left(b c^{3} d^{3} + b c d^{2} e + {\left(b c^{3} d e^{2} + b c e^{3}\right)} x^{4} + 2 \, {\left(b c^{3} d^{2} e + b c d e^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + 3 \, {\left(b c^{2} d^{3} + {\left(b c^{2} d e^{2} + b e^{3}\right)} x^{4} + b d^{2} e + 2 \, {\left(b c^{2} d^{2} e + b d e^{2}\right)} x^{2}\right)} \sqrt{e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{3} + {\left(c^{2} d - e\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{e} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)}}\right) - 2 \, {\left(8 \, b c^{3} d^{3} + 8 \, b c d^{2} e + 3 \, {\left(b c^{3} d e^{2} + b c e^{3}\right)} x^{4} + 12 \, {\left(b c^{3} d^{2} e + b c d e^{2}\right)} x^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 2 \, {\left(8 \, a c^{3} d^{3} + 8 \, a c d^{2} e + 3 \, {\left(a c^{3} d e^{2} + a c e^{3}\right)} x^{4} + 12 \, {\left(a c^{3} d^{2} e + a c d e^{2}\right)} x^{2} - {\left(b c^{2} d e^{2} x^{3} + b c^{2} d^{2} e x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{6 \, {\left(c^{3} d^{3} e^{3} + c d^{2} e^{4} + {\left(c^{3} d e^{5} + c e^{6}\right)} x^{4} + 2 \, {\left(c^{3} d^{2} e^{4} + c d e^{5}\right)} x^{2}\right)}}\right]"," ",0,"[-1/12*(3*(b*c^2*d^3 + (b*c^2*d*e^2 + b*e^3)*x^4 + b*d^2*e + 2*(b*c^2*d^2*e + b*d*e^2)*x^2)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) - 4*(8*b*c^3*d^3 + 8*b*c*d^2*e + 3*(b*c^3*d*e^2 + b*c*e^3)*x^4 + 12*(b*c^3*d^2*e + b*c*d*e^2)*x^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 8*(b*c^3*d^3 + b*c*d^2*e + (b*c^3*d*e^2 + b*c*e^3)*x^4 + 2*(b*c^3*d^2*e + b*c*d*e^2)*x^2)*sqrt(d)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 + 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) - 4*(8*a*c^3*d^3 + 8*a*c*d^2*e + 3*(a*c^3*d*e^2 + a*c*e^3)*x^4 + 12*(a*c^3*d^2*e + a*c*d*e^2)*x^2 - (b*c^2*d*e^2*x^3 + b*c^2*d^2*e*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^3*d^3*e^3 + c*d^2*e^4 + (c^3*d*e^5 + c*e^6)*x^4 + 2*(c^3*d^2*e^4 + c*d*e^5)*x^2), -1/6*(3*(b*c^2*d^3 + (b*c^2*d*e^2 + b*e^3)*x^4 + b*d^2*e + 2*(b*c^2*d^2*e + b*d*e^2)*x^2)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) - 2*(8*b*c^3*d^3 + 8*b*c*d^2*e + 3*(b*c^3*d*e^2 + b*c*e^3)*x^4 + 12*(b*c^3*d^2*e + b*c*d*e^2)*x^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 4*(b*c^3*d^3 + b*c*d^2*e + (b*c^3*d*e^2 + b*c*e^3)*x^4 + 2*(b*c^3*d^2*e + b*c*d*e^2)*x^2)*sqrt(d)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 + 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) - 2*(8*a*c^3*d^3 + 8*a*c*d^2*e + 3*(a*c^3*d*e^2 + a*c*e^3)*x^4 + 12*(a*c^3*d^2*e + a*c*d*e^2)*x^2 - (b*c^2*d*e^2*x^3 + b*c^2*d^2*e*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^3*d^3*e^3 + c*d^2*e^4 + (c^3*d*e^5 + c*e^6)*x^4 + 2*(c^3*d^2*e^4 + c*d*e^5)*x^2), -1/12*(16*(b*c^3*d^3 + b*c*d^2*e + (b*c^3*d*e^2 + b*c*e^3)*x^4 + 2*(b*c^3*d^2*e + b*c*d*e^2)*x^2)*sqrt(-d)*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + 3*(b*c^2*d^3 + (b*c^2*d*e^2 + b*e^3)*x^4 + b*d^2*e + 2*(b*c^2*d^2*e + b*d*e^2)*x^2)*sqrt(-e)*log(8*c^4*e^2*x^4 + c^4*d^2 - 6*c^2*d*e + 8*(c^4*d*e - c^2*e^2)*x^2 - 4*(2*c^4*e*x^3 + (c^4*d - c^2*e)*x)*sqrt(e*x^2 + d)*sqrt(-e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + e^2) - 4*(8*b*c^3*d^3 + 8*b*c*d^2*e + 3*(b*c^3*d*e^2 + b*c*e^3)*x^4 + 12*(b*c^3*d^2*e + b*c*d*e^2)*x^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 4*(8*a*c^3*d^3 + 8*a*c*d^2*e + 3*(a*c^3*d*e^2 + a*c*e^3)*x^4 + 12*(a*c^3*d^2*e + a*c*d*e^2)*x^2 - (b*c^2*d*e^2*x^3 + b*c^2*d^2*e*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^3*d^3*e^3 + c*d^2*e^4 + (c^3*d*e^5 + c*e^6)*x^4 + 2*(c^3*d^2*e^4 + c*d*e^5)*x^2), -1/6*(8*(b*c^3*d^3 + b*c*d^2*e + (b*c^3*d*e^2 + b*c*e^3)*x^4 + 2*(b*c^3*d^2*e + b*c*d*e^2)*x^2)*sqrt(-d)*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + 3*(b*c^2*d^3 + (b*c^2*d*e^2 + b*e^3)*x^4 + b*d^2*e + 2*(b*c^2*d^2*e + b*d*e^2)*x^2)*sqrt(e)*arctan(1/2*(2*c^2*e*x^3 + (c^2*d - e)*x)*sqrt(e*x^2 + d)*sqrt(e)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)) - 2*(8*b*c^3*d^3 + 8*b*c*d^2*e + 3*(b*c^3*d*e^2 + b*c*e^3)*x^4 + 12*(b*c^3*d^2*e + b*c*d*e^2)*x^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 2*(8*a*c^3*d^3 + 8*a*c*d^2*e + 3*(a*c^3*d*e^2 + a*c*e^3)*x^4 + 12*(a*c^3*d^2*e + a*c*d*e^2)*x^2 - (b*c^2*d*e^2*x^3 + b*c^2*d^2*e*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^3*d^3*e^3 + c*d^2*e^4 + (c^3*d*e^5 + c*e^6)*x^4 + 2*(c^3*d^2*e^4 + c*d*e^5)*x^2)]","B",0
169,1,786,0,0.778974," ","integrate(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(2 \, b c^{2} d^{3} + 2 \, b d^{2} e + 3 \, {\left(b c^{2} d^{2} e + b d e^{2}\right)} x^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(b c^{2} d^{3} + {\left(b c^{2} d e^{2} + b e^{3}\right)} x^{4} + b d^{2} e + 2 \, {\left(b c^{2} d^{2} e + b d e^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} - 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) + 2 \, {\left(2 \, a c^{2} d^{3} + 2 \, a d^{2} e + 3 \, {\left(a c^{2} d^{2} e + a d e^{2}\right)} x^{2} - {\left(b c d e^{2} x^{3} + b c d^{2} e x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{6 \, {\left(c^{2} d^{4} e^{2} + d^{3} e^{3} + {\left(c^{2} d^{2} e^{4} + d e^{5}\right)} x^{4} + 2 \, {\left(c^{2} d^{3} e^{3} + d^{2} e^{4}\right)} x^{2}\right)}}, \frac{{\left(b c^{2} d^{3} + {\left(b c^{2} d e^{2} + b e^{3}\right)} x^{4} + b d^{2} e + 2 \, {\left(b c^{2} d^{2} e + b d e^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) - {\left(2 \, b c^{2} d^{3} + 2 \, b d^{2} e + 3 \, {\left(b c^{2} d^{2} e + b d e^{2}\right)} x^{2}\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(2 \, a c^{2} d^{3} + 2 \, a d^{2} e + 3 \, {\left(a c^{2} d^{2} e + a d e^{2}\right)} x^{2} - {\left(b c d e^{2} x^{3} + b c d^{2} e x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{3 \, {\left(c^{2} d^{4} e^{2} + d^{3} e^{3} + {\left(c^{2} d^{2} e^{4} + d e^{5}\right)} x^{4} + 2 \, {\left(c^{2} d^{3} e^{3} + d^{2} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[-1/6*(2*(2*b*c^2*d^3 + 2*b*d^2*e + 3*(b*c^2*d^2*e + b*d*e^2)*x^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (b*c^2*d^3 + (b*c^2*d*e^2 + b*e^3)*x^4 + b*d^2*e + 2*(b*c^2*d^2*e + b*d*e^2)*x^2)*sqrt(d)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 - 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) + 2*(2*a*c^2*d^3 + 2*a*d^2*e + 3*(a*c^2*d^2*e + a*d*e^2)*x^2 - (b*c*d*e^2*x^3 + b*c*d^2*e*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^2*d^4*e^2 + d^3*e^3 + (c^2*d^2*e^4 + d*e^5)*x^4 + 2*(c^2*d^3*e^3 + d^2*e^4)*x^2), 1/3*((b*c^2*d^3 + (b*c^2*d*e^2 + b*e^3)*x^4 + b*d^2*e + 2*(b*c^2*d^2*e + b*d*e^2)*x^2)*sqrt(-d)*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) - (2*b*c^2*d^3 + 2*b*d^2*e + 3*(b*c^2*d^2*e + b*d*e^2)*x^2)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (2*a*c^2*d^3 + 2*a*d^2*e + 3*(a*c^2*d^2*e + a*d*e^2)*x^2 - (b*c*d*e^2*x^3 + b*c*d^2*e*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^2*d^4*e^2 + d^3*e^3 + (c^2*d^2*e^4 + d*e^5)*x^4 + 2*(c^2*d^3*e^3 + d^2*e^4)*x^2)]","B",0
170,1,692,0,1.407201," ","integrate(x*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(b c^{2} d^{3} + b d^{2} e\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(b c^{2} d^{3} + {\left(b c^{2} d e^{2} + b e^{3}\right)} x^{4} + b d^{2} e + 2 \, {\left(b c^{2} d^{2} e + b d e^{2}\right)} x^{2}\right)} \sqrt{d} \log\left(\frac{{\left(c^{4} d^{2} - 6 \, c^{2} d e + e^{2}\right)} x^{4} - 8 \, {\left(c^{2} d^{2} - d e\right)} x^{2} - 4 \, {\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 8 \, d^{2}}{x^{4}}\right) + 4 \, {\left(a c^{2} d^{3} + a d^{2} e + {\left(b c d e^{2} x^{3} + b c d^{2} e x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{12 \, {\left(c^{2} d^{5} e + d^{4} e^{2} + {\left(c^{2} d^{3} e^{3} + d^{2} e^{4}\right)} x^{4} + 2 \, {\left(c^{2} d^{4} e^{2} + d^{3} e^{3}\right)} x^{2}\right)}}, \frac{{\left(b c^{2} d^{3} + {\left(b c^{2} d e^{2} + b e^{3}\right)} x^{4} + b d^{2} e + 2 \, {\left(b c^{2} d^{2} e + b d e^{2}\right)} x^{2}\right)} \sqrt{-d} \arctan\left(-\frac{{\left({\left(c^{3} d - c e\right)} x^{3} - 2 \, c d x\right)} \sqrt{e x^{2} + d} \sqrt{-d} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) - 2 \, {\left(b c^{2} d^{3} + b d^{2} e\right)} \sqrt{e x^{2} + d} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - 2 \, {\left(a c^{2} d^{3} + a d^{2} e + {\left(b c d e^{2} x^{3} + b c d^{2} e x\right)} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}}\right)} \sqrt{e x^{2} + d}}{6 \, {\left(c^{2} d^{5} e + d^{4} e^{2} + {\left(c^{2} d^{3} e^{3} + d^{2} e^{4}\right)} x^{4} + 2 \, {\left(c^{2} d^{4} e^{2} + d^{3} e^{3}\right)} x^{2}\right)}}\right]"," ",0,"[-1/12*(4*(b*c^2*d^3 + b*d^2*e)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (b*c^2*d^3 + (b*c^2*d*e^2 + b*e^3)*x^4 + b*d^2*e + 2*(b*c^2*d^2*e + b*d*e^2)*x^2)*sqrt(d)*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 - 4*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 8*d^2)/x^4) + 4*(a*c^2*d^3 + a*d^2*e + (b*c*d*e^2*x^3 + b*c*d^2*e*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^2*d^5*e + d^4*e^2 + (c^2*d^3*e^3 + d^2*e^4)*x^4 + 2*(c^2*d^4*e^2 + d^3*e^3)*x^2), 1/6*((b*c^2*d^3 + (b*c^2*d*e^2 + b*e^3)*x^4 + b*d^2*e + 2*(b*c^2*d^2*e + b*d*e^2)*x^2)*sqrt(-d)*arctan(-1/2*((c^3*d - c*e)*x^3 - 2*c*d*x)*sqrt(e*x^2 + d)*sqrt(-d)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2))/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) - 2*(b*c^2*d^3 + b*d^2*e)*sqrt(e*x^2 + d)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - 2*(a*c^2*d^3 + a*d^2*e + (b*c*d*e^2*x^3 + b*c*d^2*e*x)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)))*sqrt(e*x^2 + d))/(c^2*d^5*e + d^4*e^2 + (c^2*d^3*e^3 + d^2*e^4)*x^4 + 2*(c^2*d^4*e^2 + d^3*e^3)*x^2)]","B",0
171,0,0,0,0.553130," ","integrate((a+b*arcsech(c*x))/x/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{e^{3} x^{7} + 3 \, d e^{2} x^{5} + 3 \, d^{2} e x^{3} + d^{3} x}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)/(e^3*x^7 + 3*d*e^2*x^5 + 3*d^2*e*x^3 + d^3*x), x)","F",0
172,0,0,0,0.617073," ","integrate((a+b*arcsech(c*x))/x^3/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{e^{3} x^{9} + 3 \, d e^{2} x^{7} + 3 \, d^{2} e x^{5} + d^{3} x^{3}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)/(e^3*x^9 + 3*d*e^2*x^7 + 3*d^2*e*x^5 + d^3*x^3), x)","F",0
173,0,0,0,1.648940," ","integrate(x^6*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{6} \operatorname{arsech}\left(c x\right) + a x^{6}\right)} \sqrt{e x^{2} + d}}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral((b*x^6*arcsech(c*x) + a*x^6)*sqrt(e*x^2 + d)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
174,0,0,0,0.620179," ","integrate(x^4*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} \operatorname{arsech}\left(c x\right) + a x^{4}\right)} \sqrt{e x^{2} + d}}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral((b*x^4*arcsech(c*x) + a*x^4)*sqrt(e*x^2 + d)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
175,0,0,0,0.716367," ","integrate(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} \operatorname{arsech}\left(c x\right) + a x^{2}\right)} \sqrt{e x^{2} + d}}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral((b*x^2*arcsech(c*x) + a*x^2)*sqrt(e*x^2 + d)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
176,0,0,0,0.731381," ","integrate((a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
177,0,0,0,1.510711," ","integrate((f*x)^m*(e*x^2+d)^3*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e^{3} x^{6} + 3 \, a d e^{2} x^{4} + 3 \, a d^{2} e x^{2} + a d^{3} + {\left(b e^{3} x^{6} + 3 \, b d e^{2} x^{4} + 3 \, b d^{2} e x^{2} + b d^{3}\right)} \operatorname{arsech}\left(c x\right)\right)} \left(f x\right)^{m}, x\right)"," ",0,"integral((a*e^3*x^6 + 3*a*d*e^2*x^4 + 3*a*d^2*e*x^2 + a*d^3 + (b*e^3*x^6 + 3*b*d*e^2*x^4 + 3*b*d^2*e*x^2 + b*d^3)*arcsech(c*x))*(f*x)^m, x)","F",0
178,0,0,0,0.710273," ","integrate((f*x)^m*(e*x^2+d)^2*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e^{2} x^{4} + 2 \, a d e x^{2} + a d^{2} + {\left(b e^{2} x^{4} + 2 \, b d e x^{2} + b d^{2}\right)} \operatorname{arsech}\left(c x\right)\right)} \left(f x\right)^{m}, x\right)"," ",0,"integral((a*e^2*x^4 + 2*a*d*e*x^2 + a*d^2 + (b*e^2*x^4 + 2*b*d*e*x^2 + b*d^2)*arcsech(c*x))*(f*x)^m, x)","F",0
179,0,0,0,0.489256," ","integrate((f*x)^m*(e*x^2+d)*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \operatorname{arsech}\left(c x\right)\right)} \left(f x\right)^{m}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsech(c*x))*(f*x)^m, x)","F",0
180,0,0,0,0.721836," ","integrate((f*x)^m*(a+b*arcsech(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \operatorname{arsech}\left(c x\right) + a\right)} \left(f x\right)^{m}}{e x^{2} + d}, x\right)"," ",0,"integral((b*arcsech(c*x) + a)*(f*x)^m/(e*x^2 + d), x)","F",0
181,0,0,0,1.046047," ","integrate((f*x)^m*(a+b*arcsech(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \operatorname{arsech}\left(c x\right) + a\right)} \left(f x\right)^{m}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*arcsech(c*x) + a)*(f*x)^m/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
182,0,0,0,0.610917," ","integrate((f*x)^m*(e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \operatorname{arsech}\left(c x\right)\right)} \sqrt{e x^{2} + d} \left(f x\right)^{m}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsech(c*x))*sqrt(e*x^2 + d)*(f*x)^m, x)","F",0
183,0,0,0,0.613679," ","integrate((f*x)^m*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)} \left(f x\right)^{m}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)*(f*x)^m, x)","F",0
184,0,0,0,1.649663," ","integrate((f*x)^m*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \operatorname{arsech}\left(c x\right) + a\right)} \left(f x\right)^{m}}{\sqrt{e x^{2} + d}}, x\right)"," ",0,"integral((b*arcsech(c*x) + a)*(f*x)^m/sqrt(e*x^2 + d), x)","F",0
185,0,0,0,0.663520," ","integrate((f*x)^m*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arsech}\left(c x\right) + a\right)} \left(f x\right)^{m}}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsech(c*x) + a)*(f*x)^m/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
186,1,393,0,0.671148," ","integrate(x^11*(a+b*arcsech(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{105 \, {\left(3 \, b c^{10} x^{10} - 3 \, b c^{8} x^{8} + 4 \, b c^{6} x^{6} - 4 \, b c^{4} x^{4} + 8 \, b c^{2} x^{2} - 8 \, b\right)} \sqrt{-c^{4} x^{4} + 1} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(35 \, b c^{9} x^{9} + 5 \, b c^{7} x^{7} + 78 \, b c^{5} x^{5} + 36 \, b c^{3} x^{3} + 768 \, b c x\right)} \sqrt{-c^{4} x^{4} + 1} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 420 \, {\left(b c^{2} x^{2} - b\right)} \log\left(\frac{c^{2} x^{2} + \sqrt{-c^{4} x^{4} + 1} c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c^{2} x^{2} - 1}\right) - 420 \, {\left(b c^{2} x^{2} - b\right)} \log\left(-\frac{c^{2} x^{2} - \sqrt{-c^{4} x^{4} + 1} c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c^{2} x^{2} - 1}\right) + 105 \, {\left(3 \, a c^{10} x^{10} - 3 \, a c^{8} x^{8} + 4 \, a c^{6} x^{6} - 4 \, a c^{4} x^{4} + 8 \, a c^{2} x^{2} - 8 \, a\right)} \sqrt{-c^{4} x^{4} + 1}}{3150 \, {\left(c^{14} x^{2} - c^{12}\right)}}"," ",0,"-1/3150*(105*(3*b*c^10*x^10 - 3*b*c^8*x^8 + 4*b*c^6*x^6 - 4*b*c^4*x^4 + 8*b*c^2*x^2 - 8*b)*sqrt(-c^4*x^4 + 1)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (35*b*c^9*x^9 + 5*b*c^7*x^7 + 78*b*c^5*x^5 + 36*b*c^3*x^3 + 768*b*c*x)*sqrt(-c^4*x^4 + 1)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 420*(b*c^2*x^2 - b)*log((c^2*x^2 + sqrt(-c^4*x^4 + 1)*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c^2*x^2 - 1)) - 420*(b*c^2*x^2 - b)*log(-(c^2*x^2 - sqrt(-c^4*x^4 + 1)*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c^2*x^2 - 1)) + 105*(3*a*c^10*x^10 - 3*a*c^8*x^8 + 4*a*c^6*x^6 - 4*a*c^4*x^4 + 8*a*c^2*x^2 - 8*a)*sqrt(-c^4*x^4 + 1))/(c^14*x^2 - c^12)","A",0
187,1,336,0,0.578670," ","integrate(x^7*(a+b*arcsech(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""fricas"")","-\frac{15 \, {\left(b c^{6} x^{6} - b c^{4} x^{4} + 2 \, b c^{2} x^{2} - 2 \, b\right)} \sqrt{-c^{4} x^{4} + 1} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(3 \, b c^{5} x^{5} + b c^{3} x^{3} + 28 \, b c x\right)} \sqrt{-c^{4} x^{4} + 1} \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 15 \, {\left(b c^{2} x^{2} - b\right)} \log\left(\frac{c^{2} x^{2} + \sqrt{-c^{4} x^{4} + 1} c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c^{2} x^{2} - 1}\right) - 15 \, {\left(b c^{2} x^{2} - b\right)} \log\left(-\frac{c^{2} x^{2} - \sqrt{-c^{4} x^{4} + 1} c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c^{2} x^{2} - 1}\right) + 15 \, {\left(a c^{6} x^{6} - a c^{4} x^{4} + 2 \, a c^{2} x^{2} - 2 \, a\right)} \sqrt{-c^{4} x^{4} + 1}}{90 \, {\left(c^{10} x^{2} - c^{8}\right)}}"," ",0,"-1/90*(15*(b*c^6*x^6 - b*c^4*x^4 + 2*b*c^2*x^2 - 2*b)*sqrt(-c^4*x^4 + 1)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (3*b*c^5*x^5 + b*c^3*x^3 + 28*b*c*x)*sqrt(-c^4*x^4 + 1)*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 15*(b*c^2*x^2 - b)*log((c^2*x^2 + sqrt(-c^4*x^4 + 1)*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c^2*x^2 - 1)) - 15*(b*c^2*x^2 - b)*log(-(c^2*x^2 - sqrt(-c^4*x^4 + 1)*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c^2*x^2 - 1)) + 15*(a*c^6*x^6 - a*c^4*x^4 + 2*a*c^2*x^2 - 2*a)*sqrt(-c^4*x^4 + 1))/(c^10*x^2 - c^8)","A",0
188,1,279,0,0.670182," ","integrate(x^3*(a+b*arcsech(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{-c^{4} x^{4} + 1} b c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 2 \, \sqrt{-c^{4} x^{4} + 1} {\left(b c^{2} x^{2} - b\right)} \log\left(\frac{c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} + 1}{c x}\right) - {\left(b c^{2} x^{2} - b\right)} \log\left(\frac{c^{2} x^{2} + \sqrt{-c^{4} x^{4} + 1} c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c^{2} x^{2} - 1}\right) + {\left(b c^{2} x^{2} - b\right)} \log\left(-\frac{c^{2} x^{2} - \sqrt{-c^{4} x^{4} + 1} c x \sqrt{-\frac{c^{2} x^{2} - 1}{c^{2} x^{2}}} - 1}{c^{2} x^{2} - 1}\right) - 2 \, \sqrt{-c^{4} x^{4} + 1} {\left(a c^{2} x^{2} - a\right)}}{4 \, {\left(c^{6} x^{2} - c^{4}\right)}}"," ",0,"1/4*(2*sqrt(-c^4*x^4 + 1)*b*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 2*sqrt(-c^4*x^4 + 1)*(b*c^2*x^2 - b)*log((c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) + 1)/(c*x)) - (b*c^2*x^2 - b)*log((c^2*x^2 + sqrt(-c^4*x^4 + 1)*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c^2*x^2 - 1)) + (b*c^2*x^2 - b)*log(-(c^2*x^2 - sqrt(-c^4*x^4 + 1)*c*x*sqrt(-(c^2*x^2 - 1)/(c^2*x^2)) - 1)/(c^2*x^2 - 1)) - 2*sqrt(-c^4*x^4 + 1)*(a*c^2*x^2 - a))/(c^6*x^2 - c^4)","B",0
189,0,0,0,1.083250," ","integrate((a+b*arcsech(c*x))/x/(-c^4*x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{4} x^{4} + 1} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{c^{4} x^{5} - x}, x\right)"," ",0,"integral(-sqrt(-c^4*x^4 + 1)*(b*arcsech(c*x) + a)/(c^4*x^5 - x), x)","F",0
190,0,0,0,1.244333," ","integrate((a+b*arcsech(c*x))/x^5/(-c^4*x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{4} x^{4} + 1} {\left(b \operatorname{arsech}\left(c x\right) + a\right)}}{c^{4} x^{9} - x^{5}}, x\right)"," ",0,"integral(-sqrt(-c^4*x^4 + 1)*(b*arcsech(c*x) + a)/(c^4*x^9 - x^5), x)","F",0
