1,1,116,0,0.942853," ","integrate(x^6*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\frac{48 \, a c^{7} x^{7} + 96 \, b c^{7} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + 48 \, {\left(b c^{7} x^{7} - b c^{7}\right)} \operatorname{arcsec}\left(c x\right) + 15 \, b \log\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) - {\left(8 \, b c^{5} x^{5} + 10 \, b c^{3} x^{3} + 15 \, b c x\right)} \sqrt{c^{2} x^{2} - 1}}{336 \, c^{7}}"," ",0,"1/336*(48*a*c^7*x^7 + 96*b*c^7*arctan(-c*x + sqrt(c^2*x^2 - 1)) + 48*(b*c^7*x^7 - b*c^7)*arcsec(c*x) + 15*b*log(-c*x + sqrt(c^2*x^2 - 1)) - (8*b*c^5*x^5 + 10*b*c^3*x^3 + 15*b*c*x)*sqrt(c^2*x^2 - 1))/c^7","A",0
2,1,63,0,0.713449," ","integrate(x^5*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\frac{15 \, b c^{6} x^{6} \operatorname{arcsec}\left(c x\right) + 15 \, a c^{6} x^{6} - {\left(3 \, b c^{4} x^{4} + 4 \, b c^{2} x^{2} + 8 \, b\right)} \sqrt{c^{2} x^{2} - 1}}{90 \, c^{6}}"," ",0,"1/90*(15*b*c^6*x^6*arcsec(c*x) + 15*a*c^6*x^6 - (3*b*c^4*x^4 + 4*b*c^2*x^2 + 8*b)*sqrt(c^2*x^2 - 1))/c^6","A",0
3,1,107,0,0.686304," ","integrate(x^4*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\frac{8 \, a c^{5} x^{5} + 16 \, b c^{5} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + 8 \, {\left(b c^{5} x^{5} - b c^{5}\right)} \operatorname{arcsec}\left(c x\right) + 3 \, b \log\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) - {\left(2 \, b c^{3} x^{3} + 3 \, b c x\right)} \sqrt{c^{2} x^{2} - 1}}{40 \, c^{5}}"," ",0,"1/40*(8*a*c^5*x^5 + 16*b*c^5*arctan(-c*x + sqrt(c^2*x^2 - 1)) + 8*(b*c^5*x^5 - b*c^5)*arcsec(c*x) + 3*b*log(-c*x + sqrt(c^2*x^2 - 1)) - (2*b*c^3*x^3 + 3*b*c*x)*sqrt(c^2*x^2 - 1))/c^5","A",0
4,1,53,0,0.698069," ","integrate(x^3*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\frac{3 \, b c^{4} x^{4} \operatorname{arcsec}\left(c x\right) + 3 \, a c^{4} x^{4} - {\left(b c^{2} x^{2} + 2 \, b\right)} \sqrt{c^{2} x^{2} - 1}}{12 \, c^{4}}"," ",0,"1/12*(3*b*c^4*x^4*arcsec(c*x) + 3*a*c^4*x^4 - (b*c^2*x^2 + 2*b)*sqrt(c^2*x^2 - 1))/c^4","A",0
5,1,94,0,0.759522," ","integrate(x^2*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\frac{2 \, a c^{3} x^{3} + 4 \, b c^{3} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) - \sqrt{c^{2} x^{2} - 1} b c x + 2 \, {\left(b c^{3} x^{3} - b c^{3}\right)} \operatorname{arcsec}\left(c x\right) + b \log\left(-c x + \sqrt{c^{2} x^{2} - 1}\right)}{6 \, c^{3}}"," ",0,"1/6*(2*a*c^3*x^3 + 4*b*c^3*arctan(-c*x + sqrt(c^2*x^2 - 1)) - sqrt(c^2*x^2 - 1)*b*c*x + 2*(b*c^3*x^3 - b*c^3)*arcsec(c*x) + b*log(-c*x + sqrt(c^2*x^2 - 1)))/c^3","A",0
6,1,40,0,0.545113," ","integrate(x*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\frac{b c^{2} x^{2} \operatorname{arcsec}\left(c x\right) + a c^{2} x^{2} - \sqrt{c^{2} x^{2} - 1} b}{2 \, c^{2}}"," ",0,"1/2*(b*c^2*x^2*arcsec(c*x) + a*c^2*x^2 - sqrt(c^2*x^2 - 1)*b)/c^2","A",0
7,1,63,0,0.989903," ","integrate(a+b*arcsec(c*x),x, algorithm=""fricas"")","\frac{a c x + 2 \, b c \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + {\left(b c x - b c\right)} \operatorname{arcsec}\left(c x\right) + b \log\left(-c x + \sqrt{c^{2} x^{2} - 1}\right)}{c}"," ",0,"(a*c*x + 2*b*c*arctan(-c*x + sqrt(c^2*x^2 - 1)) + (b*c*x - b*c)*arcsec(c*x) + b*log(-c*x + sqrt(c^2*x^2 - 1)))/c","B",0
8,0,0,0,0.576334," ","integrate((a+b*arcsec(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arcsec}\left(c x\right) + a}{x}, x\right)"," ",0,"integral((b*arcsec(c*x) + a)/x, x)","F",0
9,1,27,0,1.226083," ","integrate((a+b*arcsec(c*x))/x^2,x, algorithm=""fricas"")","-\frac{b \operatorname{arcsec}\left(c x\right) - \sqrt{c^{2} x^{2} - 1} b + a}{x}"," ",0,"-(b*arcsec(c*x) - sqrt(c^2*x^2 - 1)*b + a)/x","A",0
10,1,39,0,0.581279," ","integrate((a+b*arcsec(c*x))/x^3,x, algorithm=""fricas"")","\frac{{\left(b c^{2} x^{2} - 2 \, b\right)} \operatorname{arcsec}\left(c x\right) + \sqrt{c^{2} x^{2} - 1} b - 2 \, a}{4 \, x^{2}}"," ",0,"1/4*((b*c^2*x^2 - 2*b)*arcsec(c*x) + sqrt(c^2*x^2 - 1)*b - 2*a)/x^2","A",0
11,1,40,0,0.679540," ","integrate((a+b*arcsec(c*x))/x^4,x, algorithm=""fricas"")","-\frac{3 \, b \operatorname{arcsec}\left(c x\right) - {\left(2 \, b c^{2} x^{2} + b\right)} \sqrt{c^{2} x^{2} - 1} + 3 \, a}{9 \, x^{3}}"," ",0,"-1/9*(3*b*arcsec(c*x) - (2*b*c^2*x^2 + b)*sqrt(c^2*x^2 - 1) + 3*a)/x^3","A",0
12,1,52,0,0.708756," ","integrate((a+b*arcsec(c*x))/x^5,x, algorithm=""fricas"")","\frac{{\left(3 \, b c^{4} x^{4} - 8 \, b\right)} \operatorname{arcsec}\left(c x\right) + {\left(3 \, b c^{2} x^{2} + 2 \, b\right)} \sqrt{c^{2} x^{2} - 1} - 8 \, a}{32 \, x^{4}}"," ",0,"1/32*((3*b*c^4*x^4 - 8*b)*arcsec(c*x) + (3*b*c^2*x^2 + 2*b)*sqrt(c^2*x^2 - 1) - 8*a)/x^4","A",0
13,1,51,0,0.796358," ","integrate((a+b*arcsec(c*x))/x^6,x, algorithm=""fricas"")","-\frac{15 \, b \operatorname{arcsec}\left(c x\right) - {\left(8 \, b c^{4} x^{4} + 4 \, b c^{2} x^{2} + 3 \, b\right)} \sqrt{c^{2} x^{2} - 1} + 15 \, a}{75 \, x^{5}}"," ",0,"-1/75*(15*b*arcsec(c*x) - (8*b*c^4*x^4 + 4*b*c^2*x^2 + 3*b)*sqrt(c^2*x^2 - 1) + 15*a)/x^5","A",0
14,1,62,0,0.762611," ","integrate((a+b*arcsec(c*x))/x^7,x, algorithm=""fricas"")","\frac{3 \, {\left(5 \, b c^{6} x^{6} - 16 \, b\right)} \operatorname{arcsec}\left(c x\right) + {\left(15 \, b c^{4} x^{4} + 10 \, b c^{2} x^{2} + 8 \, b\right)} \sqrt{c^{2} x^{2} - 1} - 48 \, a}{288 \, x^{6}}"," ",0,"1/288*(3*(5*b*c^6*x^6 - 16*b)*arcsec(c*x) + (15*b*c^4*x^4 + 10*b*c^2*x^2 + 8*b)*sqrt(c^2*x^2 - 1) - 48*a)/x^6","A",0
15,1,146,0,0.915249," ","integrate(x^3*(a+b*arcsec(c*x))^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} c^{4} x^{4} \operatorname{arcsec}\left(c x\right)^{2} + 3 \, a^{2} c^{4} x^{4} + 12 \, a b c^{4} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + b^{2} c^{2} x^{2} + 4 \, b^{2} \log\left(x\right) + 6 \, {\left(a b c^{4} x^{4} - a b c^{4}\right)} \operatorname{arcsec}\left(c x\right) - 2 \, {\left(a b c^{2} x^{2} + 2 \, a b + {\left(b^{2} c^{2} x^{2} + 2 \, b^{2}\right)} \operatorname{arcsec}\left(c x\right)\right)} \sqrt{c^{2} x^{2} - 1}}{12 \, c^{4}}"," ",0,"1/12*(3*b^2*c^4*x^4*arcsec(c*x)^2 + 3*a^2*c^4*x^4 + 12*a*b*c^4*arctan(-c*x + sqrt(c^2*x^2 - 1)) + b^2*c^2*x^2 + 4*b^2*log(x) + 6*(a*b*c^4*x^4 - a*b*c^4)*arcsec(c*x) - 2*(a*b*c^2*x^2 + 2*a*b + (b^2*c^2*x^2 + 2*b^2)*arcsec(c*x))*sqrt(c^2*x^2 - 1))/c^4","A",0
16,0,0,0,0.490530," ","integrate(x^2*(a+b*arcsec(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \operatorname{arcsec}\left(c x\right)^{2} + 2 \, a b x^{2} \operatorname{arcsec}\left(c x\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*arcsec(c*x)^2 + 2*a*b*x^2*arcsec(c*x) + a^2*x^2, x)","F",0
17,1,111,0,0.763721," ","integrate(x*(a+b*arcsec(c*x))^2,x, algorithm=""fricas"")","\frac{b^{2} c^{2} x^{2} \operatorname{arcsec}\left(c x\right)^{2} + a^{2} c^{2} x^{2} + 4 \, a b c^{2} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + 2 \, b^{2} \log\left(x\right) + 2 \, {\left(a b c^{2} x^{2} - a b c^{2}\right)} \operatorname{arcsec}\left(c x\right) - 2 \, \sqrt{c^{2} x^{2} - 1} {\left(b^{2} \operatorname{arcsec}\left(c x\right) + a b\right)}}{2 \, c^{2}}"," ",0,"1/2*(b^2*c^2*x^2*arcsec(c*x)^2 + a^2*c^2*x^2 + 4*a*b*c^2*arctan(-c*x + sqrt(c^2*x^2 - 1)) + 2*b^2*log(x) + 2*(a*b*c^2*x^2 - a*b*c^2)*arcsec(c*x) - 2*sqrt(c^2*x^2 - 1)*(b^2*arcsec(c*x) + a*b))/c^2","B",0
18,0,0,0,1.022373," ","integrate((a+b*arcsec(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \operatorname{arcsec}\left(c x\right)^{2} + 2 \, a b \operatorname{arcsec}\left(c x\right) + a^{2}, x\right)"," ",0,"integral(b^2*arcsec(c*x)^2 + 2*a*b*arcsec(c*x) + a^2, x)","F",0
19,0,0,0,0.413324," ","integrate((a+b*arcsec(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{arcsec}\left(c x\right)^{2} + 2 \, a b \operatorname{arcsec}\left(c x\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*arcsec(c*x)^2 + 2*a*b*arcsec(c*x) + a^2)/x, x)","F",0
20,1,57,0,0.481220," ","integrate((a+b*arcsec(c*x))^2/x^2,x, algorithm=""fricas"")","-\frac{b^{2} \operatorname{arcsec}\left(c x\right)^{2} + 2 \, a b \operatorname{arcsec}\left(c x\right) + a^{2} - 2 \, b^{2} - 2 \, \sqrt{c^{2} x^{2} - 1} {\left(b^{2} \operatorname{arcsec}\left(c x\right) + a b\right)}}{x}"," ",0,"-(b^2*arcsec(c*x)^2 + 2*a*b*arcsec(c*x) + a^2 - 2*b^2 - 2*sqrt(c^2*x^2 - 1)*(b^2*arcsec(c*x) + a*b))/x","A",0
21,1,82,0,0.589158," ","integrate((a+b*arcsec(c*x))^2/x^3,x, algorithm=""fricas"")","\frac{{\left(b^{2} c^{2} x^{2} - 2 \, b^{2}\right)} \operatorname{arcsec}\left(c x\right)^{2} - 2 \, a^{2} + b^{2} + 2 \, {\left(a b c^{2} x^{2} - 2 \, a b\right)} \operatorname{arcsec}\left(c x\right) + 2 \, \sqrt{c^{2} x^{2} - 1} {\left(b^{2} \operatorname{arcsec}\left(c x\right) + a b\right)}}{4 \, x^{2}}"," ",0,"1/4*((b^2*c^2*x^2 - 2*b^2)*arcsec(c*x)^2 - 2*a^2 + b^2 + 2*(a*b*c^2*x^2 - 2*a*b)*arcsec(c*x) + 2*sqrt(c^2*x^2 - 1)*(b^2*arcsec(c*x) + a*b))/x^2","A",0
22,1,93,0,0.617641," ","integrate((a+b*arcsec(c*x))^2/x^4,x, algorithm=""fricas"")","\frac{12 \, b^{2} c^{2} x^{2} - 9 \, b^{2} \operatorname{arcsec}\left(c x\right)^{2} - 18 \, a b \operatorname{arcsec}\left(c x\right) - 9 \, a^{2} + 2 \, b^{2} + 6 \, {\left(2 \, a b c^{2} x^{2} + a b + {\left(2 \, b^{2} c^{2} x^{2} + b^{2}\right)} \operatorname{arcsec}\left(c x\right)\right)} \sqrt{c^{2} x^{2} - 1}}{27 \, x^{3}}"," ",0,"1/27*(12*b^2*c^2*x^2 - 9*b^2*arcsec(c*x)^2 - 18*a*b*arcsec(c*x) - 9*a^2 + 2*b^2 + 6*(2*a*b*c^2*x^2 + a*b + (2*b^2*c^2*x^2 + b^2)*arcsec(c*x))*sqrt(c^2*x^2 - 1))/x^3","A",0
23,1,120,0,0.707869," ","integrate((a+b*arcsec(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)} \operatorname{arcsec}\left(c x\right)^{2} - 8 \, a^{2} + b^{2} + 2 \, {\left(3 \, a b c^{4} x^{4} - 8 \, a b\right)} \operatorname{arcsec}\left(c x\right) + 2 \, {\left(3 \, a b c^{2} x^{2} + 2 \, a b + {\left(3 \, b^{2} c^{2} x^{2} + 2 \, b^{2}\right)} \operatorname{arcsec}\left(c x\right)\right)} \sqrt{c^{2} x^{2} - 1}}{32 \, x^{4}}"," ",0,"1/32*(3*b^2*c^2*x^2 + (3*b^2*c^4*x^4 - 8*b^2)*arcsec(c*x)^2 - 8*a^2 + b^2 + 2*(3*a*b*c^4*x^4 - 8*a*b)*arcsec(c*x) + 2*(3*a*b*c^2*x^2 + 2*a*b + (3*b^2*c^2*x^2 + 2*b^2)*arcsec(c*x))*sqrt(c^2*x^2 - 1))/x^4","A",0
24,0,0,0,0.662467," ","integrate(x^3*(a+b*arcsec(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{3} \operatorname{arcsec}\left(c x\right)^{3} + 3 \, a b^{2} x^{3} \operatorname{arcsec}\left(c x\right)^{2} + 3 \, a^{2} b x^{3} \operatorname{arcsec}\left(c x\right) + a^{3} x^{3}, x\right)"," ",0,"integral(b^3*x^3*arcsec(c*x)^3 + 3*a*b^2*x^3*arcsec(c*x)^2 + 3*a^2*b*x^3*arcsec(c*x) + a^3*x^3, x)","F",0
25,0,0,0,0.682062," ","integrate(x^2*(a+b*arcsec(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{2} \operatorname{arcsec}\left(c x\right)^{3} + 3 \, a b^{2} x^{2} \operatorname{arcsec}\left(c x\right)^{2} + 3 \, a^{2} b x^{2} \operatorname{arcsec}\left(c x\right) + a^{3} x^{2}, x\right)"," ",0,"integral(b^3*x^2*arcsec(c*x)^3 + 3*a*b^2*x^2*arcsec(c*x)^2 + 3*a^2*b*x^2*arcsec(c*x) + a^3*x^2, x)","F",0
26,0,0,0,0.657887," ","integrate(x*(a+b*arcsec(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x \operatorname{arcsec}\left(c x\right)^{3} + 3 \, a b^{2} x \operatorname{arcsec}\left(c x\right)^{2} + 3 \, a^{2} b x \operatorname{arcsec}\left(c x\right) + a^{3} x, x\right)"," ",0,"integral(b^3*x*arcsec(c*x)^3 + 3*a*b^2*x*arcsec(c*x)^2 + 3*a^2*b*x*arcsec(c*x) + a^3*x, x)","F",0
27,0,0,0,0.631320," ","integrate((a+b*arcsec(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} \operatorname{arcsec}\left(c x\right)^{3} + 3 \, a b^{2} \operatorname{arcsec}\left(c x\right)^{2} + 3 \, a^{2} b \operatorname{arcsec}\left(c x\right) + a^{3}, x\right)"," ",0,"integral(b^3*arcsec(c*x)^3 + 3*a*b^2*arcsec(c*x)^2 + 3*a^2*b*arcsec(c*x) + a^3, x)","F",0
28,0,0,0,0.472823," ","integrate((a+b*arcsec(c*x))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{arcsec}\left(c x\right)^{3} + 3 \, a b^{2} \operatorname{arcsec}\left(c x\right)^{2} + 3 \, a^{2} b \operatorname{arcsec}\left(c x\right) + a^{3}}{x}, x\right)"," ",0,"integral((b^3*arcsec(c*x)^3 + 3*a*b^2*arcsec(c*x)^2 + 3*a^2*b*arcsec(c*x) + a^3)/x, x)","F",0
29,1,98,0,0.687553," ","integrate((a+b*arcsec(c*x))^3/x^2,x, algorithm=""fricas"")","-\frac{b^{3} \operatorname{arcsec}\left(c x\right)^{3} + 3 \, a b^{2} \operatorname{arcsec}\left(c x\right)^{2} + a^{3} - 6 \, a b^{2} + 3 \, {\left(a^{2} b - 2 \, b^{3}\right)} \operatorname{arcsec}\left(c x\right) - 3 \, {\left(b^{3} \operatorname{arcsec}\left(c x\right)^{2} + 2 \, a b^{2} \operatorname{arcsec}\left(c x\right) + a^{2} b - 2 \, b^{3}\right)} \sqrt{c^{2} x^{2} - 1}}{x}"," ",0,"-(b^3*arcsec(c*x)^3 + 3*a*b^2*arcsec(c*x)^2 + a^3 - 6*a*b^2 + 3*(a^2*b - 2*b^3)*arcsec(c*x) - 3*(b^3*arcsec(c*x)^2 + 2*a*b^2*arcsec(c*x) + a^2*b - 2*b^3)*sqrt(c^2*x^2 - 1))/x","A",0
30,1,150,0,0.673728," ","integrate((a+b*arcsec(c*x))^3/x^3,x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} c^{2} x^{2} - 2 \, b^{3}\right)} \operatorname{arcsec}\left(c x\right)^{3} - 4 \, a^{3} + 6 \, a b^{2} + 6 \, {\left(a b^{2} c^{2} x^{2} - 2 \, a b^{2}\right)} \operatorname{arcsec}\left(c x\right)^{2} + 3 \, {\left({\left(2 \, a^{2} b - b^{3}\right)} c^{2} x^{2} - 4 \, a^{2} b + 2 \, b^{3}\right)} \operatorname{arcsec}\left(c x\right) + 3 \, {\left(2 \, b^{3} \operatorname{arcsec}\left(c x\right)^{2} + 4 \, a b^{2} \operatorname{arcsec}\left(c x\right) + 2 \, a^{2} b - b^{3}\right)} \sqrt{c^{2} x^{2} - 1}}{8 \, x^{2}}"," ",0,"1/8*(2*(b^3*c^2*x^2 - 2*b^3)*arcsec(c*x)^3 - 4*a^3 + 6*a*b^2 + 6*(a*b^2*c^2*x^2 - 2*a*b^2)*arcsec(c*x)^2 + 3*((2*a^2*b - b^3)*c^2*x^2 - 4*a^2*b + 2*b^3)*arcsec(c*x) + 3*(2*b^3*arcsec(c*x)^2 + 4*a*b^2*arcsec(c*x) + 2*a^2*b - b^3)*sqrt(c^2*x^2 - 1))/x^2","A",0
31,1,172,0,0.705618," ","integrate((a+b*arcsec(c*x))^3/x^4,x, algorithm=""fricas"")","\frac{36 \, a b^{2} c^{2} x^{2} - 9 \, b^{3} \operatorname{arcsec}\left(c x\right)^{3} - 27 \, a b^{2} \operatorname{arcsec}\left(c x\right)^{2} - 9 \, a^{3} + 6 \, a b^{2} + 3 \, {\left(12 \, b^{3} c^{2} x^{2} - 9 \, a^{2} b + 2 \, b^{3}\right)} \operatorname{arcsec}\left(c x\right) + {\left(2 \, {\left(9 \, a^{2} b - 20 \, b^{3}\right)} c^{2} x^{2} + 9 \, a^{2} b - 2 \, b^{3} + 9 \, {\left(2 \, b^{3} c^{2} x^{2} + b^{3}\right)} \operatorname{arcsec}\left(c x\right)^{2} + 18 \, {\left(2 \, a b^{2} c^{2} x^{2} + a b^{2}\right)} \operatorname{arcsec}\left(c x\right)\right)} \sqrt{c^{2} x^{2} - 1}}{27 \, x^{3}}"," ",0,"1/27*(36*a*b^2*c^2*x^2 - 9*b^3*arcsec(c*x)^3 - 27*a*b^2*arcsec(c*x)^2 - 9*a^3 + 6*a*b^2 + 3*(12*b^3*c^2*x^2 - 9*a^2*b + 2*b^3)*arcsec(c*x) + (2*(9*a^2*b - 20*b^3)*c^2*x^2 + 9*a^2*b - 2*b^3 + 9*(2*b^3*c^2*x^2 + b^3)*arcsec(c*x)^2 + 18*(2*a*b^2*c^2*x^2 + a*b^2)*arcsec(c*x))*sqrt(c^2*x^2 - 1))/x^3","A",0
32,1,225,0,0.724889," ","integrate((a+b*arcsec(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)} \operatorname{arcsec}\left(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}\right)} \operatorname{arcsec}\left(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}\right)} \operatorname{arcsec}\left(c x\right) + 3 \, {\left(3 \, {\left(8 \, a^{2} b - 5 \, b^{3}\right)} c^{2} x^{2} + 16 \, a^{2} b - 2 \, b^{3} + 8 \, {\left(3 \, b^{3} c^{2} x^{2} + 2 \, b^{3}\right)} \operatorname{arcsec}\left(c x\right)^{2} + 16 \, {\left(3 \, a b^{2} c^{2} x^{2} + 2 \, a b^{2}\right)} \operatorname{arcsec}\left(c x\right)\right)} \sqrt{c^{2} x^{2} - 1}}{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)*arcsec(c*x)^3 - 64*a^3 + 24*a*b^2 + 24*(3*a*b^2*c^4*x^4 - 8*a*b^2)*arcsec(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)*arcsec(c*x) + 3*(3*(8*a^2*b - 5*b^3)*c^2*x^2 + 16*a^2*b - 2*b^3 + 8*(3*b^3*c^2*x^2 + 2*b^3)*arcsec(c*x)^2 + 16*(3*a*b^2*c^2*x^2 + 2*a*b^2)*arcsec(c*x))*sqrt(c^2*x^2 - 1))/x^4","A",0
33,0,0,0,0.720340," ","integrate(x/(a+b*arcsec(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b \operatorname{arcsec}\left(c x\right) + a}, x\right)"," ",0,"integral(x/(b*arcsec(c*x) + a), x)","F",0
34,0,0,0,0.599708," ","integrate(1/(a+b*arcsec(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b \operatorname{arcsec}\left(c x\right) + a}, x\right)"," ",0,"integral(1/(b*arcsec(c*x) + a), x)","F",0
35,0,0,0,0.516038," ","integrate(1/x/(a+b*arcsec(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x \operatorname{arcsec}\left(c x\right) + a x}, x\right)"," ",0,"integral(1/(b*x*arcsec(c*x) + a*x), x)","F",0
36,0,0,0,0.673977," ","integrate(1/x^2/(a+b*arcsec(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x^{2} \operatorname{arcsec}\left(c x\right) + a x^{2}}, x\right)"," ",0,"integral(1/(b*x^2*arcsec(c*x) + a*x^2), x)","F",0
37,0,0,0,0.535221," ","integrate(1/x^3/(a+b*arcsec(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x^{3} \operatorname{arcsec}\left(c x\right) + a x^{3}}, x\right)"," ",0,"integral(1/(b*x^3*arcsec(c*x) + a*x^3), x)","F",0
38,0,0,0,0.426325," ","integrate(1/x^4/(a+b*arcsec(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x^{4} \operatorname{arcsec}\left(c x\right) + a x^{4}}, x\right)"," ",0,"integral(1/(b*x^4*arcsec(c*x) + a*x^4), x)","F",0
39,0,0,0,0.458787," ","integrate(x/(a+b*arcsec(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b^{2} \operatorname{arcsec}\left(c x\right)^{2} + 2 \, a b \operatorname{arcsec}\left(c x\right) + a^{2}}, x\right)"," ",0,"integral(x/(b^2*arcsec(c*x)^2 + 2*a*b*arcsec(c*x) + a^2), x)","F",0
40,0,0,0,0.592169," ","integrate(1/(a+b*arcsec(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} \operatorname{arcsec}\left(c x\right)^{2} + 2 \, a b \operatorname{arcsec}\left(c x\right) + a^{2}}, x\right)"," ",0,"integral(1/(b^2*arcsec(c*x)^2 + 2*a*b*arcsec(c*x) + a^2), x)","F",0
41,0,0,0,0.981447," ","integrate(1/x/(a+b*arcsec(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x \operatorname{arcsec}\left(c x\right)^{2} + 2 \, a b x \operatorname{arcsec}\left(c x\right) + a^{2} x}, x\right)"," ",0,"integral(1/(b^2*x*arcsec(c*x)^2 + 2*a*b*x*arcsec(c*x) + a^2*x), x)","F",0
42,0,0,0,1.433224," ","integrate(1/x^2/(a+b*arcsec(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{2} \operatorname{arcsec}\left(c x\right)^{2} + 2 \, a b x^{2} \operatorname{arcsec}\left(c x\right) + a^{2} x^{2}}, x\right)"," ",0,"integral(1/(b^2*x^2*arcsec(c*x)^2 + 2*a*b*x^2*arcsec(c*x) + a^2*x^2), x)","F",0
43,0,0,0,0.674232," ","integrate(1/x^3/(a+b*arcsec(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{3} \operatorname{arcsec}\left(c x\right)^{2} + 2 \, a b x^{3} \operatorname{arcsec}\left(c x\right) + a^{2} x^{3}}, x\right)"," ",0,"integral(1/(b^2*x^3*arcsec(c*x)^2 + 2*a*b*x^3*arcsec(c*x) + a^2*x^3), x)","F",0
44,0,0,0,0.704604," ","integrate(1/x^4/(a+b*arcsec(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{4} \operatorname{arcsec}\left(c x\right)^{2} + 2 \, a b x^{4} \operatorname{arcsec}\left(c x\right) + a^{2} x^{4}}, x\right)"," ",0,"integral(1/(b^2*x^4*arcsec(c*x)^2 + 2*a*b*x^4*arcsec(c*x) + a^2*x^4), x)","F",0
45,0,0,0,0.487573," ","integrate(x/(a+b*arcsec(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b^{3} \operatorname{arcsec}\left(c x\right)^{3} + 3 \, a b^{2} \operatorname{arcsec}\left(c x\right)^{2} + 3 \, a^{2} b \operatorname{arcsec}\left(c x\right) + a^{3}}, x\right)"," ",0,"integral(x/(b^3*arcsec(c*x)^3 + 3*a*b^2*arcsec(c*x)^2 + 3*a^2*b*arcsec(c*x) + a^3), x)","F",0
46,0,0,0,0.545511," ","integrate(1/(a+b*arcsec(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} \operatorname{arcsec}\left(c x\right)^{3} + 3 \, a b^{2} \operatorname{arcsec}\left(c x\right)^{2} + 3 \, a^{2} b \operatorname{arcsec}\left(c x\right) + a^{3}}, x\right)"," ",0,"integral(1/(b^3*arcsec(c*x)^3 + 3*a*b^2*arcsec(c*x)^2 + 3*a^2*b*arcsec(c*x) + a^3), x)","F",0
47,0,0,0,0.814556," ","integrate(1/x/(a+b*arcsec(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} x \operatorname{arcsec}\left(c x\right)^{3} + 3 \, a b^{2} x \operatorname{arcsec}\left(c x\right)^{2} + 3 \, a^{2} b x \operatorname{arcsec}\left(c x\right) + a^{3} x}, x\right)"," ",0,"integral(1/(b^3*x*arcsec(c*x)^3 + 3*a*b^2*x*arcsec(c*x)^2 + 3*a^2*b*x*arcsec(c*x) + a^3*x), x)","F",0
48,0,0,0,0.457469," ","integrate(1/x^2/(a+b*arcsec(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} x^{2} \operatorname{arcsec}\left(c x\right)^{3} + 3 \, a b^{2} x^{2} \operatorname{arcsec}\left(c x\right)^{2} + 3 \, a^{2} b x^{2} \operatorname{arcsec}\left(c x\right) + a^{3} x^{2}}, x\right)"," ",0,"integral(1/(b^3*x^2*arcsec(c*x)^3 + 3*a*b^2*x^2*arcsec(c*x)^2 + 3*a^2*b*x^2*arcsec(c*x) + a^3*x^2), x)","F",0
49,0,0,0,0.437261," ","integrate(1/x^3/(a+b*arcsec(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} x^{3} \operatorname{arcsec}\left(c x\right)^{3} + 3 \, a b^{2} x^{3} \operatorname{arcsec}\left(c x\right)^{2} + 3 \, a^{2} b x^{3} \operatorname{arcsec}\left(c x\right) + a^{3} x^{3}}, x\right)"," ",0,"integral(1/(b^3*x^3*arcsec(c*x)^3 + 3*a*b^2*x^3*arcsec(c*x)^2 + 3*a^2*b*x^3*arcsec(c*x) + a^3*x^3), x)","F",0
50,0,0,0,0.434628," ","integrate(1/x^4/(a+b*arcsec(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} x^{4} \operatorname{arcsec}\left(c x\right)^{3} + 3 \, a b^{2} x^{4} \operatorname{arcsec}\left(c x\right)^{2} + 3 \, a^{2} b x^{4} \operatorname{arcsec}\left(c x\right) + a^{3} x^{4}}, x\right)"," ",0,"integral(1/(b^3*x^4*arcsec(c*x)^3 + 3*a*b^2*x^4*arcsec(c*x)^2 + 3*a^2*b*x^4*arcsec(c*x) + a^3*x^4), x)","F",0
51,0,0,0,0.466608," ","integrate((d*x)^m*(a+b*arcsec(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \operatorname{arcsec}\left(c x\right)^{3} + 3 \, a b^{2} \operatorname{arcsec}\left(c x\right)^{2} + 3 \, a^{2} b \operatorname{arcsec}\left(c x\right) + a^{3}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^3*arcsec(c*x)^3 + 3*a*b^2*arcsec(c*x)^2 + 3*a^2*b*arcsec(c*x) + a^3)*(d*x)^m, x)","F",0
52,0,0,0,0.472666," ","integrate((d*x)^m*(a+b*arcsec(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \operatorname{arcsec}\left(c x\right)^{2} + 2 \, a b \operatorname{arcsec}\left(c x\right) + a^{2}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^2*arcsec(c*x)^2 + 2*a*b*arcsec(c*x) + a^2)*(d*x)^m, x)","F",0
53,0,0,0,0.428646," ","integrate((d*x)^m*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b*arcsec(c*x) + a)*(d*x)^m, x)","F",0
54,0,0,0,0.400566," ","integrate((d*x)^m/(a+b*arcsec(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b \operatorname{arcsec}\left(c x\right) + a}, x\right)"," ",0,"integral((d*x)^m/(b*arcsec(c*x) + a), x)","F",0
55,0,0,0,0.406957," ","integrate((d*x)^m/(a+b*arcsec(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b^{2} \operatorname{arcsec}\left(c x\right)^{2} + 2 \, a b \operatorname{arcsec}\left(c x\right) + a^{2}}, x\right)"," ",0,"integral((d*x)^m/(b^2*arcsec(c*x)^2 + 2*a*b*arcsec(c*x) + a^2), x)","F",0
56,1,291,0,0.655533," ","integrate((e*x+d)^3*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\frac{3 \, a c^{4} e^{3} x^{4} + 12 \, a c^{4} d e^{2} x^{3} + 18 \, a c^{4} d^{2} e x^{2} + 12 \, a c^{4} d^{3} x + 3 \, {\left(b c^{4} e^{3} x^{4} + 4 \, b c^{4} d e^{2} x^{3} + 6 \, b c^{4} d^{2} e x^{2} + 4 \, b c^{4} d^{3} x - 4 \, b c^{4} d^{3} - 6 \, b c^{4} d^{2} e - 4 \, b c^{4} d e^{2} - b c^{4} e^{3}\right)} \operatorname{arcsec}\left(c x\right) + 6 \, {\left(4 \, b c^{4} d^{3} + 6 \, b c^{4} d^{2} e + 4 \, b c^{4} d e^{2} + b c^{4} e^{3}\right)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + 6 \, {\left(2 \, b c^{3} d^{3} + b c d e^{2}\right)} \log\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) - {\left(b c^{2} e^{3} x^{2} + 6 \, b c^{2} d e^{2} x + 18 \, b c^{2} d^{2} e + 2 \, b e^{3}\right)} \sqrt{c^{2} x^{2} - 1}}{12 \, c^{4}}"," ",0,"1/12*(3*a*c^4*e^3*x^4 + 12*a*c^4*d*e^2*x^3 + 18*a*c^4*d^2*e*x^2 + 12*a*c^4*d^3*x + 3*(b*c^4*e^3*x^4 + 4*b*c^4*d*e^2*x^3 + 6*b*c^4*d^2*e*x^2 + 4*b*c^4*d^3*x - 4*b*c^4*d^3 - 6*b*c^4*d^2*e - 4*b*c^4*d*e^2 - b*c^4*e^3)*arcsec(c*x) + 6*(4*b*c^4*d^3 + 6*b*c^4*d^2*e + 4*b*c^4*d*e^2 + b*c^4*e^3)*arctan(-c*x + sqrt(c^2*x^2 - 1)) + 6*(2*b*c^3*d^3 + b*c*d*e^2)*log(-c*x + sqrt(c^2*x^2 - 1)) - (b*c^2*e^3*x^2 + 6*b*c^2*d*e^2*x + 18*b*c^2*d^2*e + 2*b*e^3)*sqrt(c^2*x^2 - 1))/c^4","A",0
57,1,209,0,0.575516," ","integrate((e*x+d)^2*(a+b*arcsec(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(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)} \operatorname{arcsec}\left(c x\right) + 4 \, {\left(3 \, b c^{3} d^{2} + 3 \, b c^{3} d e + b c^{3} e^{2}\right)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + {\left(6 \, b c^{2} d^{2} + b e^{2}\right)} \log\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) - {\left(b c e^{2} x + 6 \, b c d e\right)} \sqrt{c^{2} x^{2} - 1}}{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*(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)*arcsec(c*x) + 4*(3*b*c^3*d^2 + 3*b*c^3*d*e + b*c^3*e^2)*arctan(-c*x + sqrt(c^2*x^2 - 1)) + (6*b*c^2*d^2 + b*e^2)*log(-c*x + sqrt(c^2*x^2 - 1)) - (b*c*e^2*x + 6*b*c*d*e)*sqrt(c^2*x^2 - 1))/c^3","A",0
58,1,130,0,0.448824," ","integrate((e*x+d)*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\frac{a c^{2} e x^{2} + 2 \, a c^{2} d x + 2 \, b c d \log\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) - \sqrt{c^{2} x^{2} - 1} b e + {\left(b c^{2} e x^{2} + 2 \, b c^{2} d x - 2 \, b c^{2} d - b c^{2} e\right)} \operatorname{arcsec}\left(c x\right) + 2 \, {\left(2 \, b c^{2} d + b c^{2} e\right)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right)}{2 \, c^{2}}"," ",0,"1/2*(a*c^2*e*x^2 + 2*a*c^2*d*x + 2*b*c*d*log(-c*x + sqrt(c^2*x^2 - 1)) - sqrt(c^2*x^2 - 1)*b*e + (b*c^2*e*x^2 + 2*b*c^2*d*x - 2*b*c^2*d - b*c^2*e)*arcsec(c*x) + 2*(2*b*c^2*d + b*c^2*e)*arctan(-c*x + sqrt(c^2*x^2 - 1)))/c^2","A",0
59,1,63,0,0.431925," ","integrate(a+b*arcsec(c*x),x, algorithm=""fricas"")","\frac{a c x + 2 \, b c \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + {\left(b c x - b c\right)} \operatorname{arcsec}\left(c x\right) + b \log\left(-c x + \sqrt{c^{2} x^{2} - 1}\right)}{c}"," ",0,"(a*c*x + 2*b*c*arctan(-c*x + sqrt(c^2*x^2 - 1)) + (b*c*x - b*c)*arcsec(c*x) + b*log(-c*x + sqrt(c^2*x^2 - 1)))/c","B",0
60,0,0,0,0.434014," ","integrate((a+b*arcsec(c*x))/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arcsec}\left(c x\right) + a}{e x + d}, x\right)"," ",0,"integral((b*arcsec(c*x) + a)/(e*x + d), x)","F",0
61,1,477,0,0.487009," ","integrate((a+b*arcsec(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^{3} d^{2} x + c d e - \sqrt{c^{2} d^{2} - e^{2}} {\left(c^{2} d x + e\right)} + {\left(c^{2} d^{2} - \sqrt{c^{2} d^{2} - e^{2}} c d - e^{2}\right)} \sqrt{c^{2} x^{2} - 1}}{e x + d}\right) + {\left(b c^{2} d^{3} - b d e^{2}\right)} \operatorname{arcsec}\left(c x\right) - 2 \, {\left(b c^{2} d^{3} - b d e^{2} + {\left(b c^{2} d^{2} e - b e^{3}\right)} x\right)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\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}} \sqrt{c^{2} x^{2} - 1} e - \sqrt{-c^{2} d^{2} + e^{2}} {\left(c e x + c d\right)}}{c^{2} d^{2} - e^{2}}\right) + {\left(b c^{2} d^{3} - b d e^{2}\right)} \operatorname{arcsec}\left(c x\right) - 2 \, {\left(b c^{2} d^{3} - b d e^{2} + {\left(b c^{2} d^{2} e - b e^{3}\right)} x\right)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\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^3*d^2*x + c*d*e - sqrt(c^2*d^2 - e^2)*(c^2*d*x + e) + (c^2*d^2 - sqrt(c^2*d^2 - e^2)*c*d - e^2)*sqrt(c^2*x^2 - 1))/(e*x + d)) + (b*c^2*d^3 - b*d*e^2)*arcsec(c*x) - 2*(b*c^2*d^3 - b*d*e^2 + (b*c^2*d^2*e - b*e^3)*x)*arctan(-c*x + sqrt(c^2*x^2 - 1)))/(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)*sqrt(c^2*x^2 - 1)*e - sqrt(-c^2*d^2 + e^2)*(c*e*x + c*d))/(c^2*d^2 - e^2)) + (b*c^2*d^3 - b*d*e^2)*arcsec(c*x) - 2*(b*c^2*d^3 - b*d*e^2 + (b*c^2*d^2*e - b*e^3)*x)*arctan(-c*x + sqrt(c^2*x^2 - 1)))/(c^2*d^4*e - d^2*e^3 + (c^2*d^3*e^2 - d*e^4)*x)]","B",0
62,1,1117,0,0.994135," ","integrate((a+b*arcsec(c*x))/(e*x+d)^3,x, algorithm=""fricas"")","\left[-\frac{a c^{4} d^{6} - b c^{3} d^{5} e - 2 \, a c^{2} d^{4} e^{2} + b c d^{3} e^{3} + a d^{2} e^{4} - {\left(b c^{3} d^{3} e^{3} - b c d e^{5}\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^{3} d^{2} x + c d e - \sqrt{c^{2} d^{2} - e^{2}} {\left(c^{2} d x + e\right)} + {\left(c^{2} d^{2} - \sqrt{c^{2} d^{2} - e^{2}} c d - e^{2}\right)} \sqrt{c^{2} x^{2} - 1}}{e x + d}\right) - 2 \, {\left(b c^{3} d^{4} e^{2} - b c d^{2} e^{4}\right)} x + {\left(b c^{4} d^{6} - 2 \, b c^{2} d^{4} e^{2} + b d^{2} e^{4}\right)} \operatorname{arcsec}\left(c x\right) - 2 \, {\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)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) - {\left(b c^{2} d^{4} e^{2} - b d^{2} e^{4} + {\left(b c^{2} d^{3} e^{3} - b d e^{5}\right)} x\right)} \sqrt{c^{2} x^{2} - 1}}{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} - b c^{3} d^{5} e - 2 \, a c^{2} d^{4} e^{2} + b c d^{3} e^{3} + a d^{2} e^{4} - {\left(b c^{3} d^{3} e^{3} - b c d e^{5}\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}} \sqrt{c^{2} x^{2} - 1} e - \sqrt{-c^{2} d^{2} + e^{2}} {\left(c e x + c d\right)}}{c^{2} d^{2} - e^{2}}\right) - 2 \, {\left(b c^{3} d^{4} e^{2} - b c d^{2} e^{4}\right)} x + {\left(b c^{4} d^{6} - 2 \, b c^{2} d^{4} e^{2} + b d^{2} e^{4}\right)} \operatorname{arcsec}\left(c x\right) - 2 \, {\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)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) - {\left(b c^{2} d^{4} e^{2} - b d^{2} e^{4} + {\left(b c^{2} d^{3} e^{3} - b d e^{5}\right)} x\right)} \sqrt{c^{2} x^{2} - 1}}{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 - b*c^3*d^5*e - 2*a*c^2*d^4*e^2 + b*c*d^3*e^3 + a*d^2*e^4 - (b*c^3*d^3*e^3 - b*c*d*e^5)*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^3*d^2*x + c*d*e - sqrt(c^2*d^2 - e^2)*(c^2*d*x + e) + (c^2*d^2 - sqrt(c^2*d^2 - e^2)*c*d - e^2)*sqrt(c^2*x^2 - 1))/(e*x + d)) - 2*(b*c^3*d^4*e^2 - b*c*d^2*e^4)*x + (b*c^4*d^6 - 2*b*c^2*d^4*e^2 + b*d^2*e^4)*arcsec(c*x) - 2*(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)*arctan(-c*x + sqrt(c^2*x^2 - 1)) - (b*c^2*d^4*e^2 - b*d^2*e^4 + (b*c^2*d^3*e^3 - b*d*e^5)*x)*sqrt(c^2*x^2 - 1))/(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 - b*c^3*d^5*e - 2*a*c^2*d^4*e^2 + b*c*d^3*e^3 + a*d^2*e^4 - (b*c^3*d^3*e^3 - b*c*d*e^5)*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)*sqrt(c^2*x^2 - 1)*e - sqrt(-c^2*d^2 + e^2)*(c*e*x + c*d))/(c^2*d^2 - e^2)) - 2*(b*c^3*d^4*e^2 - b*c*d^2*e^4)*x + (b*c^4*d^6 - 2*b*c^2*d^4*e^2 + b*d^2*e^4)*arcsec(c*x) - 2*(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)*arctan(-c*x + sqrt(c^2*x^2 - 1)) - (b*c^2*d^4*e^2 - b*d^2*e^4 + (b*c^2*d^3*e^3 - b*d*e^5)*x)*sqrt(c^2*x^2 - 1))/(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
63,-1,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,-1,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,0,0,0,1.848853," ","integrate((a+b*arcsec(c*x))/(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arcsec}\left(c x\right) + a}{\sqrt{e x + d}}, x\right)"," ",0,"integral((b*arcsec(c*x) + a)/sqrt(e*x + d), x)","F",0
66,-1,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x+d)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
67,0,0,0,1.407200," ","integrate((a+b*arcsec(c*x))/(e*x+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x + d} {\left(b \operatorname{arcsec}\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*arcsec(c*x) + a)/(e^3*x^3 + 3*d*e^2*x^2 + 3*d^2*e*x + d^3), x)","F",0
68,-1,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x+d)^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,1,192,0,1.928592," ","integrate(x^4*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\frac{240 \, a c^{7} e x^{7} + 336 \, a c^{7} d x^{5} + 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)} \operatorname{arcsec}\left(c x\right) + 96 \, {\left(7 \, b c^{7} d + 5 \, b c^{7} e\right)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + 3 \, {\left(42 \, b c^{2} d + 25 \, b e\right)} \log\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) - {\left(40 \, b c^{5} e x^{5} + 2 \, {\left(42 \, b c^{5} d + 25 \, b c^{3} e\right)} x^{3} + 3 \, {\left(42 \, b c^{3} d + 25 \, b c e\right)} x\right)} \sqrt{c^{2} x^{2} - 1}}{1680 \, c^{7}}"," ",0,"1/1680*(240*a*c^7*e*x^7 + 336*a*c^7*d*x^5 + 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)*arcsec(c*x) + 96*(7*b*c^7*d + 5*b*c^7*e)*arctan(-c*x + sqrt(c^2*x^2 - 1)) + 3*(42*b*c^2*d + 25*b*e)*log(-c*x + sqrt(c^2*x^2 - 1)) - (40*b*c^5*e*x^5 + 2*(42*b*c^5*d + 25*b*c^3*e)*x^3 + 3*(42*b*c^3*d + 25*b*c*e)*x)*sqrt(c^2*x^2 - 1))/c^7","A",0
70,1,170,0,2.032002," ","integrate(x^2*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\frac{24 \, a c^{5} e x^{5} + 40 \, a c^{5} d x^{3} + 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)} \operatorname{arcsec}\left(c x\right) + 16 \, {\left(5 \, b c^{5} d + 3 \, b c^{5} e\right)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + {\left(20 \, b c^{2} d + 9 \, b e\right)} \log\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) - {\left(6 \, b c^{3} e x^{3} + {\left(20 \, b c^{3} d + 9 \, b c e\right)} x\right)} \sqrt{c^{2} x^{2} - 1}}{120 \, c^{5}}"," ",0,"1/120*(24*a*c^5*e*x^5 + 40*a*c^5*d*x^3 + 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)*arcsec(c*x) + 16*(5*b*c^5*d + 3*b*c^5*e)*arctan(-c*x + sqrt(c^2*x^2 - 1)) + (20*b*c^2*d + 9*b*e)*log(-c*x + sqrt(c^2*x^2 - 1)) - (6*b*c^3*e*x^3 + (20*b*c^3*d + 9*b*c*e)*x)*sqrt(c^2*x^2 - 1))/c^5","A",0
71,1,141,0,2.085628," ","integrate((e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\frac{2 \, a c^{3} e x^{3} + 6 \, a c^{3} d x - \sqrt{c^{2} x^{2} - 1} b c e x + 2 \, {\left(b c^{3} e x^{3} + 3 \, b c^{3} d x - 3 \, b c^{3} d - b c^{3} e\right)} \operatorname{arcsec}\left(c x\right) + 4 \, {\left(3 \, b c^{3} d + b c^{3} e\right)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + {\left(6 \, b c^{2} d + b e\right)} \log\left(-c x + \sqrt{c^{2} x^{2} - 1}\right)}{6 \, c^{3}}"," ",0,"1/6*(2*a*c^3*e*x^3 + 6*a*c^3*d*x - sqrt(c^2*x^2 - 1)*b*c*e*x + 2*(b*c^3*e*x^3 + 3*b*c^3*d*x - 3*b*c^3*d - b*c^3*e)*arcsec(c*x) + 4*(3*b*c^3*d + b*c^3*e)*arctan(-c*x + sqrt(c^2*x^2 - 1)) + (6*b*c^2*d + b*e)*log(-c*x + sqrt(c^2*x^2 - 1)))/c^3","A",0
72,1,123,0,0.453952," ","integrate((e*x^2+d)*(a+b*arcsec(c*x))/x^2,x, algorithm=""fricas"")","\frac{b c^{2} d x + a c e x^{2} + b e x \log\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + \sqrt{c^{2} x^{2} - 1} b c d - a c d - 2 \, {\left(b c d - b c e\right)} x \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + {\left(b c e x^{2} - b c d + {\left(b c d - b c e\right)} x\right)} \operatorname{arcsec}\left(c x\right)}{c x}"," ",0,"(b*c^2*d*x + a*c*e*x^2 + b*e*x*log(-c*x + sqrt(c^2*x^2 - 1)) + sqrt(c^2*x^2 - 1)*b*c*d - a*c*d - 2*(b*c*d - b*c*e)*x*arctan(-c*x + sqrt(c^2*x^2 - 1)) + (b*c*e*x^2 - b*c*d + (b*c*d - b*c*e)*x)*arcsec(c*x))/(c*x)","A",0
73,1,67,0,2.057683," ","integrate((e*x^2+d)*(a+b*arcsec(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)} \operatorname{arcsec}\left(c x\right) - \sqrt{c^{2} x^{2} - 1} {\left({\left(2 \, b c^{2} d + 9 \, b e\right)} x^{2} + b d\right)}}{9 \, x^{3}}"," ",0,"-1/9*(9*a*e*x^2 + 3*a*d + 3*(3*b*e*x^2 + b*d)*arcsec(c*x) - sqrt(c^2*x^2 - 1)*((2*b*c^2*d + 9*b*e)*x^2 + b*d))/x^3","A",0
74,1,89,0,1.066005," ","integrate((e*x^2+d)*(a+b*arcsec(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)} \operatorname{arcsec}\left(c x\right) - {\left(2 \, {\left(12 \, b c^{4} d + 25 \, b c^{2} e\right)} x^{4} + {\left(12 \, b c^{2} d + 25 \, b e\right)} x^{2} + 9 \, b d\right)} \sqrt{c^{2} x^{2} - 1}}{225 \, x^{5}}"," ",0,"-1/225*(75*a*e*x^2 + 45*a*d + 15*(5*b*e*x^2 + 3*b*d)*arcsec(c*x) - (2*(12*b*c^4*d + 25*b*c^2*e)*x^4 + (12*b*c^2*d + 25*b*e)*x^2 + 9*b*d)*sqrt(c^2*x^2 - 1))/x^5","A",0
75,1,110,0,1.486367," ","integrate((e*x^2+d)*(a+b*arcsec(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)} \operatorname{arcsec}\left(c x\right) - {\left(8 \, {\left(30 \, b c^{6} d + 49 \, b c^{4} e\right)} x^{6} + 4 \, {\left(30 \, b c^{4} d + 49 \, b c^{2} e\right)} x^{4} + 3 \, {\left(30 \, b c^{2} d + 49 \, b e\right)} x^{2} + 75 \, b d\right)} \sqrt{c^{2} x^{2} - 1}}{3675 \, x^{7}}"," ",0,"-1/3675*(735*a*e*x^2 + 525*a*d + 105*(7*b*e*x^2 + 5*b*d)*arcsec(c*x) - (8*(30*b*c^6*d + 49*b*c^4*e)*x^6 + 4*(30*b*c^4*d + 49*b*c^2*e)*x^4 + 3*(30*b*c^2*d + 49*b*e)*x^2 + 75*b*d)*sqrt(c^2*x^2 - 1))/x^7","A",0
76,1,128,0,1.976521," ","integrate(x^5*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\frac{315 \, a c^{8} e x^{8} + 420 \, a c^{8} d x^{6} + 105 \, {\left(3 \, b c^{8} e x^{8} + 4 \, b c^{8} d x^{6}\right)} \operatorname{arcsec}\left(c x\right) - {\left(45 \, b c^{6} e x^{6} + 6 \, {\left(14 \, b c^{6} d + 9 \, b c^{4} e\right)} x^{4} + 224 \, b c^{2} d + 8 \, {\left(14 \, b c^{4} d + 9 \, b c^{2} e\right)} x^{2} + 144 \, b e\right)} \sqrt{c^{2} x^{2} - 1}}{2520 \, c^{8}}"," ",0,"1/2520*(315*a*c^8*e*x^8 + 420*a*c^8*d*x^6 + 105*(3*b*c^8*e*x^8 + 4*b*c^8*d*x^6)*arcsec(c*x) - (45*b*c^6*e*x^6 + 6*(14*b*c^6*d + 9*b*c^4*e)*x^4 + 224*b*c^2*d + 8*(14*b*c^4*d + 9*b*c^2*e)*x^2 + 144*b*e)*sqrt(c^2*x^2 - 1))/c^8","A",0
77,1,107,0,0.647131," ","integrate(x^3*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\frac{30 \, a c^{6} e x^{6} + 45 \, a c^{6} d x^{4} + 15 \, {\left(2 \, b c^{6} e x^{6} + 3 \, b c^{6} d x^{4}\right)} \operatorname{arcsec}\left(c x\right) - {\left(6 \, b c^{4} e x^{4} + 30 \, b c^{2} d + {\left(15 \, b c^{4} d + 8 \, b c^{2} e\right)} x^{2} + 16 \, b e\right)} \sqrt{c^{2} x^{2} - 1}}{180 \, c^{6}}"," ",0,"1/180*(30*a*c^6*e*x^6 + 45*a*c^6*d*x^4 + 15*(2*b*c^6*e*x^6 + 3*b*c^6*d*x^4)*arcsec(c*x) - (6*b*c^4*e*x^4 + 30*b*c^2*d + (15*b*c^4*d + 8*b*c^2*e)*x^2 + 16*b*e)*sqrt(c^2*x^2 - 1))/c^6","A",0
78,1,86,0,0.669947," ","integrate(x*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\frac{3 \, a c^{4} e x^{4} + 6 \, a c^{4} d x^{2} + 3 \, {\left(b c^{4} e x^{4} + 2 \, b c^{4} d x^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(b c^{2} e x^{2} + 6 \, b c^{2} d + 2 \, b e\right)} \sqrt{c^{2} x^{2} - 1}}{12 \, c^{4}}"," ",0,"1/12*(3*a*c^4*e*x^4 + 6*a*c^4*d*x^2 + 3*(b*c^4*e*x^4 + 2*b*c^4*d*x^2)*arcsec(c*x) - (b*c^2*e*x^2 + 6*b*c^2*d + 2*b*e)*sqrt(c^2*x^2 - 1))/c^4","A",0
79,0,0,0,1.980857," ","integrate((e*x^2+d)*(a+b*arcsec(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{arcsec}\left(c x\right)}{x}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsec(c*x))/x, x)","F",0
80,0,0,0,0.579297," ","integrate((e*x^2+d)*(a+b*arcsec(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{arcsec}\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a*e*x^2 + a*d + (b*e*x^2 + b*d)*arcsec(c*x))/x^3, x)","F",0
81,1,273,0,4.040318," ","integrate(x^2*(e*x^2+d)^2*(a+b*arcsec(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} + 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)} \operatorname{arcsec}\left(c x\right) + 32 \, {\left(35 \, b c^{7} d^{2} + 42 \, b c^{7} d e + 15 \, b c^{7} e^{2}\right)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + {\left(280 \, b c^{4} d^{2} + 252 \, b c^{2} d e + 75 \, b e^{2}\right)} \log\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) - {\left(40 \, b c^{5} e^{2} x^{5} + 2 \, {\left(84 \, b c^{5} d e + 25 \, b c^{3} e^{2}\right)} x^{3} + {\left(280 \, b c^{5} d^{2} + 252 \, b c^{3} d e + 75 \, b c e^{2}\right)} x\right)} \sqrt{c^{2} x^{2} - 1}}{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 + 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)*arcsec(c*x) + 32*(35*b*c^7*d^2 + 42*b*c^7*d*e + 15*b*c^7*e^2)*arctan(-c*x + sqrt(c^2*x^2 - 1)) + (280*b*c^4*d^2 + 252*b*c^2*d*e + 75*b*e^2)*log(-c*x + sqrt(c^2*x^2 - 1)) - (40*b*c^5*e^2*x^5 + 2*(84*b*c^5*d*e + 25*b*c^3*e^2)*x^3 + (280*b*c^5*d^2 + 252*b*c^3*d*e + 75*b*c*e^2)*x)*sqrt(c^2*x^2 - 1))/c^7","A",0
82,1,237,0,2.284940," ","integrate((e*x^2+d)^2*(a+b*arcsec(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 + 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)} \operatorname{arcsec}\left(c x\right) + 16 \, {\left(15 \, b c^{5} d^{2} + 10 \, b c^{5} d e + 3 \, b c^{5} e^{2}\right)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + {\left(120 \, b c^{4} d^{2} + 40 \, b c^{2} d e + 9 \, b e^{2}\right)} \log\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) - {\left(6 \, b c^{3} e^{2} x^{3} + {\left(40 \, b c^{3} d e + 9 \, b c e^{2}\right)} x\right)} \sqrt{c^{2} x^{2} - 1}}{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 + 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)*arcsec(c*x) + 16*(15*b*c^5*d^2 + 10*b*c^5*d*e + 3*b*c^5*e^2)*arctan(-c*x + sqrt(c^2*x^2 - 1)) + (120*b*c^4*d^2 + 40*b*c^2*d*e + 9*b*e^2)*log(-c*x + sqrt(c^2*x^2 - 1)) - (6*b*c^3*e^2*x^3 + (40*b*c^3*d*e + 9*b*c*e^2)*x)*sqrt(c^2*x^2 - 1))/c^5","A",0
83,1,230,0,1.106029," ","integrate((e*x^2+d)^2*(a+b*arcsec(c*x))/x^2,x, algorithm=""fricas"")","\frac{2 \, a c^{3} e^{2} x^{4} + 6 \, b c^{4} d^{2} x + 12 \, a c^{3} d e x^{2} - 6 \, a c^{3} d^{2} - 4 \, {\left(3 \, b c^{3} d^{2} - 6 \, b c^{3} d e - b c^{3} e^{2}\right)} x \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + {\left(12 \, b c^{2} d e + b e^{2}\right)} x \log\left(-c x + \sqrt{c^{2} x^{2} - 1}\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)} \operatorname{arcsec}\left(c x\right) + {\left(6 \, b c^{3} d^{2} - b c e^{2} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}}{6 \, c^{3} x}"," ",0,"1/6*(2*a*c^3*e^2*x^4 + 6*b*c^4*d^2*x + 12*a*c^3*d*e*x^2 - 6*a*c^3*d^2 - 4*(3*b*c^3*d^2 - 6*b*c^3*d*e - b*c^3*e^2)*x*arctan(-c*x + sqrt(c^2*x^2 - 1)) + (12*b*c^2*d*e + b*e^2)*x*log(-c*x + sqrt(c^2*x^2 - 1)) + 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)*arcsec(c*x) + (6*b*c^3*d^2 - b*c*e^2*x^2)*sqrt(c^2*x^2 - 1))/(c^3*x)","A",0
84,1,221,0,3.063752," ","integrate((e*x^2+d)^2*(a+b*arcsec(c*x))/x^4,x, algorithm=""fricas"")","\frac{9 \, a c e^{2} x^{4} + 9 \, b e^{2} x^{3} \log\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) - 18 \, a c d e x^{2} - 6 \, {\left(b c d^{2} + 6 \, b c d e - 3 \, b c e^{2}\right)} x^{3} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) - 3 \, a c d^{2} + 2 \, {\left(b c^{4} d^{2} + 9 \, b c^{2} d e\right)} x^{3} + 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)} \operatorname{arcsec}\left(c x\right) + {\left(b c d^{2} + 2 \, {\left(b c^{3} d^{2} + 9 \, b c d e\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}}{9 \, c x^{3}}"," ",0,"1/9*(9*a*c*e^2*x^4 + 9*b*e^2*x^3*log(-c*x + sqrt(c^2*x^2 - 1)) - 18*a*c*d*e*x^2 - 6*(b*c*d^2 + 6*b*c*d*e - 3*b*c*e^2)*x^3*arctan(-c*x + sqrt(c^2*x^2 - 1)) - 3*a*c*d^2 + 2*(b*c^4*d^2 + 9*b*c^2*d*e)*x^3 + 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)*arcsec(c*x) + (b*c*d^2 + 2*(b*c^3*d^2 + 9*b*c*d*e)*x^2)*sqrt(c^2*x^2 - 1))/(c*x^3)","A",0
85,1,127,0,1.321934," ","integrate((e*x^2+d)^2*(a+b*arcsec(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)} \operatorname{arcsec}\left(c x\right) - {\left({\left(24 \, b c^{4} d^{2} + 100 \, b c^{2} d e + 225 \, b e^{2}\right)} x^{4} + 9 \, b d^{2} + 2 \, {\left(6 \, b c^{2} d^{2} + 25 \, b d e\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}}{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)*arcsec(c*x) - ((24*b*c^4*d^2 + 100*b*c^2*d*e + 225*b*e^2)*x^4 + 9*b*d^2 + 2*(6*b*c^2*d^2 + 25*b*d*e)*x^2)*sqrt(c^2*x^2 - 1))/x^5","A",0
86,1,159,0,1.547959," ","integrate((e*x^2+d)^2*(a+b*arcsec(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)} \operatorname{arcsec}\left(c x\right) - {\left(2 \, {\left(360 \, b c^{6} d^{2} + 1176 \, b c^{4} d e + 1225 \, b c^{2} e^{2}\right)} x^{6} + {\left(360 \, b c^{4} d^{2} + 1176 \, b c^{2} d e + 1225 \, b e^{2}\right)} x^{4} + 225 \, b d^{2} + 18 \, {\left(15 \, b c^{2} d^{2} + 49 \, b d e\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}}{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)*arcsec(c*x) - (2*(360*b*c^6*d^2 + 1176*b*c^4*d*e + 1225*b*c^2*e^2)*x^6 + (360*b*c^4*d^2 + 1176*b*c^2*d*e + 1225*b*e^2)*x^4 + 225*b*d^2 + 18*(15*b*c^2*d^2 + 49*b*d*e)*x^2)*sqrt(c^2*x^2 - 1))/x^7","A",0
87,1,187,0,0.982839," ","integrate(x^3*(e*x^2+d)^2*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\frac{315 \, a c^{8} e^{2} x^{8} + 840 \, a c^{8} d e x^{6} + 630 \, a c^{8} d^{2} x^{4} + 105 \, {\left(3 \, b c^{8} e^{2} x^{8} + 8 \, b c^{8} d e x^{6} + 6 \, b c^{8} d^{2} x^{4}\right)} \operatorname{arcsec}\left(c x\right) - {\left(45 \, b c^{6} e^{2} x^{6} + 420 \, b c^{4} d^{2} + 448 \, b c^{2} d e + 6 \, {\left(28 \, b c^{6} d e + 9 \, b c^{4} e^{2}\right)} x^{4} + 144 \, b e^{2} + 2 \, {\left(105 \, b c^{6} d^{2} + 112 \, b c^{4} d e + 36 \, b c^{2} e^{2}\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}}{2520 \, c^{8}}"," ",0,"1/2520*(315*a*c^8*e^2*x^8 + 840*a*c^8*d*e*x^6 + 630*a*c^8*d^2*x^4 + 105*(3*b*c^8*e^2*x^8 + 8*b*c^8*d*e*x^6 + 6*b*c^8*d^2*x^4)*arcsec(c*x) - (45*b*c^6*e^2*x^6 + 420*b*c^4*d^2 + 448*b*c^2*d*e + 6*(28*b*c^6*d*e + 9*b*c^4*e^2)*x^4 + 144*b*e^2 + 2*(105*b*c^6*d^2 + 112*b*c^4*d*e + 36*b*c^2*e^2)*x^2)*sqrt(c^2*x^2 - 1))/c^8","A",0
88,1,153,0,1.438289," ","integrate(x*(e*x^2+d)^2*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\frac{15 \, a c^{6} e^{2} x^{6} + 45 \, a c^{6} d e x^{4} + 45 \, a c^{6} d^{2} x^{2} + 15 \, {\left(b c^{6} e^{2} x^{6} + 3 \, b c^{6} d e x^{4} + 3 \, b c^{6} d^{2} x^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(3 \, b c^{4} e^{2} x^{4} + 45 \, b c^{4} d^{2} + 30 \, b c^{2} d e + 8 \, b e^{2} + {\left(15 \, b c^{4} d e + 4 \, b c^{2} e^{2}\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}}{90 \, c^{6}}"," ",0,"1/90*(15*a*c^6*e^2*x^6 + 45*a*c^6*d*e*x^4 + 45*a*c^6*d^2*x^2 + 15*(b*c^6*e^2*x^6 + 3*b*c^6*d*e*x^4 + 3*b*c^6*d^2*x^2)*arcsec(c*x) - (3*b*c^4*e^2*x^4 + 45*b*c^4*d^2 + 30*b*c^2*d*e + 8*b*e^2 + (15*b*c^4*d*e + 4*b*c^2*e^2)*x^2)*sqrt(c^2*x^2 - 1))/c^6","A",0
89,0,0,0,0.446258," ","integrate((e*x^2+d)^2*(a+b*arcsec(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{arcsec}\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)*arcsec(c*x))/x, x)","F",0
90,0,0,0,0.497891," ","integrate((e*x^2+d)^2*(a+b*arcsec(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{arcsec}\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)*arcsec(c*x))/x^3, x)","F",0
91,0,0,0,0.522412," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \operatorname{arcsec}\left(c x\right) + a x^{2}}{e x^{2} + d}, x\right)"," ",0,"integral((b*x^2*arcsec(c*x) + a*x^2)/(e*x^2 + d), x)","F",0
92,0,0,0,0.605269," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x \operatorname{arcsec}\left(c x\right) + a x}{e x^{2} + d}, x\right)"," ",0,"integral((b*x*arcsec(c*x) + a*x)/(e*x^2 + d), x)","F",0
93,0,0,0,0.600169," ","integrate((a+b*arcsec(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arcsec}\left(c x\right) + a}{e x^{2} + d}, x\right)"," ",0,"integral((b*arcsec(c*x) + a)/(e*x^2 + d), x)","F",0
94,0,0,0,0.501977," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arcsec}\left(c x\right) + a}{e x^{3} + d x}, x\right)"," ",0,"integral((b*arcsec(c*x) + a)/(e*x^3 + d*x), x)","F",0
95,0,0,0,0.847971," ","integrate((a+b*arcsec(c*x))/x^2/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arcsec}\left(c x\right) + a}{e x^{4} + d x^{2}}, x\right)"," ",0,"integral((b*arcsec(c*x) + a)/(e*x^4 + d*x^2), x)","F",0
96,0,0,0,0.594178," ","integrate(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{5} \operatorname{arcsec}\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*arcsec(c*x) + a*x^5)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
97,0,0,0,0.844449," ","integrate(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{3} \operatorname{arcsec}\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*arcsec(c*x) + a*x^3)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
98,1,384,0,0.605992," ","integrate(x*(a+b*arcsec(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^{2} e x^{2} - c^{2} d + 2 \, \sqrt{-c^{2} d e - e^{2}} \sqrt{c^{2} x^{2} - 1} - 2 \, e}{e x^{2} + d}\right) + 2 \, {\left(b c^{2} d^{2} + b d e\right)} \operatorname{arcsec}\left(c x\right) - 4 \, {\left(b c^{2} d^{2} + b d e + {\left(b c^{2} d e + b e^{2}\right)} x^{2}\right)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\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}} \sqrt{c^{2} x^{2} - 1}}{c^{2} d + e}\right) + {\left(b c^{2} d^{2} + b d e\right)} \operatorname{arcsec}\left(c x\right) - 2 \, {\left(b c^{2} d^{2} + b d e + {\left(b c^{2} d e + b e^{2}\right)} x^{2}\right)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\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^2*e*x^2 - c^2*d + 2*sqrt(-c^2*d*e - e^2)*sqrt(c^2*x^2 - 1) - 2*e)/(e*x^2 + d)) + 2*(b*c^2*d^2 + b*d*e)*arcsec(c*x) - 4*(b*c^2*d^2 + b*d*e + (b*c^2*d*e + b*e^2)*x^2)*arctan(-c*x + sqrt(c^2*x^2 - 1)))/(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)*sqrt(c^2*x^2 - 1)/(c^2*d + e)) + (b*c^2*d^2 + b*d*e)*arcsec(c*x) - 2*(b*c^2*d^2 + b*d*e + (b*c^2*d*e + b*e^2)*x^2)*arctan(-c*x + sqrt(c^2*x^2 - 1)))/(c^2*d^3*e + d^2*e^2 + (c^2*d^2*e^2 + d*e^3)*x^2)]","A",0
99,0,0,0,0.528179," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arcsec}\left(c x\right) + a}{e^{2} x^{5} + 2 \, d e x^{3} + d^{2} x}, x\right)"," ",0,"integral((b*arcsec(c*x) + a)/(e^2*x^5 + 2*d*e*x^3 + d^2*x), x)","F",0
100,0,0,0,0.646244," ","integrate(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{4} \operatorname{arcsec}\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*arcsec(c*x) + a*x^4)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
101,0,0,0,1.362184," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \operatorname{arcsec}\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*arcsec(c*x) + a*x^2)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
102,0,0,0,0.622780," ","integrate((a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arcsec}\left(c x\right) + a}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}, x\right)"," ",0,"integral((b*arcsec(c*x) + a)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
103,0,0,0,0.771169," ","integrate((a+b*arcsec(c*x))/x^2/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arcsec}\left(c x\right) + a}{e^{2} x^{6} + 2 \, d e x^{4} + d^{2} x^{2}}, x\right)"," ",0,"integral((b*arcsec(c*x) + a)/(e^2*x^6 + 2*d*e*x^4 + d^2*x^2), x)","F",0
104,0,0,0,0.709508," ","integrate(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{5} \operatorname{arcsec}\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*arcsec(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
105,1,1015,0,1.797111," ","integrate(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, a c^{4} d^{4} + 8 \, a c^{2} d^{3} e + 4 \, a d^{2} e^{2} + 8 \, {\left(a c^{4} d^{3} e + 2 \, a c^{2} d^{2} e^{2} + a 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^{2} e x^{2} - c^{2} d + 2 \, \sqrt{-c^{2} d e - e^{2}} \sqrt{c^{2} x^{2} - 1} - 2 \, e}{e x^{2} + d}\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)} \operatorname{arcsec}\left(c x\right) - 8 \, {\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)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) - 2 \, {\left(b c^{2} d^{3} e + b d^{2} e^{2} + {\left(b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}}{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} + 4 \, a c^{2} d^{3} e + 2 \, a d^{2} e^{2} + 4 \, {\left(a c^{4} d^{3} e + 2 \, a c^{2} d^{2} e^{2} + a 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}} \sqrt{c^{2} x^{2} - 1}}{c^{2} d + e}\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)} \operatorname{arcsec}\left(c x\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)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) - {\left(b c^{2} d^{3} e + b d^{2} e^{2} + {\left(b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}}{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 + 8*a*c^2*d^3*e + 4*a*d^2*e^2 + 8*(a*c^4*d^3*e + 2*a*c^2*d^2*e^2 + a*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^2*e*x^2 - c^2*d + 2*sqrt(-c^2*d*e - e^2)*sqrt(c^2*x^2 - 1) - 2*e)/(e*x^2 + d)) + 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)*arcsec(c*x) - 8*(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)*arctan(-c*x + sqrt(c^2*x^2 - 1)) - 2*(b*c^2*d^3*e + b*d^2*e^2 + (b*c^2*d^2*e^2 + b*d*e^3)*x^2)*sqrt(c^2*x^2 - 1))/(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*c^2*d^3*e + 2*a*d^2*e^2 + 4*(a*c^4*d^3*e + 2*a*c^2*d^2*e^2 + a*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)*sqrt(c^2*x^2 - 1)/(c^2*d + e)) + 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)*arcsec(c*x) - 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)*arctan(-c*x + sqrt(c^2*x^2 - 1)) - (b*c^2*d^3*e + b*d^2*e^2 + (b*c^2*d^2*e^2 + b*d*e^3)*x^2)*sqrt(c^2*x^2 - 1))/(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
106,1,888,0,1.888267," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, a c^{4} d^{4} + 8 \, a c^{2} d^{3} e + 4 \, a d^{2} e^{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^{2} e x^{2} - c^{2} d + 2 \, \sqrt{-c^{2} d e - e^{2}} \sqrt{c^{2} x^{2} - 1} - 2 \, e}{e x^{2} + d}\right) + 4 \, {\left(b c^{4} d^{4} + 2 \, b c^{2} d^{3} e + b d^{2} e^{2}\right)} \operatorname{arcsec}\left(c x\right) - 8 \, {\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)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + 2 \, {\left(b c^{2} d^{3} e + b d^{2} e^{2} + {\left(b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}}{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} + 4 \, a c^{2} d^{3} e + 2 \, a d^{2} e^{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}} \sqrt{c^{2} x^{2} - 1}}{c^{2} d + e}\right) + 2 \, {\left(b c^{4} d^{4} + 2 \, b c^{2} d^{3} e + b d^{2} e^{2}\right)} \operatorname{arcsec}\left(c x\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)} \arctan\left(-c x + \sqrt{c^{2} x^{2} - 1}\right) + {\left(b c^{2} d^{3} e + b d^{2} e^{2} + {\left(b c^{2} d^{2} e^{2} + b d e^{3}\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}}{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 + 8*a*c^2*d^3*e + 4*a*d^2*e^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^2*e*x^2 - c^2*d + 2*sqrt(-c^2*d*e - e^2)*sqrt(c^2*x^2 - 1) - 2*e)/(e*x^2 + d)) + 4*(b*c^4*d^4 + 2*b*c^2*d^3*e + b*d^2*e^2)*arcsec(c*x) - 8*(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)*arctan(-c*x + sqrt(c^2*x^2 - 1)) + 2*(b*c^2*d^3*e + b*d^2*e^2 + (b*c^2*d^2*e^2 + b*d*e^3)*x^2)*sqrt(c^2*x^2 - 1))/(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*c^2*d^3*e + 2*a*d^2*e^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)*sqrt(c^2*x^2 - 1)/(c^2*d + e)) + 2*(b*c^4*d^4 + 2*b*c^2*d^3*e + b*d^2*e^2)*arcsec(c*x) - 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)*arctan(-c*x + sqrt(c^2*x^2 - 1)) + (b*c^2*d^3*e + b*d^2*e^2 + (b*c^2*d^2*e^2 + b*d*e^3)*x^2)*sqrt(c^2*x^2 - 1))/(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
107,0,0,0,0.672402," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arcsec}\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*arcsec(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
108,0,0,0,0.657054," ","integrate(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{4} \operatorname{arcsec}\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*arcsec(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
109,0,0,0,1.111787," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \operatorname{arcsec}\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*arcsec(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
110,0,0,0,0.651330," ","integrate((a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arcsec}\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*arcsec(c*x) + a)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
111,1,1701,0,7.030898," ","integrate(x^5*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{128 \, b c^{7} \sqrt{-d} d^{3} \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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\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} + 16 \, {\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)} \operatorname{arcsec}\left(c x\right) - {\left(40 \, b c^{5} e^{3} x^{4} - 41 \, b c^{5} d^{2} e + 38 \, b c^{3} d e^{2} + 75 \, b c e^{3} + 2 \, {\left(11 \, b c^{5} d e^{2} + 25 \, b c^{3} e^{3}\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{6720 \, c^{7} e^{3}}, \frac{256 \, b c^{7} d^{\frac{7}{2}} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\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} + 16 \, {\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)} \operatorname{arcsec}\left(c x\right) - {\left(40 \, b c^{5} e^{3} x^{4} - 41 \, b c^{5} d^{2} e + 38 \, b c^{3} d e^{2} + 75 \, b c e^{3} + 2 \, {\left(11 \, b c^{5} d e^{2} + 25 \, b c^{3} e^{3}\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{6720 \, c^{7} e^{3}}, \frac{64 \, b c^{7} \sqrt{-d} d^{3} \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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\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} + 16 \, {\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)} \operatorname{arcsec}\left(c x\right) - {\left(40 \, b c^{5} e^{3} x^{4} - 41 \, b c^{5} d^{2} e + 38 \, b c^{3} d e^{2} + 75 \, b c e^{3} + 2 \, {\left(11 \, b c^{5} d e^{2} + 25 \, b c^{3} e^{3}\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{3360 \, c^{7} e^{3}}, \frac{128 \, b c^{7} d^{\frac{7}{2}} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\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} + 16 \, {\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)} \operatorname{arcsec}\left(c x\right) - {\left(40 \, b c^{5} e^{3} x^{4} - 41 \, b c^{5} d^{2} e + 38 \, b c^{3} d e^{2} + 75 \, b c e^{3} + 2 \, {\left(11 \, b c^{5} d e^{2} + 25 \, b c^{3} e^{3}\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{3360 \, c^{7} e^{3}}\right]"," ",0,"[1/6720*(128*b*c^7*sqrt(-d)*d^3*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 - 4*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 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 + 16*(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)*arcsec(c*x) - (40*b*c^5*e^3*x^4 - 41*b*c^5*d^2*e + 38*b*c^3*d*e^2 + 75*b*c*e^3 + 2*(11*b*c^5*d*e^2 + 25*b*c^3*e^3)*x^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^7*e^3), 1/6720*(256*b*c^7*d^(7/2)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 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 + 16*(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)*arcsec(c*x) - (40*b*c^5*e^3*x^4 - 41*b*c^5*d^2*e + 38*b*c^3*d*e^2 + 75*b*c*e^3 + 2*(11*b*c^5*d*e^2 + 25*b*c^3*e^3)*x^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^7*e^3), 1/3360*(64*b*c^7*sqrt(-d)*d^3*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 - 4*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 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 + 16*(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)*arcsec(c*x) - (40*b*c^5*e^3*x^4 - 41*b*c^5*d^2*e + 38*b*c^3*d*e^2 + 75*b*c*e^3 + 2*(11*b*c^5*d*e^2 + 25*b*c^3*e^3)*x^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^7*e^3), 1/3360*(128*b*c^7*d^(7/2)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 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 + 16*(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)*arcsec(c*x) - (40*b*c^5*e^3*x^4 - 41*b*c^5*d^2*e + 38*b*c^3*d*e^2 + 75*b*c*e^3 + 2*(11*b*c^5*d*e^2 + 25*b*c^3*e^3)*x^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^7*e^3)]","A",0
112,1,1383,0,4.130048," ","integrate(x^3*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{16 \, b c^{5} \sqrt{-d} d^{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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\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} + 8 \, {\left(3 \, b c^{5} e^{2} x^{4} + b c^{5} d e x^{2} - 2 \, b c^{5} d^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(6 \, b c^{3} e^{2} x^{2} + 7 \, b c^{3} d e + 9 \, b c e^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{480 \, c^{5} e^{2}}, -\frac{32 \, b c^{5} d^{\frac{5}{2}} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\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} + 8 \, {\left(3 \, b c^{5} e^{2} x^{4} + b c^{5} d e x^{2} - 2 \, b c^{5} d^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(6 \, b c^{3} e^{2} x^{2} + 7 \, b c^{3} d e + 9 \, b c e^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{480 \, c^{5} e^{2}}, \frac{8 \, b c^{5} \sqrt{-d} d^{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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\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} + 8 \, {\left(3 \, b c^{5} e^{2} x^{4} + b c^{5} d e x^{2} - 2 \, b c^{5} d^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(6 \, b c^{3} e^{2} x^{2} + 7 \, b c^{3} d e + 9 \, b c e^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{240 \, c^{5} e^{2}}, -\frac{16 \, b c^{5} d^{\frac{5}{2}} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\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} + 8 \, {\left(3 \, b c^{5} e^{2} x^{4} + b c^{5} d e x^{2} - 2 \, b c^{5} d^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(6 \, b c^{3} e^{2} x^{2} + 7 \, b c^{3} d e + 9 \, b c e^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{240 \, c^{5} e^{2}}\right]"," ",0,"[1/480*(16*b*c^5*sqrt(-d)*d^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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 4*(24*a*c^5*e^2*x^4 + 8*a*c^5*d*e*x^2 - 16*a*c^5*d^2 + 8*(3*b*c^5*e^2*x^4 + b*c^5*d*e*x^2 - 2*b*c^5*d^2)*arcsec(c*x) - (6*b*c^3*e^2*x^2 + 7*b*c^3*d*e + 9*b*c*e^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^5*e^2), -1/480*(32*b*c^5*d^(5/2)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) - 4*(24*a*c^5*e^2*x^4 + 8*a*c^5*d*e*x^2 - 16*a*c^5*d^2 + 8*(3*b*c^5*e^2*x^4 + b*c^5*d*e*x^2 - 2*b*c^5*d^2)*arcsec(c*x) - (6*b*c^3*e^2*x^2 + 7*b*c^3*d*e + 9*b*c*e^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^5*e^2), 1/240*(8*b*c^5*sqrt(-d)*d^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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 2*(24*a*c^5*e^2*x^4 + 8*a*c^5*d*e*x^2 - 16*a*c^5*d^2 + 8*(3*b*c^5*e^2*x^4 + b*c^5*d*e*x^2 - 2*b*c^5*d^2)*arcsec(c*x) - (6*b*c^3*e^2*x^2 + 7*b*c^3*d*e + 9*b*c*e^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^5*e^2), -1/240*(16*b*c^5*d^(5/2)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) - 2*(24*a*c^5*e^2*x^4 + 8*a*c^5*d*e*x^2 - 16*a*c^5*d^2 + 8*(3*b*c^5*e^2*x^4 + b*c^5*d*e*x^2 - 2*b*c^5*d^2)*arcsec(c*x) - (6*b*c^3*e^2*x^2 + 7*b*c^3*d*e + 9*b*c*e^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^5*e^2)]","A",0
113,1,1100,0,2.292635," ","integrate(x*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, b c^{3} \sqrt{-d} 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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\right) + 4 \, {\left(2 \, a c^{3} e x^{2} + 2 \, a c^{3} d - \sqrt{c^{2} x^{2} - 1} b c e + 2 \, {\left(b c^{3} e x^{2} + b c^{3} d\right)} \operatorname{arcsec}\left(c x\right)\right)} \sqrt{e x^{2} + d}}{24 \, c^{3} e}, \frac{4 \, b c^{3} d^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\right) + 4 \, {\left(2 \, a c^{3} e x^{2} + 2 \, a c^{3} d - \sqrt{c^{2} x^{2} - 1} b c e + 2 \, {\left(b c^{3} e x^{2} + b c^{3} d\right)} \operatorname{arcsec}\left(c x\right)\right)} \sqrt{e x^{2} + d}}{24 \, c^{3} e}, \frac{b c^{3} \sqrt{-d} 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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(2 \, a c^{3} e x^{2} + 2 \, a c^{3} d - \sqrt{c^{2} x^{2} - 1} b c e + 2 \, {\left(b c^{3} e x^{2} + b c^{3} d\right)} \operatorname{arcsec}\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, c^{3} e}, \frac{2 \, b c^{3} d^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(2 \, a c^{3} e x^{2} + 2 \, a c^{3} d - \sqrt{c^{2} x^{2} - 1} b c e + 2 \, {\left(b c^{3} e x^{2} + b c^{3} d\right)} \operatorname{arcsec}\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, c^{3} e}\right]"," ",0,"[1/24*(2*b*c^3*sqrt(-d)*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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 4*(2*a*c^3*e*x^2 + 2*a*c^3*d - sqrt(c^2*x^2 - 1)*b*c*e + 2*(b*c^3*e*x^2 + b*c^3*d)*arcsec(c*x))*sqrt(e*x^2 + d))/(c^3*e), 1/24*(4*b*c^3*d^(3/2)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 4*(2*a*c^3*e*x^2 + 2*a*c^3*d - sqrt(c^2*x^2 - 1)*b*c*e + 2*(b*c^3*e*x^2 + b*c^3*d)*arcsec(c*x))*sqrt(e*x^2 + d))/(c^3*e), 1/12*(b*c^3*sqrt(-d)*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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 8*d^2)/x^4) + (3*b*c^2*d + b*e)*sqrt(-e)*arctan(1/2*(2*c^2*e*x^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 2*(2*a*c^3*e*x^2 + 2*a*c^3*d - sqrt(c^2*x^2 - 1)*b*c*e + 2*(b*c^3*e*x^2 + b*c^3*d)*arcsec(c*x))*sqrt(e*x^2 + d))/(c^3*e), 1/12*(2*b*c^3*d^(3/2)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 2*(2*a*c^3*e*x^2 + 2*a*c^3*d - sqrt(c^2*x^2 - 1)*b*c*e + 2*(b*c^3*e*x^2 + b*c^3*d)*arcsec(c*x))*sqrt(e*x^2 + d))/(c^3*e)]","A",0
114,0,0,0,0.956071," ","integrate((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{x}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/x, x)","F",0
115,0,0,0,0.742635," ","integrate((a+b*arcsec(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{arcsec}\left(c x\right) + a\right)}}{x^{3}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/x^3, x)","F",0
116,0,0,0,1.001517," ","integrate(x^2*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{2} \operatorname{arcsec}\left(c x\right) + a x^{2}\right)} \sqrt{e x^{2} + d}, x\right)"," ",0,"integral((b*x^2*arcsec(c*x) + a*x^2)*sqrt(e*x^2 + d), x)","F",0
117,0,0,0,0.623792," ","integrate((a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a), x)","F",0
118,0,0,0,0.531157," ","integrate((a+b*arcsec(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{arcsec}\left(c x\right) + a\right)}}{x^{2}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/x^2, x)","F",0
119,0,0,0,1.427069," ","integrate((a+b*arcsec(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{arcsec}\left(c x\right) + a\right)}}{x^{4}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/x^4, x)","F",0
120,0,0,0,0.673375," ","integrate((a+b*arcsec(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{arcsec}\left(c x\right) + a\right)}}{x^{6}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/x^6, x)","F",0
121,1,1701,0,12.021292," ","integrate(x^3*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\left[\frac{96 \, b c^{7} \sqrt{-d} d^{3} \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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\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} + 48 \, {\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)} \operatorname{arcsec}\left(c x\right) - {\left(40 \, b c^{5} e^{3} x^{4} + 57 \, b c^{5} d^{2} e + 164 \, b c^{3} d e^{2} + 75 \, b c e^{3} + 2 \, {\left(53 \, b c^{5} d e^{2} + 25 \, b c^{3} e^{3}\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{6720 \, c^{7} e^{2}}, -\frac{192 \, b c^{7} d^{\frac{7}{2}} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\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} + 48 \, {\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)} \operatorname{arcsec}\left(c x\right) - {\left(40 \, b c^{5} e^{3} x^{4} + 57 \, b c^{5} d^{2} e + 164 \, b c^{3} d e^{2} + 75 \, b c e^{3} + 2 \, {\left(53 \, b c^{5} d e^{2} + 25 \, b c^{3} e^{3}\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{6720 \, c^{7} e^{2}}, \frac{48 \, b c^{7} \sqrt{-d} d^{3} \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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\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} + 48 \, {\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)} \operatorname{arcsec}\left(c x\right) - {\left(40 \, b c^{5} e^{3} x^{4} + 57 \, b c^{5} d^{2} e + 164 \, b c^{3} d e^{2} + 75 \, b c e^{3} + 2 \, {\left(53 \, b c^{5} d e^{2} + 25 \, b c^{3} e^{3}\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{3360 \, c^{7} e^{2}}, -\frac{96 \, b c^{7} d^{\frac{7}{2}} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\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} + 48 \, {\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)} \operatorname{arcsec}\left(c x\right) - {\left(40 \, b c^{5} e^{3} x^{4} + 57 \, b c^{5} d^{2} e + 164 \, b c^{3} d e^{2} + 75 \, b c e^{3} + 2 \, {\left(53 \, b c^{5} d e^{2} + 25 \, b c^{3} e^{3}\right)} x^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{3360 \, c^{7} e^{2}}\right]"," ",0,"[1/6720*(96*b*c^7*sqrt(-d)*d^3*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 + 4*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 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 + 48*(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)*arcsec(c*x) - (40*b*c^5*e^3*x^4 + 57*b*c^5*d^2*e + 164*b*c^3*d*e^2 + 75*b*c*e^3 + 2*(53*b*c^5*d*e^2 + 25*b*c^3*e^3)*x^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^7*e^2), -1/6720*(192*b*c^7*d^(7/2)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) - 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 + 48*(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)*arcsec(c*x) - (40*b*c^5*e^3*x^4 + 57*b*c^5*d^2*e + 164*b*c^3*d*e^2 + 75*b*c*e^3 + 2*(53*b*c^5*d*e^2 + 25*b*c^3*e^3)*x^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^7*e^2), 1/3360*(48*b*c^7*sqrt(-d)*d^3*log(((c^4*d^2 - 6*c^2*d*e + e^2)*x^4 - 8*(c^2*d^2 - d*e)*x^2 + 4*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 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 + 48*(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)*arcsec(c*x) - (40*b*c^5*e^3*x^4 + 57*b*c^5*d^2*e + 164*b*c^3*d*e^2 + 75*b*c*e^3 + 2*(53*b*c^5*d*e^2 + 25*b*c^3*e^3)*x^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^7*e^2), -1/3360*(96*b*c^7*d^(7/2)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) - 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 + 48*(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)*arcsec(c*x) - (40*b*c^5*e^3*x^4 + 57*b*c^5*d^2*e + 164*b*c^3*d*e^2 + 75*b*c*e^3 + 2*(53*b*c^5*d*e^2 + 25*b*c^3*e^3)*x^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^7*e^2)]","A",0
122,1,1377,0,3.165513," ","integrate(x*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","\left[\frac{8 \, b c^{5} \sqrt{-d} d^{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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\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} + 8 \, {\left(b c^{5} e^{2} x^{4} + 2 \, b c^{5} d e x^{2} + b c^{5} d^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(2 \, b c^{3} e^{2} x^{2} + 9 \, b c^{3} d e + 3 \, b c e^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{160 \, c^{5} e}, \frac{16 \, b c^{5} d^{\frac{5}{2}} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\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} + 8 \, {\left(b c^{5} e^{2} x^{4} + 2 \, b c^{5} d e x^{2} + b c^{5} d^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(2 \, b c^{3} e^{2} x^{2} + 9 \, b c^{3} d e + 3 \, b c e^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{160 \, c^{5} e}, \frac{4 \, b c^{5} \sqrt{-d} d^{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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\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} + 8 \, {\left(b c^{5} e^{2} x^{4} + 2 \, b c^{5} d e x^{2} + b c^{5} d^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(2 \, b c^{3} e^{2} x^{2} + 9 \, b c^{3} d e + 3 \, b c e^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{80 \, c^{5} e}, \frac{8 \, b c^{5} d^{\frac{5}{2}} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\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} + 8 \, {\left(b c^{5} e^{2} x^{4} + 2 \, b c^{5} d e x^{2} + b c^{5} d^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(2 \, b c^{3} e^{2} x^{2} + 9 \, b c^{3} d e + 3 \, b c e^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{80 \, c^{5} e}\right]"," ",0,"[1/160*(8*b*c^5*sqrt(-d)*d^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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 4*(8*a*c^5*e^2*x^4 + 16*a*c^5*d*e*x^2 + 8*a*c^5*d^2 + 8*(b*c^5*e^2*x^4 + 2*b*c^5*d*e*x^2 + b*c^5*d^2)*arcsec(c*x) - (2*b*c^3*e^2*x^2 + 9*b*c^3*d*e + 3*b*c*e^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^5*e), 1/160*(16*b*c^5*d^(5/2)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 4*(8*a*c^5*e^2*x^4 + 16*a*c^5*d*e*x^2 + 8*a*c^5*d^2 + 8*(b*c^5*e^2*x^4 + 2*b*c^5*d*e*x^2 + b*c^5*d^2)*arcsec(c*x) - (2*b*c^3*e^2*x^2 + 9*b*c^3*d*e + 3*b*c*e^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^5*e), 1/80*(4*b*c^5*sqrt(-d)*d^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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 2*(8*a*c^5*e^2*x^4 + 16*a*c^5*d*e*x^2 + 8*a*c^5*d^2 + 8*(b*c^5*e^2*x^4 + 2*b*c^5*d*e*x^2 + b*c^5*d^2)*arcsec(c*x) - (2*b*c^3*e^2*x^2 + 9*b*c^3*d*e + 3*b*c*e^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^5*e), 1/80*(8*b*c^5*d^(5/2)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 2*(8*a*c^5*e^2*x^4 + 16*a*c^5*d*e*x^2 + 8*a*c^5*d^2 + 8*(b*c^5*e^2*x^4 + 2*b*c^5*d*e*x^2 + b*c^5*d^2)*arcsec(c*x) - (2*b*c^3*e^2*x^2 + 9*b*c^3*d*e + 3*b*c*e^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^5*e)]","A",0
123,0,0,0,0.593092," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(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{arcsec}\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)*arcsec(c*x))*sqrt(e*x^2 + d)/x, x)","F",0
124,0,0,0,0.693084," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(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{arcsec}\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)*arcsec(c*x))*sqrt(e*x^2 + d)/x^3, x)","F",0
125,0,0,0,0.813043," ","integrate(x^2*(e*x^2+d)^(3/2)*(a+b*arcsec(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{arcsec}\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)*arcsec(c*x))*sqrt(e*x^2 + d), x)","F",0
126,0,0,0,0.775421," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \operatorname{arcsec}\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)*arcsec(c*x))*sqrt(e*x^2 + d), x)","F",0
127,0,0,0,1.038565," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(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{arcsec}\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)*arcsec(c*x))*sqrt(e*x^2 + d)/x^2, x)","F",0
128,0,0,0,0.643884," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(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{arcsec}\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)*arcsec(c*x))*sqrt(e*x^2 + d)/x^4, x)","F",0
129,0,0,0,1.221312," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(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{arcsec}\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)*arcsec(c*x))*sqrt(e*x^2 + d)/x^6, x)","F",0
130,0,0,0,1.148998," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(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{arcsec}\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)*arcsec(c*x))*sqrt(e*x^2 + d)/x^8, x)","F",0
131,1,1385,0,5.854733," ","integrate(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{64 \, b c^{5} \sqrt{-d} d^{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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\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} + 8 \, {\left(3 \, b c^{5} e^{2} x^{4} - 4 \, b c^{5} d e x^{2} + 8 \, b c^{5} d^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(6 \, b c^{3} e^{2} x^{2} - 13 \, b c^{3} d e + 9 \, b c e^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{480 \, c^{5} e^{3}}, \frac{128 \, b c^{5} d^{\frac{5}{2}} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\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} + 8 \, {\left(3 \, b c^{5} e^{2} x^{4} - 4 \, b c^{5} d e x^{2} + 8 \, b c^{5} d^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(6 \, b c^{3} e^{2} x^{2} - 13 \, b c^{3} d e + 9 \, b c e^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{480 \, c^{5} e^{3}}, \frac{32 \, b c^{5} \sqrt{-d} d^{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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\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} + 8 \, {\left(3 \, b c^{5} e^{2} x^{4} - 4 \, b c^{5} d e x^{2} + 8 \, b c^{5} d^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(6 \, b c^{3} e^{2} x^{2} - 13 \, b c^{3} d e + 9 \, b c e^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{240 \, c^{5} e^{3}}, \frac{64 \, b c^{5} d^{\frac{5}{2}} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\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} + 8 \, {\left(3 \, b c^{5} e^{2} x^{4} - 4 \, b c^{5} d e x^{2} + 8 \, b c^{5} d^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(6 \, b c^{3} e^{2} x^{2} - 13 \, b c^{3} d e + 9 \, b c e^{2}\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{240 \, c^{5} e^{3}}\right]"," ",0,"[1/480*(64*b*c^5*sqrt(-d)*d^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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 4*(24*a*c^5*e^2*x^4 - 32*a*c^5*d*e*x^2 + 64*a*c^5*d^2 + 8*(3*b*c^5*e^2*x^4 - 4*b*c^5*d*e*x^2 + 8*b*c^5*d^2)*arcsec(c*x) - (6*b*c^3*e^2*x^2 - 13*b*c^3*d*e + 9*b*c*e^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^5*e^3), 1/480*(128*b*c^5*d^(5/2)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 4*(24*a*c^5*e^2*x^4 - 32*a*c^5*d*e*x^2 + 64*a*c^5*d^2 + 8*(3*b*c^5*e^2*x^4 - 4*b*c^5*d*e*x^2 + 8*b*c^5*d^2)*arcsec(c*x) - (6*b*c^3*e^2*x^2 - 13*b*c^3*d*e + 9*b*c*e^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^5*e^3), 1/240*(32*b*c^5*sqrt(-d)*d^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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 2*(24*a*c^5*e^2*x^4 - 32*a*c^5*d*e*x^2 + 64*a*c^5*d^2 + 8*(3*b*c^5*e^2*x^4 - 4*b*c^5*d*e*x^2 + 8*b*c^5*d^2)*arcsec(c*x) - (6*b*c^3*e^2*x^2 - 13*b*c^3*d*e + 9*b*c*e^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^5*e^3), 1/240*(64*b*c^5*d^(5/2)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 2*(24*a*c^5*e^2*x^4 - 32*a*c^5*d*e*x^2 + 64*a*c^5*d^2 + 8*(3*b*c^5*e^2*x^4 - 4*b*c^5*d*e*x^2 + 8*b*c^5*d^2)*arcsec(c*x) - (6*b*c^3*e^2*x^2 - 13*b*c^3*d*e + 9*b*c*e^2)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^5*e^3)]","A",0
132,1,1111,0,1.400929," ","integrate(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, b c^{3} \sqrt{-d} 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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\right) + 4 \, {\left(2 \, a c^{3} e x^{2} - 4 \, a c^{3} d - \sqrt{c^{2} x^{2} - 1} b c e + 2 \, {\left(b c^{3} e x^{2} - 2 \, b c^{3} d\right)} \operatorname{arcsec}\left(c x\right)\right)} \sqrt{e x^{2} + d}}{24 \, c^{3} e^{2}}, -\frac{8 \, b c^{3} d^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\right) - 4 \, {\left(2 \, a c^{3} e x^{2} - 4 \, a c^{3} d - \sqrt{c^{2} x^{2} - 1} b c e + 2 \, {\left(b c^{3} e x^{2} - 2 \, b c^{3} d\right)} \operatorname{arcsec}\left(c x\right)\right)} \sqrt{e x^{2} + d}}{24 \, c^{3} e^{2}}, \frac{2 \, b c^{3} \sqrt{-d} 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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(2 \, a c^{3} e x^{2} - 4 \, a c^{3} d - \sqrt{c^{2} x^{2} - 1} b c e + 2 \, {\left(b c^{3} e x^{2} - 2 \, b c^{3} d\right)} \operatorname{arcsec}\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, c^{3} e^{2}}, -\frac{4 \, b c^{3} d^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) - 2 \, {\left(2 \, a c^{3} e x^{2} - 4 \, a c^{3} d - \sqrt{c^{2} x^{2} - 1} b c e + 2 \, {\left(b c^{3} e x^{2} - 2 \, b c^{3} d\right)} \operatorname{arcsec}\left(c x\right)\right)} \sqrt{e x^{2} + d}}{12 \, c^{3} e^{2}}\right]"," ",0,"[1/24*(4*b*c^3*sqrt(-d)*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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 4*(2*a*c^3*e*x^2 - 4*a*c^3*d - sqrt(c^2*x^2 - 1)*b*c*e + 2*(b*c^3*e*x^2 - 2*b*c^3*d)*arcsec(c*x))*sqrt(e*x^2 + d))/(c^3*e^2), -1/24*(8*b*c^3*d^(3/2)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) - 4*(2*a*c^3*e*x^2 - 4*a*c^3*d - sqrt(c^2*x^2 - 1)*b*c*e + 2*(b*c^3*e*x^2 - 2*b*c^3*d)*arcsec(c*x))*sqrt(e*x^2 + d))/(c^3*e^2), 1/12*(2*b*c^3*sqrt(-d)*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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 8*d^2)/x^4) - (3*b*c^2*d - b*e)*sqrt(-e)*arctan(1/2*(2*c^2*e*x^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 2*(2*a*c^3*e*x^2 - 4*a*c^3*d - sqrt(c^2*x^2 - 1)*b*c*e + 2*(b*c^3*e*x^2 - 2*b*c^3*d)*arcsec(c*x))*sqrt(e*x^2 + d))/(c^3*e^2), -1/12*(4*b*c^3*d^(3/2)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) - 2*(2*a*c^3*e*x^2 - 4*a*c^3*d - sqrt(c^2*x^2 - 1)*b*c*e + 2*(b*c^3*e*x^2 - 2*b*c^3*d)*arcsec(c*x))*sqrt(e*x^2 + d))/(c^3*e^2)]","A",0
133,1,869,0,0.880229," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 8 \, d^{2}}{x^{4}}\right) + 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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\right) + 4 \, \sqrt{e x^{2} + d} {\left(b c \operatorname{arcsec}\left(c x\right) + a c\right)}}{4 \, c e}, \frac{2 \, b c \sqrt{d} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + 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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\right) + 4 \, \sqrt{e x^{2} + d} {\left(b c \operatorname{arcsec}\left(c x\right) + a c\right)}}{4 \, c e}, \frac{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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 8 \, d^{2}}{x^{4}}\right) + 2 \, b \sqrt{-e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + 4 \, \sqrt{e x^{2} + d} {\left(b c \operatorname{arcsec}\left(c x\right) + a c\right)}}{4 \, c e}, \frac{b c \sqrt{d} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + b \sqrt{-e} \arctan\left(\frac{{\left(2 \, c^{2} e x^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + 2 \, \sqrt{e x^{2} + d} {\left(b c \operatorname{arcsec}\left(c x\right) + a c\right)}}{2 \, c e}\right]"," ",0,"[1/4*(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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 8*d^2)/x^4) + 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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 4*sqrt(e*x^2 + d)*(b*c*arcsec(c*x) + a*c))/(c*e), 1/4*(2*b*c*sqrt(d)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + 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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 4*sqrt(e*x^2 + d)*(b*c*arcsec(c*x) + a*c))/(c*e), 1/4*(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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 8*d^2)/x^4) + 2*b*sqrt(-e)*arctan(1/2*(2*c^2*e*x^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 4*sqrt(e*x^2 + d)*(b*c*arcsec(c*x) + a*c))/(c*e), 1/2*(b*c*sqrt(d)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + b*sqrt(-e)*arctan(1/2*(2*c^2*e*x^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 2*sqrt(e*x^2 + d)*(b*c*arcsec(c*x) + a*c))/(c*e)]","A",0
134,0,0,0,1.365856," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{e x^{3} + d x}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/(e*x^3 + d*x), x)","F",0
135,0,0,0,1.015164," ","integrate((a+b*arcsec(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{arcsec}\left(c x\right) + a\right)}}{e x^{5} + d x^{3}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/(e*x^5 + d*x^3), x)","F",0
136,0,0,0,0.549856," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \operatorname{arcsec}\left(c x\right) + a x^{2}}{\sqrt{e x^{2} + d}}, x\right)"," ",0,"integral((b*x^2*arcsec(c*x) + a*x^2)/sqrt(e*x^2 + d), x)","F",0
137,0,0,0,1.979166," ","integrate((a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arcsec}\left(c x\right) + a}{\sqrt{e x^{2} + d}}, x\right)"," ",0,"integral((b*arcsec(c*x) + a)/sqrt(e*x^2 + d), x)","F",0
138,0,0,0,0.846481," ","integrate((a+b*arcsec(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{arcsec}\left(c x\right) + a\right)}}{e x^{4} + d x^{2}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/(e*x^4 + d*x^2), x)","F",0
139,0,0,0,1.379716," ","integrate((a+b*arcsec(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{arcsec}\left(c x\right) + a\right)}}{e x^{6} + d x^{4}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/(e*x^6 + d*x^4), x)","F",0
140,0,0,0,0.808417," ","integrate((a+b*arcsec(c*x))/x^6/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{e x^{8} + d x^{6}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/(e*x^8 + d*x^6), x)","F",0
141,1,1483,0,1.032575," ","integrate(x^5*(a+b*arcsec(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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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} + 2 \, {\left(b c^{3} e^{2} x^{4} - 4 \, b c^{3} d e x^{2} - 8 \, b c^{3} d^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(b c e^{2} x^{2} + b c d e\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{24 \, {\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{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\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} + 2 \, {\left(b c^{3} e^{2} x^{4} - 4 \, b c^{3} d e x^{2} - 8 \, b c^{3} d^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(b c e^{2} x^{2} + b c d e\right)} \sqrt{c^{2} x^{2} - 1}\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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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} + 2 \, {\left(b c^{3} e^{2} x^{4} - 4 \, b c^{3} d e x^{2} - 8 \, b c^{3} d^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(b c e^{2} x^{2} + b c d e\right)} \sqrt{c^{2} x^{2} - 1}\right)} \sqrt{e x^{2} + d}}{12 \, {\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{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\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} + 2 \, {\left(b c^{3} e^{2} x^{4} - 4 \, b c^{3} d e x^{2} - 8 \, b c^{3} d^{2}\right)} \operatorname{arcsec}\left(c x\right) - {\left(b c e^{2} x^{2} + b c d e\right)} \sqrt{c^{2} x^{2} - 1}\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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) - 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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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 + 2*(b*c^3*e^2*x^4 - 4*b*c^3*d*e*x^2 - 8*b*c^3*d^2)*arcsec(c*x) - (b*c*e^2*x^2 + b*c*d*e)*sqrt(c^2*x^2 - 1))*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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) - 4*(2*a*c^3*e^2*x^4 - 8*a*c^3*d*e*x^2 - 16*a*c^3*d^2 + 2*(b*c^3*e^2*x^4 - 4*b*c^3*d*e*x^2 - 8*b*c^3*d^2)*arcsec(c*x) - (b*c*e^2*x^2 + b*c*d*e)*sqrt(c^2*x^2 - 1))*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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) - 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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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 + 2*(b*c^3*e^2*x^4 - 4*b*c^3*d*e*x^2 - 8*b*c^3*d^2)*arcsec(c*x) - (b*c*e^2*x^2 + b*c*d*e)*sqrt(c^2*x^2 - 1))*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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) - 2*(2*a*c^3*e^2*x^4 - 8*a*c^3*d*e*x^2 - 16*a*c^3*d^2 + 2*(b*c^3*e^2*x^4 - 4*b*c^3*d*e*x^2 - 8*b*c^3*d^2)*arcsec(c*x) - (b*c*e^2*x^2 + b*c*d*e)*sqrt(c^2*x^2 - 1))*sqrt(e*x^2 + d))/(c^3*e^4*x^2 + c^3*d*e^3)]","A",0
142,1,1070,0,1.002773," ","integrate(x^3*(a+b*arcsec(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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 8 \, d^{2}}{x^{4}}\right) + 4 \, {\left(a c e x^{2} + 2 \, a c d + {\left(b c e x^{2} + 2 \, b c d\right)} \operatorname{arcsec}\left(c x\right)\right)} \sqrt{e x^{2} + d}}{4 \, {\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{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\right) + 4 \, {\left(a c e x^{2} + 2 \, a c d + {\left(b c e x^{2} + 2 \, b c d\right)} \operatorname{arcsec}\left(c x\right)\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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 8 \, d^{2}}{x^{4}}\right) + 2 \, {\left(a c e x^{2} + 2 \, a c d + {\left(b c e x^{2} + 2 \, b c d\right)} \operatorname{arcsec}\left(c x\right)\right)} \sqrt{e x^{2} + d}}{2 \, {\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{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\right) + 2 \, {\left(a c e x^{2} + 2 \, a c d + {\left(b c e x^{2} + 2 \, b c d\right)} \operatorname{arcsec}\left(c x\right)\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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 8*d^2)/x^4) + 4*(a*c*e*x^2 + 2*a*c*d + (b*c*e*x^2 + 2*b*c*d)*arcsec(c*x))*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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 4*(a*c*e*x^2 + 2*a*c*d + (b*c*e*x^2 + 2*b*c*d)*arcsec(c*x))*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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 8*d^2)/x^4) + 2*(a*c*e*x^2 + 2*a*c*d + (b*c*e*x^2 + 2*b*c*d)*arcsec(c*x))*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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 2*(a*c*e*x^2 + 2*a*c*d + (b*c*e*x^2 + 2*b*c*d)*arcsec(c*x))*sqrt(e*x^2 + d))/(c*e^3*x^2 + c*d*e^2)]","A",0
143,1,283,0,0.641396," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 8 \, d^{2}}{x^{4}}\right) + 4 \, \sqrt{e x^{2} + d} {\left(b d \operatorname{arcsec}\left(c x\right) + a d\right)}}{4 \, {\left(d e^{2} x^{2} + d^{2} e\right)}}, -\frac{{\left(b e x^{2} + b d\right)} \sqrt{d} \arctan\left(-\frac{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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} {\left(b d \operatorname{arcsec}\left(c x\right) + a d\right)}}{2 \, {\left(d e^{2} x^{2} + d^{2} e\right)}}\right]"," ",0,"[-1/4*((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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 8*d^2)/x^4) + 4*sqrt(e*x^2 + d)*(b*d*arcsec(c*x) + a*d))/(d*e^2*x^2 + d^2*e), -1/2*((b*e*x^2 + b*d)*sqrt(d)*arctan(-1/2*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + 2*sqrt(e*x^2 + d)*(b*d*arcsec(c*x) + a*d))/(d*e^2*x^2 + d^2*e)]","A",0
144,0,0,0,0.608971," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\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*arcsec(c*x) + a)/(e^2*x^5 + 2*d*e*x^3 + d^2*x), x)","F",0
145,0,0,0,0.886698," ","integrate((a+b*arcsec(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{arcsec}\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*arcsec(c*x) + a)/(e^2*x^7 + 2*d*e*x^5 + d^2*x^3), x)","F",0
146,0,0,0,0.581644," ","integrate(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} \operatorname{arcsec}\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*arcsec(c*x) + a*x^4)*sqrt(e*x^2 + d)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
147,0,0,0,1.299420," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} \operatorname{arcsec}\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*arcsec(c*x) + a*x^2)*sqrt(e*x^2 + d)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
148,0,0,0,0.685100," ","integrate((a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\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*arcsec(c*x) + a)/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
149,0,0,0,0.782027," ","integrate((a+b*arcsec(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{arcsec}\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*arcsec(c*x) + a)/(e^2*x^6 + 2*d*e*x^4 + d^2*x^2), x)","F",0
150,0,0,0,1.106726," ","integrate((a+b*arcsec(c*x))/x^4/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{e^{2} x^{8} + 2 \, d e x^{6} + d^{2} x^{4}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/(e^2*x^8 + 2*d*e*x^6 + d^2*x^4), x)","F",0
151,1,2123,0,1.257172," ","integrate(x^5*(a+b*arcsec(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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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(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)} \operatorname{arcsec}\left(c x\right) - {\left(b c d e^{2} x^{2} + b c d^{2} e\right)} \sqrt{c^{2} x^{2} - 1}\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{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{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{3} e x^{2} + c^{3} d - c e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{e} + e^{2}\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(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)} \operatorname{arcsec}\left(c x\right) - {\left(b c d e^{2} x^{2} + b c d^{2} e\right)} \sqrt{c^{2} x^{2} - 1}\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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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(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)} \operatorname{arcsec}\left(c x\right) - {\left(b c d e^{2} x^{2} + b c d^{2} e\right)} \sqrt{c^{2} x^{2} - 1}\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{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{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{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^{2} + c^{2} d - e\right)} \sqrt{c^{2} x^{2} - 1} \sqrt{e x^{2} + d} \sqrt{-e}}{2 \, {\left(c^{3} e^{2} x^{4} - c d e + {\left(c^{3} d e - c e^{2}\right)} x^{2}\right)}}\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(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)} \operatorname{arcsec}\left(c x\right) - {\left(b c d e^{2} x^{2} + b c d^{2} e\right)} \sqrt{c^{2} x^{2} - 1}\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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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 + (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)*arcsec(c*x) - (b*c*d*e^2*x^2 + b*c*d^2*e)*sqrt(c^2*x^2 - 1))*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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^3*e*x^2 + c^3*d - c*e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(e) + e^2) + 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 + (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)*arcsec(c*x) - (b*c*d*e^2*x^2 + b*c*d^2*e)*sqrt(c^2*x^2 - 1))*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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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 + (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)*arcsec(c*x) - (b*c*d*e^2*x^2 + b*c*d^2*e)*sqrt(c^2*x^2 - 1))*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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(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^2 + c^2*d - e)*sqrt(c^2*x^2 - 1)*sqrt(e*x^2 + d)*sqrt(-e)/(c^3*e^2*x^4 - c*d*e + (c^3*d*e - c*e^2)*x^2)) + 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 + (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)*arcsec(c*x) - (b*c*d*e^2*x^2 + b*c*d^2*e)*sqrt(c^2*x^2 - 1))*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
152,1,664,0,0.977112," ","integrate(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[-\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} \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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 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(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)} \operatorname{arcsec}\left(c x\right) - {\left(b d e^{2} x^{2} + b d^{2} e\right)} \sqrt{c^{2} x^{2} - 1}\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{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\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(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)} \operatorname{arcsec}\left(c x\right) - {\left(b d e^{2} x^{2} + b d^{2} e\right)} \sqrt{c^{2} x^{2} - 1}\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*((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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 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 + (2*b*c^2*d^3 + 2*b*d^2*e + 3*(b*c^2*d^2*e + b*d*e^2)*x^2)*arcsec(c*x) - (b*d*e^2*x^2 + b*d^2*e)*sqrt(c^2*x^2 - 1))*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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^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 + (2*b*c^2*d^3 + 2*b*d^2*e + 3*(b*c^2*d^2*e + b*d*e^2)*x^2)*arcsec(c*x) - (b*d*e^2*x^2 + b*d^2*e)*sqrt(c^2*x^2 - 1))*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
153,1,571,0,1.537326," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[-\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} \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 \, \sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{-d} + 8 \, d^{2}}{x^{4}}\right) + 4 \, {\left(a c^{2} d^{3} + a d^{2} e + {\left(b c^{2} d^{3} + b d^{2} e\right)} \operatorname{arcsec}\left(c x\right) + {\left(b d e^{2} x^{2} + b d^{2} e\right)} \sqrt{c^{2} x^{2} - 1}\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{\sqrt{c^{2} x^{2} - 1} {\left({\left(c^{2} d - e\right)} x^{2} - 2 \, d\right)} \sqrt{e x^{2} + d} \sqrt{d}}{2 \, {\left(c^{2} d e x^{4} + {\left(c^{2} d^{2} - d e\right)} x^{2} - d^{2}\right)}}\right) + 2 \, {\left(a c^{2} d^{3} + a d^{2} e + {\left(b c^{2} d^{3} + b d^{2} e\right)} \operatorname{arcsec}\left(c x\right) + {\left(b d e^{2} x^{2} + b d^{2} e\right)} \sqrt{c^{2} x^{2} - 1}\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*((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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(-d) + 8*d^2)/x^4) + 4*(a*c^2*d^3 + a*d^2*e + (b*c^2*d^3 + b*d^2*e)*arcsec(c*x) + (b*d*e^2*x^2 + b*d^2*e)*sqrt(c^2*x^2 - 1))*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*sqrt(c^2*x^2 - 1)*((c^2*d - e)*x^2 - 2*d)*sqrt(e*x^2 + d)*sqrt(d)/(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)) + 2*(a*c^2*d^3 + a*d^2*e + (b*c^2*d^3 + b*d^2*e)*arcsec(c*x) + (b*d*e^2*x^2 + b*d^2*e)*sqrt(c^2*x^2 - 1))*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
154,0,0,0,0.566936," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\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*arcsec(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
155,0,0,0,0.503088," ","integrate((a+b*arcsec(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{arcsec}\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*arcsec(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
156,0,0,0,1.490115," ","integrate(x^6*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{6} \operatorname{arcsec}\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*arcsec(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
157,0,0,0,1.649768," ","integrate(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} \operatorname{arcsec}\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*arcsec(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
158,0,0,0,0.906256," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{2} \operatorname{arcsec}\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*arcsec(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
159,0,0,0,2.144240," ","integrate((a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\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*arcsec(c*x) + a)/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
160,0,0,0,0.806754," ","integrate((a+b*arcsec(c*x))/x^2/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)}}{e^{3} x^{8} + 3 \, d e^{2} x^{6} + 3 \, d^{2} e x^{4} + d^{3} x^{2}}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)/(e^3*x^8 + 3*d*e^2*x^6 + 3*d^2*e*x^4 + d^3*x^2), x)","F",0
161,0,0,0,1.768394," ","integrate((f*x)^m*(e*x^2+d)^3*(a+b*arcsec(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{arcsec}\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)*arcsec(c*x))*(f*x)^m, x)","F",0
162,0,0,0,0.864856," ","integrate((f*x)^m*(e*x^2+d)^2*(a+b*arcsec(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{arcsec}\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)*arcsec(c*x))*(f*x)^m, x)","F",0
163,0,0,0,1.527446," ","integrate((f*x)^m*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \operatorname{arcsec}\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)*arcsec(c*x))*(f*x)^m, x)","F",0
164,0,0,0,0.560812," ","integrate((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}}{e x^{2} + d}, x\right)"," ",0,"integral((b*arcsec(c*x) + a)*(f*x)^m/(e*x^2 + d), x)","F",0
165,0,0,0,0.554981," ","integrate((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \operatorname{arcsec}\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*arcsec(c*x) + a)*(f*x)^m/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
166,0,0,0,0.545961," ","integrate((f*x)^m*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a e x^{2} + a d + {\left(b e x^{2} + b d\right)} \operatorname{arcsec}\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)*arcsec(c*x))*sqrt(e*x^2 + d)*(f*x)^m, x)","F",0
167,0,0,0,1.015256," ","integrate((f*x)^m*(e*x^2+d)^(1/2)*(a+b*arcsec(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}, x\right)"," ",0,"integral(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)*(f*x)^m, x)","F",0
168,0,0,0,0.880548," ","integrate((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}}{\sqrt{e x^{2} + d}}, x\right)"," ",0,"integral((b*arcsec(c*x) + a)*(f*x)^m/sqrt(e*x^2 + d), x)","F",0
169,0,0,0,1.647138," ","integrate((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\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*arcsec(c*x) + a)*(f*x)^m/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
170,-2,0,0,0.000000," ","integrate(x^11*(a+b*arcsec(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> the translation of the FriCAS object sage2 to sage is not yet implemented","F(-2)",0
171,-2,0,0,0.000000," ","integrate(x^7*(a+b*arcsec(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> the translation of the FriCAS object sage2 to sage is not yet implemented","F(-2)",0
172,-2,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> the translation of the FriCAS object sage2 to sage is not yet implemented","F(-2)",0
173,0,0,0,1.766572," ","integrate((a+b*arcsec(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{arcsec}\left(c x\right) + a\right)}}{c^{4} x^{5} - x}, x\right)"," ",0,"integral(-sqrt(-c^4*x^4 + 1)*(b*arcsec(c*x) + a)/(c^4*x^5 - x), x)","F",0
174,0,0,0,1.771537," ","integrate((a+b*arcsec(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{arcsec}\left(c x\right) + a\right)}}{c^{4} x^{9} - x^{5}}, x\right)"," ",0,"integral(-sqrt(-c^4*x^4 + 1)*(b*arcsec(c*x) + a)/(c^4*x^9 - x^5), x)","F",0
