1,1,162,0,0.418267," ","integrate(x^6*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a x^{7} + \frac{1}{672} \, {\left(96 \, x^{7} \operatorname{arcsec}\left(c x\right) - \frac{\frac{2 \, {\left(15 \, {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} - 40 \, {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 33 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right)}}{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} + 3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{6}} + \frac{15 \, \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{6}} - \frac{15 \, \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{6}}}{c}\right)} b"," ",0,"1/7*a*x^7 + 1/672*(96*x^7*arcsec(c*x) - (2*(15*(-1/(c^2*x^2) + 1)^(5/2) - 40*(-1/(c^2*x^2) + 1)^(3/2) + 33*sqrt(-1/(c^2*x^2) + 1))/(c^6*(1/(c^2*x^2) - 1)^3 + 3*c^6*(1/(c^2*x^2) - 1)^2 + 3*c^6*(1/(c^2*x^2) - 1) + c^6) + 15*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^6 - 15*log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^6)/c)*b","A",0
2,1,81,0,0.326451," ","integrate(x^5*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a x^{6} + \frac{1}{90} \, {\left(15 \, x^{6} \operatorname{arcsec}\left(c x\right) - \frac{3 \, c^{4} x^{5} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} + 10 \, c^{2} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 15 \, x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{5}}\right)} b"," ",0,"1/6*a*x^6 + 1/90*(15*x^6*arcsec(c*x) - (3*c^4*x^5*(-1/(c^2*x^2) + 1)^(5/2) + 10*c^2*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 15*x*sqrt(-1/(c^2*x^2) + 1))/c^5)*b","A",0
3,1,131,0,0.309427," ","integrate(x^4*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a x^{5} + \frac{1}{80} \, {\left(16 \, x^{5} \operatorname{arcsec}\left(c x\right) + \frac{\frac{2 \, {\left(3 \, {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 5 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right)}}{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{4}} - \frac{3 \, \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{4}} + \frac{3 \, \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{4}}}{c}\right)} b"," ",0,"1/5*a*x^5 + 1/80*(16*x^5*arcsec(c*x) + (2*(3*(-1/(c^2*x^2) + 1)^(3/2) - 5*sqrt(-1/(c^2*x^2) + 1))/(c^4*(1/(c^2*x^2) - 1)^2 + 2*c^4*(1/(c^2*x^2) - 1) + c^4) - 3*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^4 + 3*log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^4)/c)*b","A",0
4,1,60,0,0.308460," ","integrate(x^3*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{12} \, {\left(3 \, x^{4} \operatorname{arcsec}\left(c x\right) - \frac{c^{2} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 3 \, x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{3}}\right)} b"," ",0,"1/4*a*x^4 + 1/12*(3*x^4*arcsec(c*x) - (c^2*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 3*x*sqrt(-1/(c^2*x^2) + 1))/c^3)*b","A",0
5,1,98,0,0.314128," ","integrate(x^2*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{1}{12} \, {\left(4 \, x^{3} \operatorname{arcsec}\left(c x\right) - \frac{\frac{2 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}} - \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{2}}}{c}\right)} b"," ",0,"1/3*a*x^3 + 1/12*(4*x^3*arcsec(c*x) - (2*sqrt(-1/(c^2*x^2) + 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 - log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^2)/c)*b","A",0
6,1,37,0,0.314358," ","integrate(x*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{1}{2} \, {\left(x^{2} \operatorname{arcsec}\left(c x\right) - \frac{x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c}\right)} b"," ",0,"1/2*a*x^2 + 1/2*(x^2*arcsec(c*x) - x*sqrt(-1/(c^2*x^2) + 1)/c)*b","A",0
7,1,53,0,0.313723," ","integrate(a+b*arcsec(c*x),x, algorithm=""maxima"")","a x + \frac{{\left(2 \, c x \operatorname{arcsec}\left(c x\right) - \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right) + \log\left(-\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)\right)} b}{2 \, c}"," ",0,"a*x + 1/2*(2*c*x*arcsec(c*x) - log(sqrt(-1/(c^2*x^2) + 1) + 1) + log(-sqrt(-1/(c^2*x^2) + 1) + 1))*b/c","A",0
8,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x,x, algorithm=""maxima"")","-{\left(c^{2} \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \log\left(x\right)}{c^{4} x^{3} - c^{2} x}\,{d x} - \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)\right)} b + a \log\left(x\right)"," ",0,"-(c^2*integrate(sqrt(c*x + 1)*sqrt(c*x - 1)*log(x)/(c^4*x^3 - c^2*x), x) - arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x))*b + a*log(x)","F",0
9,1,33,0,0.312738," ","integrate((a+b*arcsec(c*x))/x^2,x, algorithm=""maxima"")","{\left(c \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{\operatorname{arcsec}\left(c x\right)}{x}\right)} b - \frac{a}{x}"," ",0,"(c*sqrt(-1/(c^2*x^2) + 1) - arcsec(c*x)/x)*b - a/x","A",0
10,1,83,0,0.412156," ","integrate((a+b*arcsec(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{4} \, b {\left(\frac{\frac{c^{4} x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} - 1} - c^{3} \arctan\left(c x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right)}{c} + \frac{2 \, \operatorname{arcsec}\left(c x\right)}{x^{2}}\right)} - \frac{a}{2 \, x^{2}}"," ",0,"-1/4*b*((c^4*x*sqrt(-1/(c^2*x^2) + 1)/(c^2*x^2*(1/(c^2*x^2) - 1) - 1) - c^3*arctan(c*x*sqrt(-1/(c^2*x^2) + 1)))/c + 2*arcsec(c*x)/x^2) - 1/2*a/x^2","A",0
11,1,58,0,0.317981," ","integrate((a+b*arcsec(c*x))/x^4,x, algorithm=""maxima"")","-\frac{1}{9} \, b {\left(\frac{c^{4} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 3 \, c^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c} + \frac{3 \, \operatorname{arcsec}\left(c x\right)}{x^{3}}\right)} - \frac{a}{3 \, x^{3}}"," ",0,"-1/9*b*((c^4*(-1/(c^2*x^2) + 1)^(3/2) - 3*c^4*sqrt(-1/(c^2*x^2) + 1))/c + 3*arcsec(c*x)/x^3) - 1/3*a/x^3","A",0
12,1,125,0,0.421851," ","integrate((a+b*arcsec(c*x))/x^5,x, algorithm=""maxima"")","\frac{1}{32} \, b {\left(\frac{3 \, c^{5} \arctan\left(c x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right) + \frac{3 \, c^{8} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 5 \, c^{6} x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{4} x^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} - 2 \, c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + 1}}{c} - \frac{8 \, \operatorname{arcsec}\left(c x\right)}{x^{4}}\right)} - \frac{a}{4 \, x^{4}}"," ",0,"1/32*b*((3*c^5*arctan(c*x*sqrt(-1/(c^2*x^2) + 1)) + (3*c^8*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 5*c^6*x*sqrt(-1/(c^2*x^2) + 1))/(c^4*x^4*(1/(c^2*x^2) - 1)^2 - 2*c^2*x^2*(1/(c^2*x^2) - 1) + 1))/c - 8*arcsec(c*x)/x^4) - 1/4*a/x^4","A",0
13,1,76,0,0.335295," ","integrate((a+b*arcsec(c*x))/x^6,x, algorithm=""maxima"")","\frac{1}{75} \, b {\left(\frac{3 \, c^{6} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} - 10 \, c^{6} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 15 \, c^{6} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c} - \frac{15 \, \operatorname{arcsec}\left(c x\right)}{x^{5}}\right)} - \frac{a}{5 \, x^{5}}"," ",0,"1/75*b*((3*c^6*(-1/(c^2*x^2) + 1)^(5/2) - 10*c^6*(-1/(c^2*x^2) + 1)^(3/2) + 15*c^6*sqrt(-1/(c^2*x^2) + 1))/c - 15*arcsec(c*x)/x^5) - 1/5*a/x^5","A",0
14,1,165,0,0.426090," ","integrate((a+b*arcsec(c*x))/x^7,x, algorithm=""maxima"")","\frac{1}{288} \, b {\left(\frac{15 \, c^{7} \arctan\left(c x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right) - \frac{15 \, c^{12} x^{5} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} + 40 \, c^{10} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 33 \, c^{8} x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{6} x^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} - 3 \, c^{4} x^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 3 \, c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} - 1}}{c} - \frac{48 \, \operatorname{arcsec}\left(c x\right)}{x^{6}}\right)} - \frac{a}{6 \, x^{6}}"," ",0,"1/288*b*((15*c^7*arctan(c*x*sqrt(-1/(c^2*x^2) + 1)) - (15*c^12*x^5*(-1/(c^2*x^2) + 1)^(5/2) + 40*c^10*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 33*c^8*x*sqrt(-1/(c^2*x^2) + 1))/(c^6*x^6*(1/(c^2*x^2) - 1)^3 - 3*c^4*x^4*(1/(c^2*x^2) - 1)^2 + 3*c^2*x^2*(1/(c^2*x^2) - 1) - 1))/c - 48*arcsec(c*x)/x^6) - 1/6*a/x^6","A",0
15,1,163,0,0.687774," ","integrate(x^3*(a+b*arcsec(c*x))^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} x^{4} \operatorname{arcsec}\left(c x\right)^{2} + \frac{1}{4} \, a^{2} x^{4} + \frac{1}{6} \, {\left(3 \, x^{4} \operatorname{arcsec}\left(c x\right) - \frac{c^{2} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 3 \, x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{3}}\right)} a b + \frac{{\left({\left(c^{2} x^{2} + 2 \, \log\left(x^{2}\right)\right)} \sqrt{c x + 1} \sqrt{c x - 1} - 2 \, {\left(c^{4} x^{4} + c^{2} x^{2} - 2\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b^{2}}{12 \, \sqrt{c x + 1} \sqrt{c x - 1} c^{4}}"," ",0,"1/4*b^2*x^4*arcsec(c*x)^2 + 1/4*a^2*x^4 + 1/6*(3*x^4*arcsec(c*x) - (c^2*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 3*x*sqrt(-1/(c^2*x^2) + 1))/c^3)*a*b + 1/12*((c^2*x^2 + 2*log(x^2))*sqrt(c*x + 1)*sqrt(c*x - 1) - 2*(c^4*x^4 + c^2*x^2 - 2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b^2/(sqrt(c*x + 1)*sqrt(c*x - 1)*c^4)","A",0
16,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} x^{3} + \frac{1}{6} \, {\left(4 \, x^{3} \operatorname{arcsec}\left(c x\right) - \frac{\frac{2 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}} - \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{2}}}{c}\right)} a b + \frac{1}{12} \, {\left(4 \, x^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - x^{3} \log\left(c^{2} x^{2}\right)^{2} - 2 \, c^{2} {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)} \log\left(c\right)^{2} + 36 \, c^{2} \int \frac{x^{4} \log\left(c^{2} x^{2}\right)}{3 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) - 72 \, c^{2} \int \frac{x^{4} \log\left(x\right)}{3 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) + 36 \, c^{2} \int \frac{x^{4} \log\left(c^{2} x^{2}\right) \log\left(x\right)}{3 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 36 \, c^{2} \int \frac{x^{4} \log\left(x\right)^{2}}{3 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + 12 \, c^{2} \int \frac{x^{4} \log\left(c^{2} x^{2}\right)}{3 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + 6 \, {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)} \log\left(c\right)^{2} - 36 \, \int \frac{x^{2} \log\left(c^{2} x^{2}\right)}{3 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) + 72 \, \int \frac{x^{2} \log\left(x\right)}{3 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) - 24 \, \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{3 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 36 \, \int \frac{x^{2} \log\left(c^{2} x^{2}\right) \log\left(x\right)}{3 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + 36 \, \int \frac{x^{2} \log\left(x\right)^{2}}{3 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 12 \, \int \frac{x^{2} \log\left(c^{2} x^{2}\right)}{3 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}\right)} b^{2}"," ",0,"1/3*a^2*x^3 + 1/6*(4*x^3*arcsec(c*x) - (2*sqrt(-1/(c^2*x^2) + 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 - log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^2)/c)*a*b + 1/12*(4*x^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - x^3*log(c^2*x^2)^2 - 2*c^2*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5)*log(c)^2 + 36*c^2*integrate(1/3*x^4*log(c^2*x^2)/(c^2*x^2 - 1), x)*log(c) - 72*c^2*integrate(1/3*x^4*log(x)/(c^2*x^2 - 1), x)*log(c) + 36*c^2*integrate(1/3*x^4*log(c^2*x^2)*log(x)/(c^2*x^2 - 1), x) - 36*c^2*integrate(1/3*x^4*log(x)^2/(c^2*x^2 - 1), x) + 12*c^2*integrate(1/3*x^4*log(c^2*x^2)/(c^2*x^2 - 1), x) + 6*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3)*log(c)^2 - 36*integrate(1/3*x^2*log(c^2*x^2)/(c^2*x^2 - 1), x)*log(c) + 72*integrate(1/3*x^2*log(x)/(c^2*x^2 - 1), x)*log(c) - 24*integrate(1/3*sqrt(c*x + 1)*sqrt(c*x - 1)*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^2 - 1), x) - 36*integrate(1/3*x^2*log(c^2*x^2)*log(x)/(c^2*x^2 - 1), x) + 36*integrate(1/3*x^2*log(x)^2/(c^2*x^2 - 1), x) - 12*integrate(1/3*x^2*log(c^2*x^2)/(c^2*x^2 - 1), x))*b^2","F",0
17,1,87,0,0.327650," ","integrate(x*(a+b*arcsec(c*x))^2,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} x^{2} \operatorname{arcsec}\left(c x\right)^{2} + \frac{1}{2} \, a^{2} x^{2} + {\left(x^{2} \operatorname{arcsec}\left(c x\right) - \frac{x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c}\right)} a b - {\left(\frac{x \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \operatorname{arcsec}\left(c x\right)}{c} - \frac{\log\left(x\right)}{c^{2}}\right)} b^{2}"," ",0,"1/2*b^2*x^2*arcsec(c*x)^2 + 1/2*a^2*x^2 + (x^2*arcsec(c*x) - x*sqrt(-1/(c^2*x^2) + 1)/c)*a*b - (x*sqrt(-1/(c^2*x^2) + 1)*arcsec(c*x)/c - log(x)/c^2)*b^2","A",0
18,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(2 \, c^{2} {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)} \log\left(c\right)^{2} - 4 \, c^{2} \int \frac{x^{2} \log\left(c^{2} x^{2}\right)}{c^{2} x^{2} - 1}\,{d x} \log\left(c\right) + 8 \, c^{2} \int \frac{x^{2} \log\left(x\right)}{c^{2} x^{2} - 1}\,{d x} \log\left(c\right) - 4 \, x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - 4 \, c^{2} \int \frac{x^{2} \log\left(c^{2} x^{2}\right) \log\left(x\right)}{c^{2} x^{2} - 1}\,{d x} + 4 \, c^{2} \int \frac{x^{2} \log\left(x\right)^{2}}{c^{2} x^{2} - 1}\,{d x} - 4 \, c^{2} \int \frac{x^{2} \log\left(c^{2} x^{2}\right)}{c^{2} x^{2} - 1}\,{d x} + x \log\left(c^{2} x^{2}\right)^{2} + 2 \, {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} \log\left(c\right)^{2} + 4 \, \int \frac{\log\left(c^{2} x^{2}\right)}{c^{2} x^{2} - 1}\,{d x} \log\left(c\right) - 8 \, \int \frac{\log\left(x\right)}{c^{2} x^{2} - 1}\,{d x} \log\left(c\right) + 8 \, \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{2} x^{2} - 1}\,{d x} + 4 \, \int \frac{\log\left(c^{2} x^{2}\right) \log\left(x\right)}{c^{2} x^{2} - 1}\,{d x} - 4 \, \int \frac{\log\left(x\right)^{2}}{c^{2} x^{2} - 1}\,{d x} + 4 \, \int \frac{\log\left(c^{2} x^{2}\right)}{c^{2} x^{2} - 1}\,{d x}\right)} b^{2} + a^{2} x + \frac{{\left(2 \, c x \operatorname{arcsec}\left(c x\right) - \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right) + \log\left(-\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)\right)} a b}{c}"," ",0,"-1/4*(2*c^2*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3)*log(c)^2 - 4*c^2*integrate(x^2*log(c^2*x^2)/(c^2*x^2 - 1), x)*log(c) + 8*c^2*integrate(x^2*log(x)/(c^2*x^2 - 1), x)*log(c) - 4*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - 4*c^2*integrate(x^2*log(c^2*x^2)*log(x)/(c^2*x^2 - 1), x) + 4*c^2*integrate(x^2*log(x)^2/(c^2*x^2 - 1), x) - 4*c^2*integrate(x^2*log(c^2*x^2)/(c^2*x^2 - 1), x) + x*log(c^2*x^2)^2 + 2*(log(c*x + 1)/c - log(c*x - 1)/c)*log(c)^2 + 4*integrate(log(c^2*x^2)/(c^2*x^2 - 1), x)*log(c) - 8*integrate(log(x)/(c^2*x^2 - 1), x)*log(c) + 8*integrate(sqrt(c*x + 1)*sqrt(c*x - 1)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^2 - 1), x) + 4*integrate(log(c^2*x^2)*log(x)/(c^2*x^2 - 1), x) - 4*integrate(log(x)^2/(c^2*x^2 - 1), x) + 4*integrate(log(c^2*x^2)/(c^2*x^2 - 1), x))*b^2 + a^2*x + (2*c*x*arcsec(c*x) - log(sqrt(-1/(c^2*x^2) + 1) + 1) + log(-sqrt(-1/(c^2*x^2) + 1) + 1))*a*b/c","F",0
19,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))^2/x,x, algorithm=""maxima"")","-\frac{1}{2} \, b^{2} c^{2} {\left(\frac{\log\left(c x + 1\right)}{c^{2}} + \frac{\log\left(c x - 1\right)}{c^{2}}\right)} \log\left(c\right)^{2} + b^{2} c^{2} \int \frac{x^{2} \log\left(c^{2} x^{2}\right)}{c^{2} x^{3} - x}\,{d x} \log\left(c\right) - 2 \, b^{2} c^{2} \int \frac{x^{2} \log\left(x\right)}{c^{2} x^{3} - x}\,{d x} \log\left(c\right) + 2 \, b^{2} c^{2} \int \frac{x^{2} \log\left(c^{2} x^{2}\right) \log\left(x\right)}{c^{2} x^{3} - x}\,{d x} - b^{2} c^{2} \int \frac{x^{2} \log\left(x\right)^{2}}{c^{2} x^{3} - x}\,{d x} + 2 \, a b c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{2} x^{3} - x}\,{d x} + \frac{1}{2} \, b^{2} {\left(\log\left(c x + 1\right) + \log\left(c x - 1\right) - 2 \, \log\left(x\right)\right)} \log\left(c\right)^{2} + b^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} \log\left(x\right) - \frac{1}{4} \, b^{2} \log\left(c^{2} x^{2}\right)^{2} \log\left(x\right) - b^{2} \int \frac{\log\left(c^{2} x^{2}\right)}{c^{2} x^{3} - x}\,{d x} \log\left(c\right) + 2 \, b^{2} \int \frac{\log\left(x\right)}{c^{2} x^{3} - x}\,{d x} \log\left(c\right) - 2 \, b^{2} \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)}{c^{2} x^{3} - x}\,{d x} - 2 \, b^{2} \int \frac{\log\left(c^{2} x^{2}\right) \log\left(x\right)}{c^{2} x^{3} - x}\,{d x} + b^{2} \int \frac{\log\left(x\right)^{2}}{c^{2} x^{3} - x}\,{d x} - 2 \, a b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{2} x^{3} - x}\,{d x} + a^{2} \log\left(x\right)"," ",0,"-1/2*b^2*c^2*(log(c*x + 1)/c^2 + log(c*x - 1)/c^2)*log(c)^2 + b^2*c^2*integrate(x^2*log(c^2*x^2)/(c^2*x^3 - x), x)*log(c) - 2*b^2*c^2*integrate(x^2*log(x)/(c^2*x^3 - x), x)*log(c) + 2*b^2*c^2*integrate(x^2*log(c^2*x^2)*log(x)/(c^2*x^3 - x), x) - b^2*c^2*integrate(x^2*log(x)^2/(c^2*x^3 - x), x) + 2*a*b*c^2*integrate(x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^3 - x), x) + 1/2*b^2*(log(c*x + 1) + log(c*x - 1) - 2*log(x))*log(c)^2 + b^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2*log(x) - 1/4*b^2*log(c^2*x^2)^2*log(x) - b^2*integrate(log(c^2*x^2)/(c^2*x^3 - x), x)*log(c) + 2*b^2*integrate(log(x)/(c^2*x^3 - x), x)*log(c) - 2*b^2*integrate(sqrt(c*x + 1)*sqrt(c*x - 1)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)/(c^2*x^3 - x), x) - 2*b^2*integrate(log(c^2*x^2)*log(x)/(c^2*x^3 - x), x) + b^2*integrate(log(x)^2/(c^2*x^3 - x), x) - 2*a*b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^3 - x), x) + a^2*log(x)","F",0
20,1,78,0,0.328156," ","integrate((a+b*arcsec(c*x))^2/x^2,x, algorithm=""maxima"")","2 \, {\left(c \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{\operatorname{arcsec}\left(c x\right)}{x}\right)} a b + 2 \, {\left(c \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \operatorname{arcsec}\left(c x\right) + \frac{1}{x}\right)} b^{2} - \frac{b^{2} \operatorname{arcsec}\left(c x\right)^{2}}{x} - \frac{a^{2}}{x}"," ",0,"2*(c*sqrt(-1/(c^2*x^2) + 1) - arcsec(c*x)/x)*a*b + 2*(c*sqrt(-1/(c^2*x^2) + 1)*arcsec(c*x) + 1/x)*b^2 - b^2*arcsec(c*x)^2/x - a^2/x","A",0
21,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))^2/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, a b {\left(\frac{\frac{c^{4} x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} - 1} - c^{3} \arctan\left(c x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right)}{c} + \frac{2 \, \operatorname{arcsec}\left(c x\right)}{x^{2}}\right)} - \frac{\frac{1}{3} \, {\left(2 \, {\left(6 \, c^{2} {\left(\log\left(c x + 1\right) + \log\left(c x - 1\right) - 2 \, \log\left(x\right)\right)} \log\left(c\right)^{2} + 4 \, c^{2} \log\left(x\right)^{3} - 6 \, {\left({\left(\log\left(c x + 1\right) + \log\left(c x - 1\right) - 2 \, \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) - 2 \, \log\left(c x - 1\right) \log\left(x\right) + 2 \, \log\left(-c x + 1\right) \log\left(x\right) + 2 \, \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) + 2 \, {\rm Li}_2\left(-c x\right)\right)} c^{2} \log\left(c\right) + 12 \, {\left({\left(\log\left(c x + 1\right) + \log\left(c x - 1\right) - 2 \, \log\left(x\right)\right)} \log\left(x\right) - \log\left(c x - 1\right) \log\left(x\right) + \log\left(-c x + 1\right) \log\left(x\right) + \log\left(x\right)^{2} + {\rm Li}_2\left(c x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} \log\left(c\right) + 12 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} \log\left(c\right) + 12 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} \log\left(c\right) + 2 \, {\left({\left(3 i \, \pi - 6 \, \log\left(c\right)\right)} \log\left(x\right)^{2} - 6 \, \log\left(c x + 1\right) \log\left(x\right)^{2} - 3 \, \log\left(-c x + 1\right) \log\left(x\right)^{2} - 2 \, \log\left(x\right)^{3} + 6 \, {\left(\log\left(c\right) \log\left(x\right) + \log\left(x\right)^{2}\right)} \log\left(c x + 1\right) + 3 \, {\left(2 \, \log\left(c\right) \log\left(x\right) + \log\left(x\right)^{2}\right)} \log\left(c x - 1\right) - 6 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} \log\left(c\right) - 6 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} \log\left(c\right) - 3 \, {\left({\left(\log\left(c x + 1\right) + \log\left(c x - 1\right) - 2 \, \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) - 2 \, \log\left(c x - 1\right) \log\left(x\right) + 2 \, \log\left(-c x + 1\right) \log\left(x\right) + 2 \, \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) + 2 \, {\rm Li}_2\left(-c x\right)\right)} \log\left(x\right) - 6 \, {\rm Li}_2\left(c x\right) \log\left(x\right) - 6 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) + 12 \, {\rm Li}_{3}(c x) + 12 \, {\rm Li}_{3}(-c x)\right)} c^{2} + 2 \, {\left(3 \, \log\left(c x + 1\right) \log\left(x\right)^{2} + 3 \, \log\left(-c x + 1\right) \log\left(x\right)^{2} - 2 \, \log\left(x\right)^{3} + 6 \, {\rm Li}_2\left(c x\right) \log\left(x\right) + 6 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) - 6 \, {\rm Li}_{3}(c x) - 6 \, {\rm Li}_{3}(-c x)\right)} c^{2} + 6 \, {\left(\log\left(c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(-c x)\right)} c^{2} + 6 \, {\left(\log\left(-c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(c x)\right)} c^{2} + 3 \, {\left({\left(\log\left(c x + 1\right) + \log\left(c x - 1\right) - 2 \, \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) - 2 \, \log\left(c x - 1\right) \log\left(x\right) + 2 \, \log\left(-c x + 1\right) \log\left(x\right) + 2 \, \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) + 2 \, {\rm Li}_2\left(-c x\right)\right)} c^{2} - 6 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} - 6 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} - 6 \, {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(c\right)^{2} - 3 \, {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(c^{2} x^{2}\right) + 6 \, {\left(2 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} + 2 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} + {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(c^{2} x^{2}\right) - \frac{2 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right) + 2 \, c^{2} x^{2} \log\left(c x - 1\right) \log\left(x\right) - 2 \, c^{2} x^{2} \log\left(x\right)^{2} - 1}{x^{2}}\right)} \log\left(c\right) - 6 \, {\left(2 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} + 2 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} + 2 \, {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(x\right) - \frac{2 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right) + 2 \, c^{2} x^{2} \log\left(c x - 1\right) \log\left(x\right) - 2 \, c^{2} x^{2} \log\left(x\right)^{2} - 1}{x^{2}}\right)} \log\left(c\right) + 6 \, {\left(2 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} + 2 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} + {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(c^{2} x^{2}\right) - \frac{2 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right) + 2 \, c^{2} x^{2} \log\left(c x - 1\right) \log\left(x\right) - 2 \, c^{2} x^{2} \log\left(x\right)^{2} - 1}{x^{2}}\right)} \log\left(x\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} \log\left(-c x + 1\right) \log\left(x\right)^{2} - 2 \, c^{2} x^{2} \log\left(x\right)^{3} + 6 \, c^{2} x^{2} {\rm Li}_2\left(c x\right) \log\left(x\right) + 6 \, c^{2} x^{2} {\rm Li}_2\left(-c x\right) \log\left(x\right) - 3 \, {\left(-i \, \pi c^{2} + 2 \, c^{2} \log\left(c\right)\right)} x^{2} \log\left(x\right)^{2} + 6 \, {\left(c^{2} x^{2} \log\left(c\right) \log\left(x\right) + c^{2} x^{2} \log\left(x\right)^{2}\right)} \log\left(c x + 1\right) + 3 \, {\left(2 \, c^{2} x^{2} \log\left(c\right) \log\left(x\right) + c^{2} x^{2} \log\left(x\right)^{2}\right)} \log\left(c x - 1\right) - 3 \, \log\left(c\right) - 3 \, \log\left(x\right) - 3\right)}}{x^{2}} + \frac{3 \, {\left(2 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right) + 2 \, c^{2} x^{2} \log\left(c x - 1\right) \log\left(x\right) - 2 \, c^{2} x^{2} \log\left(x\right)^{2} - 1\right)}}{x^{2}} - \frac{3 \, {\left(2 \, \log\left(x\right)^{2} + 2 \, \log\left(x\right) + 1\right)}}{x^{2}} - 12 \, \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{2} x^{5} - x^{3}}\,{d x}\right)} x^{2} + 12 \, \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - 3 \, \log\left(c^{2} x^{2}\right)^{2}\right)} b^{2}}{8 \, x^{2}} - \frac{a^{2}}{2 \, x^{2}}"," ",0,"-1/2*a*b*((c^4*x*sqrt(-1/(c^2*x^2) + 1)/(c^2*x^2*(1/(c^2*x^2) - 1) - 1) - c^3*arctan(c*x*sqrt(-1/(c^2*x^2) + 1)))/c + 2*arcsec(c*x)/x^2) - 1/8*(4*(c^2*(log(c*x + 1) + log(c*x - 1) - 2*log(x))*log(c)^2 - 4*c^2*integrate(1/2*x^2*log(c^2*x^2)/(c^2*x^5 - x^3), x)*log(c) + 8*c^2*integrate(1/2*x^2*log(x)/(c^2*x^5 - x^3), x)*log(c) - 4*c^2*integrate(1/2*x^2*log(c^2*x^2)*log(x)/(c^2*x^5 - x^3), x) + 4*c^2*integrate(1/2*x^2*log(x)^2/(c^2*x^5 - x^3), x) + 2*c^2*integrate(1/2*x^2*log(c^2*x^2)/(c^2*x^5 - x^3), x) - (c^2*log(c*x + 1) + c^2*log(c*x - 1) - 2*c^2*log(x) + 1/x^2)*log(c)^2 + 4*integrate(1/2*log(c^2*x^2)/(c^2*x^5 - x^3), x)*log(c) - 8*integrate(1/2*log(x)/(c^2*x^5 - x^3), x)*log(c) - 4*integrate(1/2*sqrt(c*x + 1)*sqrt(c*x - 1)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^5 - x^3), x) + 4*integrate(1/2*log(c^2*x^2)*log(x)/(c^2*x^5 - x^3), x) - 4*integrate(1/2*log(x)^2/(c^2*x^5 - x^3), x) - 2*integrate(1/2*log(c^2*x^2)/(c^2*x^5 - x^3), x))*x^2 + 4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - log(c^2*x^2)^2)*b^2/x^2 - 1/2*a^2/x^2","F",0
22,1,164,0,0.704250," ","integrate((a+b*arcsec(c*x))^2/x^4,x, algorithm=""maxima"")","-\frac{2}{9} \, a b {\left(\frac{c^{4} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 3 \, c^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c} + \frac{3 \, \operatorname{arcsec}\left(c x\right)}{x^{3}}\right)} - \frac{b^{2} \operatorname{arcsec}\left(c x\right)^{2}}{3 \, x^{3}} - \frac{a^{2}}{3 \, x^{3}} + \frac{2 \, {\left({\left(6 \, c^{3} x^{2} + c\right)} \sqrt{c x + 1} \sqrt{c x - 1} + 3 \, {\left(2 \, c^{5} x^{4} - c^{3} x^{2} - c\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b^{2}}{27 \, \sqrt{c x + 1} \sqrt{c x - 1} c x^{3}}"," ",0,"-2/9*a*b*((c^4*(-1/(c^2*x^2) + 1)^(3/2) - 3*c^4*sqrt(-1/(c^2*x^2) + 1))/c + 3*arcsec(c*x)/x^3) - 1/3*b^2*arcsec(c*x)^2/x^3 - 1/3*a^2/x^3 + 2/27*((6*c^3*x^2 + c)*sqrt(c*x + 1)*sqrt(c*x - 1) + 3*(2*c^5*x^4 - c^3*x^2 - c)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b^2/(sqrt(c*x + 1)*sqrt(c*x - 1)*c*x^3)","A",0
23,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))^2/x^5,x, algorithm=""maxima"")","\frac{1}{16} \, a b {\left(\frac{3 \, c^{5} \arctan\left(c x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right) + \frac{3 \, c^{8} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 5 \, c^{6} x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{4} x^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} - 2 \, c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + 1}}{c} - \frac{8 \, \operatorname{arcsec}\left(c x\right)}{x^{4}}\right)} - \frac{\frac{1}{6} \, {\left({\left(32 \, c^{4} \log\left(x\right)^{3} + 96 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{4} \log\left(c\right) + 96 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{4} \log\left(c\right) + 48 \, {\left(\log\left(c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(-c x)\right)} c^{4} + 48 \, {\left(\log\left(-c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(c x)\right)} c^{4} - 24 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{4} - 24 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{4} + 48 \, {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} c^{2} \log\left(c\right)^{2} - 48 \, {\left(2 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} + 2 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} + {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(c^{2} x^{2}\right) - \frac{2 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right) + 2 \, c^{2} x^{2} \log\left(c x - 1\right) \log\left(x\right) - 2 \, c^{2} x^{2} \log\left(x\right)^{2} - 1}{x^{2}}\right)} c^{2} \log\left(c\right) + 48 \, {\left(2 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} + 2 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} + 2 \, {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(x\right) - \frac{2 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right) + 2 \, c^{2} x^{2} \log\left(c x - 1\right) \log\left(x\right) - 2 \, c^{2} x^{2} \log\left(x\right)^{2} - 1}{x^{2}}\right)} c^{2} \log\left(c\right) - 8 \, {\left(4 \, c^{2} \log\left(x\right)^{3} - 6 \, {\left(\log\left(c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(-c x)\right)} c^{2} - 6 \, {\left(\log\left(-c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(c x)\right)} c^{2} - \frac{3 \, {\left(2 \, \log\left(x\right)^{2} + 2 \, \log\left(x\right) + 1\right)}}{x^{2}}\right)} c^{2} - 16 \, {\left(6 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} \log\left(c\right) + 6 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} \log\left(c\right) + 6 \, {\left(\log\left(c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(-c x)\right)} c^{2} + 6 \, {\left(\log\left(-c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(c x)\right)} c^{2} + 3 \, {\left(2 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} + 2 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} + {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(c^{2} x^{2}\right) - \frac{2 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right) + 2 \, c^{2} x^{2} \log\left(c x - 1\right) \log\left(x\right) - 2 \, c^{2} x^{2} \log\left(x\right)^{2} - 1}{x^{2}}\right)} \log\left(x\right) - \frac{3 \, c^{2} x^{2} \log\left(-c x + 1\right) \log\left(x\right)^{2} - 2 \, c^{2} x^{2} \log\left(x\right)^{3} + 6 \, c^{2} x^{2} {\rm Li}_2\left(c x\right) \log\left(x\right) + 6 \, c^{2} x^{2} {\rm Li}_2\left(-c x\right) \log\left(x\right) - 3 \, {\left(-i \, \pi c^{2} + 2 \, c^{2} \log\left(c\right)\right)} x^{2} \log\left(x\right)^{2} + 6 \, {\left(c^{2} x^{2} \log\left(c\right) \log\left(x\right) + c^{2} x^{2} \log\left(x\right)^{2}\right)} \log\left(c x + 1\right) + 3 \, {\left(2 \, c^{2} x^{2} \log\left(c\right) \log\left(x\right) + c^{2} x^{2} \log\left(x\right)^{2}\right)} \log\left(c x - 1\right) - 3 \, \log\left(c\right) - 3 \, \log\left(x\right) - 3}{x^{2}}\right)} c^{2} + 12 \, {\left(2 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} + 2 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} + {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(c^{2} x^{2}\right) - \frac{2 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right) + 2 \, c^{2} x^{2} \log\left(c x - 1\right) \log\left(x\right) - 2 \, c^{2} x^{2} \log\left(x\right)^{2} - 1}{x^{2}}\right)} c^{2} - 24 \, {\left(2 \, c^{4} \log\left(c x + 1\right) + 2 \, c^{4} \log\left(c x - 1\right) - 4 \, c^{4} \log\left(x\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} \log\left(c\right)^{2} - 6 \, {\left(2 \, c^{4} \log\left(c x + 1\right) + 2 \, c^{4} \log\left(c x - 1\right) - 4 \, c^{4} \log\left(x\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} \log\left(c^{2} x^{2}\right) + 12 \, {\left(8 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{4} + 8 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{4} + 2 \, {\left(2 \, c^{4} \log\left(c x + 1\right) + 2 \, c^{4} \log\left(c x - 1\right) - 4 \, c^{4} \log\left(x\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} \log\left(c^{2} x^{2}\right) - \frac{8 \, c^{4} x^{4} \log\left(c x + 1\right) \log\left(x\right) + 8 \, c^{4} x^{4} \log\left(c x - 1\right) \log\left(x\right) - 8 \, c^{4} x^{4} \log\left(x\right)^{2} - 4 \, c^{2} x^{2} - 1}{x^{4}}\right)} \log\left(c\right) - 12 \, {\left(8 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{4} + 8 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{4} + 4 \, {\left(2 \, c^{4} \log\left(c x + 1\right) + 2 \, c^{4} \log\left(c x - 1\right) - 4 \, c^{4} \log\left(x\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} \log\left(x\right) - \frac{8 \, c^{4} x^{4} \log\left(c x + 1\right) \log\left(x\right) + 8 \, c^{4} x^{4} \log\left(c x - 1\right) \log\left(x\right) - 8 \, c^{4} x^{4} \log\left(x\right)^{2} - 4 \, c^{2} x^{2} - 1}{x^{4}}\right)} \log\left(c\right) + 12 \, {\left(8 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{4} + 8 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{4} + 2 \, {\left(2 \, c^{4} \log\left(c x + 1\right) + 2 \, c^{4} \log\left(c x - 1\right) - 4 \, c^{4} \log\left(x\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} \log\left(c^{2} x^{2}\right) - \frac{8 \, c^{4} x^{4} \log\left(c x + 1\right) \log\left(x\right) + 8 \, c^{4} x^{4} \log\left(c x - 1\right) \log\left(x\right) - 8 \, c^{4} x^{4} \log\left(x\right)^{2} - 4 \, c^{2} x^{2} - 1}{x^{4}}\right)} \log\left(x\right) - \frac{24 \, {\left(2 \, c^{2} \log\left(x\right)^{2} + 2 \, c^{2} \log\left(x\right) + c^{2}\right)}}{x^{2}} - \frac{2 \, {\left(24 \, c^{4} x^{4} \log\left(-c x + 1\right) \log\left(x\right)^{2} - 16 \, c^{4} x^{4} \log\left(x\right)^{3} + 48 \, c^{4} x^{4} {\rm Li}_2\left(c x\right) \log\left(x\right) + 48 \, c^{4} x^{4} {\rm Li}_2\left(-c x\right) \log\left(x\right) - 24 \, {\left(-i \, \pi c^{4} + 2 \, c^{4} \log\left(c\right)\right)} x^{4} \log\left(x\right)^{2} - 24 \, {\left(c^{2} \log\left(c\right) + c^{2}\right)} x^{2} + 48 \, {\left(c^{4} x^{4} \log\left(c\right) \log\left(x\right) + c^{4} x^{4} \log\left(x\right)^{2}\right)} \log\left(c x + 1\right) + 24 \, {\left(2 \, c^{4} x^{4} \log\left(c\right) \log\left(x\right) + c^{4} x^{4} \log\left(x\right)^{2}\right)} \log\left(c x - 1\right) - 6 \, {\left(4 \, c^{2} x^{2} + 1\right)} \log\left(x\right) - 6 \, \log\left(c\right) - 3\right)}}{x^{4}} + \frac{3 \, {\left(8 \, c^{4} x^{4} \log\left(c x + 1\right) \log\left(x\right) + 8 \, c^{4} x^{4} \log\left(c x - 1\right) \log\left(x\right) - 8 \, c^{4} x^{4} \log\left(x\right)^{2} - 4 \, c^{2} x^{2} - 1\right)}}{x^{4}} - \frac{3 \, {\left(8 \, \log\left(x\right)^{2} + 4 \, \log\left(x\right) + 1\right)}}{x^{4}} - 48 \, \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{2} x^{7} - x^{5}}\,{d x}\right)} x^{4} + 24 \, \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - 6 \, \log\left(c^{2} x^{2}\right)^{2}\right)} b^{2}}{16 \, x^{4}} - \frac{a^{2}}{4 \, x^{4}}"," ",0,"1/16*a*b*((3*c^5*arctan(c*x*sqrt(-1/(c^2*x^2) + 1)) + (3*c^8*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 5*c^6*x*sqrt(-1/(c^2*x^2) + 1))/(c^4*x^4*(1/(c^2*x^2) - 1)^2 - 2*c^2*x^2*(1/(c^2*x^2) - 1) + 1))/c - 8*arcsec(c*x)/x^4) - 1/16*(4*(2*(c^2*log(c*x + 1) + c^2*log(c*x - 1) - 2*c^2*log(x) + 1/x^2)*c^2*log(c)^2 - 16*c^2*integrate(1/4*x^2*log(c^2*x^2)/(c^2*x^7 - x^5), x)*log(c) + 32*c^2*integrate(1/4*x^2*log(x)/(c^2*x^7 - x^5), x)*log(c) - 16*c^2*integrate(1/4*x^2*log(c^2*x^2)*log(x)/(c^2*x^7 - x^5), x) + 16*c^2*integrate(1/4*x^2*log(x)^2/(c^2*x^7 - x^5), x) + 4*c^2*integrate(1/4*x^2*log(c^2*x^2)/(c^2*x^7 - x^5), x) - (2*c^4*log(c*x + 1) + 2*c^4*log(c*x - 1) - 4*c^4*log(x) + (2*c^2*x^2 + 1)/x^4)*log(c)^2 + 16*integrate(1/4*log(c^2*x^2)/(c^2*x^7 - x^5), x)*log(c) - 32*integrate(1/4*log(x)/(c^2*x^7 - x^5), x)*log(c) - 8*integrate(1/4*sqrt(c*x + 1)*sqrt(c*x - 1)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^7 - x^5), x) + 16*integrate(1/4*log(c^2*x^2)*log(x)/(c^2*x^7 - x^5), x) - 16*integrate(1/4*log(x)^2/(c^2*x^7 - x^5), x) - 4*integrate(1/4*log(c^2*x^2)/(c^2*x^7 - x^5), x))*x^4 + 4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - log(c^2*x^2)^2)*b^2/x^4 - 1/4*a^2/x^4","F",0
24,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))^3,x, algorithm=""maxima"")","\frac{3}{4} \, a b^{2} x^{4} \operatorname{arcsec}\left(c x\right)^{2} + \frac{1}{4} \, a^{3} x^{4} + \frac{1}{4} \, {\left(3 \, x^{4} \operatorname{arcsec}\left(c x\right) - \frac{c^{2} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 3 \, x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{3}}\right)} a^{2} b + \frac{1}{16} \, {\left(4 \, x^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} - 3 \, x^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)^{2} - 16 \, \int \frac{3 \, {\left({\left(4 \, x^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - x^{3} \log\left(c^{2} x^{2}\right)^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + 4 \, {\left(4 \, c^{2} x^{5} \log\left(c\right)^{2} - 4 \, x^{3} \log\left(c\right)^{2} + 4 \, {\left(c^{2} x^{5} - x^{3}\right)} \log\left(x\right)^{2} - {\left({\left(4 \, c^{2} \log\left(c\right) + c^{2}\right)} x^{5} - x^{3} {\left(4 \, \log\left(c\right) + 1\right)} + 4 \, {\left(c^{2} x^{5} - x^{3}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + 8 \, {\left(c^{2} x^{5} \log\left(c\right) - x^{3} \log\left(c\right)\right)} \log\left(x\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)}}{16 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}\right)} b^{3} + \frac{{\left({\left(c^{2} x^{2} + 2 \, \log\left(x^{2}\right)\right)} \sqrt{c x + 1} \sqrt{c x - 1} - 2 \, {\left(c^{4} x^{4} + c^{2} x^{2} - 2\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} a b^{2}}{4 \, \sqrt{c x + 1} \sqrt{c x - 1} c^{4}}"," ",0,"3/4*a*b^2*x^4*arcsec(c*x)^2 + 1/4*a^3*x^4 + 1/4*(3*x^4*arcsec(c*x) - (c^2*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 3*x*sqrt(-1/(c^2*x^2) + 1))/c^3)*a^2*b + 1/16*(4*x^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 - 3*x^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)^2 - 16*integrate(3/16*((4*x^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - x^3*log(c^2*x^2)^2)*sqrt(c*x + 1)*sqrt(c*x - 1) + 4*(4*c^2*x^5*log(c)^2 - 4*x^3*log(c)^2 + 4*(c^2*x^5 - x^3)*log(x)^2 - ((4*c^2*log(c) + c^2)*x^5 - x^3*(4*log(c) + 1) + 4*(c^2*x^5 - x^3)*log(x))*log(c^2*x^2) + 8*(c^2*x^5*log(c) - x^3*log(c))*log(x))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))/(c^2*x^2 - 1), x))*b^3 + 1/4*((c^2*x^2 + 2*log(x^2))*sqrt(c*x + 1)*sqrt(c*x - 1) - 2*(c^4*x^4 + c^2*x^2 - 2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*a*b^2/(sqrt(c*x + 1)*sqrt(c*x - 1)*c^4)","F",0
25,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))^3,x, algorithm=""maxima"")","\frac{1}{3} \, b^{3} x^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} - \frac{1}{4} \, b^{3} x^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)^{2} - \frac{1}{2} \, a b^{2} c^{2} {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)} \log\left(c\right)^{2} - 12 \, b^{3} c^{2} \int \frac{x^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right)^{2} + 12 \, b^{3} c^{2} \int \frac{x^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) - 24 \, b^{3} c^{2} \int \frac{x^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) + 12 \, a b^{2} c^{2} \int \frac{x^{4} \log\left(c^{2} x^{2}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) - 24 \, a b^{2} c^{2} \int \frac{x^{4} \log\left(x\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) + \frac{1}{3} \, a^{3} x^{3} + 12 \, b^{3} c^{2} \int \frac{x^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 12 \, b^{3} c^{2} \int \frac{x^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + 12 \, a b^{2} c^{2} \int \frac{x^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + 4 \, b^{3} c^{2} \int \frac{x^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 3 \, a b^{2} c^{2} \int \frac{x^{4} \log\left(c^{2} x^{2}\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + 12 \, a b^{2} c^{2} \int \frac{x^{4} \log\left(c^{2} x^{2}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 12 \, a b^{2} c^{2} \int \frac{x^{4} \log\left(x\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + \frac{3}{2} \, a b^{2} {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)} \log\left(c\right)^{2} + 12 \, b^{3} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right)^{2} - 12 \, b^{3} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) + 24 \, b^{3} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) - 12 \, a b^{2} \int \frac{x^{2} \log\left(c^{2} x^{2}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) + 24 \, a b^{2} \int \frac{x^{2} \log\left(x\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) + \frac{1}{4} \, {\left(4 \, x^{3} \operatorname{arcsec}\left(c x\right) - \frac{\frac{2 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}} - \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{2}}}{c}\right)} a^{2} b - 4 \, b^{3} \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + b^{3} \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} x^{2} \log\left(c^{2} x^{2}\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 12 \, b^{3} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + 12 \, b^{3} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 12 \, a b^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 4 \, b^{3} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + 3 \, a b^{2} \int \frac{x^{2} \log\left(c^{2} x^{2}\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 12 \, a b^{2} \int \frac{x^{2} \log\left(c^{2} x^{2}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + 12 \, a b^{2} \int \frac{x^{2} \log\left(x\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}"," ",0,"1/3*b^3*x^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 - 1/4*b^3*x^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)^2 - 1/2*a*b^2*c^2*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5)*log(c)^2 - 12*b^3*c^2*integrate(1/4*x^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^2 - 1), x)*log(c)^2 + 12*b^3*c^2*integrate(1/4*x^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^2 - 1), x)*log(c) - 24*b^3*c^2*integrate(1/4*x^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)/(c^2*x^2 - 1), x)*log(c) + 12*a*b^2*c^2*integrate(1/4*x^4*log(c^2*x^2)/(c^2*x^2 - 1), x)*log(c) - 24*a*b^2*c^2*integrate(1/4*x^4*log(x)/(c^2*x^2 - 1), x)*log(c) + 1/3*a^3*x^3 + 12*b^3*c^2*integrate(1/4*x^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)*log(x)/(c^2*x^2 - 1), x) - 12*b^3*c^2*integrate(1/4*x^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)^2/(c^2*x^2 - 1), x) + 12*a*b^2*c^2*integrate(1/4*x^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2/(c^2*x^2 - 1), x) + 4*b^3*c^2*integrate(1/4*x^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^2 - 1), x) - 3*a*b^2*c^2*integrate(1/4*x^4*log(c^2*x^2)^2/(c^2*x^2 - 1), x) + 12*a*b^2*c^2*integrate(1/4*x^4*log(c^2*x^2)*log(x)/(c^2*x^2 - 1), x) - 12*a*b^2*c^2*integrate(1/4*x^4*log(x)^2/(c^2*x^2 - 1), x) + 3/2*a*b^2*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3)*log(c)^2 + 12*b^3*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^2 - 1), x)*log(c)^2 - 12*b^3*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^2 - 1), x)*log(c) + 24*b^3*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)/(c^2*x^2 - 1), x)*log(c) - 12*a*b^2*integrate(1/4*x^2*log(c^2*x^2)/(c^2*x^2 - 1), x)*log(c) + 24*a*b^2*integrate(1/4*x^2*log(x)/(c^2*x^2 - 1), x)*log(c) + 1/4*(4*x^3*arcsec(c*x) - (2*sqrt(-1/(c^2*x^2) + 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 - log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^2)/c)*a^2*b - 4*b^3*integrate(1/4*sqrt(c*x + 1)*sqrt(c*x - 1)*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2/(c^2*x^2 - 1), x) + b^3*integrate(1/4*sqrt(c*x + 1)*sqrt(c*x - 1)*x^2*log(c^2*x^2)^2/(c^2*x^2 - 1), x) - 12*b^3*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)*log(x)/(c^2*x^2 - 1), x) + 12*b^3*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)^2/(c^2*x^2 - 1), x) - 12*a*b^2*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2/(c^2*x^2 - 1), x) - 4*b^3*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^2 - 1), x) + 3*a*b^2*integrate(1/4*x^2*log(c^2*x^2)^2/(c^2*x^2 - 1), x) - 12*a*b^2*integrate(1/4*x^2*log(c^2*x^2)*log(x)/(c^2*x^2 - 1), x) + 12*a*b^2*integrate(1/4*x^2*log(x)^2/(c^2*x^2 - 1), x)","F",0
26,0,0,0,0.000000," ","integrate(x*(a+b*arcsec(c*x))^3,x, algorithm=""maxima"")","\frac{3}{2} \, a b^{2} x^{2} \operatorname{arcsec}\left(c x\right)^{2} + \frac{1}{2} \, a^{3} x^{2} + \frac{3}{2} \, {\left(x^{2} \operatorname{arcsec}\left(c x\right) - \frac{x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c}\right)} a^{2} b - 3 \, {\left(\frac{x \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \operatorname{arcsec}\left(c x\right)}{c} - \frac{\log\left(x\right)}{c^{2}}\right)} a b^{2} + \frac{1}{8} \, {\left(4 \, x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} - 3 \, x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)^{2} - 8 \, \int \frac{3 \, {\left({\left(4 \, x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - x \log\left(c^{2} x^{2}\right)^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + 4 \, {\left(2 \, c^{2} x^{3} \log\left(c\right)^{2} - 2 \, x \log\left(c\right)^{2} + 2 \, {\left(c^{2} x^{3} - x\right)} \log\left(x\right)^{2} - {\left({\left(2 \, c^{2} \log\left(c\right) + c^{2}\right)} x^{3} - x {\left(2 \, \log\left(c\right) + 1\right)} + 2 \, {\left(c^{2} x^{3} - x\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + 4 \, {\left(c^{2} x^{3} \log\left(c\right) - x \log\left(c\right)\right)} \log\left(x\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)}}{8 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}\right)} b^{3}"," ",0,"3/2*a*b^2*x^2*arcsec(c*x)^2 + 1/2*a^3*x^2 + 3/2*(x^2*arcsec(c*x) - x*sqrt(-1/(c^2*x^2) + 1)/c)*a^2*b - 3*(x*sqrt(-1/(c^2*x^2) + 1)*arcsec(c*x)/c - log(x)/c^2)*a*b^2 + 1/8*(4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 - 3*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)^2 - 8*integrate(3/8*((4*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - x*log(c^2*x^2)^2)*sqrt(c*x + 1)*sqrt(c*x - 1) + 4*(2*c^2*x^3*log(c)^2 - 2*x*log(c)^2 + 2*(c^2*x^3 - x)*log(x)^2 - ((2*c^2*log(c) + c^2)*x^3 - x*(2*log(c) + 1) + 2*(c^2*x^3 - x)*log(x))*log(c^2*x^2) + 4*(c^2*x^3*log(c) - x*log(c))*log(x))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))/(c^2*x^2 - 1), x))*b^3","F",0
27,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))^3,x, algorithm=""maxima"")","-\frac{3}{2} \, a b^{2} c^{2} {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)} \log\left(c\right)^{2} - 12 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right)^{2} + b^{3} x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} - \frac{3}{4} \, b^{3} x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)^{2} + 12 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) - 24 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) + 12 \, a b^{2} c^{2} \int \frac{x^{2} \log\left(c^{2} x^{2}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) - 24 \, a b^{2} c^{2} \int \frac{x^{2} \log\left(x\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) + 12 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 12 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + 12 \, a b^{2} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + 12 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 3 \, a b^{2} c^{2} \int \frac{x^{2} \log\left(c^{2} x^{2}\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + 12 \, a b^{2} c^{2} \int \frac{x^{2} \log\left(c^{2} x^{2}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 12 \, a b^{2} c^{2} \int \frac{x^{2} \log\left(x\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - \frac{3}{2} \, a b^{2} {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} \log\left(c\right)^{2} + 12 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right)^{2} - 12 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) + 24 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) - 12 \, a b^{2} \int \frac{\log\left(c^{2} x^{2}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) + 24 \, a b^{2} \int \frac{\log\left(x\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} \log\left(c\right) + a^{3} x - 12 \, b^{3} \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + 3 \, b^{3} \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \log\left(c^{2} x^{2}\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 12 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + 12 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 12 \, a b^{2} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 12 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + 3 \, a b^{2} \int \frac{\log\left(c^{2} x^{2}\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} - 12 \, a b^{2} \int \frac{\log\left(c^{2} x^{2}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + 12 \, a b^{2} \int \frac{\log\left(x\right)^{2}}{4 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x} + \frac{3 \, {\left(2 \, c x \operatorname{arcsec}\left(c x\right) - \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right) + \log\left(-\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)\right)} a^{2} b}{2 \, c}"," ",0,"-3/2*a*b^2*c^2*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3)*log(c)^2 - 12*b^3*c^2*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^2 - 1), x)*log(c)^2 + b^3*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 - 3/4*b^3*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)^2 + 12*b^3*c^2*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^2 - 1), x)*log(c) - 24*b^3*c^2*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)/(c^2*x^2 - 1), x)*log(c) + 12*a*b^2*c^2*integrate(1/4*x^2*log(c^2*x^2)/(c^2*x^2 - 1), x)*log(c) - 24*a*b^2*c^2*integrate(1/4*x^2*log(x)/(c^2*x^2 - 1), x)*log(c) + 12*b^3*c^2*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)*log(x)/(c^2*x^2 - 1), x) - 12*b^3*c^2*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)^2/(c^2*x^2 - 1), x) + 12*a*b^2*c^2*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2/(c^2*x^2 - 1), x) + 12*b^3*c^2*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^2 - 1), x) - 3*a*b^2*c^2*integrate(1/4*x^2*log(c^2*x^2)^2/(c^2*x^2 - 1), x) + 12*a*b^2*c^2*integrate(1/4*x^2*log(c^2*x^2)*log(x)/(c^2*x^2 - 1), x) - 12*a*b^2*c^2*integrate(1/4*x^2*log(x)^2/(c^2*x^2 - 1), x) - 3/2*a*b^2*(log(c*x + 1)/c - log(c*x - 1)/c)*log(c)^2 + 12*b^3*integrate(1/4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^2 - 1), x)*log(c)^2 - 12*b^3*integrate(1/4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^2 - 1), x)*log(c) + 24*b^3*integrate(1/4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)/(c^2*x^2 - 1), x)*log(c) - 12*a*b^2*integrate(1/4*log(c^2*x^2)/(c^2*x^2 - 1), x)*log(c) + 24*a*b^2*integrate(1/4*log(x)/(c^2*x^2 - 1), x)*log(c) + a^3*x - 12*b^3*integrate(1/4*sqrt(c*x + 1)*sqrt(c*x - 1)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2/(c^2*x^2 - 1), x) + 3*b^3*integrate(1/4*sqrt(c*x + 1)*sqrt(c*x - 1)*log(c^2*x^2)^2/(c^2*x^2 - 1), x) - 12*b^3*integrate(1/4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)*log(x)/(c^2*x^2 - 1), x) + 12*b^3*integrate(1/4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)^2/(c^2*x^2 - 1), x) - 12*a*b^2*integrate(1/4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2/(c^2*x^2 - 1), x) - 12*b^3*integrate(1/4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^2 - 1), x) + 3*a*b^2*integrate(1/4*log(c^2*x^2)^2/(c^2*x^2 - 1), x) - 12*a*b^2*integrate(1/4*log(c^2*x^2)*log(x)/(c^2*x^2 - 1), x) + 12*a*b^2*integrate(1/4*log(x)^2/(c^2*x^2 - 1), x) + 3/2*(2*c*x*arcsec(c*x) - log(sqrt(-1/(c^2*x^2) + 1) + 1) + log(-sqrt(-1/(c^2*x^2) + 1) + 1))*a^2*b/c","F",0
28,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))^3/x,x, algorithm=""maxima"")","-\frac{3}{2} \, a b^{2} c^{2} {\left(\frac{\log\left(c x + 1\right)}{c^{2}} + \frac{\log\left(c x - 1\right)}{c^{2}}\right)} \log\left(c\right)^{2} - 12 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} \log\left(c\right)^{2} + 12 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} \log\left(c\right) - 24 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} \log\left(c\right) + 12 \, a b^{2} c^{2} \int \frac{x^{2} \log\left(c^{2} x^{2}\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} \log\left(c\right) - 24 \, a b^{2} c^{2} \int \frac{x^{2} \log\left(x\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} \log\left(c\right) + b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} \log\left(x\right) - \frac{3}{4} \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)^{2} \log\left(x\right) + 24 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} - 12 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)^{2}}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} + 12 \, a b^{2} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} - 3 \, a b^{2} c^{2} \int \frac{x^{2} \log\left(c^{2} x^{2}\right)^{2}}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} + 12 \, a b^{2} c^{2} \int \frac{x^{2} \log\left(c^{2} x^{2}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} - 12 \, a b^{2} c^{2} \int \frac{x^{2} \log\left(x\right)^{2}}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} + 12 \, a^{2} b c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} + \frac{3}{2} \, a b^{2} {\left(\log\left(c x + 1\right) + \log\left(c x - 1\right) - 2 \, \log\left(x\right)\right)} \log\left(c\right)^{2} + 12 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} \log\left(c\right)^{2} - 12 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} \log\left(c\right) + 24 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} \log\left(c\right) - 12 \, a b^{2} \int \frac{\log\left(c^{2} x^{2}\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} \log\left(c\right) + 24 \, a b^{2} \int \frac{\log\left(x\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} \log\left(c\right) - 12 \, b^{3} \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} \log\left(x\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} + 3 \, b^{3} \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \log\left(c^{2} x^{2}\right)^{2} \log\left(x\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} - 24 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} + 12 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)^{2}}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} - 12 \, a b^{2} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} + 3 \, a b^{2} \int \frac{\log\left(c^{2} x^{2}\right)^{2}}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} - 12 \, a b^{2} \int \frac{\log\left(c^{2} x^{2}\right) \log\left(x\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} + 12 \, a b^{2} \int \frac{\log\left(x\right)^{2}}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} - 12 \, a^{2} b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{4 \, {\left(c^{2} x^{3} - x\right)}}\,{d x} + a^{3} \log\left(x\right)"," ",0,"-3/2*a*b^2*c^2*(log(c*x + 1)/c^2 + log(c*x - 1)/c^2)*log(c)^2 - 12*b^3*c^2*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^3 - x), x)*log(c)^2 + 12*b^3*c^2*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^3 - x), x)*log(c) - 24*b^3*c^2*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)/(c^2*x^3 - x), x)*log(c) + 12*a*b^2*c^2*integrate(1/4*x^2*log(c^2*x^2)/(c^2*x^3 - x), x)*log(c) - 24*a*b^2*c^2*integrate(1/4*x^2*log(x)/(c^2*x^3 - x), x)*log(c) + b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3*log(x) - 3/4*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)^2*log(x) + 24*b^3*c^2*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)*log(x)/(c^2*x^3 - x), x) - 12*b^3*c^2*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)^2/(c^2*x^3 - x), x) + 12*a*b^2*c^2*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2/(c^2*x^3 - x), x) - 3*a*b^2*c^2*integrate(1/4*x^2*log(c^2*x^2)^2/(c^2*x^3 - x), x) + 12*a*b^2*c^2*integrate(1/4*x^2*log(c^2*x^2)*log(x)/(c^2*x^3 - x), x) - 12*a*b^2*c^2*integrate(1/4*x^2*log(x)^2/(c^2*x^3 - x), x) + 12*a^2*b*c^2*integrate(1/4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^3 - x), x) + 3/2*a*b^2*(log(c*x + 1) + log(c*x - 1) - 2*log(x))*log(c)^2 + 12*b^3*integrate(1/4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^3 - x), x)*log(c)^2 - 12*b^3*integrate(1/4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^3 - x), x)*log(c) + 24*b^3*integrate(1/4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)/(c^2*x^3 - x), x)*log(c) - 12*a*b^2*integrate(1/4*log(c^2*x^2)/(c^2*x^3 - x), x)*log(c) + 24*a*b^2*integrate(1/4*log(x)/(c^2*x^3 - x), x)*log(c) - 12*b^3*integrate(1/4*sqrt(c*x + 1)*sqrt(c*x - 1)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2*log(x)/(c^2*x^3 - x), x) + 3*b^3*integrate(1/4*sqrt(c*x + 1)*sqrt(c*x - 1)*log(c^2*x^2)^2*log(x)/(c^2*x^3 - x), x) - 24*b^3*integrate(1/4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)*log(x)/(c^2*x^3 - x), x) + 12*b^3*integrate(1/4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)^2/(c^2*x^3 - x), x) - 12*a*b^2*integrate(1/4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2/(c^2*x^3 - x), x) + 3*a*b^2*integrate(1/4*log(c^2*x^2)^2/(c^2*x^3 - x), x) - 12*a*b^2*integrate(1/4*log(c^2*x^2)*log(x)/(c^2*x^3 - x), x) + 12*a*b^2*integrate(1/4*log(x)^2/(c^2*x^3 - x), x) - 12*a^2*b*integrate(1/4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^3 - x), x) + a^3*log(x)","F",0
29,1,146,0,0.334749," ","integrate((a+b*arcsec(c*x))^3/x^2,x, algorithm=""maxima"")","-\frac{b^{3} \operatorname{arcsec}\left(c x\right)^{3}}{x} + 3 \, {\left(c \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{\operatorname{arcsec}\left(c x\right)}{x}\right)} a^{2} b + 6 \, {\left(c \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \operatorname{arcsec}\left(c x\right) + \frac{1}{x}\right)} a b^{2} + 3 \, {\left(c \sqrt{-\frac{1}{c^{2} x^{2}} + 1} \operatorname{arcsec}\left(c x\right)^{2} - 2 \, c \sqrt{-\frac{1}{c^{2} x^{2}} + 1} + \frac{2 \, \operatorname{arcsec}\left(c x\right)}{x}\right)} b^{3} - \frac{3 \, a b^{2} \operatorname{arcsec}\left(c x\right)^{2}}{x} - \frac{a^{3}}{x}"," ",0,"-b^3*arcsec(c*x)^3/x + 3*(c*sqrt(-1/(c^2*x^2) + 1) - arcsec(c*x)/x)*a^2*b + 6*(c*sqrt(-1/(c^2*x^2) + 1)*arcsec(c*x) + 1/x)*a*b^2 + 3*(c*sqrt(-1/(c^2*x^2) + 1)*arcsec(c*x)^2 - 2*c*sqrt(-1/(c^2*x^2) + 1) + 2*arcsec(c*x)/x)*b^3 - 3*a*b^2*arcsec(c*x)^2/x - a^3/x","A",0
30,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))^3/x^3,x, algorithm=""maxima"")","-\frac{3}{4} \, a^{2} b {\left(\frac{\frac{c^{4} x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} - 1} - c^{3} \arctan\left(c x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right)}{c} + \frac{2 \, \operatorname{arcsec}\left(c x\right)}{x^{2}}\right)} - \frac{a^{3}}{2 \, x^{2}} - \frac{4 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} - 3 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)^{2} + {\left(12 \, a b^{2} c^{2} {\left(\log\left(c x + 1\right) + \log\left(c x - 1\right) - 2 \, \log\left(x\right)\right)} \log\left(c\right)^{2} + 24 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{2} x^{5} - x^{3}}\,{d x} \log\left(c\right)^{2} - 12 \, {\left({\left(\log\left(c x + 1\right) + \log\left(c x - 1\right) - 2 \, \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) - 2 \, \log\left(c x - 1\right) \log\left(x\right) + 2 \, \log\left(-c x + 1\right) \log\left(x\right) + 2 \, \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) + 2 \, {\rm Li}_2\left(-c x\right)\right)} a b^{2} c^{2} \log\left(c\right) + 24 \, {\left({\left(\log\left(c x + 1\right) + \log\left(c x - 1\right) - 2 \, \log\left(x\right)\right)} \log\left(x\right) - \log\left(c x - 1\right) \log\left(x\right) + \log\left(-c x + 1\right) \log\left(x\right) + \log\left(x\right)^{2} + {\rm Li}_2\left(c x\right) + {\rm Li}_2\left(-c x\right)\right)} a b^{2} c^{2} \log\left(c\right) - 24 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{c^{2} x^{5} - x^{3}}\,{d x} \log\left(c\right) + 48 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)}{c^{2} x^{5} - x^{3}}\,{d x} \log\left(c\right) + {\left(3 \, {\left(\log\left(c x + 1\right) + \log\left(c x - 1\right) - 2 \, \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)^{2} - 12 i \, \pi \log\left(x\right)^{2} - 8 \, \log\left(x\right)^{3} - 12 \, {\left(\log\left(c x - 1\right) \log\left(x\right) - \log\left(-c x + 1\right) \log\left(x\right) - \log\left(x\right)^{2} - {\rm Li}_2\left(c x\right) - {\rm Li}_2\left(-c x\right)\right)} \log\left(c^{2} x^{2}\right) - 24 \, {\rm Li}_{3}(c x) - 24 \, {\rm Li}_{3}(-c x)\right)} a b^{2} c^{2} + 4 \, {\left({\left(3 i \, \pi - 6 \, \log\left(c\right)\right)} \log\left(x\right)^{2} - 6 \, \log\left(c x + 1\right) \log\left(x\right)^{2} - 3 \, \log\left(-c x + 1\right) \log\left(x\right)^{2} - 2 \, \log\left(x\right)^{3} + 6 \, {\left(\log\left(c\right) \log\left(x\right) + \log\left(x\right)^{2}\right)} \log\left(c x + 1\right) + 3 \, {\left(2 \, \log\left(c\right) \log\left(x\right) + \log\left(x\right)^{2}\right)} \log\left(c x - 1\right) - 6 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} \log\left(c\right) - 6 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} \log\left(c\right) - 3 \, {\left({\left(\log\left(c x + 1\right) + \log\left(c x - 1\right) - 2 \, \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) - 2 \, \log\left(c x - 1\right) \log\left(x\right) + 2 \, \log\left(-c x + 1\right) \log\left(x\right) + 2 \, \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) + 2 \, {\rm Li}_2\left(-c x\right)\right)} \log\left(x\right) - 6 \, {\rm Li}_2\left(c x\right) \log\left(x\right) - 6 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) + 12 \, {\rm Li}_{3}(c x) + 12 \, {\rm Li}_{3}(-c x)\right)} a b^{2} c^{2} + 4 \, {\left(3 \, \log\left(c x + 1\right) \log\left(x\right)^{2} + 3 \, \log\left(-c x + 1\right) \log\left(x\right)^{2} - 2 \, \log\left(x\right)^{3} + 6 \, {\rm Li}_2\left(c x\right) \log\left(x\right) + 6 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) - 6 \, {\rm Li}_{3}(c x) - 6 \, {\rm Li}_{3}(-c x)\right)} a b^{2} c^{2} - 24 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right) \log\left(x\right)}{c^{2} x^{5} - x^{3}}\,{d x} + 24 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)^{2}}{c^{2} x^{5} - x^{3}}\,{d x} - 24 \, a b^{2} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{c^{2} x^{5} - x^{3}}\,{d x} + 12 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{c^{2} x^{5} - x^{3}}\,{d x} - 12 \, {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} a b^{2} \log\left(c\right)^{2} - 24 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{2} x^{5} - x^{3}}\,{d x} \log\left(c\right)^{2} + 12 \, {\left(2 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} + 2 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} + {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(c^{2} x^{2}\right) - \frac{2 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right) + 2 \, c^{2} x^{2} \log\left(c x - 1\right) \log\left(x\right) - 2 \, c^{2} x^{2} \log\left(x\right)^{2} - 1}{x^{2}}\right)} a b^{2} \log\left(c\right) - 12 \, {\left(2 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} + 2 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} + 2 \, {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(x\right) - \frac{2 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right) + 2 \, c^{2} x^{2} \log\left(c x - 1\right) \log\left(x\right) - 2 \, c^{2} x^{2} \log\left(x\right)^{2} - 1}{x^{2}}\right)} a b^{2} \log\left(c\right) + 24 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{c^{2} x^{5} - x^{3}}\,{d x} \log\left(c\right) - 48 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)}{c^{2} x^{5} - x^{3}}\,{d x} \log\left(c\right) + 2 \, {\left(4 \, c^{2} \log\left(x\right)^{3} - 6 \, {\left(\log\left(c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(-c x)\right)} c^{2} - 6 \, {\left(\log\left(-c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(c x)\right)} c^{2} - \frac{3 \, {\left(2 \, \log\left(x\right)^{2} + 2 \, \log\left(x\right) + 1\right)}}{x^{2}}\right)} a b^{2} + 4 \, {\left(6 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} \log\left(c\right) + 6 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} \log\left(c\right) + 6 \, {\left(\log\left(c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(-c x)\right)} c^{2} + 6 \, {\left(\log\left(-c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(c x)\right)} c^{2} + 3 \, {\left(2 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} + 2 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} + {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(c^{2} x^{2}\right) - \frac{2 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right) + 2 \, c^{2} x^{2} \log\left(c x - 1\right) \log\left(x\right) - 2 \, c^{2} x^{2} \log\left(x\right)^{2} - 1}{x^{2}}\right)} \log\left(x\right) - \frac{3 \, c^{2} x^{2} \log\left(-c x + 1\right) \log\left(x\right)^{2} - 2 \, c^{2} x^{2} \log\left(x\right)^{3} + 6 \, c^{2} x^{2} {\rm Li}_2\left(c x\right) \log\left(x\right) + 6 \, c^{2} x^{2} {\rm Li}_2\left(-c x\right) \log\left(x\right) - 3 \, {\left(-i \, \pi c^{2} + 2 \, c^{2} \log\left(c\right)\right)} x^{2} \log\left(x\right)^{2} + 6 \, {\left(c^{2} x^{2} \log\left(c\right) \log\left(x\right) + c^{2} x^{2} \log\left(x\right)^{2}\right)} \log\left(c x + 1\right) + 3 \, {\left(2 \, c^{2} x^{2} \log\left(c\right) \log\left(x\right) + c^{2} x^{2} \log\left(x\right)^{2}\right)} \log\left(c x - 1\right) - 3 \, \log\left(c\right) - 3 \, \log\left(x\right) - 3}{x^{2}}\right)} a b^{2} - {\left(12 \, {\left(\log\left(c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(-c x)\right)} c^{2} + 12 \, {\left(\log\left(-c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(c x)\right)} c^{2} + 3 \, {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(c^{2} x^{2}\right)^{2} + 6 \, {\left(2 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} + 2 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} - \frac{2 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right) + 2 \, c^{2} x^{2} \log\left(c x - 1\right) \log\left(x\right) - 2 \, c^{2} x^{2} \log\left(x\right)^{2} - 1}{x^{2}}\right)} \log\left(c^{2} x^{2}\right) - \frac{2 \, {\left(6 i \, \pi c^{2} x^{2} \log\left(x\right)^{2} + 6 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right)^{2} + 6 \, c^{2} x^{2} \log\left(-c x + 1\right) \log\left(x\right)^{2} + 4 \, c^{2} x^{2} \log\left(x\right)^{3} + 12 \, c^{2} x^{2} {\rm Li}_2\left(c x\right) \log\left(x\right) + 12 \, c^{2} x^{2} {\rm Li}_2\left(-c x\right) \log\left(x\right) - 3\right)}}{x^{2}}\right)} a b^{2} - 12 \, b^{3} \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{c^{2} x^{5} - x^{3}}\,{d x} + 3 \, b^{3} \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \log\left(c^{2} x^{2}\right)^{2}}{c^{2} x^{5} - x^{3}}\,{d x} + 24 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right) \log\left(x\right)}{c^{2} x^{5} - x^{3}}\,{d x} - 24 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)^{2}}{c^{2} x^{5} - x^{3}}\,{d x} + 24 \, a b^{2} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{c^{2} x^{5} - x^{3}}\,{d x} - 12 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{c^{2} x^{5} - x^{3}}\,{d x}\right)} x^{2}}{8 \, x^{2}}"," ",0,"-3/4*a^2*b*((c^4*x*sqrt(-1/(c^2*x^2) + 1)/(c^2*x^2*(1/(c^2*x^2) - 1) - 1) - c^3*arctan(c*x*sqrt(-1/(c^2*x^2) + 1)))/c + 2*arcsec(c*x)/x^2) - 1/2*a^3/x^2 - 1/8*(4*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 - 3*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)^2 + 12*(a*b^2*c^2*(log(c*x + 1) + log(c*x - 1) - 2*log(x))*log(c)^2 + 16*b^3*c^2*integrate(1/8*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^5 - x^3), x)*log(c)^2 - 16*b^3*c^2*integrate(1/8*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^5 - x^3), x)*log(c) + 32*b^3*c^2*integrate(1/8*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)/(c^2*x^5 - x^3), x)*log(c) - 16*a*b^2*c^2*integrate(1/8*x^2*log(c^2*x^2)/(c^2*x^5 - x^3), x)*log(c) + 32*a*b^2*c^2*integrate(1/8*x^2*log(x)/(c^2*x^5 - x^3), x)*log(c) - 16*b^3*c^2*integrate(1/8*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)*log(x)/(c^2*x^5 - x^3), x) + 16*b^3*c^2*integrate(1/8*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)^2/(c^2*x^5 - x^3), x) - 16*a*b^2*c^2*integrate(1/8*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2/(c^2*x^5 - x^3), x) + 8*b^3*c^2*integrate(1/8*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^5 - x^3), x) + 4*a*b^2*c^2*integrate(1/8*x^2*log(c^2*x^2)^2/(c^2*x^5 - x^3), x) - 16*a*b^2*c^2*integrate(1/8*x^2*log(c^2*x^2)*log(x)/(c^2*x^5 - x^3), x) + 16*a*b^2*c^2*integrate(1/8*x^2*log(x)^2/(c^2*x^5 - x^3), x) - (c^2*log(c*x + 1) + c^2*log(c*x - 1) - 2*c^2*log(x) + 1/x^2)*a*b^2*log(c)^2 - 16*b^3*integrate(1/8*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^5 - x^3), x)*log(c)^2 + 16*b^3*integrate(1/8*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^5 - x^3), x)*log(c) - 32*b^3*integrate(1/8*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)/(c^2*x^5 - x^3), x)*log(c) + 16*a*b^2*integrate(1/8*log(c^2*x^2)/(c^2*x^5 - x^3), x)*log(c) - 32*a*b^2*integrate(1/8*log(x)/(c^2*x^5 - x^3), x)*log(c) - 8*b^3*integrate(1/8*sqrt(c*x + 1)*sqrt(c*x - 1)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2/(c^2*x^5 - x^3), x) + 2*b^3*integrate(1/8*sqrt(c*x + 1)*sqrt(c*x - 1)*log(c^2*x^2)^2/(c^2*x^5 - x^3), x) + 16*b^3*integrate(1/8*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)*log(x)/(c^2*x^5 - x^3), x) - 16*b^3*integrate(1/8*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)^2/(c^2*x^5 - x^3), x) + 16*a*b^2*integrate(1/8*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2/(c^2*x^5 - x^3), x) - 8*b^3*integrate(1/8*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^5 - x^3), x) - 4*a*b^2*integrate(1/8*log(c^2*x^2)^2/(c^2*x^5 - x^3), x) + 16*a*b^2*integrate(1/8*log(c^2*x^2)*log(x)/(c^2*x^5 - x^3), x) - 16*a*b^2*integrate(1/8*log(x)^2/(c^2*x^5 - x^3), x))*x^2)/x^2","F",0
31,1,575,0,0.980652," ","integrate((a+b*arcsec(c*x))^3/x^4,x, algorithm=""maxima"")","-\frac{1}{216} \, {\left(\frac{72 \, {\left(c^{4} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 3 \, c^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right)} \operatorname{arcsec}\left(c x\right)^{2}}{c} + \frac{72 \, c^{4} {\left(\frac{c^{2} \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{2 \, \sqrt{c^{2} x^{2} - 1} c}{x} - \frac{\sqrt{c^{2} x^{2} - 1}}{x^{2}}}{c} - \frac{c^{2} \arcsin\left(\frac{1}{c {\left| x \right|}}\right) - \frac{2 \, \sqrt{c^{2} x^{2} - 1} c}{x} - \frac{\sqrt{c^{2} x^{2} - 1}}{x^{2}}}{c} - \frac{4 \, \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\right)} + c^{2} {\left(\frac{9 \, c^{4} \arcsin\left(\frac{1}{c {\left| x \right|}}\right) + \frac{16 \, \sqrt{c^{2} x^{2} - 1} c^{3}}{x} - \frac{9 \, \sqrt{c^{2} x^{2} - 1} c^{2}}{x^{2}} + \frac{8 \, \sqrt{c^{2} x^{2} - 1} c}{x^{3}} - \frac{6 \, \sqrt{c^{2} x^{2} - 1}}{x^{4}}}{c} - \frac{9 \, c^{4} \arcsin\left(\frac{1}{c {\left| x \right|}}\right) - \frac{16 \, \sqrt{c^{2} x^{2} - 1} c^{3}}{x} - \frac{9 \, \sqrt{c^{2} x^{2} - 1} c^{2}}{x^{2}} - \frac{8 \, \sqrt{c^{2} x^{2} - 1} c}{x^{3}} - \frac{6 \, \sqrt{c^{2} x^{2} - 1}}{x^{4}}}{c} - \frac{48 \, \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{3}}\right)}}{c^{2}}\right)} b^{3} - \frac{1}{3} \, a^{2} b {\left(\frac{c^{4} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 3 \, c^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c} + \frac{3 \, \operatorname{arcsec}\left(c x\right)}{x^{3}}\right)} - \frac{b^{3} \operatorname{arcsec}\left(c x\right)^{3}}{3 \, x^{3}} - \frac{a b^{2} \operatorname{arcsec}\left(c x\right)^{2}}{x^{3}} - \frac{a^{3}}{3 \, x^{3}} + \frac{2 \, {\left({\left(6 \, c^{3} x^{2} + c\right)} \sqrt{c x + 1} \sqrt{c x - 1} + 3 \, {\left(2 \, c^{5} x^{4} - c^{3} x^{2} - c\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} a b^{2}}{9 \, \sqrt{c x + 1} \sqrt{c x - 1} c x^{3}}"," ",0,"-1/216*(72*(c^4*(-1/(c^2*x^2) + 1)^(3/2) - 3*c^4*sqrt(-1/(c^2*x^2) + 1))*arcsec(c*x)^2/c + (72*c^4*((c^2*arcsin(1/(c*abs(x))) + 2*sqrt(c^2*x^2 - 1)*c/x - sqrt(c^2*x^2 - 1)/x^2)/c - (c^2*arcsin(1/(c*abs(x))) - 2*sqrt(c^2*x^2 - 1)*c/x - sqrt(c^2*x^2 - 1)/x^2)/c - 4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/x) + c^2*((9*c^4*arcsin(1/(c*abs(x))) + 16*sqrt(c^2*x^2 - 1)*c^3/x - 9*sqrt(c^2*x^2 - 1)*c^2/x^2 + 8*sqrt(c^2*x^2 - 1)*c/x^3 - 6*sqrt(c^2*x^2 - 1)/x^4)/c - (9*c^4*arcsin(1/(c*abs(x))) - 16*sqrt(c^2*x^2 - 1)*c^3/x - 9*sqrt(c^2*x^2 - 1)*c^2/x^2 - 8*sqrt(c^2*x^2 - 1)*c/x^3 - 6*sqrt(c^2*x^2 - 1)/x^4)/c - 48*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/x^3))/c^2)*b^3 - 1/3*a^2*b*((c^4*(-1/(c^2*x^2) + 1)^(3/2) - 3*c^4*sqrt(-1/(c^2*x^2) + 1))/c + 3*arcsec(c*x)/x^3) - 1/3*b^3*arcsec(c*x)^3/x^3 - a*b^2*arcsec(c*x)^2/x^3 - 1/3*a^3/x^3 + 2/9*((6*c^3*x^2 + c)*sqrt(c*x + 1)*sqrt(c*x - 1) + 3*(2*c^5*x^4 - c^3*x^2 - c)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*a*b^2/(sqrt(c*x + 1)*sqrt(c*x - 1)*c*x^3)","B",0
32,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))^3/x^5,x, algorithm=""maxima"")","\frac{3}{32} \, a^{2} b {\left(\frac{3 \, c^{5} \arctan\left(c x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right) + \frac{3 \, c^{8} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 5 \, c^{6} x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{4} x^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} - 2 \, c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + 1}}{c} - \frac{8 \, \operatorname{arcsec}\left(c x\right)}{x^{4}}\right)} - \frac{a^{3}}{4 \, x^{4}} - \frac{4 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} - 3 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)^{2} + \frac{1}{2} \, {\left(48 \, {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} a b^{2} c^{2} \log\left(c\right)^{2} + 96 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{2} x^{7} - x^{5}}\,{d x} \log\left(c\right)^{2} - 48 \, {\left(2 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} + 2 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} + {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(c^{2} x^{2}\right) - \frac{2 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right) + 2 \, c^{2} x^{2} \log\left(c x - 1\right) \log\left(x\right) - 2 \, c^{2} x^{2} \log\left(x\right)^{2} - 1}{x^{2}}\right)} a b^{2} c^{2} \log\left(c\right) + 48 \, {\left(2 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} + 2 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} + 2 \, {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(x\right) - \frac{2 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right) + 2 \, c^{2} x^{2} \log\left(c x - 1\right) \log\left(x\right) - 2 \, c^{2} x^{2} \log\left(x\right)^{2} - 1}{x^{2}}\right)} a b^{2} c^{2} \log\left(c\right) - 96 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{c^{2} x^{7} - x^{5}}\,{d x} \log\left(c\right) + 192 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)}{c^{2} x^{7} - x^{5}}\,{d x} \log\left(c\right) - 8 \, {\left(4 \, c^{2} \log\left(x\right)^{3} - 6 \, {\left(\log\left(c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(-c x)\right)} c^{2} - 6 \, {\left(\log\left(-c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(c x)\right)} c^{2} - \frac{3 \, {\left(2 \, \log\left(x\right)^{2} + 2 \, \log\left(x\right) + 1\right)}}{x^{2}}\right)} a b^{2} c^{2} - 16 \, {\left(6 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} \log\left(c\right) + 6 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} \log\left(c\right) + 6 \, {\left(\log\left(c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(-c x)\right)} c^{2} + 6 \, {\left(\log\left(-c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(c x)\right)} c^{2} + 3 \, {\left(2 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} + 2 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} + {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(c^{2} x^{2}\right) - \frac{2 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right) + 2 \, c^{2} x^{2} \log\left(c x - 1\right) \log\left(x\right) - 2 \, c^{2} x^{2} \log\left(x\right)^{2} - 1}{x^{2}}\right)} \log\left(x\right) - \frac{3 \, c^{2} x^{2} \log\left(-c x + 1\right) \log\left(x\right)^{2} - 2 \, c^{2} x^{2} \log\left(x\right)^{3} + 6 \, c^{2} x^{2} {\rm Li}_2\left(c x\right) \log\left(x\right) + 6 \, c^{2} x^{2} {\rm Li}_2\left(-c x\right) \log\left(x\right) - 3 \, {\left(-i \, \pi c^{2} + 2 \, c^{2} \log\left(c\right)\right)} x^{2} \log\left(x\right)^{2} + 6 \, {\left(c^{2} x^{2} \log\left(c\right) \log\left(x\right) + c^{2} x^{2} \log\left(x\right)^{2}\right)} \log\left(c x + 1\right) + 3 \, {\left(2 \, c^{2} x^{2} \log\left(c\right) \log\left(x\right) + c^{2} x^{2} \log\left(x\right)^{2}\right)} \log\left(c x - 1\right) - 3 \, \log\left(c\right) - 3 \, \log\left(x\right) - 3}{x^{2}}\right)} a b^{2} c^{2} + 4 \, {\left(12 \, {\left(\log\left(c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(-c x)\right)} c^{2} + 12 \, {\left(\log\left(-c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(c x)\right)} c^{2} + 3 \, {\left(c^{2} \log\left(c x + 1\right) + c^{2} \log\left(c x - 1\right) - 2 \, c^{2} \log\left(x\right) + \frac{1}{x^{2}}\right)} \log\left(c^{2} x^{2}\right)^{2} + 6 \, {\left(2 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{2} + 2 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{2} - \frac{2 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right) + 2 \, c^{2} x^{2} \log\left(c x - 1\right) \log\left(x\right) - 2 \, c^{2} x^{2} \log\left(x\right)^{2} - 1}{x^{2}}\right)} \log\left(c^{2} x^{2}\right) - \frac{2 \, {\left(6 i \, \pi c^{2} x^{2} \log\left(x\right)^{2} + 6 \, c^{2} x^{2} \log\left(c x + 1\right) \log\left(x\right)^{2} + 6 \, c^{2} x^{2} \log\left(-c x + 1\right) \log\left(x\right)^{2} + 4 \, c^{2} x^{2} \log\left(x\right)^{3} + 12 \, c^{2} x^{2} {\rm Li}_2\left(c x\right) \log\left(x\right) + 12 \, c^{2} x^{2} {\rm Li}_2\left(-c x\right) \log\left(x\right) - 3\right)}}{x^{2}}\right)} a b^{2} c^{2} - 96 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right) \log\left(x\right)}{c^{2} x^{7} - x^{5}}\,{d x} + 96 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)^{2}}{c^{2} x^{7} - x^{5}}\,{d x} - 96 \, a b^{2} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{c^{2} x^{7} - x^{5}}\,{d x} + 24 \, b^{3} c^{2} \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{c^{2} x^{7} - x^{5}}\,{d x} - 24 \, {\left(2 \, c^{4} \log\left(c x + 1\right) + 2 \, c^{4} \log\left(c x - 1\right) - 4 \, c^{4} \log\left(x\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} a b^{2} \log\left(c\right)^{2} - 96 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{c^{2} x^{7} - x^{5}}\,{d x} \log\left(c\right)^{2} + 12 \, {\left(8 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{4} + 8 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{4} + 2 \, {\left(2 \, c^{4} \log\left(c x + 1\right) + 2 \, c^{4} \log\left(c x - 1\right) - 4 \, c^{4} \log\left(x\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} \log\left(c^{2} x^{2}\right) - \frac{8 \, c^{4} x^{4} \log\left(c x + 1\right) \log\left(x\right) + 8 \, c^{4} x^{4} \log\left(c x - 1\right) \log\left(x\right) - 8 \, c^{4} x^{4} \log\left(x\right)^{2} - 4 \, c^{2} x^{2} - 1}{x^{4}}\right)} a b^{2} \log\left(c\right) - 12 \, {\left(8 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{4} + 8 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{4} + 4 \, {\left(2 \, c^{4} \log\left(c x + 1\right) + 2 \, c^{4} \log\left(c x - 1\right) - 4 \, c^{4} \log\left(x\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} \log\left(x\right) - \frac{8 \, c^{4} x^{4} \log\left(c x + 1\right) \log\left(x\right) + 8 \, c^{4} x^{4} \log\left(c x - 1\right) \log\left(x\right) - 8 \, c^{4} x^{4} \log\left(x\right)^{2} - 4 \, c^{2} x^{2} - 1}{x^{4}}\right)} a b^{2} \log\left(c\right) + 96 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{c^{2} x^{7} - x^{5}}\,{d x} \log\left(c\right) - 192 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)}{c^{2} x^{7} - x^{5}}\,{d x} \log\left(c\right) + {\left(32 \, c^{4} \log\left(x\right)^{3} - 48 \, {\left(\log\left(c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(-c x)\right)} c^{4} - 48 \, {\left(\log\left(-c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(c x)\right)} c^{4} - \frac{24 \, {\left(2 \, c^{2} \log\left(x\right)^{2} + 2 \, c^{2} \log\left(x\right) + c^{2}\right)}}{x^{2}} - \frac{3 \, {\left(8 \, \log\left(x\right)^{2} + 4 \, \log\left(x\right) + 1\right)}}{x^{4}}\right)} a b^{2} + 2 \, {\left(48 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{4} \log\left(c\right) + 48 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{4} \log\left(c\right) + 48 \, {\left(\log\left(c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(-c x)\right)} c^{4} + 48 \, {\left(\log\left(-c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(c x)\right)} c^{4} + 6 \, {\left(8 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{4} + 8 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{4} + 2 \, {\left(2 \, c^{4} \log\left(c x + 1\right) + 2 \, c^{4} \log\left(c x - 1\right) - 4 \, c^{4} \log\left(x\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} \log\left(c^{2} x^{2}\right) - \frac{8 \, c^{4} x^{4} \log\left(c x + 1\right) \log\left(x\right) + 8 \, c^{4} x^{4} \log\left(c x - 1\right) \log\left(x\right) - 8 \, c^{4} x^{4} \log\left(x\right)^{2} - 4 \, c^{2} x^{2} - 1}{x^{4}}\right)} \log\left(x\right) - \frac{24 \, c^{4} x^{4} \log\left(-c x + 1\right) \log\left(x\right)^{2} - 16 \, c^{4} x^{4} \log\left(x\right)^{3} + 48 \, c^{4} x^{4} {\rm Li}_2\left(c x\right) \log\left(x\right) + 48 \, c^{4} x^{4} {\rm Li}_2\left(-c x\right) \log\left(x\right) - 24 \, {\left(-i \, \pi c^{4} + 2 \, c^{4} \log\left(c\right)\right)} x^{4} \log\left(x\right)^{2} - 24 \, {\left(c^{2} \log\left(c\right) + c^{2}\right)} x^{2} + 48 \, {\left(c^{4} x^{4} \log\left(c\right) \log\left(x\right) + c^{4} x^{4} \log\left(x\right)^{2}\right)} \log\left(c x + 1\right) + 24 \, {\left(2 \, c^{4} x^{4} \log\left(c\right) \log\left(x\right) + c^{4} x^{4} \log\left(x\right)^{2}\right)} \log\left(c x - 1\right) - 6 \, {\left(4 \, c^{2} x^{2} + 1\right)} \log\left(x\right) - 6 \, \log\left(c\right) - 3}{x^{4}}\right)} a b^{2} - {\left(48 \, {\left(\log\left(c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(-c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(-c x)\right)} c^{4} + 48 \, {\left(\log\left(-c x + 1\right) \log\left(x\right)^{2} + 2 \, {\rm Li}_2\left(c x\right) \log\left(x\right) - 2 \, {\rm Li}_{3}(c x)\right)} c^{4} + 6 \, {\left(2 \, c^{4} \log\left(c x + 1\right) + 2 \, c^{4} \log\left(c x - 1\right) - 4 \, c^{4} \log\left(x\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} \log\left(c^{2} x^{2}\right)^{2} + 6 \, {\left(8 \, {\left(\log\left(c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-c x\right)\right)} c^{4} + 8 \, {\left(\log\left(-c x + 1\right) \log\left(x\right) + {\rm Li}_2\left(c x\right)\right)} c^{4} - \frac{8 \, c^{4} x^{4} \log\left(c x + 1\right) \log\left(x\right) + 8 \, c^{4} x^{4} \log\left(c x - 1\right) \log\left(x\right) - 8 \, c^{4} x^{4} \log\left(x\right)^{2} - 4 \, c^{2} x^{2} - 1}{x^{4}}\right)} \log\left(c^{2} x^{2}\right) - \frac{48 i \, \pi c^{4} x^{4} \log\left(x\right)^{2} + 48 \, c^{4} x^{4} \log\left(c x + 1\right) \log\left(x\right)^{2} + 48 \, c^{4} x^{4} \log\left(-c x + 1\right) \log\left(x\right)^{2} + 32 \, c^{4} x^{4} \log\left(x\right)^{3} + 96 \, c^{4} x^{4} {\rm Li}_2\left(c x\right) \log\left(x\right) + 96 \, c^{4} x^{4} {\rm Li}_2\left(-c x\right) \log\left(x\right) - 24 \, c^{2} x^{2} - 3}{x^{4}}\right)} a b^{2} - 24 \, b^{3} \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{c^{2} x^{7} - x^{5}}\,{d x} + 6 \, b^{3} \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \log\left(c^{2} x^{2}\right)^{2}}{c^{2} x^{7} - x^{5}}\,{d x} + 96 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right) \log\left(x\right)}{c^{2} x^{7} - x^{5}}\,{d x} - 96 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)^{2}}{c^{2} x^{7} - x^{5}}\,{d x} + 96 \, a b^{2} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2}}{c^{2} x^{7} - x^{5}}\,{d x} - 24 \, b^{3} \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)}{c^{2} x^{7} - x^{5}}\,{d x}\right)} x^{4}}{16 \, x^{4}}"," ",0,"3/32*a^2*b*((3*c^5*arctan(c*x*sqrt(-1/(c^2*x^2) + 1)) + (3*c^8*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 5*c^6*x*sqrt(-1/(c^2*x^2) + 1))/(c^4*x^4*(1/(c^2*x^2) - 1)^2 - 2*c^2*x^2*(1/(c^2*x^2) - 1) + 1))/c - 8*arcsec(c*x)/x^4) - 1/4*a^3/x^4 - 1/16*(4*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 - 3*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)^2 + 12*(2*(c^2*log(c*x + 1) + c^2*log(c*x - 1) - 2*c^2*log(x) + 1/x^2)*a*b^2*c^2*log(c)^2 + 64*b^3*c^2*integrate(1/16*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^7 - x^5), x)*log(c)^2 - 64*b^3*c^2*integrate(1/16*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^7 - x^5), x)*log(c) + 128*b^3*c^2*integrate(1/16*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)/(c^2*x^7 - x^5), x)*log(c) - 64*a*b^2*c^2*integrate(1/16*x^2*log(c^2*x^2)/(c^2*x^7 - x^5), x)*log(c) + 128*a*b^2*c^2*integrate(1/16*x^2*log(x)/(c^2*x^7 - x^5), x)*log(c) - 64*b^3*c^2*integrate(1/16*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)*log(x)/(c^2*x^7 - x^5), x) + 64*b^3*c^2*integrate(1/16*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)^2/(c^2*x^7 - x^5), x) - 64*a*b^2*c^2*integrate(1/16*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2/(c^2*x^7 - x^5), x) + 16*b^3*c^2*integrate(1/16*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^7 - x^5), x) + 16*a*b^2*c^2*integrate(1/16*x^2*log(c^2*x^2)^2/(c^2*x^7 - x^5), x) - 64*a*b^2*c^2*integrate(1/16*x^2*log(c^2*x^2)*log(x)/(c^2*x^7 - x^5), x) + 64*a*b^2*c^2*integrate(1/16*x^2*log(x)^2/(c^2*x^7 - x^5), x) - (2*c^4*log(c*x + 1) + 2*c^4*log(c*x - 1) - 4*c^4*log(x) + (2*c^2*x^2 + 1)/x^4)*a*b^2*log(c)^2 - 64*b^3*integrate(1/16*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(c^2*x^7 - x^5), x)*log(c)^2 + 64*b^3*integrate(1/16*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^7 - x^5), x)*log(c) - 128*b^3*integrate(1/16*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)/(c^2*x^7 - x^5), x)*log(c) + 64*a*b^2*integrate(1/16*log(c^2*x^2)/(c^2*x^7 - x^5), x)*log(c) - 128*a*b^2*integrate(1/16*log(x)/(c^2*x^7 - x^5), x)*log(c) - 16*b^3*integrate(1/16*sqrt(c*x + 1)*sqrt(c*x - 1)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2/(c^2*x^7 - x^5), x) + 4*b^3*integrate(1/16*sqrt(c*x + 1)*sqrt(c*x - 1)*log(c^2*x^2)^2/(c^2*x^7 - x^5), x) + 64*b^3*integrate(1/16*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)*log(x)/(c^2*x^7 - x^5), x) - 64*b^3*integrate(1/16*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x)^2/(c^2*x^7 - x^5), x) + 64*a*b^2*integrate(1/16*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2/(c^2*x^7 - x^5), x) - 16*b^3*integrate(1/16*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)/(c^2*x^7 - x^5), x) - 16*a*b^2*integrate(1/16*log(c^2*x^2)^2/(c^2*x^7 - x^5), x) + 64*a*b^2*integrate(1/16*log(c^2*x^2)*log(x)/(c^2*x^7 - x^5), x) - 64*a*b^2*integrate(1/16*log(x)^2/(c^2*x^7 - x^5), x))*x^4)/x^4","F",0
33,0,0,0,0.000000," ","integrate(x/(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\int \frac{x}{b \operatorname{arcsec}\left(c x\right) + a}\,{d x}"," ",0,"integrate(x/(b*arcsec(c*x) + a), x)","F",0
34,0,0,0,0.000000," ","integrate(1/(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\int \frac{1}{b \operatorname{arcsec}\left(c x\right) + a}\,{d x}"," ",0,"integrate(1/(b*arcsec(c*x) + a), x)","F",0
35,0,0,0,0.000000," ","integrate(1/x/(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/((b*arcsec(c*x) + a)*x), x)","F",0
36,0,0,0,0.000000," ","integrate(1/x^2/(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{2}}\,{d x}"," ",0,"integrate(1/((b*arcsec(c*x) + a)*x^2), x)","F",0
37,0,0,0,0.000000," ","integrate(1/x^3/(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{3}}\,{d x}"," ",0,"integrate(1/((b*arcsec(c*x) + a)*x^3), x)","F",0
38,0,0,0,0.000000," ","integrate(1/x^4/(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} x^{4}}\,{d x}"," ",0,"integrate(1/((b*arcsec(c*x) + a)*x^4), x)","F",0
39,0,0,0,0.000000," ","integrate(x/(a+b*arcsec(c*x))^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(b x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + a x^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1} + 4 \, {\left(4 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{3} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{3} \log\left(c\right)^{2} + 8 \, b^{3} \log\left(c\right) \log\left(x\right) + 4 \, b^{3} \log\left(x\right)^{2} + 8 \, a b^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, a^{2} b - 4 \, {\left(b^{3} \log\left(c\right) + b^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \int \frac{{\left(3 \, a c^{2} x^{3} - 2 \, a x + {\left(3 \, b c^{2} x^{3} - 2 \, b x\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{4 \, b^{3} \log\left(c\right)^{2} + 4 \, a^{2} b - 4 \, {\left(b^{3} c^{2} \log\left(c\right)^{2} + a^{2} b c^{2}\right)} x^{2} - 4 \, {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(c^{2} x^{2}\right)^{2} - 4 \, {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)^{2} - 8 \, {\left(a b^{2} c^{2} x^{2} - a b^{2}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, {\left(b^{3} c^{2} x^{2} \log\left(c\right) - b^{3} \log\left(c\right) + {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) - 8 \, {\left(b^{3} c^{2} x^{2} \log\left(c\right) - b^{3} \log\left(c\right)\right)} \log\left(x\right)}\,{d x}}{4 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{3} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{3} \log\left(c\right)^{2} + 8 \, b^{3} \log\left(c\right) \log\left(x\right) + 4 \, b^{3} \log\left(x\right)^{2} + 8 \, a b^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, a^{2} b - 4 \, {\left(b^{3} \log\left(c\right) + b^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)}"," ",0,"-(4*(b*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + a*x^2)*sqrt(c*x + 1)*sqrt(c*x - 1) - (4*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^3*log(c^2*x^2)^2 + 4*b^3*log(c)^2 + 8*b^3*log(c)*log(x) + 4*b^3*log(x)^2 + 8*a*b^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*a^2*b - 4*(b^3*log(c) + b^3*log(x))*log(c^2*x^2))*integrate(-4*(3*a*c^2*x^3 - 2*a*x + (3*b*c^2*x^3 - 2*b*x)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*sqrt(c*x + 1)*sqrt(c*x - 1)/(4*b^3*log(c)^2 + 4*a^2*b - 4*(b^3*c^2*log(c)^2 + a^2*b*c^2)*x^2 - 4*(b^3*c^2*x^2 - b^3)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - (b^3*c^2*x^2 - b^3)*log(c^2*x^2)^2 - 4*(b^3*c^2*x^2 - b^3)*log(x)^2 - 8*(a*b^2*c^2*x^2 - a*b^2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*(b^3*c^2*x^2*log(c) - b^3*log(c) + (b^3*c^2*x^2 - b^3)*log(x))*log(c^2*x^2) - 8*(b^3*c^2*x^2*log(c) - b^3*log(c))*log(x)), x))/(4*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^3*log(c^2*x^2)^2 + 4*b^3*log(c)^2 + 8*b^3*log(c)*log(x) + 4*b^3*log(x)^2 + 8*a*b^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*a^2*b - 4*(b^3*log(c) + b^3*log(x))*log(c^2*x^2))","F",0
40,0,0,0,0.000000," ","integrate(1/(a+b*arcsec(c*x))^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(b x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + a x\right)} \sqrt{c x + 1} \sqrt{c x - 1} + 4 \, {\left(4 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{3} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{3} \log\left(c\right)^{2} + 8 \, b^{3} \log\left(c\right) \log\left(x\right) + 4 \, b^{3} \log\left(x\right)^{2} + 8 \, a b^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, a^{2} b - 4 \, {\left(b^{3} \log\left(c\right) + b^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \int \frac{{\left(2 \, a c^{2} x^{2} + {\left(2 \, b c^{2} x^{2} - b\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - a\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{4 \, b^{3} \log\left(c\right)^{2} + 4 \, a^{2} b - 4 \, {\left(b^{3} c^{2} \log\left(c\right)^{2} + a^{2} b c^{2}\right)} x^{2} - 4 \, {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(c^{2} x^{2}\right)^{2} - 4 \, {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)^{2} - 8 \, {\left(a b^{2} c^{2} x^{2} - a b^{2}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, {\left(b^{3} c^{2} x^{2} \log\left(c\right) - b^{3} \log\left(c\right) + {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) - 8 \, {\left(b^{3} c^{2} x^{2} \log\left(c\right) - b^{3} \log\left(c\right)\right)} \log\left(x\right)}\,{d x}}{4 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{3} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{3} \log\left(c\right)^{2} + 8 \, b^{3} \log\left(c\right) \log\left(x\right) + 4 \, b^{3} \log\left(x\right)^{2} + 8 \, a b^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, a^{2} b - 4 \, {\left(b^{3} \log\left(c\right) + b^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)}"," ",0,"-(4*(b*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + a*x)*sqrt(c*x + 1)*sqrt(c*x - 1) - (4*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^3*log(c^2*x^2)^2 + 4*b^3*log(c)^2 + 8*b^3*log(c)*log(x) + 4*b^3*log(x)^2 + 8*a*b^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*a^2*b - 4*(b^3*log(c) + b^3*log(x))*log(c^2*x^2))*integrate(-4*(2*a*c^2*x^2 + (2*b*c^2*x^2 - b)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - a)*sqrt(c*x + 1)*sqrt(c*x - 1)/(4*b^3*log(c)^2 + 4*a^2*b - 4*(b^3*c^2*log(c)^2 + a^2*b*c^2)*x^2 - 4*(b^3*c^2*x^2 - b^3)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - (b^3*c^2*x^2 - b^3)*log(c^2*x^2)^2 - 4*(b^3*c^2*x^2 - b^3)*log(x)^2 - 8*(a*b^2*c^2*x^2 - a*b^2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*(b^3*c^2*x^2*log(c) - b^3*log(c) + (b^3*c^2*x^2 - b^3)*log(x))*log(c^2*x^2) - 8*(b^3*c^2*x^2*log(c) - b^3*log(c))*log(x)), x))/(4*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^3*log(c^2*x^2)^2 + 4*b^3*log(c)^2 + 8*b^3*log(c)*log(x) + 4*b^3*log(x)^2 + 8*a*b^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*a^2*b - 4*(b^3*log(c) + b^3*log(x))*log(c^2*x^2))","F",0
41,0,0,0,0.000000," ","integrate(1/x/(a+b*arcsec(c*x))^2,x, algorithm=""maxima"")","-\frac{4 \, \sqrt{c x + 1} \sqrt{c x - 1} {\left(b \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + a\right)} + 4 \, {\left(4 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{3} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{3} \log\left(c\right)^{2} + 8 \, b^{3} \log\left(c\right) \log\left(x\right) + 4 \, b^{3} \log\left(x\right)^{2} + 8 \, a b^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, a^{2} b - 4 \, {\left(b^{3} \log\left(c\right) + b^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \int \frac{{\left(b c^{2} x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + a c^{2} x\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{4 \, b^{3} \log\left(c\right)^{2} + 4 \, a^{2} b - 4 \, {\left(b^{3} c^{2} \log\left(c\right)^{2} + a^{2} b c^{2}\right)} x^{2} - 4 \, {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(c^{2} x^{2}\right)^{2} - 4 \, {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)^{2} - 8 \, {\left(a b^{2} c^{2} x^{2} - a b^{2}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, {\left(b^{3} c^{2} x^{2} \log\left(c\right) - b^{3} \log\left(c\right) + {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) - 8 \, {\left(b^{3} c^{2} x^{2} \log\left(c\right) - b^{3} \log\left(c\right)\right)} \log\left(x\right)}\,{d x}}{4 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{3} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{3} \log\left(c\right)^{2} + 8 \, b^{3} \log\left(c\right) \log\left(x\right) + 4 \, b^{3} \log\left(x\right)^{2} + 8 \, a b^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, a^{2} b - 4 \, {\left(b^{3} \log\left(c\right) + b^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)}"," ",0,"-(4*sqrt(c*x + 1)*sqrt(c*x - 1)*(b*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + a) - (4*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^3*log(c^2*x^2)^2 + 4*b^3*log(c)^2 + 8*b^3*log(c)*log(x) + 4*b^3*log(x)^2 + 8*a*b^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*a^2*b - 4*(b^3*log(c) + b^3*log(x))*log(c^2*x^2))*integrate(-4*(b*c^2*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + a*c^2*x)*sqrt(c*x + 1)*sqrt(c*x - 1)/(4*b^3*log(c)^2 + 4*a^2*b - 4*(b^3*c^2*log(c)^2 + a^2*b*c^2)*x^2 - 4*(b^3*c^2*x^2 - b^3)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - (b^3*c^2*x^2 - b^3)*log(c^2*x^2)^2 - 4*(b^3*c^2*x^2 - b^3)*log(x)^2 - 8*(a*b^2*c^2*x^2 - a*b^2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*(b^3*c^2*x^2*log(c) - b^3*log(c) + (b^3*c^2*x^2 - b^3)*log(x))*log(c^2*x^2) - 8*(b^3*c^2*x^2*log(c) - b^3*log(c))*log(x)), x))/(4*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^3*log(c^2*x^2)^2 + 4*b^3*log(c)^2 + 8*b^3*log(c)*log(x) + 4*b^3*log(x)^2 + 8*a*b^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*a^2*b - 4*(b^3*log(c) + b^3*log(x))*log(c^2*x^2))","F",0
42,0,0,0,0.000000," ","integrate(1/x^2/(a+b*arcsec(c*x))^2,x, algorithm=""maxima"")","-\frac{4 \, \sqrt{c x + 1} \sqrt{c x - 1} {\left(b \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + a\right)} - 4 \, {\left(4 \, b^{3} x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{3} x \log\left(c^{2} x^{2}\right)^{2} + 8 \, b^{3} x \log\left(c\right) \log\left(x\right) + 4 \, b^{3} x \log\left(x\right)^{2} + 8 \, a b^{2} x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, {\left(b^{3} \log\left(c\right)^{2} + a^{2} b\right)} x - 4 \, {\left(b^{3} x \log\left(c\right) + b^{3} x \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} {\left(b \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + a\right)}}{4 \, {\left(b^{3} c^{2} \log\left(c\right)^{2} + a^{2} b c^{2}\right)} x^{4} - 4 \, {\left(b^{3} \log\left(c\right)^{2} + a^{2} b\right)} x^{2} + 4 \, {\left(b^{3} c^{2} x^{4} - b^{3} x^{2}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + {\left(b^{3} c^{2} x^{4} - b^{3} x^{2}\right)} \log\left(c^{2} x^{2}\right)^{2} + 4 \, {\left(b^{3} c^{2} x^{4} - b^{3} x^{2}\right)} \log\left(x\right)^{2} + 8 \, {\left(a b^{2} c^{2} x^{4} - a b^{2} x^{2}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 4 \, {\left(b^{3} c^{2} x^{4} \log\left(c\right) - b^{3} x^{2} \log\left(c\right) + {\left(b^{3} c^{2} x^{4} - b^{3} x^{2}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + 8 \, {\left(b^{3} c^{2} x^{4} \log\left(c\right) - b^{3} x^{2} \log\left(c\right)\right)} \log\left(x\right)}\,{d x}}{4 \, b^{3} x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{3} x \log\left(c^{2} x^{2}\right)^{2} + 8 \, b^{3} x \log\left(c\right) \log\left(x\right) + 4 \, b^{3} x \log\left(x\right)^{2} + 8 \, a b^{2} x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, {\left(b^{3} \log\left(c\right)^{2} + a^{2} b\right)} x - 4 \, {\left(b^{3} x \log\left(c\right) + b^{3} x \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)}"," ",0,"-(4*sqrt(c*x + 1)*sqrt(c*x - 1)*(b*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + a) - (4*b^3*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^3*x*log(c^2*x^2)^2 + 8*b^3*x*log(c)*log(x) + 4*b^3*x*log(x)^2 + 8*a*b^2*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*(b^3*log(c)^2 + a^2*b)*x - 4*(b^3*x*log(c) + b^3*x*log(x))*log(c^2*x^2))*integrate(4*sqrt(c*x + 1)*sqrt(c*x - 1)*(b*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + a)/(4*(b^3*c^2*log(c)^2 + a^2*b*c^2)*x^4 - 4*(b^3*log(c)^2 + a^2*b)*x^2 + 4*(b^3*c^2*x^4 - b^3*x^2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + (b^3*c^2*x^4 - b^3*x^2)*log(c^2*x^2)^2 + 4*(b^3*c^2*x^4 - b^3*x^2)*log(x)^2 + 8*(a*b^2*c^2*x^4 - a*b^2*x^2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 4*(b^3*c^2*x^4*log(c) - b^3*x^2*log(c) + (b^3*c^2*x^4 - b^3*x^2)*log(x))*log(c^2*x^2) + 8*(b^3*c^2*x^4*log(c) - b^3*x^2*log(c))*log(x)), x))/(4*b^3*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^3*x*log(c^2*x^2)^2 + 8*b^3*x*log(c)*log(x) + 4*b^3*x*log(x)^2 + 8*a*b^2*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*(b^3*log(c)^2 + a^2*b)*x - 4*(b^3*x*log(c) + b^3*x*log(x))*log(c^2*x^2))","F",0
43,0,0,0,0.000000," ","integrate(1/x^3/(a+b*arcsec(c*x))^2,x, algorithm=""maxima"")","-\frac{4 \, \sqrt{c x + 1} \sqrt{c x - 1} {\left(b \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + a\right)} + 4 \, {\left(4 \, b^{3} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{3} x^{2} \log\left(c^{2} x^{2}\right)^{2} + 8 \, b^{3} x^{2} \log\left(c\right) \log\left(x\right) + 4 \, b^{3} x^{2} \log\left(x\right)^{2} + 8 \, a b^{2} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, {\left(b^{3} \log\left(c\right)^{2} + a^{2} b\right)} x^{2} - 4 \, {\left(b^{3} x^{2} \log\left(c\right) + b^{3} x^{2} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \int \frac{{\left(a c^{2} x^{2} + {\left(b c^{2} x^{2} - 2 \, b\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 2 \, a\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{4 \, {\left(b^{3} c^{2} \log\left(c\right)^{2} + a^{2} b c^{2}\right)} x^{5} - 4 \, {\left(b^{3} \log\left(c\right)^{2} + a^{2} b\right)} x^{3} + 4 \, {\left(b^{3} c^{2} x^{5} - b^{3} x^{3}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + {\left(b^{3} c^{2} x^{5} - b^{3} x^{3}\right)} \log\left(c^{2} x^{2}\right)^{2} + 4 \, {\left(b^{3} c^{2} x^{5} - b^{3} x^{3}\right)} \log\left(x\right)^{2} + 8 \, {\left(a b^{2} c^{2} x^{5} - a b^{2} x^{3}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 4 \, {\left(b^{3} c^{2} x^{5} \log\left(c\right) - b^{3} x^{3} \log\left(c\right) + {\left(b^{3} c^{2} x^{5} - b^{3} x^{3}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + 8 \, {\left(b^{3} c^{2} x^{5} \log\left(c\right) - b^{3} x^{3} \log\left(c\right)\right)} \log\left(x\right)}\,{d x}}{4 \, b^{3} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{3} x^{2} \log\left(c^{2} x^{2}\right)^{2} + 8 \, b^{3} x^{2} \log\left(c\right) \log\left(x\right) + 4 \, b^{3} x^{2} \log\left(x\right)^{2} + 8 \, a b^{2} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, {\left(b^{3} \log\left(c\right)^{2} + a^{2} b\right)} x^{2} - 4 \, {\left(b^{3} x^{2} \log\left(c\right) + b^{3} x^{2} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)}"," ",0,"-(4*sqrt(c*x + 1)*sqrt(c*x - 1)*(b*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + a) + (4*b^3*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^3*x^2*log(c^2*x^2)^2 + 8*b^3*x^2*log(c)*log(x) + 4*b^3*x^2*log(x)^2 + 8*a*b^2*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*(b^3*log(c)^2 + a^2*b)*x^2 - 4*(b^3*x^2*log(c) + b^3*x^2*log(x))*log(c^2*x^2))*integrate(4*(a*c^2*x^2 + (b*c^2*x^2 - 2*b)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 2*a)*sqrt(c*x + 1)*sqrt(c*x - 1)/(4*(b^3*c^2*log(c)^2 + a^2*b*c^2)*x^5 - 4*(b^3*log(c)^2 + a^2*b)*x^3 + 4*(b^3*c^2*x^5 - b^3*x^3)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + (b^3*c^2*x^5 - b^3*x^3)*log(c^2*x^2)^2 + 4*(b^3*c^2*x^5 - b^3*x^3)*log(x)^2 + 8*(a*b^2*c^2*x^5 - a*b^2*x^3)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 4*(b^3*c^2*x^5*log(c) - b^3*x^3*log(c) + (b^3*c^2*x^5 - b^3*x^3)*log(x))*log(c^2*x^2) + 8*(b^3*c^2*x^5*log(c) - b^3*x^3*log(c))*log(x)), x))/(4*b^3*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^3*x^2*log(c^2*x^2)^2 + 8*b^3*x^2*log(c)*log(x) + 4*b^3*x^2*log(x)^2 + 8*a*b^2*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*(b^3*log(c)^2 + a^2*b)*x^2 - 4*(b^3*x^2*log(c) + b^3*x^2*log(x))*log(c^2*x^2))","F",0
44,0,0,0,0.000000," ","integrate(1/x^4/(a+b*arcsec(c*x))^2,x, algorithm=""maxima"")","-\frac{4 \, \sqrt{c x + 1} \sqrt{c x - 1} {\left(b \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + a\right)} + 4 \, {\left(4 \, b^{3} x^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{3} x^{3} \log\left(c^{2} x^{2}\right)^{2} + 8 \, b^{3} x^{3} \log\left(c\right) \log\left(x\right) + 4 \, b^{3} x^{3} \log\left(x\right)^{2} + 8 \, a b^{2} x^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, {\left(b^{3} \log\left(c\right)^{2} + a^{2} b\right)} x^{3} - 4 \, {\left(b^{3} x^{3} \log\left(c\right) + b^{3} x^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \int \frac{{\left(2 \, a c^{2} x^{2} + {\left(2 \, b c^{2} x^{2} - 3 \, b\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 3 \, a\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{4 \, {\left(b^{3} c^{2} \log\left(c\right)^{2} + a^{2} b c^{2}\right)} x^{6} - 4 \, {\left(b^{3} \log\left(c\right)^{2} + a^{2} b\right)} x^{4} + 4 \, {\left(b^{3} c^{2} x^{6} - b^{3} x^{4}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + {\left(b^{3} c^{2} x^{6} - b^{3} x^{4}\right)} \log\left(c^{2} x^{2}\right)^{2} + 4 \, {\left(b^{3} c^{2} x^{6} - b^{3} x^{4}\right)} \log\left(x\right)^{2} + 8 \, {\left(a b^{2} c^{2} x^{6} - a b^{2} x^{4}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 4 \, {\left(b^{3} c^{2} x^{6} \log\left(c\right) - b^{3} x^{4} \log\left(c\right) + {\left(b^{3} c^{2} x^{6} - b^{3} x^{4}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + 8 \, {\left(b^{3} c^{2} x^{6} \log\left(c\right) - b^{3} x^{4} \log\left(c\right)\right)} \log\left(x\right)}\,{d x}}{4 \, b^{3} x^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{3} x^{3} \log\left(c^{2} x^{2}\right)^{2} + 8 \, b^{3} x^{3} \log\left(c\right) \log\left(x\right) + 4 \, b^{3} x^{3} \log\left(x\right)^{2} + 8 \, a b^{2} x^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, {\left(b^{3} \log\left(c\right)^{2} + a^{2} b\right)} x^{3} - 4 \, {\left(b^{3} x^{3} \log\left(c\right) + b^{3} x^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)}"," ",0,"-(4*sqrt(c*x + 1)*sqrt(c*x - 1)*(b*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + a) + (4*b^3*x^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^3*x^3*log(c^2*x^2)^2 + 8*b^3*x^3*log(c)*log(x) + 4*b^3*x^3*log(x)^2 + 8*a*b^2*x^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*(b^3*log(c)^2 + a^2*b)*x^3 - 4*(b^3*x^3*log(c) + b^3*x^3*log(x))*log(c^2*x^2))*integrate(4*(2*a*c^2*x^2 + (2*b*c^2*x^2 - 3*b)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 3*a)*sqrt(c*x + 1)*sqrt(c*x - 1)/(4*(b^3*c^2*log(c)^2 + a^2*b*c^2)*x^6 - 4*(b^3*log(c)^2 + a^2*b)*x^4 + 4*(b^3*c^2*x^6 - b^3*x^4)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + (b^3*c^2*x^6 - b^3*x^4)*log(c^2*x^2)^2 + 4*(b^3*c^2*x^6 - b^3*x^4)*log(x)^2 + 8*(a*b^2*c^2*x^6 - a*b^2*x^4)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 4*(b^3*c^2*x^6*log(c) - b^3*x^4*log(c) + (b^3*c^2*x^6 - b^3*x^4)*log(x))*log(c^2*x^2) + 8*(b^3*c^2*x^6*log(c) - b^3*x^4*log(c))*log(x)), x))/(4*b^3*x^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^3*x^3*log(c^2*x^2)^2 + 8*b^3*x^3*log(c)*log(x) + 4*b^3*x^3*log(x)^2 + 8*a*b^2*x^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*(b^3*log(c)^2 + a^2*b)*x^3 - 4*(b^3*x^3*log(c) + b^3*x^3*log(x))*log(c^2*x^2))","F",0
45,0,0,0,0.000000," ","integrate(x/(a+b*arcsec(c*x))^3,x, algorithm=""maxima"")","-\frac{24 \, {\left(a b^{2} c^{2} \log\left(c\right)^{2} + a^{3} c^{2}\right)} x^{4} + 8 \, {\left(3 \, b^{3} c^{2} x^{4} - 2 \, b^{3} x^{2}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} - 16 \, {\left(a b^{2} \log\left(c\right)^{2} + a^{3}\right)} x^{2} + 24 \, {\left(3 \, a b^{2} c^{2} x^{4} - 2 \, a b^{2} x^{2}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 2 \, {\left(3 \, a b^{2} c^{2} x^{4} - 2 \, a b^{2} x^{2}\right)} \log\left(c^{2} x^{2}\right)^{2} + 8 \, {\left(3 \, a b^{2} c^{2} x^{4} - 2 \, a b^{2} x^{2}\right)} \log\left(x\right)^{2} + 2 \, {\left(4 \, b^{3} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - b^{3} x^{2} \log\left(c^{2} x^{2}\right)^{2} - 8 \, b^{3} x^{2} \log\left(c\right) \log\left(x\right) - 4 \, b^{3} x^{2} \log\left(x\right)^{2} + 8 \, a b^{2} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 4 \, {\left(b^{3} \log\left(c\right)^{2} - a^{2} b\right)} x^{2} + 4 \, {\left(b^{3} x^{2} \log\left(c\right) + b^{3} x^{2} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \sqrt{c x + 1} \sqrt{c x - 1} + 2 \, {\left(12 \, {\left(b^{3} c^{2} \log\left(c\right)^{2} + 3 \, a^{2} b c^{2}\right)} x^{4} - 8 \, {\left(b^{3} \log\left(c\right)^{2} + 3 \, a^{2} b\right)} x^{2} + {\left(3 \, b^{3} c^{2} x^{4} - 2 \, b^{3} x^{2}\right)} \log\left(c^{2} x^{2}\right)^{2} + 4 \, {\left(3 \, b^{3} c^{2} x^{4} - 2 \, b^{3} x^{2}\right)} \log\left(x\right)^{2} - 4 \, {\left(3 \, b^{3} c^{2} x^{4} \log\left(c\right) - 2 \, b^{3} x^{2} \log\left(c\right) + {\left(3 \, b^{3} c^{2} x^{4} - 2 \, b^{3} x^{2}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + 8 \, {\left(3 \, b^{3} c^{2} x^{4} \log\left(c\right) - 2 \, b^{3} x^{2} \log\left(c\right)\right)} \log\left(x\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 8 \, {\left(16 \, b^{6} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{4} + b^{6} \log\left(c^{2} x^{2}\right)^{4} + 16 \, b^{6} \log\left(c\right)^{4} + 64 \, b^{6} \log\left(c\right) \log\left(x\right)^{3} + 16 \, b^{6} \log\left(x\right)^{4} + 64 \, a b^{5} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} + 32 \, a^{2} b^{4} \log\left(c\right)^{2} + 16 \, a^{4} b^{2} - 8 \, {\left(b^{6} \log\left(c\right) + b^{6} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)^{3} + 8 \, {\left(b^{6} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{6} \log\left(c\right)^{2} + 8 \, b^{6} \log\left(c\right) \log\left(x\right) + 4 \, b^{6} \log\left(x\right)^{2} + 12 \, a^{2} b^{4} - 4 \, {\left(b^{6} \log\left(c\right) + b^{6} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 8 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + 6 \, b^{6} \log\left(c\right) \log\left(x\right) + 3 \, b^{6} \log\left(x\right)^{2} + a^{2} b^{4}\right)} \log\left(c^{2} x^{2}\right)^{2} + 32 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} \log\left(x\right)^{2} + 16 \, {\left(a b^{5} \log\left(c^{2} x^{2}\right)^{2} + 4 \, a b^{5} \log\left(c\right)^{2} + 8 \, a b^{5} \log\left(c\right) \log\left(x\right) + 4 \, a b^{5} \log\left(x\right)^{2} + 4 \, a^{3} b^{3} - 4 \, {\left(a b^{5} \log\left(c\right) + a b^{5} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 32 \, {\left(b^{6} \log\left(c\right)^{3} + 3 \, b^{6} \log\left(c\right) \log\left(x\right)^{2} + b^{6} \log\left(x\right)^{3} + a^{2} b^{4} \log\left(c\right) + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + 64 \, {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} \log\left(x\right)\right)} \int \frac{3 \, a c^{2} x^{3} - a x + {\left(3 \, b c^{2} x^{3} - b x\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{4 \, b^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{4} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{4} \log\left(c\right)^{2} + 8 \, b^{4} \log\left(c\right) \log\left(x\right) + 4 \, b^{4} \log\left(x\right)^{2} + 8 \, a b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, a^{2} b^{2} - 4 \, {\left(b^{4} \log\left(c\right) + b^{4} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)}\,{d x} - 8 \, {\left(3 \, a b^{2} c^{2} x^{4} \log\left(c\right) - 2 \, a b^{2} x^{2} \log\left(c\right) + {\left(3 \, a b^{2} c^{2} x^{4} - 2 \, a b^{2} x^{2}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + 16 \, {\left(3 \, a b^{2} c^{2} x^{4} \log\left(c\right) - 2 \, a b^{2} x^{2} \log\left(c\right)\right)} \log\left(x\right)}{16 \, b^{6} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{4} + b^{6} \log\left(c^{2} x^{2}\right)^{4} + 16 \, b^{6} \log\left(c\right)^{4} + 64 \, b^{6} \log\left(c\right) \log\left(x\right)^{3} + 16 \, b^{6} \log\left(x\right)^{4} + 64 \, a b^{5} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} + 32 \, a^{2} b^{4} \log\left(c\right)^{2} + 16 \, a^{4} b^{2} - 8 \, {\left(b^{6} \log\left(c\right) + b^{6} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)^{3} + 8 \, {\left(b^{6} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{6} \log\left(c\right)^{2} + 8 \, b^{6} \log\left(c\right) \log\left(x\right) + 4 \, b^{6} \log\left(x\right)^{2} + 12 \, a^{2} b^{4} - 4 \, {\left(b^{6} \log\left(c\right) + b^{6} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 8 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + 6 \, b^{6} \log\left(c\right) \log\left(x\right) + 3 \, b^{6} \log\left(x\right)^{2} + a^{2} b^{4}\right)} \log\left(c^{2} x^{2}\right)^{2} + 32 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} \log\left(x\right)^{2} + 16 \, {\left(a b^{5} \log\left(c^{2} x^{2}\right)^{2} + 4 \, a b^{5} \log\left(c\right)^{2} + 8 \, a b^{5} \log\left(c\right) \log\left(x\right) + 4 \, a b^{5} \log\left(x\right)^{2} + 4 \, a^{3} b^{3} - 4 \, {\left(a b^{5} \log\left(c\right) + a b^{5} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 32 \, {\left(b^{6} \log\left(c\right)^{3} + 3 \, b^{6} \log\left(c\right) \log\left(x\right)^{2} + b^{6} \log\left(x\right)^{3} + a^{2} b^{4} \log\left(c\right) + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + 64 \, {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} \log\left(x\right)}"," ",0,"-(24*(a*b^2*c^2*log(c)^2 + a^3*c^2)*x^4 + 8*(3*b^3*c^2*x^4 - 2*b^3*x^2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 - 16*(a*b^2*log(c)^2 + a^3)*x^2 + 24*(3*a*b^2*c^2*x^4 - 2*a*b^2*x^2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 2*(3*a*b^2*c^2*x^4 - 2*a*b^2*x^2)*log(c^2*x^2)^2 + 8*(3*a*b^2*c^2*x^4 - 2*a*b^2*x^2)*log(x)^2 + 2*(4*b^3*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - b^3*x^2*log(c^2*x^2)^2 - 8*b^3*x^2*log(c)*log(x) - 4*b^3*x^2*log(x)^2 + 8*a*b^2*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 4*(b^3*log(c)^2 - a^2*b)*x^2 + 4*(b^3*x^2*log(c) + b^3*x^2*log(x))*log(c^2*x^2))*sqrt(c*x + 1)*sqrt(c*x - 1) + 2*(12*(b^3*c^2*log(c)^2 + 3*a^2*b*c^2)*x^4 - 8*(b^3*log(c)^2 + 3*a^2*b)*x^2 + (3*b^3*c^2*x^4 - 2*b^3*x^2)*log(c^2*x^2)^2 + 4*(3*b^3*c^2*x^4 - 2*b^3*x^2)*log(x)^2 - 4*(3*b^3*c^2*x^4*log(c) - 2*b^3*x^2*log(c) + (3*b^3*c^2*x^4 - 2*b^3*x^2)*log(x))*log(c^2*x^2) + 8*(3*b^3*c^2*x^4*log(c) - 2*b^3*x^2*log(c))*log(x))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - (16*b^6*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^4 + b^6*log(c^2*x^2)^4 + 16*b^6*log(c)^4 + 64*b^6*log(c)*log(x)^3 + 16*b^6*log(x)^4 + 64*a*b^5*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 + 32*a^2*b^4*log(c)^2 + 16*a^4*b^2 - 8*(b^6*log(c) + b^6*log(x))*log(c^2*x^2)^3 + 8*(b^6*log(c^2*x^2)^2 + 4*b^6*log(c)^2 + 8*b^6*log(c)*log(x) + 4*b^6*log(x)^2 + 12*a^2*b^4 - 4*(b^6*log(c) + b^6*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 8*(3*b^6*log(c)^2 + 6*b^6*log(c)*log(x) + 3*b^6*log(x)^2 + a^2*b^4)*log(c^2*x^2)^2 + 32*(3*b^6*log(c)^2 + a^2*b^4)*log(x)^2 + 16*(a*b^5*log(c^2*x^2)^2 + 4*a*b^5*log(c)^2 + 8*a*b^5*log(c)*log(x) + 4*a*b^5*log(x)^2 + 4*a^3*b^3 - 4*(a*b^5*log(c) + a*b^5*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 32*(b^6*log(c)^3 + 3*b^6*log(c)*log(x)^2 + b^6*log(x)^3 + a^2*b^4*log(c) + (3*b^6*log(c)^2 + a^2*b^4)*log(x))*log(c^2*x^2) + 64*(b^6*log(c)^3 + a^2*b^4*log(c))*log(x))*integrate(8*(3*a*c^2*x^3 - a*x + (3*b*c^2*x^3 - b*x)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))/(4*b^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^4*log(c^2*x^2)^2 + 4*b^4*log(c)^2 + 8*b^4*log(c)*log(x) + 4*b^4*log(x)^2 + 8*a*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*a^2*b^2 - 4*(b^4*log(c) + b^4*log(x))*log(c^2*x^2)), x) - 8*(3*a*b^2*c^2*x^4*log(c) - 2*a*b^2*x^2*log(c) + (3*a*b^2*c^2*x^4 - 2*a*b^2*x^2)*log(x))*log(c^2*x^2) + 16*(3*a*b^2*c^2*x^4*log(c) - 2*a*b^2*x^2*log(c))*log(x))/(16*b^6*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^4 + b^6*log(c^2*x^2)^4 + 16*b^6*log(c)^4 + 64*b^6*log(c)*log(x)^3 + 16*b^6*log(x)^4 + 64*a*b^5*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 + 32*a^2*b^4*log(c)^2 + 16*a^4*b^2 - 8*(b^6*log(c) + b^6*log(x))*log(c^2*x^2)^3 + 8*(b^6*log(c^2*x^2)^2 + 4*b^6*log(c)^2 + 8*b^6*log(c)*log(x) + 4*b^6*log(x)^2 + 12*a^2*b^4 - 4*(b^6*log(c) + b^6*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 8*(3*b^6*log(c)^2 + 6*b^6*log(c)*log(x) + 3*b^6*log(x)^2 + a^2*b^4)*log(c^2*x^2)^2 + 32*(3*b^6*log(c)^2 + a^2*b^4)*log(x)^2 + 16*(a*b^5*log(c^2*x^2)^2 + 4*a*b^5*log(c)^2 + 8*a*b^5*log(c)*log(x) + 4*a*b^5*log(x)^2 + 4*a^3*b^3 - 4*(a*b^5*log(c) + a*b^5*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 32*(b^6*log(c)^3 + 3*b^6*log(c)*log(x)^2 + b^6*log(x)^3 + a^2*b^4*log(c) + (3*b^6*log(c)^2 + a^2*b^4)*log(x))*log(c^2*x^2) + 64*(b^6*log(c)^3 + a^2*b^4*log(c))*log(x))","F",0
46,0,0,0,0.000000," ","integrate(1/(a+b*arcsec(c*x))^3,x, algorithm=""maxima"")","-\frac{16 \, {\left(a b^{2} c^{2} \log\left(c\right)^{2} + a^{3} c^{2}\right)} x^{3} + 8 \, {\left(2 \, b^{3} c^{2} x^{3} - b^{3} x\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} + 24 \, {\left(2 \, a b^{2} c^{2} x^{3} - a b^{2} x\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 2 \, {\left(2 \, a b^{2} c^{2} x^{3} - a b^{2} x\right)} \log\left(c^{2} x^{2}\right)^{2} + 8 \, {\left(2 \, a b^{2} c^{2} x^{3} - a b^{2} x\right)} \log\left(x\right)^{2} + 2 \, {\left(4 \, b^{3} x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - b^{3} x \log\left(c^{2} x^{2}\right)^{2} - 8 \, b^{3} x \log\left(c\right) \log\left(x\right) - 4 \, b^{3} x \log\left(x\right)^{2} + 8 \, a b^{2} x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 4 \, {\left(b^{3} \log\left(c\right)^{2} - a^{2} b\right)} x + 4 \, {\left(b^{3} x \log\left(c\right) + b^{3} x \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \sqrt{c x + 1} \sqrt{c x - 1} - 8 \, {\left(a b^{2} \log\left(c\right)^{2} + a^{3}\right)} x + 2 \, {\left(8 \, {\left(b^{3} c^{2} \log\left(c\right)^{2} + 3 \, a^{2} b c^{2}\right)} x^{3} + {\left(2 \, b^{3} c^{2} x^{3} - b^{3} x\right)} \log\left(c^{2} x^{2}\right)^{2} + 4 \, {\left(2 \, b^{3} c^{2} x^{3} - b^{3} x\right)} \log\left(x\right)^{2} - 4 \, {\left(b^{3} \log\left(c\right)^{2} + 3 \, a^{2} b\right)} x - 4 \, {\left(2 \, b^{3} c^{2} x^{3} \log\left(c\right) - b^{3} x \log\left(c\right) + {\left(2 \, b^{3} c^{2} x^{3} - b^{3} x\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + 8 \, {\left(2 \, b^{3} c^{2} x^{3} \log\left(c\right) - b^{3} x \log\left(c\right)\right)} \log\left(x\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 2 \, {\left(16 \, b^{6} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{4} + b^{6} \log\left(c^{2} x^{2}\right)^{4} + 16 \, b^{6} \log\left(c\right)^{4} + 64 \, b^{6} \log\left(c\right) \log\left(x\right)^{3} + 16 \, b^{6} \log\left(x\right)^{4} + 64 \, a b^{5} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} + 32 \, a^{2} b^{4} \log\left(c\right)^{2} + 16 \, a^{4} b^{2} - 8 \, {\left(b^{6} \log\left(c\right) + b^{6} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)^{3} + 8 \, {\left(b^{6} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{6} \log\left(c\right)^{2} + 8 \, b^{6} \log\left(c\right) \log\left(x\right) + 4 \, b^{6} \log\left(x\right)^{2} + 12 \, a^{2} b^{4} - 4 \, {\left(b^{6} \log\left(c\right) + b^{6} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 8 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + 6 \, b^{6} \log\left(c\right) \log\left(x\right) + 3 \, b^{6} \log\left(x\right)^{2} + a^{2} b^{4}\right)} \log\left(c^{2} x^{2}\right)^{2} + 32 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} \log\left(x\right)^{2} + 16 \, {\left(a b^{5} \log\left(c^{2} x^{2}\right)^{2} + 4 \, a b^{5} \log\left(c\right)^{2} + 8 \, a b^{5} \log\left(c\right) \log\left(x\right) + 4 \, a b^{5} \log\left(x\right)^{2} + 4 \, a^{3} b^{3} - 4 \, {\left(a b^{5} \log\left(c\right) + a b^{5} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 32 \, {\left(b^{6} \log\left(c\right)^{3} + 3 \, b^{6} \log\left(c\right) \log\left(x\right)^{2} + b^{6} \log\left(x\right)^{3} + a^{2} b^{4} \log\left(c\right) + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + 64 \, {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} \log\left(x\right)\right)} \int \frac{6 \, a c^{2} x^{2} + {\left(6 \, b c^{2} x^{2} - b\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - a}{4 \, b^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{4} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{4} \log\left(c\right)^{2} + 8 \, b^{4} \log\left(c\right) \log\left(x\right) + 4 \, b^{4} \log\left(x\right)^{2} + 8 \, a b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, a^{2} b^{2} - 4 \, {\left(b^{4} \log\left(c\right) + b^{4} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)}\,{d x} - 8 \, {\left(2 \, a b^{2} c^{2} x^{3} \log\left(c\right) - a b^{2} x \log\left(c\right) + {\left(2 \, a b^{2} c^{2} x^{3} - a b^{2} x\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + 16 \, {\left(2 \, a b^{2} c^{2} x^{3} \log\left(c\right) - a b^{2} x \log\left(c\right)\right)} \log\left(x\right)}{16 \, b^{6} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{4} + b^{6} \log\left(c^{2} x^{2}\right)^{4} + 16 \, b^{6} \log\left(c\right)^{4} + 64 \, b^{6} \log\left(c\right) \log\left(x\right)^{3} + 16 \, b^{6} \log\left(x\right)^{4} + 64 \, a b^{5} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} + 32 \, a^{2} b^{4} \log\left(c\right)^{2} + 16 \, a^{4} b^{2} - 8 \, {\left(b^{6} \log\left(c\right) + b^{6} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)^{3} + 8 \, {\left(b^{6} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{6} \log\left(c\right)^{2} + 8 \, b^{6} \log\left(c\right) \log\left(x\right) + 4 \, b^{6} \log\left(x\right)^{2} + 12 \, a^{2} b^{4} - 4 \, {\left(b^{6} \log\left(c\right) + b^{6} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 8 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + 6 \, b^{6} \log\left(c\right) \log\left(x\right) + 3 \, b^{6} \log\left(x\right)^{2} + a^{2} b^{4}\right)} \log\left(c^{2} x^{2}\right)^{2} + 32 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} \log\left(x\right)^{2} + 16 \, {\left(a b^{5} \log\left(c^{2} x^{2}\right)^{2} + 4 \, a b^{5} \log\left(c\right)^{2} + 8 \, a b^{5} \log\left(c\right) \log\left(x\right) + 4 \, a b^{5} \log\left(x\right)^{2} + 4 \, a^{3} b^{3} - 4 \, {\left(a b^{5} \log\left(c\right) + a b^{5} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 32 \, {\left(b^{6} \log\left(c\right)^{3} + 3 \, b^{6} \log\left(c\right) \log\left(x\right)^{2} + b^{6} \log\left(x\right)^{3} + a^{2} b^{4} \log\left(c\right) + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + 64 \, {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} \log\left(x\right)}"," ",0,"-(16*(a*b^2*c^2*log(c)^2 + a^3*c^2)*x^3 + 8*(2*b^3*c^2*x^3 - b^3*x)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 + 24*(2*a*b^2*c^2*x^3 - a*b^2*x)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 2*(2*a*b^2*c^2*x^3 - a*b^2*x)*log(c^2*x^2)^2 + 8*(2*a*b^2*c^2*x^3 - a*b^2*x)*log(x)^2 + 2*(4*b^3*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - b^3*x*log(c^2*x^2)^2 - 8*b^3*x*log(c)*log(x) - 4*b^3*x*log(x)^2 + 8*a*b^2*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 4*(b^3*log(c)^2 - a^2*b)*x + 4*(b^3*x*log(c) + b^3*x*log(x))*log(c^2*x^2))*sqrt(c*x + 1)*sqrt(c*x - 1) - 8*(a*b^2*log(c)^2 + a^3)*x + 2*(8*(b^3*c^2*log(c)^2 + 3*a^2*b*c^2)*x^3 + (2*b^3*c^2*x^3 - b^3*x)*log(c^2*x^2)^2 + 4*(2*b^3*c^2*x^3 - b^3*x)*log(x)^2 - 4*(b^3*log(c)^2 + 3*a^2*b)*x - 4*(2*b^3*c^2*x^3*log(c) - b^3*x*log(c) + (2*b^3*c^2*x^3 - b^3*x)*log(x))*log(c^2*x^2) + 8*(2*b^3*c^2*x^3*log(c) - b^3*x*log(c))*log(x))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - (16*b^6*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^4 + b^6*log(c^2*x^2)^4 + 16*b^6*log(c)^4 + 64*b^6*log(c)*log(x)^3 + 16*b^6*log(x)^4 + 64*a*b^5*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 + 32*a^2*b^4*log(c)^2 + 16*a^4*b^2 - 8*(b^6*log(c) + b^6*log(x))*log(c^2*x^2)^3 + 8*(b^6*log(c^2*x^2)^2 + 4*b^6*log(c)^2 + 8*b^6*log(c)*log(x) + 4*b^6*log(x)^2 + 12*a^2*b^4 - 4*(b^6*log(c) + b^6*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 8*(3*b^6*log(c)^2 + 6*b^6*log(c)*log(x) + 3*b^6*log(x)^2 + a^2*b^4)*log(c^2*x^2)^2 + 32*(3*b^6*log(c)^2 + a^2*b^4)*log(x)^2 + 16*(a*b^5*log(c^2*x^2)^2 + 4*a*b^5*log(c)^2 + 8*a*b^5*log(c)*log(x) + 4*a*b^5*log(x)^2 + 4*a^3*b^3 - 4*(a*b^5*log(c) + a*b^5*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 32*(b^6*log(c)^3 + 3*b^6*log(c)*log(x)^2 + b^6*log(x)^3 + a^2*b^4*log(c) + (3*b^6*log(c)^2 + a^2*b^4)*log(x))*log(c^2*x^2) + 64*(b^6*log(c)^3 + a^2*b^4*log(c))*log(x))*integrate(2*(6*a*c^2*x^2 + (6*b*c^2*x^2 - b)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - a)/(4*b^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^4*log(c^2*x^2)^2 + 4*b^4*log(c)^2 + 8*b^4*log(c)*log(x) + 4*b^4*log(x)^2 + 8*a*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*a^2*b^2 - 4*(b^4*log(c) + b^4*log(x))*log(c^2*x^2)), x) - 8*(2*a*b^2*c^2*x^3*log(c) - a*b^2*x*log(c) + (2*a*b^2*c^2*x^3 - a*b^2*x)*log(x))*log(c^2*x^2) + 16*(2*a*b^2*c^2*x^3*log(c) - a*b^2*x*log(c))*log(x))/(16*b^6*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^4 + b^6*log(c^2*x^2)^4 + 16*b^6*log(c)^4 + 64*b^6*log(c)*log(x)^3 + 16*b^6*log(x)^4 + 64*a*b^5*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 + 32*a^2*b^4*log(c)^2 + 16*a^4*b^2 - 8*(b^6*log(c) + b^6*log(x))*log(c^2*x^2)^3 + 8*(b^6*log(c^2*x^2)^2 + 4*b^6*log(c)^2 + 8*b^6*log(c)*log(x) + 4*b^6*log(x)^2 + 12*a^2*b^4 - 4*(b^6*log(c) + b^6*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 8*(3*b^6*log(c)^2 + 6*b^6*log(c)*log(x) + 3*b^6*log(x)^2 + a^2*b^4)*log(c^2*x^2)^2 + 32*(3*b^6*log(c)^2 + a^2*b^4)*log(x)^2 + 16*(a*b^5*log(c^2*x^2)^2 + 4*a*b^5*log(c)^2 + 8*a*b^5*log(c)*log(x) + 4*a*b^5*log(x)^2 + 4*a^3*b^3 - 4*(a*b^5*log(c) + a*b^5*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 32*(b^6*log(c)^3 + 3*b^6*log(c)*log(x)^2 + b^6*log(x)^3 + a^2*b^4*log(c) + (3*b^6*log(c)^2 + a^2*b^4)*log(x))*log(c^2*x^2) + 64*(b^6*log(c)^3 + a^2*b^4*log(c))*log(x))","F",0
47,0,0,0,0.000000," ","integrate(1/x/(a+b*arcsec(c*x))^3,x, algorithm=""maxima"")","-\frac{8 \, b^{3} c^{2} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} + 24 \, a b^{2} c^{2} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 2 \, a b^{2} c^{2} x^{2} \log\left(c^{2} x^{2}\right)^{2} + 16 \, a b^{2} c^{2} x^{2} \log\left(c\right) \log\left(x\right) + 8 \, a b^{2} c^{2} x^{2} \log\left(x\right)^{2} + 8 \, {\left(a b^{2} c^{2} \log\left(c\right)^{2} + a^{3} c^{2}\right)} x^{2} + 2 \, {\left(4 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - b^{3} \log\left(c^{2} x^{2}\right)^{2} - 4 \, b^{3} \log\left(c\right)^{2} - 8 \, b^{3} \log\left(c\right) \log\left(x\right) - 4 \, b^{3} \log\left(x\right)^{2} + 8 \, a b^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, a^{2} b + 4 \, {\left(b^{3} \log\left(c\right) + b^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \sqrt{c x + 1} \sqrt{c x - 1} + 2 \, {\left(b^{3} c^{2} x^{2} \log\left(c^{2} x^{2}\right)^{2} + 8 \, b^{3} c^{2} x^{2} \log\left(c\right) \log\left(x\right) + 4 \, b^{3} c^{2} x^{2} \log\left(x\right)^{2} + 4 \, {\left(b^{3} c^{2} \log\left(c\right)^{2} + 3 \, a^{2} b c^{2}\right)} x^{2} - 4 \, {\left(b^{3} c^{2} x^{2} \log\left(c\right) + b^{3} c^{2} x^{2} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 4 \, {\left(16 \, b^{6} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{4} + b^{6} \log\left(c^{2} x^{2}\right)^{4} + 16 \, b^{6} \log\left(c\right)^{4} + 64 \, b^{6} \log\left(c\right) \log\left(x\right)^{3} + 16 \, b^{6} \log\left(x\right)^{4} + 64 \, a b^{5} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} + 32 \, a^{2} b^{4} \log\left(c\right)^{2} + 16 \, a^{4} b^{2} - 8 \, {\left(b^{6} \log\left(c\right) + b^{6} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)^{3} + 8 \, {\left(b^{6} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{6} \log\left(c\right)^{2} + 8 \, b^{6} \log\left(c\right) \log\left(x\right) + 4 \, b^{6} \log\left(x\right)^{2} + 12 \, a^{2} b^{4} - 4 \, {\left(b^{6} \log\left(c\right) + b^{6} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 8 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + 6 \, b^{6} \log\left(c\right) \log\left(x\right) + 3 \, b^{6} \log\left(x\right)^{2} + a^{2} b^{4}\right)} \log\left(c^{2} x^{2}\right)^{2} + 32 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} \log\left(x\right)^{2} + 16 \, {\left(a b^{5} \log\left(c^{2} x^{2}\right)^{2} + 4 \, a b^{5} \log\left(c\right)^{2} + 8 \, a b^{5} \log\left(c\right) \log\left(x\right) + 4 \, a b^{5} \log\left(x\right)^{2} + 4 \, a^{3} b^{3} - 4 \, {\left(a b^{5} \log\left(c\right) + a b^{5} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 32 \, {\left(b^{6} \log\left(c\right)^{3} + 3 \, b^{6} \log\left(c\right) \log\left(x\right)^{2} + b^{6} \log\left(x\right)^{3} + a^{2} b^{4} \log\left(c\right) + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + 64 \, {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} \log\left(x\right)\right)} \int \frac{b c^{2} x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + a c^{2} x}{4 \, b^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{4} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{4} \log\left(c\right)^{2} + 8 \, b^{4} \log\left(c\right) \log\left(x\right) + 4 \, b^{4} \log\left(x\right)^{2} + 8 \, a b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, a^{2} b^{2} - 4 \, {\left(b^{4} \log\left(c\right) + b^{4} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)}\,{d x} - 8 \, {\left(a b^{2} c^{2} x^{2} \log\left(c\right) + a b^{2} c^{2} x^{2} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)}{16 \, b^{6} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{4} + b^{6} \log\left(c^{2} x^{2}\right)^{4} + 16 \, b^{6} \log\left(c\right)^{4} + 64 \, b^{6} \log\left(c\right) \log\left(x\right)^{3} + 16 \, b^{6} \log\left(x\right)^{4} + 64 \, a b^{5} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} + 32 \, a^{2} b^{4} \log\left(c\right)^{2} + 16 \, a^{4} b^{2} - 8 \, {\left(b^{6} \log\left(c\right) + b^{6} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)^{3} + 8 \, {\left(b^{6} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{6} \log\left(c\right)^{2} + 8 \, b^{6} \log\left(c\right) \log\left(x\right) + 4 \, b^{6} \log\left(x\right)^{2} + 12 \, a^{2} b^{4} - 4 \, {\left(b^{6} \log\left(c\right) + b^{6} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 8 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + 6 \, b^{6} \log\left(c\right) \log\left(x\right) + 3 \, b^{6} \log\left(x\right)^{2} + a^{2} b^{4}\right)} \log\left(c^{2} x^{2}\right)^{2} + 32 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} \log\left(x\right)^{2} + 16 \, {\left(a b^{5} \log\left(c^{2} x^{2}\right)^{2} + 4 \, a b^{5} \log\left(c\right)^{2} + 8 \, a b^{5} \log\left(c\right) \log\left(x\right) + 4 \, a b^{5} \log\left(x\right)^{2} + 4 \, a^{3} b^{3} - 4 \, {\left(a b^{5} \log\left(c\right) + a b^{5} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 32 \, {\left(b^{6} \log\left(c\right)^{3} + 3 \, b^{6} \log\left(c\right) \log\left(x\right)^{2} + b^{6} \log\left(x\right)^{3} + a^{2} b^{4} \log\left(c\right) + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + 64 \, {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} \log\left(x\right)}"," ",0,"-(8*b^3*c^2*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 + 24*a*b^2*c^2*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 2*a*b^2*c^2*x^2*log(c^2*x^2)^2 + 16*a*b^2*c^2*x^2*log(c)*log(x) + 8*a*b^2*c^2*x^2*log(x)^2 + 8*(a*b^2*c^2*log(c)^2 + a^3*c^2)*x^2 + 2*(4*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - b^3*log(c^2*x^2)^2 - 4*b^3*log(c)^2 - 8*b^3*log(c)*log(x) - 4*b^3*log(x)^2 + 8*a*b^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*a^2*b + 4*(b^3*log(c) + b^3*log(x))*log(c^2*x^2))*sqrt(c*x + 1)*sqrt(c*x - 1) + 2*(b^3*c^2*x^2*log(c^2*x^2)^2 + 8*b^3*c^2*x^2*log(c)*log(x) + 4*b^3*c^2*x^2*log(x)^2 + 4*(b^3*c^2*log(c)^2 + 3*a^2*b*c^2)*x^2 - 4*(b^3*c^2*x^2*log(c) + b^3*c^2*x^2*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - (16*b^6*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^4 + b^6*log(c^2*x^2)^4 + 16*b^6*log(c)^4 + 64*b^6*log(c)*log(x)^3 + 16*b^6*log(x)^4 + 64*a*b^5*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 + 32*a^2*b^4*log(c)^2 + 16*a^4*b^2 - 8*(b^6*log(c) + b^6*log(x))*log(c^2*x^2)^3 + 8*(b^6*log(c^2*x^2)^2 + 4*b^6*log(c)^2 + 8*b^6*log(c)*log(x) + 4*b^6*log(x)^2 + 12*a^2*b^4 - 4*(b^6*log(c) + b^6*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 8*(3*b^6*log(c)^2 + 6*b^6*log(c)*log(x) + 3*b^6*log(x)^2 + a^2*b^4)*log(c^2*x^2)^2 + 32*(3*b^6*log(c)^2 + a^2*b^4)*log(x)^2 + 16*(a*b^5*log(c^2*x^2)^2 + 4*a*b^5*log(c)^2 + 8*a*b^5*log(c)*log(x) + 4*a*b^5*log(x)^2 + 4*a^3*b^3 - 4*(a*b^5*log(c) + a*b^5*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 32*(b^6*log(c)^3 + 3*b^6*log(c)*log(x)^2 + b^6*log(x)^3 + a^2*b^4*log(c) + (3*b^6*log(c)^2 + a^2*b^4)*log(x))*log(c^2*x^2) + 64*(b^6*log(c)^3 + a^2*b^4*log(c))*log(x))*integrate(4*(b*c^2*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + a*c^2*x)/(4*b^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^4*log(c^2*x^2)^2 + 4*b^4*log(c)^2 + 8*b^4*log(c)*log(x) + 4*b^4*log(x)^2 + 8*a*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*a^2*b^2 - 4*(b^4*log(c) + b^4*log(x))*log(c^2*x^2)), x) - 8*(a*b^2*c^2*x^2*log(c) + a*b^2*c^2*x^2*log(x))*log(c^2*x^2))/(16*b^6*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^4 + b^6*log(c^2*x^2)^4 + 16*b^6*log(c)^4 + 64*b^6*log(c)*log(x)^3 + 16*b^6*log(x)^4 + 64*a*b^5*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 + 32*a^2*b^4*log(c)^2 + 16*a^4*b^2 - 8*(b^6*log(c) + b^6*log(x))*log(c^2*x^2)^3 + 8*(b^6*log(c^2*x^2)^2 + 4*b^6*log(c)^2 + 8*b^6*log(c)*log(x) + 4*b^6*log(x)^2 + 12*a^2*b^4 - 4*(b^6*log(c) + b^6*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 8*(3*b^6*log(c)^2 + 6*b^6*log(c)*log(x) + 3*b^6*log(x)^2 + a^2*b^4)*log(c^2*x^2)^2 + 32*(3*b^6*log(c)^2 + a^2*b^4)*log(x)^2 + 16*(a*b^5*log(c^2*x^2)^2 + 4*a*b^5*log(c)^2 + 8*a*b^5*log(c)*log(x) + 4*a*b^5*log(x)^2 + 4*a^3*b^3 - 4*(a*b^5*log(c) + a*b^5*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 32*(b^6*log(c)^3 + 3*b^6*log(c)*log(x)^2 + b^6*log(x)^3 + a^2*b^4*log(c) + (3*b^6*log(c)^2 + a^2*b^4)*log(x))*log(c^2*x^2) + 64*(b^6*log(c)^3 + a^2*b^4*log(c))*log(x))","F",0
48,0,0,0,0.000000," ","integrate(1/x^2/(a+b*arcsec(c*x))^3,x, algorithm=""maxima"")","-\frac{8 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} + 24 \, a b^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 2 \, a b^{2} \log\left(c^{2} x^{2}\right)^{2} + 8 \, a b^{2} \log\left(c\right)^{2} + 16 \, a b^{2} \log\left(c\right) \log\left(x\right) + 8 \, a b^{2} \log\left(x\right)^{2} + 8 \, a^{3} + 2 \, {\left(4 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - b^{3} \log\left(c^{2} x^{2}\right)^{2} - 4 \, b^{3} \log\left(c\right)^{2} - 8 \, b^{3} \log\left(c\right) \log\left(x\right) - 4 \, b^{3} \log\left(x\right)^{2} + 8 \, a b^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, a^{2} b + 4 \, {\left(b^{3} \log\left(c\right) + b^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \sqrt{c x + 1} \sqrt{c x - 1} + 2 \, {\left(b^{3} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{3} \log\left(c\right)^{2} + 8 \, b^{3} \log\left(c\right) \log\left(x\right) + 4 \, b^{3} \log\left(x\right)^{2} + 12 \, a^{2} b - 4 \, {\left(b^{3} \log\left(c\right) + b^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 2 \, {\left(16 \, b^{6} x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{4} + b^{6} x \log\left(c^{2} x^{2}\right)^{4} + 64 \, b^{6} x \log\left(c\right) \log\left(x\right)^{3} + 16 \, b^{6} x \log\left(x\right)^{4} + 64 \, a b^{5} x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} - 8 \, {\left(b^{6} x \log\left(c\right) + b^{6} x \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)^{3} + 32 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x \log\left(x\right)^{2} + 8 \, {\left(b^{6} x \log\left(c^{2} x^{2}\right)^{2} + 8 \, b^{6} x \log\left(c\right) \log\left(x\right) + 4 \, b^{6} x \log\left(x\right)^{2} + 4 \, {\left(b^{6} \log\left(c\right)^{2} + 3 \, a^{2} b^{4}\right)} x - 4 \, {\left(b^{6} x \log\left(c\right) + b^{6} x \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 8 \, {\left(6 \, b^{6} x \log\left(c\right) \log\left(x\right) + 3 \, b^{6} x \log\left(x\right)^{2} + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x\right)} \log\left(c^{2} x^{2}\right)^{2} + 64 \, {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} x \log\left(x\right) + 16 \, {\left(b^{6} \log\left(c\right)^{4} + 2 \, a^{2} b^{4} \log\left(c\right)^{2} + a^{4} b^{2}\right)} x + 16 \, {\left(a b^{5} x \log\left(c^{2} x^{2}\right)^{2} + 8 \, a b^{5} x \log\left(c\right) \log\left(x\right) + 4 \, a b^{5} x \log\left(x\right)^{2} + 4 \, {\left(a b^{5} \log\left(c\right)^{2} + a^{3} b^{3}\right)} x - 4 \, {\left(a b^{5} x \log\left(c\right) + a b^{5} x \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 32 \, {\left(3 \, b^{6} x \log\left(c\right) \log\left(x\right)^{2} + b^{6} x \log\left(x\right)^{3} + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x \log\left(x\right) + {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} x\right)} \log\left(c^{2} x^{2}\right)\right)} \int \frac{b \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + a}{4 \, b^{4} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{4} x^{2} \log\left(c^{2} x^{2}\right)^{2} + 8 \, b^{4} x^{2} \log\left(c\right) \log\left(x\right) + 4 \, b^{4} x^{2} \log\left(x\right)^{2} + 8 \, a b^{3} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, {\left(b^{4} \log\left(c\right)^{2} + a^{2} b^{2}\right)} x^{2} - 4 \, {\left(b^{4} x^{2} \log\left(c\right) + b^{4} x^{2} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)}\,{d x} - 8 \, {\left(a b^{2} \log\left(c\right) + a b^{2} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)}{16 \, b^{6} x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{4} + b^{6} x \log\left(c^{2} x^{2}\right)^{4} + 64 \, b^{6} x \log\left(c\right) \log\left(x\right)^{3} + 16 \, b^{6} x \log\left(x\right)^{4} + 64 \, a b^{5} x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} - 8 \, {\left(b^{6} x \log\left(c\right) + b^{6} x \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)^{3} + 32 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x \log\left(x\right)^{2} + 8 \, {\left(b^{6} x \log\left(c^{2} x^{2}\right)^{2} + 8 \, b^{6} x \log\left(c\right) \log\left(x\right) + 4 \, b^{6} x \log\left(x\right)^{2} + 4 \, {\left(b^{6} \log\left(c\right)^{2} + 3 \, a^{2} b^{4}\right)} x - 4 \, {\left(b^{6} x \log\left(c\right) + b^{6} x \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 8 \, {\left(6 \, b^{6} x \log\left(c\right) \log\left(x\right) + 3 \, b^{6} x \log\left(x\right)^{2} + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x\right)} \log\left(c^{2} x^{2}\right)^{2} + 64 \, {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} x \log\left(x\right) + 16 \, {\left(b^{6} \log\left(c\right)^{4} + 2 \, a^{2} b^{4} \log\left(c\right)^{2} + a^{4} b^{2}\right)} x + 16 \, {\left(a b^{5} x \log\left(c^{2} x^{2}\right)^{2} + 8 \, a b^{5} x \log\left(c\right) \log\left(x\right) + 4 \, a b^{5} x \log\left(x\right)^{2} + 4 \, {\left(a b^{5} \log\left(c\right)^{2} + a^{3} b^{3}\right)} x - 4 \, {\left(a b^{5} x \log\left(c\right) + a b^{5} x \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 32 \, {\left(3 \, b^{6} x \log\left(c\right) \log\left(x\right)^{2} + b^{6} x \log\left(x\right)^{3} + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x \log\left(x\right) + {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} x\right)} \log\left(c^{2} x^{2}\right)}"," ",0,"-(8*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 + 24*a*b^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 2*a*b^2*log(c^2*x^2)^2 + 8*a*b^2*log(c)^2 + 16*a*b^2*log(c)*log(x) + 8*a*b^2*log(x)^2 + 8*a^3 + 2*(4*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - b^3*log(c^2*x^2)^2 - 4*b^3*log(c)^2 - 8*b^3*log(c)*log(x) - 4*b^3*log(x)^2 + 8*a*b^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*a^2*b + 4*(b^3*log(c) + b^3*log(x))*log(c^2*x^2))*sqrt(c*x + 1)*sqrt(c*x - 1) + 2*(b^3*log(c^2*x^2)^2 + 4*b^3*log(c)^2 + 8*b^3*log(c)*log(x) + 4*b^3*log(x)^2 + 12*a^2*b - 4*(b^3*log(c) + b^3*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + (16*b^6*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^4 + b^6*x*log(c^2*x^2)^4 + 64*b^6*x*log(c)*log(x)^3 + 16*b^6*x*log(x)^4 + 64*a*b^5*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 - 8*(b^6*x*log(c) + b^6*x*log(x))*log(c^2*x^2)^3 + 32*(3*b^6*log(c)^2 + a^2*b^4)*x*log(x)^2 + 8*(b^6*x*log(c^2*x^2)^2 + 8*b^6*x*log(c)*log(x) + 4*b^6*x*log(x)^2 + 4*(b^6*log(c)^2 + 3*a^2*b^4)*x - 4*(b^6*x*log(c) + b^6*x*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 8*(6*b^6*x*log(c)*log(x) + 3*b^6*x*log(x)^2 + (3*b^6*log(c)^2 + a^2*b^4)*x)*log(c^2*x^2)^2 + 64*(b^6*log(c)^3 + a^2*b^4*log(c))*x*log(x) + 16*(b^6*log(c)^4 + 2*a^2*b^4*log(c)^2 + a^4*b^2)*x + 16*(a*b^5*x*log(c^2*x^2)^2 + 8*a*b^5*x*log(c)*log(x) + 4*a*b^5*x*log(x)^2 + 4*(a*b^5*log(c)^2 + a^3*b^3)*x - 4*(a*b^5*x*log(c) + a*b^5*x*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 32*(3*b^6*x*log(c)*log(x)^2 + b^6*x*log(x)^3 + (3*b^6*log(c)^2 + a^2*b^4)*x*log(x) + (b^6*log(c)^3 + a^2*b^4*log(c))*x)*log(c^2*x^2))*integrate(2*(b*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + a)/(4*b^4*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^4*x^2*log(c^2*x^2)^2 + 8*b^4*x^2*log(c)*log(x) + 4*b^4*x^2*log(x)^2 + 8*a*b^3*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*(b^4*log(c)^2 + a^2*b^2)*x^2 - 4*(b^4*x^2*log(c) + b^4*x^2*log(x))*log(c^2*x^2)), x) - 8*(a*b^2*log(c) + a*b^2*log(x))*log(c^2*x^2))/(16*b^6*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^4 + b^6*x*log(c^2*x^2)^4 + 64*b^6*x*log(c)*log(x)^3 + 16*b^6*x*log(x)^4 + 64*a*b^5*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 - 8*(b^6*x*log(c) + b^6*x*log(x))*log(c^2*x^2)^3 + 32*(3*b^6*log(c)^2 + a^2*b^4)*x*log(x)^2 + 8*(b^6*x*log(c^2*x^2)^2 + 8*b^6*x*log(c)*log(x) + 4*b^6*x*log(x)^2 + 4*(b^6*log(c)^2 + 3*a^2*b^4)*x - 4*(b^6*x*log(c) + b^6*x*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 8*(6*b^6*x*log(c)*log(x) + 3*b^6*x*log(x)^2 + (3*b^6*log(c)^2 + a^2*b^4)*x)*log(c^2*x^2)^2 + 64*(b^6*log(c)^3 + a^2*b^4*log(c))*x*log(x) + 16*(b^6*log(c)^4 + 2*a^2*b^4*log(c)^2 + a^4*b^2)*x + 16*(a*b^5*x*log(c^2*x^2)^2 + 8*a*b^5*x*log(c)*log(x) + 4*a*b^5*x*log(x)^2 + 4*(a*b^5*log(c)^2 + a^3*b^3)*x - 4*(a*b^5*x*log(c) + a*b^5*x*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 32*(3*b^6*x*log(c)*log(x)^2 + b^6*x*log(x)^3 + (3*b^6*log(c)^2 + a^2*b^4)*x*log(x) + (b^6*log(c)^3 + a^2*b^4*log(c))*x)*log(c^2*x^2))","F",0
49,0,0,0,0.000000," ","integrate(1/x^3/(a+b*arcsec(c*x))^3,x, algorithm=""maxima"")","-\frac{16 \, a b^{2} \log\left(c\right)^{2} - 8 \, {\left(b^{3} c^{2} x^{2} - 2 \, b^{3}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} + 16 \, a^{3} - 8 \, {\left(a b^{2} c^{2} \log\left(c\right)^{2} + a^{3} c^{2}\right)} x^{2} - 24 \, {\left(a b^{2} c^{2} x^{2} - 2 \, a b^{2}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - 2 \, {\left(a b^{2} c^{2} x^{2} - 2 \, a b^{2}\right)} \log\left(c^{2} x^{2}\right)^{2} - 8 \, {\left(a b^{2} c^{2} x^{2} - 2 \, a b^{2}\right)} \log\left(x\right)^{2} + 2 \, {\left(4 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - b^{3} \log\left(c^{2} x^{2}\right)^{2} - 4 \, b^{3} \log\left(c\right)^{2} - 8 \, b^{3} \log\left(c\right) \log\left(x\right) - 4 \, b^{3} \log\left(x\right)^{2} + 8 \, a b^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, a^{2} b + 4 \, {\left(b^{3} \log\left(c\right) + b^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \sqrt{c x + 1} \sqrt{c x - 1} + 2 \, {\left(8 \, b^{3} \log\left(c\right)^{2} + 24 \, a^{2} b - 4 \, {\left(b^{3} c^{2} \log\left(c\right)^{2} + 3 \, a^{2} b c^{2}\right)} x^{2} - {\left(b^{3} c^{2} x^{2} - 2 \, b^{3}\right)} \log\left(c^{2} x^{2}\right)^{2} - 4 \, {\left(b^{3} c^{2} x^{2} - 2 \, b^{3}\right)} \log\left(x\right)^{2} + 4 \, {\left(b^{3} c^{2} x^{2} \log\left(c\right) - 2 \, b^{3} \log\left(c\right) + {\left(b^{3} c^{2} x^{2} - 2 \, b^{3}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) - 8 \, {\left(b^{3} c^{2} x^{2} \log\left(c\right) - 2 \, b^{3} \log\left(c\right)\right)} \log\left(x\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 8 \, {\left(16 \, b^{6} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{4} + b^{6} x^{2} \log\left(c^{2} x^{2}\right)^{4} + 64 \, b^{6} x^{2} \log\left(c\right) \log\left(x\right)^{3} + 16 \, b^{6} x^{2} \log\left(x\right)^{4} + 64 \, a b^{5} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} + 32 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x^{2} \log\left(x\right)^{2} - 8 \, {\left(b^{6} x^{2} \log\left(c\right) + b^{6} x^{2} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)^{3} + 64 \, {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} x^{2} \log\left(x\right) + 16 \, {\left(b^{6} \log\left(c\right)^{4} + 2 \, a^{2} b^{4} \log\left(c\right)^{2} + a^{4} b^{2}\right)} x^{2} + 8 \, {\left(b^{6} x^{2} \log\left(c^{2} x^{2}\right)^{2} + 8 \, b^{6} x^{2} \log\left(c\right) \log\left(x\right) + 4 \, b^{6} x^{2} \log\left(x\right)^{2} + 4 \, {\left(b^{6} \log\left(c\right)^{2} + 3 \, a^{2} b^{4}\right)} x^{2} - 4 \, {\left(b^{6} x^{2} \log\left(c\right) + b^{6} x^{2} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 8 \, {\left(6 \, b^{6} x^{2} \log\left(c\right) \log\left(x\right) + 3 \, b^{6} x^{2} \log\left(x\right)^{2} + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x^{2}\right)} \log\left(c^{2} x^{2}\right)^{2} + 16 \, {\left(a b^{5} x^{2} \log\left(c^{2} x^{2}\right)^{2} + 8 \, a b^{5} x^{2} \log\left(c\right) \log\left(x\right) + 4 \, a b^{5} x^{2} \log\left(x\right)^{2} + 4 \, {\left(a b^{5} \log\left(c\right)^{2} + a^{3} b^{3}\right)} x^{2} - 4 \, {\left(a b^{5} x^{2} \log\left(c\right) + a b^{5} x^{2} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 32 \, {\left(3 \, b^{6} x^{2} \log\left(c\right) \log\left(x\right)^{2} + b^{6} x^{2} \log\left(x\right)^{3} + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x^{2} \log\left(x\right) + {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} x^{2}\right)} \log\left(c^{2} x^{2}\right)\right)} \int \frac{b \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + a}{4 \, b^{4} x^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{4} x^{3} \log\left(c^{2} x^{2}\right)^{2} + 8 \, b^{4} x^{3} \log\left(c\right) \log\left(x\right) + 4 \, b^{4} x^{3} \log\left(x\right)^{2} + 8 \, a b^{3} x^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, {\left(b^{4} \log\left(c\right)^{2} + a^{2} b^{2}\right)} x^{3} - 4 \, {\left(b^{4} x^{3} \log\left(c\right) + b^{4} x^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)}\,{d x} + 8 \, {\left(a b^{2} c^{2} x^{2} \log\left(c\right) - 2 \, a b^{2} \log\left(c\right) + {\left(a b^{2} c^{2} x^{2} - 2 \, a b^{2}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) - 16 \, {\left(a b^{2} c^{2} x^{2} \log\left(c\right) - 2 \, a b^{2} \log\left(c\right)\right)} \log\left(x\right)}{16 \, b^{6} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{4} + b^{6} x^{2} \log\left(c^{2} x^{2}\right)^{4} + 64 \, b^{6} x^{2} \log\left(c\right) \log\left(x\right)^{3} + 16 \, b^{6} x^{2} \log\left(x\right)^{4} + 64 \, a b^{5} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} + 32 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x^{2} \log\left(x\right)^{2} - 8 \, {\left(b^{6} x^{2} \log\left(c\right) + b^{6} x^{2} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)^{3} + 64 \, {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} x^{2} \log\left(x\right) + 16 \, {\left(b^{6} \log\left(c\right)^{4} + 2 \, a^{2} b^{4} \log\left(c\right)^{2} + a^{4} b^{2}\right)} x^{2} + 8 \, {\left(b^{6} x^{2} \log\left(c^{2} x^{2}\right)^{2} + 8 \, b^{6} x^{2} \log\left(c\right) \log\left(x\right) + 4 \, b^{6} x^{2} \log\left(x\right)^{2} + 4 \, {\left(b^{6} \log\left(c\right)^{2} + 3 \, a^{2} b^{4}\right)} x^{2} - 4 \, {\left(b^{6} x^{2} \log\left(c\right) + b^{6} x^{2} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 8 \, {\left(6 \, b^{6} x^{2} \log\left(c\right) \log\left(x\right) + 3 \, b^{6} x^{2} \log\left(x\right)^{2} + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x^{2}\right)} \log\left(c^{2} x^{2}\right)^{2} + 16 \, {\left(a b^{5} x^{2} \log\left(c^{2} x^{2}\right)^{2} + 8 \, a b^{5} x^{2} \log\left(c\right) \log\left(x\right) + 4 \, a b^{5} x^{2} \log\left(x\right)^{2} + 4 \, {\left(a b^{5} \log\left(c\right)^{2} + a^{3} b^{3}\right)} x^{2} - 4 \, {\left(a b^{5} x^{2} \log\left(c\right) + a b^{5} x^{2} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 32 \, {\left(3 \, b^{6} x^{2} \log\left(c\right) \log\left(x\right)^{2} + b^{6} x^{2} \log\left(x\right)^{3} + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x^{2} \log\left(x\right) + {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} x^{2}\right)} \log\left(c^{2} x^{2}\right)}"," ",0,"-(16*a*b^2*log(c)^2 - 8*(b^3*c^2*x^2 - 2*b^3)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 + 16*a^3 - 8*(a*b^2*c^2*log(c)^2 + a^3*c^2)*x^2 - 24*(a*b^2*c^2*x^2 - 2*a*b^2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - 2*(a*b^2*c^2*x^2 - 2*a*b^2)*log(c^2*x^2)^2 - 8*(a*b^2*c^2*x^2 - 2*a*b^2)*log(x)^2 + 2*(4*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - b^3*log(c^2*x^2)^2 - 4*b^3*log(c)^2 - 8*b^3*log(c)*log(x) - 4*b^3*log(x)^2 + 8*a*b^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*a^2*b + 4*(b^3*log(c) + b^3*log(x))*log(c^2*x^2))*sqrt(c*x + 1)*sqrt(c*x - 1) + 2*(8*b^3*log(c)^2 + 24*a^2*b - 4*(b^3*c^2*log(c)^2 + 3*a^2*b*c^2)*x^2 - (b^3*c^2*x^2 - 2*b^3)*log(c^2*x^2)^2 - 4*(b^3*c^2*x^2 - 2*b^3)*log(x)^2 + 4*(b^3*c^2*x^2*log(c) - 2*b^3*log(c) + (b^3*c^2*x^2 - 2*b^3)*log(x))*log(c^2*x^2) - 8*(b^3*c^2*x^2*log(c) - 2*b^3*log(c))*log(x))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + (16*b^6*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^4 + b^6*x^2*log(c^2*x^2)^4 + 64*b^6*x^2*log(c)*log(x)^3 + 16*b^6*x^2*log(x)^4 + 64*a*b^5*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 + 32*(3*b^6*log(c)^2 + a^2*b^4)*x^2*log(x)^2 - 8*(b^6*x^2*log(c) + b^6*x^2*log(x))*log(c^2*x^2)^3 + 64*(b^6*log(c)^3 + a^2*b^4*log(c))*x^2*log(x) + 16*(b^6*log(c)^4 + 2*a^2*b^4*log(c)^2 + a^4*b^2)*x^2 + 8*(b^6*x^2*log(c^2*x^2)^2 + 8*b^6*x^2*log(c)*log(x) + 4*b^6*x^2*log(x)^2 + 4*(b^6*log(c)^2 + 3*a^2*b^4)*x^2 - 4*(b^6*x^2*log(c) + b^6*x^2*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 8*(6*b^6*x^2*log(c)*log(x) + 3*b^6*x^2*log(x)^2 + (3*b^6*log(c)^2 + a^2*b^4)*x^2)*log(c^2*x^2)^2 + 16*(a*b^5*x^2*log(c^2*x^2)^2 + 8*a*b^5*x^2*log(c)*log(x) + 4*a*b^5*x^2*log(x)^2 + 4*(a*b^5*log(c)^2 + a^3*b^3)*x^2 - 4*(a*b^5*x^2*log(c) + a*b^5*x^2*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 32*(3*b^6*x^2*log(c)*log(x)^2 + b^6*x^2*log(x)^3 + (3*b^6*log(c)^2 + a^2*b^4)*x^2*log(x) + (b^6*log(c)^3 + a^2*b^4*log(c))*x^2)*log(c^2*x^2))*integrate(8*(b*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + a)/(4*b^4*x^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^4*x^3*log(c^2*x^2)^2 + 8*b^4*x^3*log(c)*log(x) + 4*b^4*x^3*log(x)^2 + 8*a*b^3*x^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*(b^4*log(c)^2 + a^2*b^2)*x^3 - 4*(b^4*x^3*log(c) + b^4*x^3*log(x))*log(c^2*x^2)), x) + 8*(a*b^2*c^2*x^2*log(c) - 2*a*b^2*log(c) + (a*b^2*c^2*x^2 - 2*a*b^2)*log(x))*log(c^2*x^2) - 16*(a*b^2*c^2*x^2*log(c) - 2*a*b^2*log(c))*log(x))/(16*b^6*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^4 + b^6*x^2*log(c^2*x^2)^4 + 64*b^6*x^2*log(c)*log(x)^3 + 16*b^6*x^2*log(x)^4 + 64*a*b^5*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 + 32*(3*b^6*log(c)^2 + a^2*b^4)*x^2*log(x)^2 - 8*(b^6*x^2*log(c) + b^6*x^2*log(x))*log(c^2*x^2)^3 + 64*(b^6*log(c)^3 + a^2*b^4*log(c))*x^2*log(x) + 16*(b^6*log(c)^4 + 2*a^2*b^4*log(c)^2 + a^4*b^2)*x^2 + 8*(b^6*x^2*log(c^2*x^2)^2 + 8*b^6*x^2*log(c)*log(x) + 4*b^6*x^2*log(x)^2 + 4*(b^6*log(c)^2 + 3*a^2*b^4)*x^2 - 4*(b^6*x^2*log(c) + b^6*x^2*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 8*(6*b^6*x^2*log(c)*log(x) + 3*b^6*x^2*log(x)^2 + (3*b^6*log(c)^2 + a^2*b^4)*x^2)*log(c^2*x^2)^2 + 16*(a*b^5*x^2*log(c^2*x^2)^2 + 8*a*b^5*x^2*log(c)*log(x) + 4*a*b^5*x^2*log(x)^2 + 4*(a*b^5*log(c)^2 + a^3*b^3)*x^2 - 4*(a*b^5*x^2*log(c) + a*b^5*x^2*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 32*(3*b^6*x^2*log(c)*log(x)^2 + b^6*x^2*log(x)^3 + (3*b^6*log(c)^2 + a^2*b^4)*x^2*log(x) + (b^6*log(c)^3 + a^2*b^4*log(c))*x^2)*log(c^2*x^2))","F",0
50,0,0,0,0.000000," ","integrate(1/x^4/(a+b*arcsec(c*x))^3,x, algorithm=""maxima"")","-\frac{24 \, a b^{2} \log\left(c\right)^{2} - 8 \, {\left(2 \, b^{3} c^{2} x^{2} - 3 \, b^{3}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} + 24 \, a^{3} - 16 \, {\left(a b^{2} c^{2} \log\left(c\right)^{2} + a^{3} c^{2}\right)} x^{2} - 24 \, {\left(2 \, a b^{2} c^{2} x^{2} - 3 \, a b^{2}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - 2 \, {\left(2 \, a b^{2} c^{2} x^{2} - 3 \, a b^{2}\right)} \log\left(c^{2} x^{2}\right)^{2} - 8 \, {\left(2 \, a b^{2} c^{2} x^{2} - 3 \, a b^{2}\right)} \log\left(x\right)^{2} + 2 \, {\left(4 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - b^{3} \log\left(c^{2} x^{2}\right)^{2} - 4 \, b^{3} \log\left(c\right)^{2} - 8 \, b^{3} \log\left(c\right) \log\left(x\right) - 4 \, b^{3} \log\left(x\right)^{2} + 8 \, a b^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, a^{2} b + 4 \, {\left(b^{3} \log\left(c\right) + b^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \sqrt{c x + 1} \sqrt{c x - 1} + 2 \, {\left(12 \, b^{3} \log\left(c\right)^{2} + 36 \, a^{2} b - 8 \, {\left(b^{3} c^{2} \log\left(c\right)^{2} + 3 \, a^{2} b c^{2}\right)} x^{2} - {\left(2 \, b^{3} c^{2} x^{2} - 3 \, b^{3}\right)} \log\left(c^{2} x^{2}\right)^{2} - 4 \, {\left(2 \, b^{3} c^{2} x^{2} - 3 \, b^{3}\right)} \log\left(x\right)^{2} + 4 \, {\left(2 \, b^{3} c^{2} x^{2} \log\left(c\right) - 3 \, b^{3} \log\left(c\right) + {\left(2 \, b^{3} c^{2} x^{2} - 3 \, b^{3}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) - 8 \, {\left(2 \, b^{3} c^{2} x^{2} \log\left(c\right) - 3 \, b^{3} \log\left(c\right)\right)} \log\left(x\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 2 \, {\left(16 \, b^{6} x^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{4} + b^{6} x^{3} \log\left(c^{2} x^{2}\right)^{4} + 64 \, b^{6} x^{3} \log\left(c\right) \log\left(x\right)^{3} + 16 \, b^{6} x^{3} \log\left(x\right)^{4} + 64 \, a b^{5} x^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} + 32 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x^{3} \log\left(x\right)^{2} + 64 \, {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} x^{3} \log\left(x\right) + 16 \, {\left(b^{6} \log\left(c\right)^{4} + 2 \, a^{2} b^{4} \log\left(c\right)^{2} + a^{4} b^{2}\right)} x^{3} - 8 \, {\left(b^{6} x^{3} \log\left(c\right) + b^{6} x^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)^{3} + 8 \, {\left(b^{6} x^{3} \log\left(c^{2} x^{2}\right)^{2} + 8 \, b^{6} x^{3} \log\left(c\right) \log\left(x\right) + 4 \, b^{6} x^{3} \log\left(x\right)^{2} + 4 \, {\left(b^{6} \log\left(c\right)^{2} + 3 \, a^{2} b^{4}\right)} x^{3} - 4 \, {\left(b^{6} x^{3} \log\left(c\right) + b^{6} x^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 8 \, {\left(6 \, b^{6} x^{3} \log\left(c\right) \log\left(x\right) + 3 \, b^{6} x^{3} \log\left(x\right)^{2} + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x^{3}\right)} \log\left(c^{2} x^{2}\right)^{2} + 16 \, {\left(a b^{5} x^{3} \log\left(c^{2} x^{2}\right)^{2} + 8 \, a b^{5} x^{3} \log\left(c\right) \log\left(x\right) + 4 \, a b^{5} x^{3} \log\left(x\right)^{2} + 4 \, {\left(a b^{5} \log\left(c\right)^{2} + a^{3} b^{3}\right)} x^{3} - 4 \, {\left(a b^{5} x^{3} \log\left(c\right) + a b^{5} x^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 32 \, {\left(3 \, b^{6} x^{3} \log\left(c\right) \log\left(x\right)^{2} + b^{6} x^{3} \log\left(x\right)^{3} + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x^{3} \log\left(x\right) + {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} x^{3}\right)} \log\left(c^{2} x^{2}\right)\right)} \int \frac{2 \, a c^{2} x^{2} + {\left(2 \, b c^{2} x^{2} - 9 \, b\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 9 \, a}{4 \, b^{4} x^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{4} x^{4} \log\left(c^{2} x^{2}\right)^{2} + 8 \, b^{4} x^{4} \log\left(c\right) \log\left(x\right) + 4 \, b^{4} x^{4} \log\left(x\right)^{2} + 8 \, a b^{3} x^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, {\left(b^{4} \log\left(c\right)^{2} + a^{2} b^{2}\right)} x^{4} - 4 \, {\left(b^{4} x^{4} \log\left(c\right) + b^{4} x^{4} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)}\,{d x} + 8 \, {\left(2 \, a b^{2} c^{2} x^{2} \log\left(c\right) - 3 \, a b^{2} \log\left(c\right) + {\left(2 \, a b^{2} c^{2} x^{2} - 3 \, a b^{2}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) - 16 \, {\left(2 \, a b^{2} c^{2} x^{2} \log\left(c\right) - 3 \, a b^{2} \log\left(c\right)\right)} \log\left(x\right)}{16 \, b^{6} x^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{4} + b^{6} x^{3} \log\left(c^{2} x^{2}\right)^{4} + 64 \, b^{6} x^{3} \log\left(c\right) \log\left(x\right)^{3} + 16 \, b^{6} x^{3} \log\left(x\right)^{4} + 64 \, a b^{5} x^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} + 32 \, {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x^{3} \log\left(x\right)^{2} + 64 \, {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} x^{3} \log\left(x\right) + 16 \, {\left(b^{6} \log\left(c\right)^{4} + 2 \, a^{2} b^{4} \log\left(c\right)^{2} + a^{4} b^{2}\right)} x^{3} - 8 \, {\left(b^{6} x^{3} \log\left(c\right) + b^{6} x^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)^{3} + 8 \, {\left(b^{6} x^{3} \log\left(c^{2} x^{2}\right)^{2} + 8 \, b^{6} x^{3} \log\left(c\right) \log\left(x\right) + 4 \, b^{6} x^{3} \log\left(x\right)^{2} + 4 \, {\left(b^{6} \log\left(c\right)^{2} + 3 \, a^{2} b^{4}\right)} x^{3} - 4 \, {\left(b^{6} x^{3} \log\left(c\right) + b^{6} x^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + 8 \, {\left(6 \, b^{6} x^{3} \log\left(c\right) \log\left(x\right) + 3 \, b^{6} x^{3} \log\left(x\right)^{2} + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x^{3}\right)} \log\left(c^{2} x^{2}\right)^{2} + 16 \, {\left(a b^{5} x^{3} \log\left(c^{2} x^{2}\right)^{2} + 8 \, a b^{5} x^{3} \log\left(c\right) \log\left(x\right) + 4 \, a b^{5} x^{3} \log\left(x\right)^{2} + 4 \, {\left(a b^{5} \log\left(c\right)^{2} + a^{3} b^{3}\right)} x^{3} - 4 \, {\left(a b^{5} x^{3} \log\left(c\right) + a b^{5} x^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 32 \, {\left(3 \, b^{6} x^{3} \log\left(c\right) \log\left(x\right)^{2} + b^{6} x^{3} \log\left(x\right)^{3} + {\left(3 \, b^{6} \log\left(c\right)^{2} + a^{2} b^{4}\right)} x^{3} \log\left(x\right) + {\left(b^{6} \log\left(c\right)^{3} + a^{2} b^{4} \log\left(c\right)\right)} x^{3}\right)} \log\left(c^{2} x^{2}\right)}"," ",0,"-(24*a*b^2*log(c)^2 - 8*(2*b^3*c^2*x^2 - 3*b^3)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 + 24*a^3 - 16*(a*b^2*c^2*log(c)^2 + a^3*c^2)*x^2 - 24*(2*a*b^2*c^2*x^2 - 3*a*b^2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - 2*(2*a*b^2*c^2*x^2 - 3*a*b^2)*log(c^2*x^2)^2 - 8*(2*a*b^2*c^2*x^2 - 3*a*b^2)*log(x)^2 + 2*(4*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - b^3*log(c^2*x^2)^2 - 4*b^3*log(c)^2 - 8*b^3*log(c)*log(x) - 4*b^3*log(x)^2 + 8*a*b^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*a^2*b + 4*(b^3*log(c) + b^3*log(x))*log(c^2*x^2))*sqrt(c*x + 1)*sqrt(c*x - 1) + 2*(12*b^3*log(c)^2 + 36*a^2*b - 8*(b^3*c^2*log(c)^2 + 3*a^2*b*c^2)*x^2 - (2*b^3*c^2*x^2 - 3*b^3)*log(c^2*x^2)^2 - 4*(2*b^3*c^2*x^2 - 3*b^3)*log(x)^2 + 4*(2*b^3*c^2*x^2*log(c) - 3*b^3*log(c) + (2*b^3*c^2*x^2 - 3*b^3)*log(x))*log(c^2*x^2) - 8*(2*b^3*c^2*x^2*log(c) - 3*b^3*log(c))*log(x))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - (16*b^6*x^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^4 + b^6*x^3*log(c^2*x^2)^4 + 64*b^6*x^3*log(c)*log(x)^3 + 16*b^6*x^3*log(x)^4 + 64*a*b^5*x^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 + 32*(3*b^6*log(c)^2 + a^2*b^4)*x^3*log(x)^2 + 64*(b^6*log(c)^3 + a^2*b^4*log(c))*x^3*log(x) + 16*(b^6*log(c)^4 + 2*a^2*b^4*log(c)^2 + a^4*b^2)*x^3 - 8*(b^6*x^3*log(c) + b^6*x^3*log(x))*log(c^2*x^2)^3 + 8*(b^6*x^3*log(c^2*x^2)^2 + 8*b^6*x^3*log(c)*log(x) + 4*b^6*x^3*log(x)^2 + 4*(b^6*log(c)^2 + 3*a^2*b^4)*x^3 - 4*(b^6*x^3*log(c) + b^6*x^3*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 8*(6*b^6*x^3*log(c)*log(x) + 3*b^6*x^3*log(x)^2 + (3*b^6*log(c)^2 + a^2*b^4)*x^3)*log(c^2*x^2)^2 + 16*(a*b^5*x^3*log(c^2*x^2)^2 + 8*a*b^5*x^3*log(c)*log(x) + 4*a*b^5*x^3*log(x)^2 + 4*(a*b^5*log(c)^2 + a^3*b^3)*x^3 - 4*(a*b^5*x^3*log(c) + a*b^5*x^3*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 32*(3*b^6*x^3*log(c)*log(x)^2 + b^6*x^3*log(x)^3 + (3*b^6*log(c)^2 + a^2*b^4)*x^3*log(x) + (b^6*log(c)^3 + a^2*b^4*log(c))*x^3)*log(c^2*x^2))*integrate(2*(2*a*c^2*x^2 + (2*b*c^2*x^2 - 9*b)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 9*a)/(4*b^4*x^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^4*x^4*log(c^2*x^2)^2 + 8*b^4*x^4*log(c)*log(x) + 4*b^4*x^4*log(x)^2 + 8*a*b^3*x^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*(b^4*log(c)^2 + a^2*b^2)*x^4 - 4*(b^4*x^4*log(c) + b^4*x^4*log(x))*log(c^2*x^2)), x) + 8*(2*a*b^2*c^2*x^2*log(c) - 3*a*b^2*log(c) + (2*a*b^2*c^2*x^2 - 3*a*b^2)*log(x))*log(c^2*x^2) - 16*(2*a*b^2*c^2*x^2*log(c) - 3*a*b^2*log(c))*log(x))/(16*b^6*x^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^4 + b^6*x^3*log(c^2*x^2)^4 + 64*b^6*x^3*log(c)*log(x)^3 + 16*b^6*x^3*log(x)^4 + 64*a*b^5*x^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 + 32*(3*b^6*log(c)^2 + a^2*b^4)*x^3*log(x)^2 + 64*(b^6*log(c)^3 + a^2*b^4*log(c))*x^3*log(x) + 16*(b^6*log(c)^4 + 2*a^2*b^4*log(c)^2 + a^4*b^2)*x^3 - 8*(b^6*x^3*log(c) + b^6*x^3*log(x))*log(c^2*x^2)^3 + 8*(b^6*x^3*log(c^2*x^2)^2 + 8*b^6*x^3*log(c)*log(x) + 4*b^6*x^3*log(x)^2 + 4*(b^6*log(c)^2 + 3*a^2*b^4)*x^3 - 4*(b^6*x^3*log(c) + b^6*x^3*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + 8*(6*b^6*x^3*log(c)*log(x) + 3*b^6*x^3*log(x)^2 + (3*b^6*log(c)^2 + a^2*b^4)*x^3)*log(c^2*x^2)^2 + 16*(a*b^5*x^3*log(c^2*x^2)^2 + 8*a*b^5*x^3*log(c)*log(x) + 4*a*b^5*x^3*log(x)^2 + 4*(a*b^5*log(c)^2 + a^3*b^3)*x^3 - 4*(a*b^5*x^3*log(c) + a*b^5*x^3*log(x))*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 32*(3*b^6*x^3*log(c)*log(x)^2 + b^6*x^3*log(x)^3 + (3*b^6*log(c)^2 + a^2*b^4)*x^3*log(x) + (b^6*log(c)^3 + a^2*b^4*log(c))*x^3)*log(c^2*x^2))","F",0
51,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arcsec(c*x))^3,x, algorithm=""maxima"")","\frac{\left(d x\right)^{m + 1} a^{3}}{d {\left(m + 1\right)}} + \frac{4 \, b^{3} d^{m} x x^{m} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{3} - 3 \, b^{3} d^{m} x x^{m} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(c^{2} x^{2}\right)^{2} - 3 \, {\left(m + 1\right)} \int \frac{4 \, {\left(a b^{2} d^{m} m + a b^{2} d^{m} - {\left(a b^{2} c^{2} d^{m} m + a b^{2} c^{2} d^{m}\right)} x^{2}\right)} x^{m} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - {\left(a b^{2} d^{m} m + a b^{2} d^{m} - {\left(a b^{2} c^{2} d^{m} m + a b^{2} c^{2} d^{m}\right)} x^{2}\right)} x^{m} \log\left(c^{2} x^{2}\right)^{2} - 4 \, {\left(a b^{2} d^{m} m + a b^{2} d^{m} - {\left(a b^{2} c^{2} d^{m} m + a b^{2} c^{2} d^{m}\right)} x^{2}\right)} x^{m} \log\left(x\right)^{2} - 8 \, {\left(a b^{2} d^{m} m \log\left(c\right) + a b^{2} d^{m} \log\left(c\right) - {\left(a b^{2} c^{2} d^{m} m \log\left(c\right) + a b^{2} c^{2} d^{m} \log\left(c\right)\right)} x^{2}\right)} x^{m} \log\left(x\right) + {\left(4 \, b^{3} d^{m} x^{m} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - b^{3} d^{m} x^{m} \log\left(c^{2} x^{2}\right)^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1} - 4 \, {\left(a b^{2} d^{m} m \log\left(c\right)^{2} + a b^{2} d^{m} \log\left(c\right)^{2} - {\left(a b^{2} c^{2} d^{m} m \log\left(c\right)^{2} + a b^{2} c^{2} d^{m} \log\left(c\right)^{2}\right)} x^{2}\right)} x^{m} - 4 \, {\left({\left(b^{3} d^{m} m + b^{3} d^{m} - {\left(b^{3} c^{2} d^{m} m + b^{3} c^{2} d^{m}\right)} x^{2}\right)} x^{m} \log\left(x\right)^{2} + 2 \, {\left(b^{3} d^{m} m \log\left(c\right) + b^{3} d^{m} \log\left(c\right) - {\left(b^{3} c^{2} d^{m} m \log\left(c\right) + b^{3} c^{2} d^{m} \log\left(c\right)\right)} x^{2}\right)} x^{m} \log\left(x\right) + {\left({\left(b^{3} \log\left(c\right)^{2} - a^{2} b\right)} d^{m} m - {\left({\left(b^{3} c^{2} \log\left(c\right)^{2} - a^{2} b c^{2}\right)} d^{m} m + {\left(b^{3} c^{2} \log\left(c\right)^{2} - a^{2} b c^{2}\right)} d^{m}\right)} x^{2} + {\left(b^{3} \log\left(c\right)^{2} - a^{2} b\right)} d^{m}\right)} x^{m} - {\left({\left(b^{3} d^{m} m + b^{3} d^{m} - {\left(b^{3} c^{2} d^{m} m + b^{3} c^{2} d^{m}\right)} x^{2}\right)} x^{m} \log\left(x\right) + {\left(b^{3} d^{m} m \log\left(c\right) - {\left(b^{3} c^{2} d^{m} m \log\left(c\right) + {\left(b^{3} c^{2} \log\left(c\right) + b^{3} c^{2}\right)} d^{m}\right)} x^{2} + {\left(b^{3} \log\left(c\right) + b^{3}\right)} d^{m}\right)} x^{m}\right)} \log\left(c^{2} x^{2}\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, {\left({\left(a b^{2} d^{m} m + a b^{2} d^{m} - {\left(a b^{2} c^{2} d^{m} m + a b^{2} c^{2} d^{m}\right)} x^{2}\right)} x^{m} \log\left(x\right) + {\left(a b^{2} d^{m} m \log\left(c\right) + a b^{2} d^{m} \log\left(c\right) - {\left(a b^{2} c^{2} d^{m} m \log\left(c\right) + a b^{2} c^{2} d^{m} \log\left(c\right)\right)} x^{2}\right)} x^{m}\right)} \log\left(c^{2} x^{2}\right)}{{\left(c^{2} m + c^{2}\right)} x^{2} - m - 1}\,{d x}}{4 \, {\left(m + 1\right)}}"," ",0,"(d*x)^(m + 1)*a^3/(d*(m + 1)) + 1/4*(4*b^3*d^m*x*x^m*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^3 - 3*b^3*d^m*x*x^m*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(c^2*x^2)^2 - 4*(m + 1)*integrate(3/4*(4*(a*b^2*d^m*m + a*b^2*d^m - (a*b^2*c^2*d^m*m + a*b^2*c^2*d^m)*x^2)*x^m*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - (a*b^2*d^m*m + a*b^2*d^m - (a*b^2*c^2*d^m*m + a*b^2*c^2*d^m)*x^2)*x^m*log(c^2*x^2)^2 - 4*(a*b^2*d^m*m + a*b^2*d^m - (a*b^2*c^2*d^m*m + a*b^2*c^2*d^m)*x^2)*x^m*log(x)^2 - 8*(a*b^2*d^m*m*log(c) + a*b^2*d^m*log(c) - (a*b^2*c^2*d^m*m*log(c) + a*b^2*c^2*d^m*log(c))*x^2)*x^m*log(x) + (4*b^3*d^m*x^m*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - b^3*d^m*x^m*log(c^2*x^2)^2)*sqrt(c*x + 1)*sqrt(c*x - 1) - 4*(a*b^2*d^m*m*log(c)^2 + a*b^2*d^m*log(c)^2 - (a*b^2*c^2*d^m*m*log(c)^2 + a*b^2*c^2*d^m*log(c)^2)*x^2)*x^m - 4*((b^3*d^m*m + b^3*d^m - (b^3*c^2*d^m*m + b^3*c^2*d^m)*x^2)*x^m*log(x)^2 + 2*(b^3*d^m*m*log(c) + b^3*d^m*log(c) - (b^3*c^2*d^m*m*log(c) + b^3*c^2*d^m*log(c))*x^2)*x^m*log(x) + ((b^3*log(c)^2 - a^2*b)*d^m*m - ((b^3*c^2*log(c)^2 - a^2*b*c^2)*d^m*m + (b^3*c^2*log(c)^2 - a^2*b*c^2)*d^m)*x^2 + (b^3*log(c)^2 - a^2*b)*d^m)*x^m - ((b^3*d^m*m + b^3*d^m - (b^3*c^2*d^m*m + b^3*c^2*d^m)*x^2)*x^m*log(x) + (b^3*d^m*m*log(c) - (b^3*c^2*d^m*m*log(c) + (b^3*c^2*log(c) + b^3*c^2)*d^m)*x^2 + (b^3*log(c) + b^3)*d^m)*x^m)*log(c^2*x^2))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*((a*b^2*d^m*m + a*b^2*d^m - (a*b^2*c^2*d^m*m + a*b^2*c^2*d^m)*x^2)*x^m*log(x) + (a*b^2*d^m*m*log(c) + a*b^2*d^m*log(c) - (a*b^2*c^2*d^m*m*log(c) + a*b^2*c^2*d^m*log(c))*x^2)*x^m)*log(c^2*x^2))/((c^2*m + c^2)*x^2 - m - 1), x))/(m + 1)","F",0
52,-1,0,0,0.000000," ","integrate((d*x)^m*(a+b*arcsec(c*x))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{{\left(d^{m} x x^{m} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(c^{2} d^{m} m + c^{2} d^{m}\right)} \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} x^{m}}{c^{2} m - {\left(c^{4} m + c^{4}\right)} x^{2} + c^{2}}\,{d x}\right)} b}{m + 1} + \frac{\left(d x\right)^{m + 1} a}{d {\left(m + 1\right)}}"," ",0,"(d^m*x*x^m*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - (c^2*d^m*m + c^2*d^m)*integrate(-sqrt(c*x + 1)*sqrt(c*x - 1)*x^m/(c^2*m - (c^4*m + c^4)*x^2 + c^2), x))*b/(m + 1) + (d*x)^(m + 1)*a/(d*(m + 1))","F",0
54,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\int \frac{\left(d x\right)^{m}}{b \operatorname{arcsec}\left(c x\right) + a}\,{d x}"," ",0,"integrate((d*x)^m/(b*arcsec(c*x) + a), x)","F",0
55,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arcsec(c*x))^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(b d^{m} x x^{m} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + a d^{m} x x^{m}\right)} \sqrt{c x + 1} \sqrt{c x - 1} - 4 \, {\left(4 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{3} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{3} \log\left(c\right)^{2} + 8 \, b^{3} \log\left(c\right) \log\left(x\right) + 4 \, b^{3} \log\left(x\right)^{2} + 8 \, a b^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, a^{2} b - 4 \, {\left(b^{3} \log\left(c\right) + b^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)\right)} \int \frac{{\left({\left(b d^{m} m - {\left(b c^{2} d^{m} m + 2 \, b c^{2} d^{m}\right)} x^{2} + b d^{m}\right)} x^{m} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(a d^{m} m - {\left(a c^{2} d^{m} m + 2 \, a c^{2} d^{m}\right)} x^{2} + a d^{m}\right)} x^{m}\right)} \sqrt{c x + 1} \sqrt{c x - 1}}{4 \, b^{3} \log\left(c\right)^{2} + 4 \, a^{2} b - 4 \, {\left(b^{3} c^{2} \log\left(c\right)^{2} + a^{2} b c^{2}\right)} x^{2} - 4 \, {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} - {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(c^{2} x^{2}\right)^{2} - 4 \, {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)^{2} - 8 \, {\left(a b^{2} c^{2} x^{2} - a b^{2}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, {\left(b^{3} c^{2} x^{2} \log\left(c\right) - b^{3} \log\left(c\right) + {\left(b^{3} c^{2} x^{2} - b^{3}\right)} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) - 8 \, {\left(b^{3} c^{2} x^{2} \log\left(c\right) - b^{3} \log\left(c\right)\right)} \log\left(x\right)}\,{d x}}{4 \, b^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)^{2} + b^{3} \log\left(c^{2} x^{2}\right)^{2} + 4 \, b^{3} \log\left(c\right)^{2} + 8 \, b^{3} \log\left(c\right) \log\left(x\right) + 4 \, b^{3} \log\left(x\right)^{2} + 8 \, a b^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + 4 \, a^{2} b - 4 \, {\left(b^{3} \log\left(c\right) + b^{3} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right)}"," ",0,"-(4*(b*d^m*x*x^m*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + a*d^m*x*x^m)*sqrt(c*x + 1)*sqrt(c*x - 1) - (4*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^3*log(c^2*x^2)^2 + 4*b^3*log(c)^2 + 8*b^3*log(c)*log(x) + 4*b^3*log(x)^2 + 8*a*b^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*a^2*b - 4*(b^3*log(c) + b^3*log(x))*log(c^2*x^2))*integrate(4*((b*d^m*m - (b*c^2*d^m*m + 2*b*c^2*d^m)*x^2 + b*d^m)*x^m*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + (a*d^m*m - (a*c^2*d^m*m + 2*a*c^2*d^m)*x^2 + a*d^m)*x^m)*sqrt(c*x + 1)*sqrt(c*x - 1)/(4*b^3*log(c)^2 + 4*a^2*b - 4*(b^3*c^2*log(c)^2 + a^2*b*c^2)*x^2 - 4*(b^3*c^2*x^2 - b^3)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 - (b^3*c^2*x^2 - b^3)*log(c^2*x^2)^2 - 4*(b^3*c^2*x^2 - b^3)*log(x)^2 - 8*(a*b^2*c^2*x^2 - a*b^2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*(b^3*c^2*x^2*log(c) - b^3*log(c) + (b^3*c^2*x^2 - b^3)*log(x))*log(c^2*x^2) - 8*(b^3*c^2*x^2*log(c) - b^3*log(c))*log(x)), x))/(4*b^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))^2 + b^3*log(c^2*x^2)^2 + 4*b^3*log(c)^2 + 8*b^3*log(c)*log(x) + 4*b^3*log(x)^2 + 8*a*b^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + 4*a^2*b - 4*(b^3*log(c) + b^3*log(x))*log(c^2*x^2))","F",0
56,1,272,0,0.328964," ","integrate((e*x+d)^3*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a e^{3} x^{4} + a d e^{2} x^{3} + \frac{3}{2} \, a d^{2} e x^{2} + \frac{3}{2} \, {\left(x^{2} \operatorname{arcsec}\left(c x\right) - \frac{x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c}\right)} b d^{2} e + \frac{1}{4} \, {\left(4 \, x^{3} \operatorname{arcsec}\left(c x\right) - \frac{\frac{2 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}} - \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{2}}}{c}\right)} b d e^{2} + \frac{1}{12} \, {\left(3 \, x^{4} \operatorname{arcsec}\left(c x\right) - \frac{c^{2} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 3 \, x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{3}}\right)} b e^{3} + a d^{3} x + \frac{{\left(2 \, c x \operatorname{arcsec}\left(c x\right) - \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right) + \log\left(-\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)\right)} b d^{3}}{2 \, c}"," ",0,"1/4*a*e^3*x^4 + a*d*e^2*x^3 + 3/2*a*d^2*e*x^2 + 3/2*(x^2*arcsec(c*x) - x*sqrt(-1/(c^2*x^2) + 1)/c)*b*d^2*e + 1/4*(4*x^3*arcsec(c*x) - (2*sqrt(-1/(c^2*x^2) + 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 - log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^2)/c)*b*d*e^2 + 1/12*(3*x^4*arcsec(c*x) - (c^2*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 3*x*sqrt(-1/(c^2*x^2) + 1))/c^3)*b*e^3 + a*d^3*x + 1/2*(2*c*x*arcsec(c*x) - log(sqrt(-1/(c^2*x^2) + 1) + 1) + log(-sqrt(-1/(c^2*x^2) + 1) + 1))*b*d^3/c","A",0
57,1,200,0,0.326966," ","integrate((e*x+d)^2*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a e^{2} x^{3} + a d e x^{2} + {\left(x^{2} \operatorname{arcsec}\left(c x\right) - \frac{x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c}\right)} b d e + \frac{1}{12} \, {\left(4 \, x^{3} \operatorname{arcsec}\left(c x\right) - \frac{\frac{2 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}} - \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{2}}}{c}\right)} b e^{2} + a d^{2} x + \frac{{\left(2 \, c x \operatorname{arcsec}\left(c x\right) - \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right) + \log\left(-\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)\right)} b d^{2}}{2 \, c}"," ",0,"1/3*a*e^2*x^3 + a*d*e*x^2 + (x^2*arcsec(c*x) - x*sqrt(-1/(c^2*x^2) + 1)/c)*b*d*e + 1/12*(4*x^3*arcsec(c*x) - (2*sqrt(-1/(c^2*x^2) + 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 - log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^2)/c)*b*e^2 + a*d^2*x + 1/2*(2*c*x*arcsec(c*x) - log(sqrt(-1/(c^2*x^2) + 1) + 1) + log(-sqrt(-1/(c^2*x^2) + 1) + 1))*b*d^2/c","A",0
58,1,93,0,0.322270," ","integrate((e*x+d)*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{2} \, a e x^{2} + \frac{1}{2} \, {\left(x^{2} \operatorname{arcsec}\left(c x\right) - \frac{x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c}\right)} b e + a d x + \frac{{\left(2 \, c x \operatorname{arcsec}\left(c x\right) - \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right) + \log\left(-\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)\right)} b d}{2 \, c}"," ",0,"1/2*a*e*x^2 + 1/2*(x^2*arcsec(c*x) - x*sqrt(-1/(c^2*x^2) + 1)/c)*b*e + a*d*x + 1/2*(2*c*x*arcsec(c*x) - log(sqrt(-1/(c^2*x^2) + 1) + 1) + log(-sqrt(-1/(c^2*x^2) + 1) + 1))*b*d/c","A",0
59,1,53,0,0.322400," ","integrate(a+b*arcsec(c*x),x, algorithm=""maxima"")","a x + \frac{{\left(2 \, c x \operatorname{arcsec}\left(c x\right) - \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right) + \log\left(-\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)\right)} b}{2 \, c}"," ",0,"a*x + 1/2*(2*c*x*arcsec(c*x) - log(sqrt(-1/(c^2*x^2) + 1) + 1) + log(-sqrt(-1/(c^2*x^2) + 1) + 1))*b/c","A",0
60,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x+d),x, algorithm=""maxima"")","b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x + d}\,{d x} + \frac{a \log\left(e x + d\right)}{e}"," ",0,"b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x + d), x) + a*log(e*x + d)/e","F",0
61,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x+d)^2,x, algorithm=""maxima"")","\frac{b {\left(\frac{2 \, {\left(c^{2} e^{2} x + c^{2} d e\right)} c {\left(\frac{\arctan\left(\frac{{\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{2} e + 2 \, c d}{2 \, \sqrt{-c^{2} d^{2} + e^{2}}}\right) e}{\sqrt{-c^{2} d^{2} + e^{2}} c d} - \frac{\arctan\left(\frac{1}{2} \, {\left(\sqrt{c x + 1} - \sqrt{c x - 1}\right)}^{2}\right)}{c d}\right)}}{c^{2} e} - \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)}}{e^{2} x + d e} - \frac{a}{e^{2} x + d e}"," ",0,"((c^2*e^2*x + c^2*d*e)*integrate(x*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1))/(c^2*e^2*x^3 + c^2*d*e*x^2 - e^2*x - d*e + (c^2*e^2*x^3 + c^2*d*e*x^2 - e^2*x - d*e)*e^(log(c*x + 1) + log(c*x - 1))), x) - arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/(e^2*x + d*e) - a/(e^2*x + d*e)","F",0
62,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x+d)^3,x, algorithm=""maxima"")","\frac{{\left({\left(c^{2} e^{3} x^{2} + 2 \, c^{2} d e^{2} x + c^{2} d^{2} e\right)} \int \frac{x e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)}}{c^{2} e^{3} x^{4} + 2 \, c^{2} d e^{2} x^{3} - 2 \, d e^{2} x + {\left(c^{2} e^{3} x^{4} + 2 \, c^{2} d e^{2} x^{3} - 2 \, d e^{2} x - d^{2} e + {\left(c^{2} d^{2} e - e^{3}\right)} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - d^{2} e + {\left(c^{2} d^{2} e - e^{3}\right)} x^{2}}\,{d x} - \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b}{2 \, {\left(e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e\right)}} - \frac{a}{2 \, {\left(e^{3} x^{2} + 2 \, d e^{2} x + d^{2} e\right)}}"," ",0,"1/2*(2*(c^2*e^3*x^2 + 2*c^2*d*e^2*x + c^2*d^2*e)*integrate(1/2*x*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1))/(c^2*e^3*x^4 + 2*c^2*d*e^2*x^3 - 2*d*e^2*x - d^2*e + (c^2*d^2*e - e^3)*x^2 + (c^2*e^3*x^4 + 2*c^2*d*e^2*x^3 - 2*d*e^2*x - d^2*e + (c^2*d^2*e - e^3)*x^2)*e^(log(c*x + 1) + log(c*x - 1))), x) - arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/(e^3*x^2 + 2*d*e^2*x + d^2*e) - 1/2*a/(e^3*x^2 + 2*d*e^2*x + d^2*e)","F",0
63,-2,0,0,0.000000," ","integrate((e*x+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c*d-e>0)', see `assume?` for more details)Is c*d-e positive or negative?","F(-2)",0
64,-2,0,0,0.000000," ","integrate((e*x+d)^(1/2)*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c*d-e>0)', see `assume?` for more details)Is c*d-e positive or negative?","F(-2)",0
65,-2,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x+d)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c*d-e>0)', see `assume?` for more details)Is c*d-e positive or negative?","F(-2)",0
66,-2,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x+d)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c*d-e>0)', see `assume?` for more details)Is c*d-e positive or negative?","F(-2)",0
67,-2,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x+d)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c*d-e>0)', see `assume?` for more details)Is c*d-e positive or negative?","F(-2)",0
68,-2,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x+d)^(7/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c*d-e>0)', see `assume?` for more details)Is c*d-e positive or negative?","F(-2)",0
69,1,296,0,0.330280," ","integrate(x^4*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a e x^{7} + \frac{1}{5} \, a d x^{5} + \frac{1}{80} \, {\left(16 \, x^{5} \operatorname{arcsec}\left(c x\right) + \frac{\frac{2 \, {\left(3 \, {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 5 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right)}}{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{4}} - \frac{3 \, \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{4}} + \frac{3 \, \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{4}}}{c}\right)} b d + \frac{1}{672} \, {\left(96 \, x^{7} \operatorname{arcsec}\left(c x\right) - \frac{\frac{2 \, {\left(15 \, {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} - 40 \, {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 33 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right)}}{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} + 3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{6}} + \frac{15 \, \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{6}} - \frac{15 \, \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{6}}}{c}\right)} b e"," ",0,"1/7*a*e*x^7 + 1/5*a*d*x^5 + 1/80*(16*x^5*arcsec(c*x) + (2*(3*(-1/(c^2*x^2) + 1)^(3/2) - 5*sqrt(-1/(c^2*x^2) + 1))/(c^4*(1/(c^2*x^2) - 1)^2 + 2*c^4*(1/(c^2*x^2) - 1) + c^4) - 3*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^4 + 3*log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^4)/c)*b*d + 1/672*(96*x^7*arcsec(c*x) - (2*(15*(-1/(c^2*x^2) + 1)^(5/2) - 40*(-1/(c^2*x^2) + 1)^(3/2) + 33*sqrt(-1/(c^2*x^2) + 1))/(c^6*(1/(c^2*x^2) - 1)^3 + 3*c^6*(1/(c^2*x^2) - 1)^2 + 3*c^6*(1/(c^2*x^2) - 1) + c^6) + 15*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^6 - 15*log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^6)/c)*b*e","A",0
70,1,232,0,0.326016," ","integrate(x^2*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e x^{5} + \frac{1}{3} \, a d x^{3} + \frac{1}{12} \, {\left(4 \, x^{3} \operatorname{arcsec}\left(c x\right) - \frac{\frac{2 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}} - \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{2}}}{c}\right)} b d + \frac{1}{80} \, {\left(16 \, x^{5} \operatorname{arcsec}\left(c x\right) + \frac{\frac{2 \, {\left(3 \, {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 5 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right)}}{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{4}} - \frac{3 \, \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{4}} + \frac{3 \, \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{4}}}{c}\right)} b e"," ",0,"1/5*a*e*x^5 + 1/3*a*d*x^3 + 1/12*(4*x^3*arcsec(c*x) - (2*sqrt(-1/(c^2*x^2) + 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 - log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^2)/c)*b*d + 1/80*(16*x^5*arcsec(c*x) + (2*(3*(-1/(c^2*x^2) + 1)^(3/2) - 5*sqrt(-1/(c^2*x^2) + 1))/(c^4*(1/(c^2*x^2) - 1)^2 + 2*c^4*(1/(c^2*x^2) - 1) + c^4) - 3*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^4 + 3*log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^4)/c)*b*e","A",0
71,1,154,0,0.313205," ","integrate((e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a e x^{3} + \frac{1}{12} \, {\left(4 \, x^{3} \operatorname{arcsec}\left(c x\right) - \frac{\frac{2 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}} - \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{2}}}{c}\right)} b e + a d x + \frac{{\left(2 \, c x \operatorname{arcsec}\left(c x\right) - \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right) + \log\left(-\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)\right)} b d}{2 \, c}"," ",0,"1/3*a*e*x^3 + 1/12*(4*x^3*arcsec(c*x) - (2*sqrt(-1/(c^2*x^2) + 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 - log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^2)/c)*b*e + a*d*x + 1/2*(2*c*x*arcsec(c*x) - log(sqrt(-1/(c^2*x^2) + 1) + 1) + log(-sqrt(-1/(c^2*x^2) + 1) + 1))*b*d/c","A",0
72,1,89,0,0.319220," ","integrate((e*x^2+d)*(a+b*arcsec(c*x))/x^2,x, algorithm=""maxima"")","{\left(c \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{\operatorname{arcsec}\left(c x\right)}{x}\right)} b d + a e x + \frac{{\left(2 \, c x \operatorname{arcsec}\left(c x\right) - \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right) + \log\left(-\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)\right)} b e}{2 \, c} - \frac{a d}{x}"," ",0,"(c*sqrt(-1/(c^2*x^2) + 1) - arcsec(c*x)/x)*b*d + a*e*x + 1/2*(2*c*x*arcsec(c*x) - log(sqrt(-1/(c^2*x^2) + 1) + 1) + log(-sqrt(-1/(c^2*x^2) + 1) + 1))*b*e/c - a*d/x","A",0
73,1,94,0,0.320316," ","integrate((e*x^2+d)*(a+b*arcsec(c*x))/x^4,x, algorithm=""maxima"")","{\left(c \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{\operatorname{arcsec}\left(c x\right)}{x}\right)} b e - \frac{1}{9} \, b d {\left(\frac{c^{4} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 3 \, c^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c} + \frac{3 \, \operatorname{arcsec}\left(c x\right)}{x^{3}}\right)} - \frac{a e}{x} - \frac{a d}{3 \, x^{3}}"," ",0,"(c*sqrt(-1/(c^2*x^2) + 1) - arcsec(c*x)/x)*b*e - 1/9*b*d*((c^4*(-1/(c^2*x^2) + 1)^(3/2) - 3*c^4*sqrt(-1/(c^2*x^2) + 1))/c + 3*arcsec(c*x)/x^3) - a*e/x - 1/3*a*d/x^3","A",0
74,1,137,0,0.323420," ","integrate((e*x^2+d)*(a+b*arcsec(c*x))/x^6,x, algorithm=""maxima"")","\frac{1}{75} \, b d {\left(\frac{3 \, c^{6} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} - 10 \, c^{6} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 15 \, c^{6} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c} - \frac{15 \, \operatorname{arcsec}\left(c x\right)}{x^{5}}\right)} - \frac{1}{9} \, b e {\left(\frac{c^{4} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 3 \, c^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c} + \frac{3 \, \operatorname{arcsec}\left(c x\right)}{x^{3}}\right)} - \frac{a e}{3 \, x^{3}} - \frac{a d}{5 \, x^{5}}"," ",0,"1/75*b*d*((3*c^6*(-1/(c^2*x^2) + 1)^(5/2) - 10*c^6*(-1/(c^2*x^2) + 1)^(3/2) + 15*c^6*sqrt(-1/(c^2*x^2) + 1))/c - 15*arcsec(c*x)/x^5) - 1/9*b*e*((c^4*(-1/(c^2*x^2) + 1)^(3/2) - 3*c^4*sqrt(-1/(c^2*x^2) + 1))/c + 3*arcsec(c*x)/x^3) - 1/3*a*e/x^3 - 1/5*a*d/x^5","A",0
75,1,172,0,0.319083," ","integrate((e*x^2+d)*(a+b*arcsec(c*x))/x^8,x, algorithm=""maxima"")","-\frac{1}{245} \, b d {\left(\frac{5 \, c^{8} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{7}{2}} - 21 \, c^{8} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} + 35 \, c^{8} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 35 \, c^{8} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c} + \frac{35 \, \operatorname{arcsec}\left(c x\right)}{x^{7}}\right)} + \frac{1}{75} \, b e {\left(\frac{3 \, c^{6} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} - 10 \, c^{6} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 15 \, c^{6} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c} - \frac{15 \, \operatorname{arcsec}\left(c x\right)}{x^{5}}\right)} - \frac{a e}{5 \, x^{5}} - \frac{a d}{7 \, x^{7}}"," ",0,"-1/245*b*d*((5*c^8*(-1/(c^2*x^2) + 1)^(7/2) - 21*c^8*(-1/(c^2*x^2) + 1)^(5/2) + 35*c^8*(-1/(c^2*x^2) + 1)^(3/2) - 35*c^8*sqrt(-1/(c^2*x^2) + 1))/c + 35*arcsec(c*x)/x^7) + 1/75*b*e*((3*c^6*(-1/(c^2*x^2) + 1)^(5/2) - 10*c^6*(-1/(c^2*x^2) + 1)^(3/2) + 15*c^6*sqrt(-1/(c^2*x^2) + 1))/c - 15*arcsec(c*x)/x^5) - 1/5*a*e/x^5 - 1/7*a*d/x^7","A",0
76,1,185,0,0.333076," ","integrate(x^5*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, a e x^{8} + \frac{1}{6} \, a d x^{6} + \frac{1}{90} \, {\left(15 \, x^{6} \operatorname{arcsec}\left(c x\right) - \frac{3 \, c^{4} x^{5} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} + 10 \, c^{2} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 15 \, x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{5}}\right)} b d + \frac{1}{280} \, {\left(35 \, x^{8} \operatorname{arcsec}\left(c x\right) - \frac{5 \, c^{6} x^{7} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{7}{2}} + 21 \, c^{4} x^{5} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} + 35 \, c^{2} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 35 \, x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{7}}\right)} b e"," ",0,"1/8*a*e*x^8 + 1/6*a*d*x^6 + 1/90*(15*x^6*arcsec(c*x) - (3*c^4*x^5*(-1/(c^2*x^2) + 1)^(5/2) + 10*c^2*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 15*x*sqrt(-1/(c^2*x^2) + 1))/c^5)*b*d + 1/280*(35*x^8*arcsec(c*x) - (5*c^6*x^7*(-1/(c^2*x^2) + 1)^(7/2) + 21*c^4*x^5*(-1/(c^2*x^2) + 1)^(5/2) + 35*c^2*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 35*x*sqrt(-1/(c^2*x^2) + 1))/c^7)*b*e","A",0
77,1,144,0,0.312792," ","integrate(x^3*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a e x^{6} + \frac{1}{4} \, a d x^{4} + \frac{1}{12} \, {\left(3 \, x^{4} \operatorname{arcsec}\left(c x\right) - \frac{c^{2} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 3 \, x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{3}}\right)} b d + \frac{1}{90} \, {\left(15 \, x^{6} \operatorname{arcsec}\left(c x\right) - \frac{3 \, c^{4} x^{5} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} + 10 \, c^{2} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 15 \, x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{5}}\right)} b e"," ",0,"1/6*a*e*x^6 + 1/4*a*d*x^4 + 1/12*(3*x^4*arcsec(c*x) - (c^2*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 3*x*sqrt(-1/(c^2*x^2) + 1))/c^3)*b*d + 1/90*(15*x^6*arcsec(c*x) - (3*c^4*x^5*(-1/(c^2*x^2) + 1)^(5/2) + 10*c^2*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 15*x*sqrt(-1/(c^2*x^2) + 1))/c^5)*b*e","A",0
78,1,100,0,0.316536," ","integrate(x*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a e x^{4} + \frac{1}{2} \, a d x^{2} + \frac{1}{2} \, {\left(x^{2} \operatorname{arcsec}\left(c x\right) - \frac{x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c}\right)} b d + \frac{1}{12} \, {\left(3 \, x^{4} \operatorname{arcsec}\left(c x\right) - \frac{c^{2} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 3 \, x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{3}}\right)} b e"," ",0,"1/4*a*e*x^4 + 1/2*a*d*x^2 + 1/2*(x^2*arcsec(c*x) - x*sqrt(-1/(c^2*x^2) + 1)/c)*b*d + 1/12*(3*x^4*arcsec(c*x) - (c^2*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 3*x*sqrt(-1/(c^2*x^2) + 1))/c^3)*b*e","A",0
79,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arcsec(c*x))/x,x, algorithm=""maxima"")","\frac{1}{2} \, a e x^{2} + a d \log\left(x\right) - \frac{-2 i \, b c^{2} e x^{2} \log\left(c\right) - 2 i \, b c^{2} d \log\left(-c x + 1\right) \log\left(x\right) - 2 i \, b c^{2} d \log\left(x\right)^{2} - 2 i \, b c^{2} d {\rm Li}_2\left(c x\right) - 2 i \, b c^{2} d {\rm Li}_2\left(-c x\right) + i \, {\left(2 \, {\left({\left(\log\left(c x + 1\right) + \log\left(c x - 1\right) - 2 \, \log\left(x\right)\right)} \log\left(x\right) - \log\left(c x - 1\right) \log\left(x\right) + \log\left(-c x + 1\right) \log\left(x\right) + \log\left(x\right)^{2} + {\rm Li}_2\left(c x\right) + {\rm Li}_2\left(-c x\right)\right)} b d + b e {\left(\frac{\log\left(c x + 1\right)}{c^{2}} + \frac{\log\left(c x - 1\right)}{c^{2}}\right)}\right)} c^{2} + 2 \, {\left(2 \, b d \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \log\left(x\right)}{c^{2} x^{3} - x}\,{d x} + \frac{\sqrt{c x + 1} \sqrt{c x - 1} b e}{c^{2}}\right)} c^{2} - i \, b e \log\left(c x - 1\right) - 2 \, {\left(b c^{2} e x^{2} + 2 \, b c^{2} d \log\left(x\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(i \, b c^{2} e x^{2} + 2 i \, b c^{2} d \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + {\left(-2 i \, b c^{2} d \log\left(x\right) - i \, b e\right)} \log\left(c x + 1\right) + {\left(-2 i \, b c^{2} e x^{2} - 4 i \, b c^{2} d \log\left(c\right)\right)} \log\left(x\right)}{4 \, c^{2}}"," ",0,"1/2*a*e*x^2 + a*d*log(x) - 1/4*(-2*I*b*c^2*e*x^2*log(c) - 2*I*b*c^2*d*log(-c*x + 1)*log(x) - 2*I*b*c^2*d*log(x)^2 - 2*I*b*c^2*d*dilog(c*x) - 2*I*b*c^2*d*dilog(-c*x) + I*(b*e*(log(c*x + 1)/c^2 + log(c*x - 1)/c^2) + 8*b*d*integrate(1/2*log(x)/(c^2*x^3 - x), x))*c^2 + 4*c^2*integrate(1/2*(b*e*x^2 + 2*b*d*log(x))*sqrt(c*x + 1)*sqrt(c*x - 1)/(c^2*x^3 - x), x) - I*b*e*log(c*x - 1) - 2*(b*c^2*e*x^2 + 2*b*c^2*d*log(x))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + (I*b*c^2*e*x^2 + 2*I*b*c^2*d*log(x))*log(c^2*x^2) + (-2*I*b*c^2*d*log(x) - I*b*e)*log(c*x + 1) + (-2*I*b*c^2*e*x^2 - 4*I*b*c^2*d*log(c))*log(x))/c^2","F",0
80,0,0,0,0.000000," ","integrate((e*x^2+d)*(a+b*arcsec(c*x))/x^3,x, algorithm=""maxima"")","-{\left(c^{2} \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \log\left(x\right)}{c^{4} x^{3} - c^{2} x}\,{d x} - \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) \log\left(x\right)\right)} b e - \frac{1}{4} \, b d {\left(\frac{\frac{c^{4} x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} - 1} - c^{3} \arctan\left(c x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right)}{c} + \frac{2 \, \operatorname{arcsec}\left(c x\right)}{x^{2}}\right)} + a e \log\left(x\right) - \frac{a d}{2 \, x^{2}}"," ",0,"-(c^2*integrate(sqrt(c*x + 1)*sqrt(c*x - 1)*log(x)/(c^4*x^3 - c^2*x), x) - arctan(sqrt(c*x + 1)*sqrt(c*x - 1))*log(x))*b*e - 1/4*b*d*((c^4*x*sqrt(-1/(c^2*x^2) + 1)/(c^2*x^2*(1/(c^2*x^2) - 1) - 1) - c^3*arctan(c*x*sqrt(-1/(c^2*x^2) + 1)))/c + 2*arcsec(c*x)/x^2) + a*e*log(x) - 1/2*a*d/x^2","F",0
81,1,405,0,0.343566," ","integrate(x^2*(e*x^2+d)^2*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{7} \, a e^{2} x^{7} + \frac{2}{5} \, a d e x^{5} + \frac{1}{3} \, a d^{2} x^{3} + \frac{1}{12} \, {\left(4 \, x^{3} \operatorname{arcsec}\left(c x\right) - \frac{\frac{2 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}} - \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{2}}}{c}\right)} b d^{2} + \frac{1}{40} \, {\left(16 \, x^{5} \operatorname{arcsec}\left(c x\right) + \frac{\frac{2 \, {\left(3 \, {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 5 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right)}}{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{4}} - \frac{3 \, \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{4}} + \frac{3 \, \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{4}}}{c}\right)} b d e + \frac{1}{672} \, {\left(96 \, x^{7} \operatorname{arcsec}\left(c x\right) - \frac{\frac{2 \, {\left(15 \, {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} - 40 \, {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 33 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right)}}{c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{3} + 3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 3 \, c^{6} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{6}} + \frac{15 \, \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{6}} - \frac{15 \, \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{6}}}{c}\right)} b e^{2}"," ",0,"1/7*a*e^2*x^7 + 2/5*a*d*e*x^5 + 1/3*a*d^2*x^3 + 1/12*(4*x^3*arcsec(c*x) - (2*sqrt(-1/(c^2*x^2) + 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 - log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^2)/c)*b*d^2 + 1/40*(16*x^5*arcsec(c*x) + (2*(3*(-1/(c^2*x^2) + 1)^(3/2) - 5*sqrt(-1/(c^2*x^2) + 1))/(c^4*(1/(c^2*x^2) - 1)^2 + 2*c^4*(1/(c^2*x^2) - 1) + c^4) - 3*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^4 + 3*log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^4)/c)*b*d*e + 1/672*(96*x^7*arcsec(c*x) - (2*(15*(-1/(c^2*x^2) + 1)^(5/2) - 40*(-1/(c^2*x^2) + 1)^(3/2) + 33*sqrt(-1/(c^2*x^2) + 1))/(c^6*(1/(c^2*x^2) - 1)^3 + 3*c^6*(1/(c^2*x^2) - 1)^2 + 3*c^6*(1/(c^2*x^2) - 1) + c^6) + 15*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^6 - 15*log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^6)/c)*b*e^2","A",0
82,1,296,0,0.343522," ","integrate((e*x^2+d)^2*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a e^{2} x^{5} + \frac{2}{3} \, a d e x^{3} + \frac{1}{6} \, {\left(4 \, x^{3} \operatorname{arcsec}\left(c x\right) - \frac{\frac{2 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}} - \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{2}}}{c}\right)} b d e + \frac{1}{80} \, {\left(16 \, x^{5} \operatorname{arcsec}\left(c x\right) + \frac{\frac{2 \, {\left(3 \, {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 5 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right)}}{c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)}^{2} + 2 \, c^{4} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{4}} - \frac{3 \, \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{4}} + \frac{3 \, \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{4}}}{c}\right)} b e^{2} + a d^{2} x + \frac{{\left(2 \, c x \operatorname{arcsec}\left(c x\right) - \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right) + \log\left(-\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)\right)} b d^{2}}{2 \, c}"," ",0,"1/5*a*e^2*x^5 + 2/3*a*d*e*x^3 + 1/6*(4*x^3*arcsec(c*x) - (2*sqrt(-1/(c^2*x^2) + 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 - log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^2)/c)*b*d*e + 1/80*(16*x^5*arcsec(c*x) + (2*(3*(-1/(c^2*x^2) + 1)^(3/2) - 5*sqrt(-1/(c^2*x^2) + 1))/(c^4*(1/(c^2*x^2) - 1)^2 + 2*c^4*(1/(c^2*x^2) - 1) + c^4) - 3*log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^4 + 3*log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^4)/c)*b*e^2 + a*d^2*x + 1/2*(2*c*x*arcsec(c*x) - log(sqrt(-1/(c^2*x^2) + 1) + 1) + log(-sqrt(-1/(c^2*x^2) + 1) + 1))*b*d^2/c","A",0
83,1,198,0,0.337830," ","integrate((e*x^2+d)^2*(a+b*arcsec(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{3} \, a e^{2} x^{3} + {\left(c \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{\operatorname{arcsec}\left(c x\right)}{x}\right)} b d^{2} + \frac{1}{12} \, {\left(4 \, x^{3} \operatorname{arcsec}\left(c x\right) - \frac{\frac{2 \, \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} + c^{2}} + \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)}{c^{2}} - \frac{\log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} - 1\right)}{c^{2}}}{c}\right)} b e^{2} + 2 \, a d e x + \frac{{\left(2 \, c x \operatorname{arcsec}\left(c x\right) - \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right) + \log\left(-\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)\right)} b d e}{c} - \frac{a d^{2}}{x}"," ",0,"1/3*a*e^2*x^3 + (c*sqrt(-1/(c^2*x^2) + 1) - arcsec(c*x)/x)*b*d^2 + 1/12*(4*x^3*arcsec(c*x) - (2*sqrt(-1/(c^2*x^2) + 1)/(c^2*(1/(c^2*x^2) - 1) + c^2) + log(sqrt(-1/(c^2*x^2) + 1) + 1)/c^2 - log(sqrt(-1/(c^2*x^2) + 1) - 1)/c^2)/c)*b*e^2 + 2*a*d*e*x + (2*c*x*arcsec(c*x) - log(sqrt(-1/(c^2*x^2) + 1) + 1) + log(-sqrt(-1/(c^2*x^2) + 1) + 1))*b*d*e/c - a*d^2/x","A",0
84,1,159,0,0.319398," ","integrate((e*x^2+d)^2*(a+b*arcsec(c*x))/x^4,x, algorithm=""maxima"")","2 \, {\left(c \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{\operatorname{arcsec}\left(c x\right)}{x}\right)} b d e + a e^{2} x - \frac{1}{9} \, b d^{2} {\left(\frac{c^{4} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 3 \, c^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c} + \frac{3 \, \operatorname{arcsec}\left(c x\right)}{x^{3}}\right)} + \frac{{\left(2 \, c x \operatorname{arcsec}\left(c x\right) - \log\left(\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right) + \log\left(-\sqrt{-\frac{1}{c^{2} x^{2}} + 1} + 1\right)\right)} b e^{2}}{2 \, c} - \frac{2 \, a d e}{x} - \frac{a d^{2}}{3 \, x^{3}}"," ",0,"2*(c*sqrt(-1/(c^2*x^2) + 1) - arcsec(c*x)/x)*b*d*e + a*e^2*x - 1/9*b*d^2*((c^4*(-1/(c^2*x^2) + 1)^(3/2) - 3*c^4*sqrt(-1/(c^2*x^2) + 1))/c + 3*arcsec(c*x)/x^3) + 1/2*(2*c*x*arcsec(c*x) - log(sqrt(-1/(c^2*x^2) + 1) + 1) + log(-sqrt(-1/(c^2*x^2) + 1) + 1))*b*e^2/c - 2*a*d*e/x - 1/3*a*d^2/x^3","A",0
85,1,181,0,0.331836," ","integrate((e*x^2+d)^2*(a+b*arcsec(c*x))/x^6,x, algorithm=""maxima"")","{\left(c \sqrt{-\frac{1}{c^{2} x^{2}} + 1} - \frac{\operatorname{arcsec}\left(c x\right)}{x}\right)} b e^{2} + \frac{1}{75} \, b d^{2} {\left(\frac{3 \, c^{6} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} - 10 \, c^{6} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 15 \, c^{6} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c} - \frac{15 \, \operatorname{arcsec}\left(c x\right)}{x^{5}}\right)} - \frac{2}{9} \, b d e {\left(\frac{c^{4} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 3 \, c^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c} + \frac{3 \, \operatorname{arcsec}\left(c x\right)}{x^{3}}\right)} - \frac{a e^{2}}{x} - \frac{2 \, a d e}{3 \, x^{3}} - \frac{a d^{2}}{5 \, x^{5}}"," ",0,"(c*sqrt(-1/(c^2*x^2) + 1) - arcsec(c*x)/x)*b*e^2 + 1/75*b*d^2*((3*c^6*(-1/(c^2*x^2) + 1)^(5/2) - 10*c^6*(-1/(c^2*x^2) + 1)^(3/2) + 15*c^6*sqrt(-1/(c^2*x^2) + 1))/c - 15*arcsec(c*x)/x^5) - 2/9*b*d*e*((c^4*(-1/(c^2*x^2) + 1)^(3/2) - 3*c^4*sqrt(-1/(c^2*x^2) + 1))/c + 3*arcsec(c*x)/x^3) - a*e^2/x - 2/3*a*d*e/x^3 - 1/5*a*d^2/x^5","A",0
86,1,241,0,0.330220," ","integrate((e*x^2+d)^2*(a+b*arcsec(c*x))/x^8,x, algorithm=""maxima"")","-\frac{1}{245} \, b d^{2} {\left(\frac{5 \, c^{8} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{7}{2}} - 21 \, c^{8} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} + 35 \, c^{8} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 35 \, c^{8} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c} + \frac{35 \, \operatorname{arcsec}\left(c x\right)}{x^{7}}\right)} + \frac{2}{75} \, b d e {\left(\frac{3 \, c^{6} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} - 10 \, c^{6} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 15 \, c^{6} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c} - \frac{15 \, \operatorname{arcsec}\left(c x\right)}{x^{5}}\right)} - \frac{1}{9} \, b e^{2} {\left(\frac{c^{4} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 3 \, c^{4} \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c} + \frac{3 \, \operatorname{arcsec}\left(c x\right)}{x^{3}}\right)} - \frac{a e^{2}}{3 \, x^{3}} - \frac{2 \, a d e}{5 \, x^{5}} - \frac{a d^{2}}{7 \, x^{7}}"," ",0,"-1/245*b*d^2*((5*c^8*(-1/(c^2*x^2) + 1)^(7/2) - 21*c^8*(-1/(c^2*x^2) + 1)^(5/2) + 35*c^8*(-1/(c^2*x^2) + 1)^(3/2) - 35*c^8*sqrt(-1/(c^2*x^2) + 1))/c + 35*arcsec(c*x)/x^7) + 2/75*b*d*e*((3*c^6*(-1/(c^2*x^2) + 1)^(5/2) - 10*c^6*(-1/(c^2*x^2) + 1)^(3/2) + 15*c^6*sqrt(-1/(c^2*x^2) + 1))/c - 15*arcsec(c*x)/x^5) - 1/9*b*e^2*((c^4*(-1/(c^2*x^2) + 1)^(3/2) - 3*c^4*sqrt(-1/(c^2*x^2) + 1))/c + 3*arcsec(c*x)/x^3) - 1/3*a*e^2/x^3 - 2/5*a*d*e/x^5 - 1/7*a*d^2/x^7","A",0
87,1,256,0,0.335930," ","integrate(x^3*(e*x^2+d)^2*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, a e^{2} x^{8} + \frac{1}{3} \, a d e x^{6} + \frac{1}{4} \, a d^{2} x^{4} + \frac{1}{12} \, {\left(3 \, x^{4} \operatorname{arcsec}\left(c x\right) - \frac{c^{2} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 3 \, x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{3}}\right)} b d^{2} + \frac{1}{45} \, {\left(15 \, x^{6} \operatorname{arcsec}\left(c x\right) - \frac{3 \, c^{4} x^{5} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} + 10 \, c^{2} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 15 \, x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{5}}\right)} b d e + \frac{1}{280} \, {\left(35 \, x^{8} \operatorname{arcsec}\left(c x\right) - \frac{5 \, c^{6} x^{7} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{7}{2}} + 21 \, c^{4} x^{5} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} + 35 \, c^{2} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 35 \, x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{7}}\right)} b e^{2}"," ",0,"1/8*a*e^2*x^8 + 1/3*a*d*e*x^6 + 1/4*a*d^2*x^4 + 1/12*(3*x^4*arcsec(c*x) - (c^2*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 3*x*sqrt(-1/(c^2*x^2) + 1))/c^3)*b*d^2 + 1/45*(15*x^6*arcsec(c*x) - (3*c^4*x^5*(-1/(c^2*x^2) + 1)^(5/2) + 10*c^2*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 15*x*sqrt(-1/(c^2*x^2) + 1))/c^5)*b*d*e + 1/280*(35*x^8*arcsec(c*x) - (5*c^6*x^7*(-1/(c^2*x^2) + 1)^(7/2) + 21*c^4*x^5*(-1/(c^2*x^2) + 1)^(5/2) + 35*c^2*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 35*x*sqrt(-1/(c^2*x^2) + 1))/c^7)*b*e^2","A",0
88,1,192,0,0.333193," ","integrate(x*(e*x^2+d)^2*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a e^{2} x^{6} + \frac{1}{2} \, a d e x^{4} + \frac{1}{2} \, a d^{2} x^{2} + \frac{1}{2} \, {\left(x^{2} \operatorname{arcsec}\left(c x\right) - \frac{x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c}\right)} b d^{2} + \frac{1}{6} \, {\left(3 \, x^{4} \operatorname{arcsec}\left(c x\right) - \frac{c^{2} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 3 \, x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{3}}\right)} b d e + \frac{1}{90} \, {\left(15 \, x^{6} \operatorname{arcsec}\left(c x\right) - \frac{3 \, c^{4} x^{5} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{5}{2}} + 10 \, c^{2} x^{3} {\left(-\frac{1}{c^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + 15 \, x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{5}}\right)} b e^{2}"," ",0,"1/6*a*e^2*x^6 + 1/2*a*d*e*x^4 + 1/2*a*d^2*x^2 + 1/2*(x^2*arcsec(c*x) - x*sqrt(-1/(c^2*x^2) + 1)/c)*b*d^2 + 1/6*(3*x^4*arcsec(c*x) - (c^2*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 3*x*sqrt(-1/(c^2*x^2) + 1))/c^3)*b*d*e + 1/90*(15*x^6*arcsec(c*x) - (3*c^4*x^5*(-1/(c^2*x^2) + 1)^(5/2) + 10*c^2*x^3*(-1/(c^2*x^2) + 1)^(3/2) + 15*x*sqrt(-1/(c^2*x^2) + 1))/c^5)*b*e^2","A",0
89,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arcsec(c*x))/x,x, algorithm=""maxima"")","\frac{1}{4} \, a e^{2} x^{4} + a d e x^{2} + a d^{2} \log\left(x\right) - \frac{-2 i \, b c^{4} e^{2} x^{4} \log\left(c\right) - 4 i \, b c^{4} d^{2} \log\left(-c x + 1\right) \log\left(x\right) - 4 i \, b c^{4} d^{2} \log\left(x\right)^{2} - 4 i \, b c^{4} d^{2} {\rm Li}_2\left(c x\right) - 4 i \, b c^{4} d^{2} {\rm Li}_2\left(-c x\right) + i \, {\left(4 \, {\left({\left(\log\left(c x + 1\right) + \log\left(c x - 1\right) - 2 \, \log\left(x\right)\right)} \log\left(x\right) - \log\left(c x - 1\right) \log\left(x\right) + \log\left(-c x + 1\right) \log\left(x\right) + \log\left(x\right)^{2} + {\rm Li}_2\left(c x\right) + {\rm Li}_2\left(-c x\right)\right)} b d^{2} + b e^{2} {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c x + 1\right)}{c^{4}} + \frac{\log\left(c x - 1\right)}{c^{4}}\right)} + 4 \, b d e {\left(\frac{\log\left(c x + 1\right)}{c^{2}} + \frac{\log\left(c x - 1\right)}{c^{2}}\right)}\right)} c^{4} + \frac{2}{3} \, {\left(12 \, b d^{2} \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \log\left(x\right)}{c^{2} x^{3} - x}\,{d x} + \frac{12 \, \sqrt{c x + 1} \sqrt{c x - 1} b d e}{c^{2}} + \frac{{\left(c^{2} x^{2} + 2\right)} \sqrt{c x + 1} \sqrt{c x - 1} b e^{2}}{c^{4}}\right)} c^{4} + {\left(-8 i \, b c^{4} d e \log\left(c\right) - i \, b c^{2} e^{2}\right)} x^{2} - 2 \, {\left(b c^{4} e^{2} x^{4} + 4 \, b c^{4} d e x^{2} + 4 \, b c^{4} d^{2} \log\left(x\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(i \, b c^{4} e^{2} x^{4} + 4 i \, b c^{4} d e x^{2} + 4 i \, b c^{4} d^{2} \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + {\left(-4 i \, b c^{4} d^{2} \log\left(x\right) - 4 i \, b c^{2} d e - i \, b e^{2}\right)} \log\left(c x + 1\right) + {\left(-4 i \, b c^{2} d e - i \, b e^{2}\right)} \log\left(c x - 1\right) + {\left(-2 i \, b c^{4} e^{2} x^{4} - 8 i \, b c^{4} d e x^{2} - 8 i \, b c^{4} d^{2} \log\left(c\right)\right)} \log\left(x\right)}{8 \, c^{4}}"," ",0,"1/4*a*e^2*x^4 + a*d*e*x^2 + a*d^2*log(x) - 1/8*(-2*I*b*c^4*e^2*x^4*log(c) - 4*I*b*c^4*d^2*log(-c*x + 1)*log(x) - 4*I*b*c^4*d^2*log(x)^2 - 4*I*b*c^4*d^2*dilog(c*x) - 4*I*b*c^4*d^2*dilog(-c*x) + I*(b*e^2*(x^2/c^2 + log(c*x + 1)/c^4 + log(c*x - 1)/c^4) + 4*b*d*e*(log(c*x + 1)/c^2 + log(c*x - 1)/c^2) + 32*b*d^2*integrate(1/4*log(x)/(c^2*x^3 - x), x))*c^4 + 8*c^4*integrate(1/4*(b*e^2*x^4 + 4*b*d*e*x^2 + 4*b*d^2*log(x))*sqrt(c*x + 1)*sqrt(c*x - 1)/(c^2*x^3 - x), x) + (-8*I*b*c^4*d*e*log(c) - I*b*c^2*e^2)*x^2 - 2*(b*c^4*e^2*x^4 + 4*b*c^4*d*e*x^2 + 4*b*c^4*d^2*log(x))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + (I*b*c^4*e^2*x^4 + 4*I*b*c^4*d*e*x^2 + 4*I*b*c^4*d^2*log(x))*log(c^2*x^2) + (-4*I*b*c^4*d^2*log(x) - 4*I*b*c^2*d*e - I*b*e^2)*log(c*x + 1) + (-4*I*b*c^2*d*e - I*b*e^2)*log(c*x - 1) + (-2*I*b*c^4*e^2*x^4 - 8*I*b*c^4*d*e*x^2 - 8*I*b*c^4*d^2*log(c))*log(x))/c^4","F",0
90,0,0,0,0.000000," ","integrate((e*x^2+d)^2*(a+b*arcsec(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, a e^{2} x^{2} - \frac{1}{4} \, b d^{2} {\left(\frac{\frac{c^{4} x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}}{c^{2} x^{2} {\left(\frac{1}{c^{2} x^{2}} - 1\right)} - 1} - c^{3} \arctan\left(c x \sqrt{-\frac{1}{c^{2} x^{2}} + 1}\right)}{c} + \frac{2 \, \operatorname{arcsec}\left(c x\right)}{x^{2}}\right)} + 2 \, a d e \log\left(x\right) - \frac{a d^{2}}{2 \, x^{2}} - \frac{-2 i \, b c^{2} e^{2} x^{2} \log\left(c\right) - 4 i \, b c^{2} d e \log\left(-c x + 1\right) \log\left(x\right) - 4 i \, b c^{2} d e \log\left(x\right)^{2} - 4 i \, b c^{2} d e {\rm Li}_2\left(c x\right) - 4 i \, b c^{2} d e {\rm Li}_2\left(-c x\right) - i \, b e^{2} \log\left(c x - 1\right) + i \, {\left(4 \, {\left({\left(\log\left(c x + 1\right) + \log\left(c x - 1\right) - 2 \, \log\left(x\right)\right)} \log\left(x\right) - \log\left(c x - 1\right) \log\left(x\right) + \log\left(-c x + 1\right) \log\left(x\right) + \log\left(x\right)^{2} + {\rm Li}_2\left(c x\right) + {\rm Li}_2\left(-c x\right)\right)} b d e + b e^{2} {\left(\frac{\log\left(c x + 1\right)}{c^{2}} + \frac{\log\left(c x - 1\right)}{c^{2}}\right)}\right)} c^{2} + 2 \, {\left(4 \, b d e \int \frac{\sqrt{c x + 1} \sqrt{c x - 1} \log\left(x\right)}{c^{2} x^{3} - x}\,{d x} + \frac{\sqrt{c x + 1} \sqrt{c x - 1} b e^{2}}{c^{2}}\right)} c^{2} - 2 \, {\left(b c^{2} e^{2} x^{2} + 4 \, b c^{2} d e \log\left(x\right)\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(i \, b c^{2} e^{2} x^{2} + 4 i \, b c^{2} d e \log\left(x\right)\right)} \log\left(c^{2} x^{2}\right) + {\left(-4 i \, b c^{2} d e \log\left(x\right) - i \, b e^{2}\right)} \log\left(c x + 1\right) + {\left(-2 i \, b c^{2} e^{2} x^{2} - 8 i \, b c^{2} d e \log\left(c\right)\right)} \log\left(x\right)}{4 \, c^{2}}"," ",0,"1/2*a*e^2*x^2 - 1/4*b*d^2*((c^4*x*sqrt(-1/(c^2*x^2) + 1)/(c^2*x^2*(1/(c^2*x^2) - 1) - 1) - c^3*arctan(c*x*sqrt(-1/(c^2*x^2) + 1)))/c + 2*arcsec(c*x)/x^2) + 2*a*d*e*log(x) - 1/2*a*d^2/x^2 - 1/4*(-2*I*b*c^2*e^2*x^2*log(c) - 4*I*b*c^2*d*e*log(-c*x + 1)*log(x) - 4*I*b*c^2*d*e*log(x)^2 - 4*I*b*c^2*d*e*dilog(c*x) - 4*I*b*c^2*d*e*dilog(-c*x) - I*b*e^2*log(c*x - 1) + I*(b*e^2*(log(c*x + 1)/c^2 + log(c*x - 1)/c^2) + 16*b*d*e*integrate(1/2*log(x)/(c^2*x^3 - x), x))*c^2 + 4*c^2*integrate(1/2*(b*e^2*x^2 + 4*b*d*e*log(x))*sqrt(c*x + 1)*sqrt(c*x - 1)/(c^2*x^3 - x), x) - 2*(b*c^2*e^2*x^2 + 4*b*c^2*d*e*log(x))*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + (I*b*c^2*e^2*x^2 + 4*I*b*c^2*d*e*log(x))*log(c^2*x^2) + (-4*I*b*c^2*d*e*log(x) - I*b*e^2)*log(c*x + 1) + (-2*I*b*c^2*e^2*x^2 - 8*I*b*c^2*d*e*log(c))*log(x))/c^2","F",0
91,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d),x, algorithm=""maxima"")","-a {\left(\frac{d \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e} - \frac{x}{e}\right)} + b \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x^{2} + d}\,{d x}"," ",0,"-a*(d*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e) - x/e) + b*integrate(x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^2 + d), x)","F",0
92,0,0,0,0.000000," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d),x, algorithm=""maxima"")","b \int \frac{x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x^{2} + d}\,{d x} + \frac{a \log\left(e x^{2} + d\right)}{2 \, e}"," ",0,"b*integrate(x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^2 + d), x) + 1/2*a*log(e*x^2 + d)/e","F",0
93,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x^2+d),x, algorithm=""maxima"")","b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x^{2} + d}\,{d x} + \frac{a \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}"," ",0,"b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^2 + d), x) + a*arctan(e*x/sqrt(d*e))/sqrt(d*e)","F",0
94,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\log\left(e x^{2} + d\right)}{d} - \frac{2 \, \log\left(x\right)}{d}\right)} + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x^{3} + d x}\,{d x}"," ",0,"-1/2*a*(log(e*x^2 + d)/d - 2*log(x)/d) + b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^3 + d*x), x)","F",0
95,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^2/(e*x^2+d),x, algorithm=""maxima"")","-a {\left(\frac{e \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d} + \frac{1}{d x}\right)} + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e x^{4} + d x^{2}}\,{d x}"," ",0,"-a*(e*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d) + 1/(d*x)) + b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^4 + d*x^2), x)","F",0
96,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{d^{2}}{e^{4} x^{2} + d e^{3}} - \frac{x^{2}}{e^{2}} + \frac{2 \, d \log\left(e x^{2} + d\right)}{e^{3}}\right)} + b \int \frac{x^{5} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}"," ",0,"-1/2*a*(d^2/(e^4*x^2 + d*e^3) - x^2/e^2 + 2*d*log(e*x^2 + d)/e^3) + b*integrate(x^5*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
97,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{d}{e^{3} x^{2} + d e^{2}} + \frac{\log\left(e x^{2} + d\right)}{e^{2}}\right)} + b \int \frac{x^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}"," ",0,"1/2*a*(d/(e^3*x^2 + d*e^2) + log(e*x^2 + d)/e^2) + b*integrate(x^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
98,0,0,0,0.000000," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{{\left({\left(c^{2} e^{2} x^{2} + c^{2} d e\right)} \int \frac{x e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)}}{c^{2} e^{2} x^{4} + {\left(c^{2} e^{2} x^{4} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(c^{2} d e - e^{2}\right)} x^{2} - d e}\,{d x} - \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b}{2 \, {\left(e^{2} x^{2} + d e\right)}} - \frac{a}{2 \, {\left(e^{2} x^{2} + d e\right)}}"," ",0,"1/2*(2*(c^2*e^2*x^2 + c^2*d*e)*integrate(1/2*x*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1))/(c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e + (c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)*e^(log(c*x + 1) + log(c*x - 1))), x) - arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/(e^2*x^2 + d*e) - 1/2*a/(e^2*x^2 + d*e)","F",0
99,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{1}{d e x^{2} + d^{2}} - \frac{\log\left(e x^{2} + d\right)}{d^{2}} + \frac{2 \, \log\left(x\right)}{d^{2}}\right)} + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{2} x^{5} + 2 \, d e x^{3} + d^{2} x}\,{d x}"," ",0,"1/2*a*(1/(d*e*x^2 + d^2) - log(e*x^2 + d)/d^2 + 2*log(x)/d^2) + b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e^2*x^5 + 2*d*e*x^3 + d^2*x), x)","F",0
100,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{d x}{e^{3} x^{2} + d e^{2}} - \frac{3 \, d \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{2}} + \frac{2 \, x}{e^{2}}\right)} + b \int \frac{x^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}"," ",0,"1/2*a*(d*x/(e^3*x^2 + d*e^2) - 3*d*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^2) + 2*x/e^2) + b*integrate(x^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
101,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{x}{e^{2} x^{2} + d e} - \frac{\arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e}\right)} + b \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}"," ",0,"-1/2*a*(x/(e^2*x^2 + d*e) - arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e)) + b*integrate(x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
102,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{x}{d e x^{2} + d^{2}} + \frac{\arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d}\right)} + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}"," ",0,"1/2*a*(x/(d*e*x^2 + d^2) + arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d)) + b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e^2*x^4 + 2*d*e*x^2 + d^2), x)","F",0
103,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^2/(e*x^2+d)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{3 \, e x^{2} + 2 \, d}{d^{2} e x^{3} + d^{3} x} + \frac{3 \, e \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d^{2}}\right)} + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{2} x^{6} + 2 \, d e x^{4} + d^{2} x^{2}}\,{d x}"," ",0,"-1/2*a*((3*e*x^2 + 2*d)/(d^2*e*x^3 + d^3*x) + 3*e*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d^2)) + b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e^2*x^6 + 2*d*e*x^4 + d^2*x^2), x)","F",0
104,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{4} \, a {\left(\frac{4 \, d e x^{2} + 3 \, d^{2}}{e^{5} x^{4} + 2 \, d e^{4} x^{2} + d^{2} e^{3}} + \frac{2 \, \log\left(e x^{2} + d\right)}{e^{3}}\right)} + b \int \frac{x^{5} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}\,{d x}"," ",0,"1/4*a*((4*d*e*x^2 + 3*d^2)/(e^5*x^4 + 2*d*e^4*x^2 + d^2*e^3) + 2*log(e*x^2 + d)/e^3) + b*integrate(x^5*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
105,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","-\frac{{\left(2 \, e x^{2} + d\right)} a}{4 \, {\left(e^{4} x^{4} + 2 \, d e^{3} x^{2} + d^{2} e^{2}\right)}} - \frac{{\left({\left(2 \, e x^{2} + d\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - {\left(e^{4} x^{4} + 2 \, d e^{3} x^{2} + d^{2} e^{2}\right)} \int \frac{{\left(2 \, c^{2} e x^{3} + c^{2} d x\right)} e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)}}{c^{2} e^{4} x^{6} + {\left(2 \, c^{2} d e^{3} - e^{4}\right)} x^{4} - d^{2} e^{2} + {\left(c^{2} e^{4} x^{6} + {\left(2 \, c^{2} d e^{3} - e^{4}\right)} x^{4} - d^{2} e^{2} + {\left(c^{2} d^{2} e^{2} - 2 \, d e^{3}\right)} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} + {\left(c^{2} d^{2} e^{2} - 2 \, d e^{3}\right)} x^{2}}\,{d x}\right)} b}{4 \, {\left(e^{4} x^{4} + 2 \, d e^{3} x^{2} + d^{2} e^{2}\right)}}"," ",0,"-1/4*(2*e*x^2 + d)*a/(e^4*x^4 + 2*d*e^3*x^2 + d^2*e^2) - 1/4*((2*e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 4*(e^4*x^4 + 2*d*e^3*x^2 + d^2*e^2)*integrate(1/4*(2*c^2*e*x^3 + c^2*d*x)*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1))/(c^2*e^4*x^6 + (2*c^2*d*e^3 - e^4)*x^4 - d^2*e^2 + (c^2*d^2*e^2 - 2*d*e^3)*x^2 + (c^2*e^4*x^6 + (2*c^2*d*e^3 - e^4)*x^4 - d^2*e^2 + (c^2*d^2*e^2 - 2*d*e^3)*x^2)*e^(log(c*x + 1) + log(c*x - 1))), x))*b/(e^4*x^4 + 2*d*e^3*x^2 + d^2*e^2)","F",0
106,0,0,0,0.000000," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{{\left({\left(c^{2} e^{3} x^{4} + 2 \, c^{2} d e^{2} x^{2} + c^{2} d^{2} e\right)} \int \frac{x e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(c x - 1\right)\right)}}{c^{2} e^{3} x^{6} + {\left(2 \, c^{2} d e^{2} - e^{3}\right)} x^{4} + {\left(c^{2} e^{3} x^{6} + {\left(2 \, c^{2} d e^{2} - e^{3}\right)} x^{4} - d^{2} e + {\left(c^{2} d^{2} e - 2 \, d e^{2}\right)} x^{2}\right)} {\left(c x + 1\right)} {\left(c x - 1\right)} - d^{2} e + {\left(c^{2} d^{2} e - 2 \, d e^{2}\right)} x^{2}}\,{d x} - \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b}{4 \, {\left(e^{3} x^{4} + 2 \, d e^{2} x^{2} + d^{2} e\right)}} - \frac{a}{4 \, {\left(e^{3} x^{4} + 2 \, d e^{2} x^{2} + d^{2} e\right)}}"," ",0,"1/4*(4*(c^2*e^3*x^4 + 2*c^2*d*e^2*x^2 + c^2*d^2*e)*integrate(1/4*x*e^(1/2*log(c*x + 1) + 1/2*log(c*x - 1))/(c^2*e^3*x^6 + (2*c^2*d*e^2 - e^3)*x^4 - d^2*e + (c^2*d^2*e - 2*d*e^2)*x^2 + (c^2*e^3*x^6 + (2*c^2*d*e^2 - e^3)*x^4 - d^2*e + (c^2*d^2*e - 2*d*e^2)*x^2)*e^(log(c*x + 1) + log(c*x - 1))), x) - arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/(e^3*x^4 + 2*d*e^2*x^2 + d^2*e) - 1/4*a/(e^3*x^4 + 2*d*e^2*x^2 + d^2*e)","F",0
107,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{4} \, a {\left(\frac{2 \, e x^{2} + 3 \, d}{d^{2} e^{2} x^{4} + 2 \, d^{3} e x^{2} + d^{4}} - \frac{2 \, \log\left(e x^{2} + d\right)}{d^{3}} + \frac{4 \, \log\left(x\right)}{d^{3}}\right)} + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{3} x^{7} + 3 \, d e^{2} x^{5} + 3 \, d^{2} e x^{3} + d^{3} x}\,{d x}"," ",0,"1/4*a*((2*e*x^2 + 3*d)/(d^2*e^2*x^4 + 2*d^3*e*x^2 + d^4) - 2*log(e*x^2 + d)/d^3 + 4*log(x)/d^3) + b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e^3*x^7 + 3*d*e^2*x^5 + 3*d^2*e*x^3 + d^3*x), x)","F",0
108,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","-\frac{1}{8} \, a {\left(\frac{5 \, e x^{3} + 3 \, d x}{e^{4} x^{4} + 2 \, d e^{3} x^{2} + d^{2} e^{2}} - \frac{3 \, \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} e^{2}}\right)} + b \int \frac{x^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}\,{d x}"," ",0,"-1/8*a*((5*e*x^3 + 3*d*x)/(e^4*x^4 + 2*d*e^3*x^2 + d^2*e^2) - 3*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*e^2)) + b*integrate(x^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
109,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{e x^{3} - d x}{d e^{3} x^{4} + 2 \, d^{2} e^{2} x^{2} + d^{3} e} + \frac{\arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d e}\right)} + b \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}\,{d x}"," ",0,"1/8*a*((e*x^3 - d*x)/(d*e^3*x^4 + 2*d^2*e^2*x^2 + d^3*e) + arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d*e)) + b*integrate(x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
110,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x^2+d)^3,x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\frac{3 \, e x^{3} + 5 \, d x}{d^{2} e^{2} x^{4} + 2 \, d^{3} e x^{2} + d^{4}} + \frac{3 \, \arctan\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e} d^{2}}\right)} + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}\,{d x}"," ",0,"1/8*a*((3*e*x^3 + 5*d*x)/(d^2*e^2*x^4 + 2*d^3*e*x^2 + d^4) + 3*arctan(e*x/sqrt(d*e))/(sqrt(d*e)*d^2)) + b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3), x)","F",0
111,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{105} \, {\left(\frac{15 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} x^{4}}{e} - \frac{12 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} d x^{2}}{e^{2}} + \frac{8 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} d^{2}}{e^{3}}\right)} a - \frac{\frac{1}{2} \, {\left({\left(\frac{840 \, c^{4} d^{3} {\left(\frac{2 \, \sqrt{e x^{2} + d}}{c^{4} e} + \frac{\sqrt{c^{2} d + e} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{c^{5} e}\right)}}{e^{2}} + \frac{840 \, c^{2} d^{3} {\left(\frac{\sqrt{d} \log\left(\frac{\sqrt{e x^{2} + d} - \sqrt{d}}{\sqrt{e x^{2} + d} + \sqrt{d}}\right)}{c^{2} e^{2}} - \frac{\sqrt{c^{2} d + e} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{c^{3} e^{2}}\right)}}{e} - \frac{140 \, c^{4} d^{2} {\left(\frac{3 \, \sqrt{c^{2} d + e} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{c^{7}} + \frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} + 3 \, \sqrt{e x^{2} + d} e\right)}}{c^{6} e}\right)}}{e^{2}} + \frac{420 \, c^{2} d^{2} {\left(\frac{2 \, \sqrt{e x^{2} + d}}{c^{4} e} + \frac{\sqrt{c^{2} d + e} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{c^{5} e}\right)}}{e} + \frac{21 \, c^{4} d {\left(\frac{15 \, {\left(c^{2} d e + e^{2}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{9}} + \frac{2 \, {\left(3 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} c^{4} - 5 \, {\left(c^{4} d - c^{2} e\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}} + 15 \, \sqrt{e x^{2} + d} e^{2}\right)}}{c^{8} e}\right)}}{e^{2}} + \frac{105 \, c^{4} {\left(\frac{105 \, {\left(c^{2} d e^{2} + e^{3}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{11}} + \frac{2 \, {\left(15 \, {\left(e x^{2} + d\right)}^{\frac{7}{2}} c^{6} - 21 \, {\left(2 \, c^{6} d - c^{4} e\right)} {\left(e x^{2} + d\right)}^{\frac{5}{2}} + 105 \, \sqrt{e x^{2} + d} e^{3} + 35 \, {\left(c^{6} d^{2} - c^{4} d e + c^{2} e^{2}\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}}\right)}}{c^{10} e}\right)} \log\left(c\right)}{e^{2}} - \frac{105 \, c^{2} d {\left(\frac{3 \, \sqrt{c^{2} d + e} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{c^{7}} + \frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} + 3 \, \sqrt{e x^{2} + d} e\right)}}{c^{6} e}\right)}}{e} + \frac{15 \, c^{4} {\left(\frac{105 \, {\left(c^{2} d e^{2} + e^{3}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{11}} + \frac{2 \, {\left(15 \, {\left(e x^{2} + d\right)}^{\frac{7}{2}} c^{6} - 21 \, {\left(2 \, c^{6} d - c^{4} e\right)} {\left(e x^{2} + d\right)}^{\frac{5}{2}} + 105 \, \sqrt{e x^{2} + d} e^{3} + 35 \, {\left(c^{6} d^{2} - c^{4} d e + c^{2} e^{2}\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}}\right)}}{c^{10} e}\right)}}{e^{2}} - \frac{735 \, c^{2} {\left(\frac{15 \, {\left(c^{2} d e + e^{2}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{9}} + \frac{2 \, {\left(3 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} c^{4} - 5 \, {\left(c^{4} d - c^{2} e\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}} + 15 \, \sqrt{e x^{2} + d} e^{2}\right)}}{c^{8} e}\right)} \log\left(c\right)}{e} - \frac{105 \, c^{2} {\left(\frac{15 \, {\left(c^{2} d e + e^{2}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{9}} + \frac{2 \, {\left(3 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} c^{4} - 5 \, {\left(c^{4} d - c^{2} e\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}} + 15 \, \sqrt{e x^{2} + d} e^{2}\right)}}{c^{8} e}\right)}}{e} + 22050 \, \int \sqrt{e x^{2} + d} x^{5} \log\left(x\right)\,{d x}\right)} e^{3} - 2 \, {\left(15 \, e^{3} x^{6} + 3 \, d e^{2} x^{4} - 4 \, d^{2} e x^{2} + 8 \, d^{3}\right)} \sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b}{105 \, e^{3}}"," ",0,"1/105*(15*(e*x^2 + d)^(3/2)*x^4/e - 12*(e*x^2 + d)^(3/2)*d*x^2/e^2 + 8*(e*x^2 + d)^(3/2)*d^2/e^3)*a - 1/105*(105*e^3*integrate((105*(c^2*e^3*x^7 - e^3*x^5 + (c^2*e^3*x^7 - e^3*x^5)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)*log(x) + (105*c^2*e^3*x^7*log(c) - 105*e^3*x^5*log(c) + (15*(7*c^2*log(c) + c^2)*e^3*x^7 - 4*c^2*d^2*e*x^3 + 8*c^2*d^3*x + 3*(c^2*d*e^2 - 35*e^3*log(c))*x^5)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d))/(c^2*e^3*x^2 - e^3 + (c^2*e^3*x^2 - e^3)*e^(log(c*x + 1) + log(c*x - 1))), x) - (15*e^3*x^6 + 3*d*e^2*x^4 - 4*d^2*e*x^2 + 8*d^3)*sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/e^3","F",0
112,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{15} \, {\left(\frac{3 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} x^{2}}{e} - \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} d}{e^{2}}\right)} a - \frac{-\frac{1}{2} \, {\left({\left(\frac{30 \, c^{4} d^{2} {\left(\frac{2 \, \sqrt{e x^{2} + d}}{c^{4}} + \frac{\sqrt{c^{2} d + e} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{c^{5}}\right)}}{e^{2}} + \frac{30 \, c^{2} d^{2} {\left(\frac{\sqrt{d} \log\left(\frac{\sqrt{e x^{2} + d} - \sqrt{d}}{\sqrt{e x^{2} + d} + \sqrt{d}}\right)}{c^{2} e} - \frac{\sqrt{c^{2} d + e} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{c^{3} e}\right)}}{e} - \frac{5 \, c^{4} d {\left(\frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} + 3 \, \sqrt{e x^{2} + d} e\right)}}{c^{6}} + \frac{3 \, {\left(c^{2} d e + e^{2}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}}\right)}}{e^{2}} - \frac{15 \, c^{4} {\left(\frac{2 \, {\left(3 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} c^{4} - 5 \, {\left(c^{4} d - c^{2} e\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}} + 15 \, \sqrt{e x^{2} + d} e^{2}\right)}}{c^{8}} + \frac{15 \, {\left(c^{2} d e^{2} + e^{3}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{9}}\right)} \log\left(c\right)}{e^{2}} + \frac{15 \, c^{2} d {\left(\frac{2 \, \sqrt{e x^{2} + d}}{c^{4}} + \frac{\sqrt{c^{2} d + e} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{c^{5}}\right)}}{e} - \frac{3 \, c^{4} {\left(\frac{2 \, {\left(3 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} c^{4} - 5 \, {\left(c^{4} d - c^{2} e\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}} + 15 \, \sqrt{e x^{2} + d} e^{2}\right)}}{c^{8}} + \frac{15 \, {\left(c^{2} d e^{2} + e^{3}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{9}}\right)}}{e^{2}} + \frac{75 \, c^{2} {\left(\frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} + 3 \, \sqrt{e x^{2} + d} e\right)}}{c^{6}} + \frac{3 \, {\left(c^{2} d e + e^{2}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}}\right)} \log\left(c\right)}{e} + \frac{15 \, c^{2} {\left(\frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} + 3 \, \sqrt{e x^{2} + d} e\right)}}{c^{6}} + \frac{3 \, {\left(c^{2} d e + e^{2}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}}\right)}}{e} - 450 \, \int \sqrt{e x^{2} + d} x^{3} \log\left(x\right)\,{d x}\right)} e^{2} + 2 \, {\left(3 \, e^{2} x^{4} + d e x^{2} - 2 \, d^{2}\right)} \sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b}{15 \, e^{2}}"," ",0,"1/15*(3*(e*x^2 + d)^(3/2)*x^2/e - 2*(e*x^2 + d)^(3/2)*d/e^2)*a - 1/15*(15*e^2*integrate((15*(c^2*e^2*x^5 - e^2*x^3 + (c^2*e^2*x^5 - e^2*x^3)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)*log(x) + (15*c^2*e^2*x^5*log(c) - 15*e^2*x^3*log(c) + (3*(5*c^2*log(c) + c^2)*e^2*x^5 - 2*c^2*d^2*x + (c^2*d*e - 15*e^2*log(c))*x^3)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d))/(c^2*e^2*x^2 - e^2 + (c^2*e^2*x^2 - e^2)*e^(log(c*x + 1) + log(c*x - 1))), x) - (3*e^2*x^4 + d*e*x^2 - 2*d^2)*sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/e^2","F",0
113,0,0,0,0.000000," ","integrate(x*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} a}{3 \, e} + \frac{\frac{1}{2} \, {\left(2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - {\left(\frac{3 \, c^{4} d {\left(\frac{2 \, \sqrt{e x^{2} + d} e}{c^{4}} + \frac{{\left(c^{2} d e + e^{2}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{5}}\right)}}{e^{2}} + \frac{3 \, c^{4} {\left(\frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} e + 3 \, \sqrt{e x^{2} + d} e^{2}\right)}}{c^{6}} + \frac{3 \, {\left(c^{2} d e^{2} + e^{3}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}}\right)} \log\left(c\right)}{e^{2}} + \frac{3 \, c^{2} d {\left(\frac{\sqrt{d} \log\left(\frac{\sqrt{e x^{2} + d} - \sqrt{d}}{\sqrt{e x^{2} + d} + \sqrt{d}}\right)}{c^{2}} - \frac{\sqrt{c^{2} d + e} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{c^{3}}\right)}}{e} + \frac{c^{4} {\left(\frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} e + 3 \, \sqrt{e x^{2} + d} e^{2}\right)}}{c^{6}} + \frac{3 \, {\left(c^{2} d e^{2} + e^{3}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}}\right)}}{e^{2}} - \frac{9 \, c^{2} {\left(\frac{2 \, \sqrt{e x^{2} + d} e}{c^{4}} + \frac{{\left(c^{2} d e + e^{2}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{5}}\right)} \log\left(c\right)}{e} - \frac{3 \, c^{2} {\left(\frac{2 \, \sqrt{e x^{2} + d} e}{c^{4}} + \frac{{\left(c^{2} d e + e^{2}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{5}}\right)}}{e} + 18 \, \int \sqrt{e x^{2} + d} x \log\left(x\right)\,{d x}\right)} e\right)} b}{3 \, e}"," ",0,"1/3*(e*x^2 + d)^(3/2)*a/e + 1/3*((e*x^2 + d)^(3/2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 3*e*integrate((3*(c^2*e*x^3 - e*x + (c^2*e*x^3 - e*x)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)*log(x) + (3*c^2*e*x^3*log(c) - 3*e*x*log(c) + ((3*c^2*log(c) + c^2)*e*x^3 + (c^2*d - 3*e*log(c))*x)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d))/(c^2*e*x^2 + (c^2*e*x^2 - e)*e^(log(c*x + 1) + log(c*x - 1)) - e), x))*b/e","F",0
114,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x,x, algorithm=""maxima"")","-{\left(\sqrt{d} \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right) - \sqrt{e x^{2} + d}\right)} a + b \int \frac{\sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}"," ",0,"-(sqrt(d)*arcsinh(d/(sqrt(d*e)*abs(x))) - sqrt(e*x^2 + d))*a + b*integrate(sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/x, x)","F",0
115,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{e \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{\sqrt{d}} - \frac{\sqrt{e x^{2} + d} e}{d} + \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}{d x^{2}}\right)} a + b \int \frac{\sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{3}}\,{d x}"," ",0,"-1/2*(e*arcsinh(d/(sqrt(d*e)*abs(x)))/sqrt(d) - sqrt(e*x^2 + d)*e/d + (e*x^2 + d)^(3/2)/(d*x^2))*a + b*integrate(sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/x^3, x)","F",0
116,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(\frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} x}{e} - \frac{\sqrt{e x^{2} + d} d x}{e} - \frac{d^{2} \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{e^{\frac{3}{2}}}\right)} a + b \int \sqrt{e x^{2} + d} x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/8*(2*(e*x^2 + d)^(3/2)*x/e - sqrt(e*x^2 + d)*d*x/e - d^2*arcsinh(e*x/sqrt(d*e))/e^(3/2))*a + b*integrate(sqrt(e*x^2 + d)*x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
117,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\sqrt{e x^{2} + d} x + \frac{d \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}}\right)} a + b \int \sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/2*(sqrt(e*x^2 + d)*x + d*arcsinh(e*x/sqrt(d*e))/sqrt(e))*a + b*integrate(sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
118,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x^2,x, algorithm=""maxima"")","{\left(\sqrt{e} \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right) - \frac{\sqrt{e x^{2} + d}}{x}\right)} a + b \int \frac{\sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{2}}\,{d x}"," ",0,"(sqrt(e)*arcsinh(e*x/sqrt(d*e)) - sqrt(e*x^2 + d)/x)*a + b*integrate(sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/x^2, x)","F",0
119,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x^4,x, algorithm=""maxima"")","-\frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} a}{3 \, d x^{3}} - \frac{{\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 3 \, {\left(e x^{2} \log\left(c\right) + d \log\left(c\right) + {\left(e x^{2} + d\right)} \log\left(x\right)\right)} \sqrt{e x^{2} + d}\right)} b}{3 \, d x^{3}}"," ",0,"-1/3*(e*x^2 + d)^(3/2)*a/(d*x^3) - 1/3*(3*d*x^3*integrate((3*(c^2*d*x^2 + (c^2*d*x^2 - d)*e^(log(c*x + 1) + log(c*x - 1)) - d)*sqrt(e*x^2 + d)*log(x) + (3*c^2*d*x^2*log(c) - (c^2*e*x^4 - (3*c^2*log(c) - c^2)*d*x^2 + 3*d*log(c))*e^(log(c*x + 1) + log(c*x - 1)) - 3*d*log(c))*sqrt(e*x^2 + d))/(c^2*d*x^6 - d*x^4 + (c^2*d*x^6 - d*x^4)*e^(log(c*x + 1) + log(c*x - 1))), x) + (e*x^2 + d)^(3/2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/(d*x^3)","F",0
120,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x^6,x, algorithm=""maxima"")","\frac{1}{15} \, a {\left(\frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} e}{d^{2} x^{3}} - \frac{3 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}}}{d x^{5}}\right)} - \frac{-{\left({\left(2 \, e^{2} x^{4} - d e x^{2} - 3 \, d^{2}\right)} \sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 15 \, {\left(2 \, e^{2} x^{4} \log\left(c\right) - d e x^{2} \log\left(c\right) - 3 \, d^{2} \log\left(c\right) + {\left(2 \, e^{2} x^{4} - d e x^{2} - 3 \, d^{2}\right)} \log\left(x\right)\right)} \sqrt{e x^{2} + d}\right)} b}{15 \, d^{2} x^{5}}"," ",0,"1/15*a*(2*(e*x^2 + d)^(3/2)*e/(d^2*x^3) - 3*(e*x^2 + d)^(3/2)/(d*x^5)) - 1/15*(15*d^2*x^5*integrate((15*(c^2*d^2*x^2 - d^2 + (c^2*d^2*x^2 - d^2)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)*log(x) + (15*c^2*d^2*x^2*log(c) - 15*d^2*log(c) + (2*c^2*e^2*x^6 - c^2*d*e*x^4 + 3*(5*c^2*log(c) - c^2)*d^2*x^2 - 15*d^2*log(c))*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d))/(c^2*d^2*x^8 - d^2*x^6 + (c^2*d^2*x^8 - d^2*x^6)*e^(log(c*x + 1) + log(c*x - 1))), x) - (2*e^2*x^4 - d*e*x^2 - 3*d^2)*sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/(d^2*x^5)","F",0
121,0,0,0,0.000000," ","integrate(x^3*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{35} \, {\left(\frac{5 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} x^{2}}{e} - \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} d}{e^{2}}\right)} a - \frac{-\frac{1}{6} \, {\left({\left(\frac{210 \, c^{4} d^{3} {\left(\frac{2 \, \sqrt{e x^{2} + d}}{c^{4}} + \frac{\sqrt{c^{2} d + e} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{c^{5}}\right)}}{e^{2}} + \frac{210 \, c^{2} d^{3} {\left(\frac{\sqrt{d} \log\left(\frac{\sqrt{e x^{2} + d} - \sqrt{d}}{\sqrt{e x^{2} + d} + \sqrt{d}}\right)}{c^{2} e} - \frac{\sqrt{c^{2} d + e} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{c^{3} e}\right)}}{e} - \frac{35 \, c^{4} d^{2} {\left(\frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} + 3 \, \sqrt{e x^{2} + d} e\right)}}{c^{6}} + \frac{3 \, {\left(c^{2} d e + e^{2}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}}\right)}}{e^{2}} - \frac{245 \, c^{4} d {\left(\frac{2 \, {\left(3 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} c^{4} - 5 \, {\left(c^{4} d - c^{2} e\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}} + 15 \, \sqrt{e x^{2} + d} e^{2}\right)}}{c^{8}} + \frac{15 \, {\left(c^{2} d e^{2} + e^{3}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{9}}\right)} \log\left(c\right)}{e^{2}} + \frac{105 \, c^{2} d^{2} {\left(\frac{2 \, \sqrt{e x^{2} + d}}{c^{4}} + \frac{\sqrt{c^{2} d + e} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{c^{5}}\right)}}{e} - \frac{56 \, c^{4} d {\left(\frac{2 \, {\left(3 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} c^{4} - 5 \, {\left(c^{4} d - c^{2} e\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}} + 15 \, \sqrt{e x^{2} + d} e^{2}\right)}}{c^{8}} + \frac{15 \, {\left(c^{2} d e^{2} + e^{3}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{9}}\right)}}{e^{2}} + \frac{1225 \, c^{2} d {\left(\frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} + 3 \, \sqrt{e x^{2} + d} e\right)}}{c^{6}} + \frac{3 \, {\left(c^{2} d e + e^{2}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}}\right)} \log\left(c\right)}{e} - \frac{35 \, c^{4} {\left(\frac{2 \, {\left(15 \, {\left(e x^{2} + d\right)}^{\frac{7}{2}} c^{6} - 21 \, {\left(2 \, c^{6} d - c^{4} e\right)} {\left(e x^{2} + d\right)}^{\frac{5}{2}} + 105 \, \sqrt{e x^{2} + d} e^{3} + 35 \, {\left(c^{6} d^{2} - c^{4} d e + c^{2} e^{2}\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}}\right)}}{c^{10}} + \frac{105 \, {\left(c^{2} d e^{3} + e^{4}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{11}}\right)} \log\left(c\right)}{e^{2}} + \frac{280 \, c^{2} d {\left(\frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} + 3 \, \sqrt{e x^{2} + d} e\right)}}{c^{6}} + \frac{3 \, {\left(c^{2} d e + e^{2}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}}\right)}}{e} - \frac{5 \, c^{4} {\left(\frac{2 \, {\left(15 \, {\left(e x^{2} + d\right)}^{\frac{7}{2}} c^{6} - 21 \, {\left(2 \, c^{6} d - c^{4} e\right)} {\left(e x^{2} + d\right)}^{\frac{5}{2}} + 105 \, \sqrt{e x^{2} + d} e^{3} + 35 \, {\left(c^{6} d^{2} - c^{4} d e + c^{2} e^{2}\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}}\right)}}{c^{10}} + \frac{105 \, {\left(c^{2} d e^{3} + e^{4}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{11}}\right)}}{e^{2}} + \frac{245 \, c^{2} {\left(\frac{2 \, {\left(3 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} c^{4} - 5 \, {\left(c^{4} d - c^{2} e\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}} + 15 \, \sqrt{e x^{2} + d} e^{2}\right)}}{c^{8}} + \frac{15 \, {\left(c^{2} d e^{2} + e^{3}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{9}}\right)} \log\left(c\right)}{e} + \frac{35 \, c^{2} {\left(\frac{2 \, {\left(3 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} c^{4} - 5 \, {\left(c^{4} d - c^{2} e\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}} + 15 \, \sqrt{e x^{2} + d} e^{2}\right)}}{c^{8}} + \frac{15 \, {\left(c^{2} d e^{2} + e^{3}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{9}}\right)}}{e} - 210 \, \int 35 \, {\left(e x^{5} + d x^{3}\right)} \sqrt{e x^{2} + d} \log\left(x\right)\,{d x}\right)} e^{2} + 6 \, {\left(5 \, e^{3} x^{6} + 8 \, d e^{2} x^{4} + d^{2} e x^{2} - 2 \, d^{3}\right)} \sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b}{35 \, e^{2}}"," ",0,"1/35*(5*(e*x^2 + d)^(5/2)*x^2/e - 2*(e*x^2 + d)^(5/2)*d/e^2)*a - 1/35*(35*e^2*integrate((35*(c^2*e^3*x^7 - d*e^2*x^3 + (c^2*d*e^2 - e^3)*x^5 + (c^2*e^3*x^7 - d*e^2*x^3 + (c^2*d*e^2 - e^3)*x^5)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)*log(x) + (35*c^2*e^3*x^7*log(c) - 35*d*e^2*x^3*log(c) + 35*(c^2*d*e^2*log(c) - e^3*log(c))*x^5 + (5*(7*c^2*log(c) + c^2)*e^3*x^7 - 2*c^2*d^3*x + ((35*c^2*log(c) + 8*c^2)*d*e^2 - 35*e^3*log(c))*x^5 + (c^2*d^2*e - 35*d*e^2*log(c))*x^3)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d))/(c^2*e^2*x^2 - e^2 + (c^2*e^2*x^2 - e^2)*e^(log(c*x + 1) + log(c*x - 1))), x) - (5*e^3*x^6 + 8*d*e^2*x^4 + d^2*e*x^2 - 2*d^3)*sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/e^2","F",0
122,0,0,0,0.000000," ","integrate(x*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{{\left(e x^{2} + d\right)}^{\frac{5}{2}} a}{5 \, e} + \frac{\frac{1}{6} \, {\left(6 \, {\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - {\left(\frac{15 \, c^{4} d^{2} {\left(\frac{2 \, \sqrt{e x^{2} + d} e}{c^{4}} + \frac{{\left(c^{2} d e + e^{2}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{5}}\right)}}{e^{2}} + \frac{25 \, c^{4} d {\left(\frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} e + 3 \, \sqrt{e x^{2} + d} e^{2}\right)}}{c^{6}} + \frac{3 \, {\left(c^{2} d e^{2} + e^{3}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}}\right)} \log\left(c\right)}{e^{2}} + \frac{15 \, c^{2} d^{2} {\left(\frac{\sqrt{d} \log\left(\frac{\sqrt{e x^{2} + d} - \sqrt{d}}{\sqrt{e x^{2} + d} + \sqrt{d}}\right)}{c^{2}} - \frac{\sqrt{c^{2} d + e} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{c^{3}}\right)}}{e} + \frac{10 \, c^{4} d {\left(\frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} e + 3 \, \sqrt{e x^{2} + d} e^{2}\right)}}{c^{6}} + \frac{3 \, {\left(c^{2} d e^{2} + e^{3}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}}\right)}}{e^{2}} - \frac{75 \, c^{2} d {\left(\frac{2 \, \sqrt{e x^{2} + d} e}{c^{4}} + \frac{{\left(c^{2} d e + e^{2}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{5}}\right)} \log\left(c\right)}{e} + \frac{5 \, c^{4} {\left(\frac{2 \, {\left(3 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} c^{4} e + 15 \, \sqrt{e x^{2} + d} e^{3} - 5 \, {\left(c^{4} d e - c^{2} e^{2}\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}}\right)}}{c^{8}} + \frac{15 \, {\left(c^{2} d e^{3} + e^{4}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{9}}\right)} \log\left(c\right)}{e^{2}} - \frac{30 \, c^{2} d {\left(\frac{2 \, \sqrt{e x^{2} + d} e}{c^{4}} + \frac{{\left(c^{2} d e + e^{2}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{5}}\right)}}{e} + \frac{c^{4} {\left(\frac{2 \, {\left(3 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} c^{4} e + 15 \, \sqrt{e x^{2} + d} e^{3} - 5 \, {\left(c^{4} d e - c^{2} e^{2}\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}}\right)}}{c^{8}} + \frac{15 \, {\left(c^{2} d e^{3} + e^{4}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{9}}\right)}}{e^{2}} - \frac{25 \, c^{2} {\left(\frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} e + 3 \, \sqrt{e x^{2} + d} e^{2}\right)}}{c^{6}} + \frac{3 \, {\left(c^{2} d e^{2} + e^{3}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}}\right)} \log\left(c\right)}{e} - \frac{5 \, c^{2} {\left(\frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} e + 3 \, \sqrt{e x^{2} + d} e^{2}\right)}}{c^{6}} + \frac{3 \, {\left(c^{2} d e^{2} + e^{3}\right)} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}}\right)}}{e} + 30 \, \int 5 \, {\left(e x^{3} + d x\right)} \sqrt{e x^{2} + d} \log\left(x\right)\,{d x}\right)} e\right)} b}{5 \, e}"," ",0,"1/5*(e*x^2 + d)^(5/2)*a/e + 1/5*((e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - 5*e*integrate((5*(c^2*e^2*x^5 + (c^2*d*e - e^2)*x^3 - d*e*x + (c^2*e^2*x^5 + (c^2*d*e - e^2)*x^3 - d*e*x)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)*log(x) + (5*c^2*e^2*x^5*log(c) + 5*(c^2*d*e*log(c) - e^2*log(c))*x^3 - 5*d*e*x*log(c) + ((5*c^2*log(c) + c^2)*e^2*x^5 + ((5*c^2*log(c) + 2*c^2)*d*e - 5*e^2*log(c))*x^3 + (c^2*d^2 - 5*d*e*log(c))*x)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d))/(c^2*e*x^2 + (c^2*e*x^2 - e)*e^(log(c*x + 1) + log(c*x - 1)) - e), x))*b/e","F",0
123,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(3 \, d^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right) - {\left(e x^{2} + d\right)}^{\frac{3}{2}} - 3 \, \sqrt{e x^{2} + d} d\right)} a + {\left(e \int \sqrt{e x^{2} + d} x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x} + d \int \frac{\sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x}\right)} b"," ",0,"-1/3*(3*d^(3/2)*arcsinh(d/(sqrt(d*e)*abs(x))) - (e*x^2 + d)^(3/2) - 3*sqrt(e*x^2 + d)*d)*a + (e*integrate(sqrt(e*x^2 + d)*x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)), x) + d*integrate(sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/x, x))*b","F",0
124,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(3 \, \sqrt{d} e \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right) - 3 \, \sqrt{e x^{2} + d} e - \frac{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e}{d} + \frac{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}{d x^{2}}\right)} a + {\left(e \int \frac{\sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{x}\,{d x} + d \int \frac{\sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{3}}\,{d x}\right)} b"," ",0,"-1/2*(3*sqrt(d)*e*arcsinh(d/(sqrt(d*e)*abs(x))) - 3*sqrt(e*x^2 + d)*e - (e*x^2 + d)^(3/2)*e/d + (e*x^2 + d)^(5/2)/(d*x^2))*a + (e*integrate(sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/x, x) + d*integrate(sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/x^3, x))*b","F",0
125,0,0,0,0.000000," ","integrate(x^2*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{48} \, {\left(\frac{8 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} x}{e} - \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} d x}{e} - \frac{3 \, \sqrt{e x^{2} + d} d^{2} x}{e} - \frac{3 \, d^{3} \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{e^{\frac{3}{2}}}\right)} a + b \int {\left(e x^{4} + d x^{2}\right)} \sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/48*(8*(e*x^2 + d)^(5/2)*x/e - 2*(e*x^2 + d)^(3/2)*d*x/e - 3*sqrt(e*x^2 + d)*d^2*x/e - 3*d^3*arcsinh(e*x/sqrt(d*e))/e^(3/2))*a + b*integrate((e*x^4 + d*x^2)*sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
126,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} x + 3 \, \sqrt{e x^{2} + d} d x + \frac{3 \, d^{2} \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}}\right)} a + b \int {\left(e x^{2} + d\right)}^{\frac{3}{2}} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x}"," ",0,"1/8*(2*(e*x^2 + d)^(3/2)*x + 3*sqrt(e*x^2 + d)*d*x + 3*d^2*arcsinh(e*x/sqrt(d*e))/sqrt(e))*a + b*integrate((e*x^2 + d)^(3/2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)), x)","F",0
127,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(3 \, \sqrt{e x^{2} + d} e x + 3 \, d \sqrt{e} \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right) - \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}}}{x}\right)} a + {\left(e \int \sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\,{d x} + d \int \frac{\sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{2}}\,{d x}\right)} b"," ",0,"1/2*(3*sqrt(e*x^2 + d)*e*x + 3*d*sqrt(e)*arcsinh(e*x/sqrt(d*e)) - 2*(e*x^2 + d)^(3/2)/x)*a + (e*integrate(sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)), x) + d*integrate(sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/x^2, x))*b","F",0
128,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{3 \, \sqrt{e x^{2} + d} e^{2} x}{d} + 3 \, e^{\frac{3}{2}} \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right) - \frac{2 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} e}{d x} - \frac{{\left(e x^{2} + d\right)}^{\frac{5}{2}}}{d x^{3}}\right)} a + {\left(e \int \frac{\sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{2}}\,{d x} + d \int \frac{\sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{x^{4}}\,{d x}\right)} b"," ",0,"1/3*(3*sqrt(e*x^2 + d)*e^2*x/d + 3*e^(3/2)*arcsinh(e*x/sqrt(d*e)) - 2*(e*x^2 + d)^(3/2)*e/(d*x) - (e*x^2 + d)^(5/2)/(d*x^3))*a + (e*integrate(sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/x^2, x) + d*integrate(sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/x^4, x))*b","F",0
129,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^6,x, algorithm=""maxima"")","-\frac{{\left(e x^{2} + d\right)}^{\frac{5}{2}} a}{5 \, d x^{5}} - \frac{{\left({\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 5 \, {\left(e^{2} x^{4} \log\left(c\right) + 2 \, d e x^{2} \log\left(c\right) + d^{2} \log\left(c\right) + {\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \log\left(x\right)\right)} \sqrt{e x^{2} + d}\right)} b}{5 \, d x^{5}}"," ",0,"-1/5*(e*x^2 + d)^(5/2)*a/(d*x^5) - 1/5*(5*d*x^5*integrate((5*(c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2 + (c^2*d*e*x^4 + (c^2*d^2 - d*e)*x^2 - d^2)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)*log(x) + (5*c^2*d*e*x^4*log(c) + 5*(c^2*d^2*log(c) - d*e*log(c))*x^2 - 5*d^2*log(c) - (c^2*e^2*x^6 - (5*c^2*log(c) - 2*c^2)*d*e*x^4 - ((5*c^2*log(c) - c^2)*d^2 - 5*d*e*log(c))*x^2 + 5*d^2*log(c))*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d))/(c^2*d*x^8 - d*x^6 + (c^2*d*x^8 - d*x^6)*e^(log(c*x + 1) + log(c*x - 1))), x) + (e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/(d*x^5)","F",0
130,0,0,0,0.000000," ","integrate((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^8,x, algorithm=""maxima"")","\frac{1}{35} \, a {\left(\frac{2 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} e}{d^{2} x^{5}} - \frac{5 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}}}{d x^{7}}\right)} - \frac{-{\left({\left(2 \, e^{3} x^{6} - d e^{2} x^{4} - 8 \, d^{2} e x^{2} - 5 \, d^{3}\right)} \sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 35 \, {\left(2 \, e^{3} x^{6} \log\left(c\right) - d e^{2} x^{4} \log\left(c\right) - 8 \, d^{2} e x^{2} \log\left(c\right) - 5 \, d^{3} \log\left(c\right) + {\left(2 \, e^{3} x^{6} - d e^{2} x^{4} - 8 \, d^{2} e x^{2} - 5 \, d^{3}\right)} \log\left(x\right)\right)} \sqrt{e x^{2} + d}\right)} b}{35 \, d^{2} x^{7}}"," ",0,"1/35*a*(2*(e*x^2 + d)^(5/2)*e/(d^2*x^5) - 5*(e*x^2 + d)^(5/2)/(d*x^7)) - 1/35*(35*d^2*x^7*integrate((35*(c^2*d^2*e*x^4 - d^3 + (c^2*d^3 - d^2*e)*x^2 + (c^2*d^2*e*x^4 - d^3 + (c^2*d^3 - d^2*e)*x^2)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)*log(x) + (35*c^2*d^2*e*x^4*log(c) - 35*d^3*log(c) + 35*(c^2*d^3*log(c) - d^2*e*log(c))*x^2 + (2*c^2*e^3*x^8 - c^2*d*e^2*x^6 + (35*c^2*log(c) - 8*c^2)*d^2*e*x^4 - 35*d^3*log(c) + 5*((7*c^2*log(c) - c^2)*d^3 - 7*d^2*e*log(c))*x^2)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d))/(c^2*d^2*x^10 - d^2*x^8 + (c^2*d^2*x^10 - d^2*x^8)*e^(log(c*x + 1) + log(c*x - 1))), x) - (2*e^3*x^6 - d*e^2*x^4 - 8*d^2*e*x^2 - 5*d^3)*sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/(d^2*x^7)","F",0
131,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{15} \, {\left(\frac{3 \, \sqrt{e x^{2} + d} x^{4}}{e} - \frac{4 \, \sqrt{e x^{2} + d} d x^{2}}{e^{2}} + \frac{8 \, \sqrt{e x^{2} + d} d^{2}}{e^{3}}\right)} a - \frac{-\frac{1}{2} \, {\left({\left(\frac{120 \, c^{2} d^{3} {\left(\frac{\log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c e^{2}} - \frac{\log\left(\frac{\sqrt{e x^{2} + d} - \sqrt{d}}{\sqrt{e x^{2} + d} + \sqrt{d}}\right)}{c^{2} \sqrt{d} e^{2}}\right)}}{e} - \frac{60 \, c^{4} d^{2} {\left(\frac{2 \, \sqrt{e x^{2} + d}}{c^{4} e} + \frac{\log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{5}}\right)}}{e^{2}} + \frac{5 \, c^{4} d {\left(\frac{3 \, e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}} + \frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} - 3 \, {\left(c^{2} d - e\right)} \sqrt{e x^{2} + d}\right)}}{c^{6} e}\right)}}{e^{2}} - \frac{15 \, c^{4} {\left(\frac{15 \, e^{2} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{9}} + \frac{2 \, {\left(3 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} c^{4} - 5 \, {\left(2 \, c^{4} d - c^{2} e\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}} + 15 \, {\left(c^{4} d^{2} - c^{2} d e + e^{2}\right)} \sqrt{e x^{2} + d}\right)}}{c^{8} e}\right)} \log\left(c\right)}{e^{2}} - \frac{15 \, c^{2} d {\left(\frac{2 \, \sqrt{e x^{2} + d}}{c^{4} e} + \frac{\log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{5}}\right)}}{e} - \frac{3 \, c^{4} {\left(\frac{15 \, e^{2} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{9}} + \frac{2 \, {\left(3 \, {\left(e x^{2} + d\right)}^{\frac{5}{2}} c^{4} - 5 \, {\left(2 \, c^{4} d - c^{2} e\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}} + 15 \, {\left(c^{4} d^{2} - c^{2} d e + e^{2}\right)} \sqrt{e x^{2} + d}\right)}}{c^{8} e}\right)}}{e^{2}} + \frac{75 \, c^{2} {\left(\frac{3 \, e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}} + \frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} - 3 \, {\left(c^{2} d - e\right)} \sqrt{e x^{2} + d}\right)}}{c^{6} e}\right)} \log\left(c\right)}{e} + \frac{15 \, c^{2} {\left(\frac{3 \, e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}} + \frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} - 3 \, {\left(c^{2} d - e\right)} \sqrt{e x^{2} + d}\right)}}{c^{6} e}\right)}}{e} - \frac{120 \, c d^{3} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} e^{3}} + \frac{60 \, d^{2} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c e^{2}} - 450 \, \int \frac{x^{5} \log\left(x\right)}{\sqrt{e x^{2} + d}}\,{d x}\right)} e^{3} + 2 \, {\left(3 \, e^{2} x^{4} - 4 \, d e x^{2} + 8 \, d^{2}\right)} \sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b}{15 \, e^{3}}"," ",0,"1/15*(3*sqrt(e*x^2 + d)*x^4/e - 4*sqrt(e*x^2 + d)*d*x^2/e^2 + 8*sqrt(e*x^2 + d)*d^2/e^3)*a - 1/15*(15*e^3*integrate((15*c^2*e^3*x^7*log(c) - 15*e^3*x^5*log(c) + (3*(5*c^2*log(c) + c^2)*e^3*x^7 + 4*c^2*d^2*e*x^3 + 8*c^2*d^3*x - (c^2*d*e^2 + 15*e^3*log(c))*x^5)*e^(log(c*x + 1) + log(c*x - 1)) + 15*(c^2*e^3*x^7 - e^3*x^5 + (c^2*e^3*x^7 - e^3*x^5)*e^(log(c*x + 1) + log(c*x - 1)))*log(x))/((c^2*e^3*x^2 - e^3 + (c^2*e^3*x^2 - e^3)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)), x) - (3*e^2*x^4 - 4*d*e*x^2 + 8*d^2)*sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/e^3","F",0
132,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{\sqrt{e x^{2} + d} x^{2}}{e} - \frac{2 \, \sqrt{e x^{2} + d} d}{e^{2}}\right)} a - \frac{\frac{1}{2} \, {\left({\left(\frac{6 \, c^{2} d^{2} {\left(\frac{\log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c e} - \frac{\log\left(\frac{\sqrt{e x^{2} + d} - \sqrt{d}}{\sqrt{e x^{2} + d} + \sqrt{d}}\right)}{c^{2} \sqrt{d} e}\right)}}{e} - \frac{3 \, c^{4} d {\left(\frac{2 \, \sqrt{e x^{2} + d}}{c^{4}} + \frac{e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{5}}\right)}}{e^{2}} + \frac{3 \, c^{4} {\left(\frac{3 \, e^{2} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}} + \frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} - 3 \, {\left(c^{2} d - e\right)} \sqrt{e x^{2} + d}\right)}}{c^{6}}\right)} \log\left(c\right)}{e^{2}} + \frac{c^{4} {\left(\frac{3 \, e^{2} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{7}} + \frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} - 3 \, {\left(c^{2} d - e\right)} \sqrt{e x^{2} + d}\right)}}{c^{6}}\right)}}{e^{2}} - \frac{9 \, c^{2} {\left(\frac{2 \, \sqrt{e x^{2} + d}}{c^{4}} + \frac{e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{5}}\right)} \log\left(c\right)}{e} - \frac{3 \, c^{2} {\left(\frac{2 \, \sqrt{e x^{2} + d}}{c^{4}} + \frac{e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{5}}\right)}}{e} - \frac{6 \, c d^{2} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} e^{2}} + \frac{3 \, d \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c e} + 18 \, \int \frac{x^{3} \log\left(x\right)}{\sqrt{e x^{2} + d}}\,{d x}\right)} \sqrt{e x^{2} + d} e^{2} - 2 \, {\left(e^{2} x^{4} - d e x^{2} - 2 \, d^{2}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b}{3 \, \sqrt{e x^{2} + d} e^{2}}"," ",0,"1/3*(sqrt(e*x^2 + d)*x^2/e - 2*sqrt(e*x^2 + d)*d/e^2)*a - 1/3*(3*sqrt(e*x^2 + d)*e^2*integrate((3*c^2*e^2*x^5*log(c) - 3*e^2*x^3*log(c) + ((3*c^2*log(c) + c^2)*e^2*x^5 - 2*c^2*d^2*x - (c^2*d*e + 3*e^2*log(c))*x^3)*e^(log(c*x + 1) + log(c*x - 1)) + 3*(c^2*e^2*x^5 - e^2*x^3 + (c^2*e^2*x^5 - e^2*x^3)*e^(log(c*x + 1) + log(c*x - 1)))*log(x))/((c^2*e^2*x^2 - e^2 + (c^2*e^2*x^2 - e^2)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)), x) - (e^2*x^4 - d*e*x^2 - 2*d^2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/(sqrt(e*x^2 + d)*e^2)","F",0
133,0,0,0,0.000000," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{\frac{1}{2} \, {\left({\left(\frac{c^{4} {\left(\frac{2 \, \sqrt{e x^{2} + d} e}{c^{4}} + \frac{e^{2} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{5}}\right)} \log\left(c\right)}{e^{2}} - \frac{c^{2} d {\left(\frac{\log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c} - \frac{\log\left(\frac{\sqrt{e x^{2} + d} - \sqrt{d}}{\sqrt{e x^{2} + d} + \sqrt{d}}\right)}{c^{2} \sqrt{d}}\right)}}{e} + \frac{c^{4} {\left(\frac{2 \, \sqrt{e x^{2} + d} e}{c^{4}} + \frac{e^{2} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c^{5}}\right)}}{e^{2}} + \frac{c d \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} e} - \frac{\log\left(c\right) \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c} - \frac{\log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{\sqrt{c^{2} d + e} c} + 2 \, \int \frac{x \log\left(x\right)}{\sqrt{e x^{2} + d}}\,{d x}\right)} e - 2 \, \sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b}{e} + \frac{\sqrt{e x^{2} + d} a}{e}"," ",0,"-(e*integrate((c^2*e*x^3*log(c) - e*x*log(c) + ((c^2*log(c) + c^2)*e*x^3 + (c^2*d - e*log(c))*x)*e^(log(c*x + 1) + log(c*x - 1)) + (c^2*e*x^3 - e*x + (c^2*e*x^3 - e*x)*e^(log(c*x + 1) + log(c*x - 1)))*log(x))/((c^2*e*x^2 + (c^2*e*x^2 - e)*e^(log(c*x + 1) + log(c*x - 1)) - e)*sqrt(e*x^2 + d)), x) - sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/e + sqrt(e*x^2 + d)*a/e","F",0
134,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{e x^{2} + d} x}\,{d x} - \frac{a \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{\sqrt{d}}"," ",0,"b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(sqrt(e*x^2 + d)*x), x) - a*arcsinh(d/(sqrt(d*e)*abs(x)))/sqrt(d)","F",0
135,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^3/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{e \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{\sqrt{e x^{2} + d}}{d x^{2}}\right)} + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{e x^{2} + d} x^{3}}\,{d x}"," ",0,"1/2*a*(e*arcsinh(d/(sqrt(d*e)*abs(x)))/d^(3/2) - sqrt(e*x^2 + d)/(d*x^2)) + b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(sqrt(e*x^2 + d)*x^3), x)","F",0
136,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{\sqrt{e x^{2} + d} x}{e} - \frac{d \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{e^{\frac{3}{2}}}\right)} + b \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"1/2*a*(sqrt(e*x^2 + d)*x/e - d*arcsinh(e*x/sqrt(d*e))/e^(3/2)) + b*integrate(x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(e*x^2 + d), x)","F",0
137,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{e x^{2} + d}}\,{d x} + \frac{a \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{e}}"," ",0,"b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/sqrt(e*x^2 + d), x) + a*arcsinh(e*x/sqrt(d*e))/sqrt(e)","F",0
138,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^2/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{-{\left(\sqrt{e x^{2} + d} {\left(\log\left(c\right) + \log\left(x\right)\right)} - \sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b}{d x} - \frac{\sqrt{e x^{2} + d} a}{d x}"," ",0,"-(d*x*integrate((c^2*d*x^2*log(c) - (c^2*e*x^4 - (c^2*log(c) - c^2)*d*x^2 + d*log(c))*e^(log(c*x + 1) + log(c*x - 1)) - d*log(c) + (c^2*d*x^2 + (c^2*d*x^2 - d)*e^(log(c*x + 1) + log(c*x - 1)) - d)*log(x))/((c^2*d*x^4 - d*x^2 + (c^2*d*x^4 - d*x^2)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)), x) + sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/(d*x) - sqrt(e*x^2 + d)*a/(d*x)","F",0
139,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^4/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{2 \, \sqrt{e x^{2} + d} e}{d^{2} x} - \frac{\sqrt{e x^{2} + d}}{d x^{3}}\right)} - \frac{{\left(3 \, {\left(2 \, e x^{2} \log\left(c\right) - d \log\left(c\right) + {\left(2 \, e x^{2} - d\right)} \log\left(x\right)\right)} {\left(e x^{2} + d\right)} - {\left(2 \, e^{2} x^{4} + d e x^{2} - d^{2}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b}{3 \, \sqrt{e x^{2} + d} d^{2} x^{3}}"," ",0,"1/3*a*(2*sqrt(e*x^2 + d)*e/(d^2*x) - sqrt(e*x^2 + d)/(d*x^3)) - 1/3*(3*sqrt(e*x^2 + d)*d^2*x^3*integrate((3*c^2*d^2*x^2*log(c) - 3*d^2*log(c) + (2*c^2*e^2*x^6 + c^2*d*e*x^4 + (3*c^2*log(c) - c^2)*d^2*x^2 - 3*d^2*log(c))*e^(log(c*x + 1) + log(c*x - 1)) + 3*(c^2*d^2*x^2 - d^2 + (c^2*d^2*x^2 - d^2)*e^(log(c*x + 1) + log(c*x - 1)))*log(x))/((c^2*d^2*x^6 - d^2*x^4 + (c^2*d^2*x^6 - d^2*x^4)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)), x) - (2*e^2*x^4 + d*e*x^2 - d^2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/(sqrt(e*x^2 + d)*d^2*x^3)","F",0
140,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^6/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","-\frac{1}{15} \, a {\left(\frac{8 \, \sqrt{e x^{2} + d} e^{2}}{d^{3} x} - \frac{4 \, \sqrt{e x^{2} + d} e}{d^{2} x^{3}} + \frac{3 \, \sqrt{e x^{2} + d}}{d x^{5}}\right)} - \frac{{\left({\left(8 \, e^{2} x^{4} - 4 \, d e x^{2} + 3 \, d^{2}\right)} \sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - 15 \, {\left(8 \, e^{2} x^{4} \log\left(c\right) - 4 \, d e x^{2} \log\left(c\right) + 3 \, d^{2} \log\left(c\right) + {\left(8 \, e^{2} x^{4} - 4 \, d e x^{2} + 3 \, d^{2}\right)} \log\left(x\right)\right)} \sqrt{e x^{2} + d}\right)} b}{15 \, d^{3} x^{5}}"," ",0,"-1/15*a*(8*sqrt(e*x^2 + d)*e^2/(d^3*x) - 4*sqrt(e*x^2 + d)*e/(d^2*x^3) + 3*sqrt(e*x^2 + d)/(d*x^5)) - 1/15*(15*d^3*x^5*integrate((15*c^2*d^3*x^2*log(c) - 15*d^3*log(c) - (8*c^2*e^3*x^8 + 4*c^2*d*e^2*x^6 - c^2*d^2*e*x^4 - 3*(5*c^2*log(c) - c^2)*d^3*x^2 + 15*d^3*log(c))*e^(log(c*x + 1) + log(c*x - 1)) + 15*(c^2*d^3*x^2 - d^3 + (c^2*d^3*x^2 - d^3)*e^(log(c*x + 1) + log(c*x - 1)))*log(x))/((c^2*d^3*x^8 - d^3*x^6 + (c^2*d^3*x^8 - d^3*x^6)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)), x) + (8*e^2*x^4 - 4*d*e*x^2 + 3*d^2)*sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/(d^3*x^5)","F",0
141,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{x^{4}}{\sqrt{e x^{2} + d} e} - \frac{4 \, d x^{2}}{\sqrt{e x^{2} + d} e^{2}} - \frac{8 \, d^{2}}{\sqrt{e x^{2} + d} e^{3}}\right)} a - \frac{-\frac{1}{2} \, {\left({\left(\frac{24 \, c^{4} d^{3} {\left(\frac{2}{{\left(c^{4} d e + c^{2} e^{2}\right)} \sqrt{e x^{2} + d}} + \frac{\log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{2} d e + e^{2}\right)} \sqrt{c^{2} d + e} c}\right)}}{e^{2}} - \frac{24 \, c^{2} d^{3} {\left(\frac{c \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{2} d e^{2} + e^{3}\right)} \sqrt{c^{2} d + e}} - \frac{2}{{\left(c^{4} d^{2} e + c^{2} d e^{2}\right)} \sqrt{e x^{2} + d}} - \frac{\log\left(\frac{\sqrt{e x^{2} + d} - \sqrt{d}}{\sqrt{e x^{2} + d} + \sqrt{d}}\right)}{c^{2} d^{\frac{3}{2}} e^{2}}\right)}}{e} - \frac{36 \, c^{4} d^{2} {\left(\frac{2 \, d}{{\left(c^{4} d e + c^{2} e^{2}\right)} \sqrt{e x^{2} + d}} - \frac{\log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{4} d + c^{2} e\right)} \sqrt{c^{2} d + e} c}\right)}}{e^{2}} + \frac{9 \, c^{4} d {\left(\frac{2 \, d^{2}}{{\left(c^{4} d e + c^{2} e^{2}\right)} \sqrt{e x^{2} + d}} + \frac{e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{6} d + c^{4} e\right)} \sqrt{c^{2} d + e} c} + \frac{2 \, \sqrt{e x^{2} + d}}{c^{4} e}\right)}}{e^{2}} - \frac{36 \, c^{2} d^{2} {\left(\frac{2}{{\left(c^{4} d e + c^{2} e^{2}\right)} \sqrt{e x^{2} + d}} + \frac{\log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{2} d e + e^{2}\right)} \sqrt{c^{2} d + e} c}\right)}}{e} + \frac{3 \, {\left(\frac{6 \, d^{3}}{{\left(c^{4} d e + c^{2} e^{2}\right)} \sqrt{e x^{2} + d}} - \frac{3 \, e^{2} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{8} d + c^{6} e\right)} \sqrt{c^{2} d + e} c} - \frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} - 3 \, {\left(2 \, c^{2} d - e\right)} \sqrt{e x^{2} + d}\right)}}{c^{6} e}\right)} c^{4} \log\left(c\right)}{e^{2}} + \frac{{\left(\frac{6 \, d^{3}}{{\left(c^{4} d e + c^{2} e^{2}\right)} \sqrt{e x^{2} + d}} - \frac{3 \, e^{2} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{8} d + c^{6} e\right)} \sqrt{c^{2} d + e} c} - \frac{2 \, {\left({\left(e x^{2} + d\right)}^{\frac{3}{2}} c^{2} - 3 \, {\left(2 \, c^{2} d - e\right)} \sqrt{e x^{2} + d}\right)}}{c^{6} e}\right)} c^{4}}{e^{2}} + \frac{9 \, c^{2} d {\left(\frac{2 \, d}{{\left(c^{4} d e + c^{2} e^{2}\right)} \sqrt{e x^{2} + d}} - \frac{\log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{4} d + c^{2} e\right)} \sqrt{c^{2} d + e} c}\right)}}{e} + \frac{9 \, c^{2} {\left(\frac{2 \, d^{2}}{{\left(c^{4} d e + c^{2} e^{2}\right)} \sqrt{e x^{2} + d}} + \frac{e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{6} d + c^{4} e\right)} \sqrt{c^{2} d + e} c} + \frac{2 \, \sqrt{e x^{2} + d}}{c^{4} e}\right)} \log\left(c\right)}{e} + \frac{3 \, c^{2} {\left(\frac{2 \, d^{2}}{{\left(c^{4} d e + c^{2} e^{2}\right)} \sqrt{e x^{2} + d}} + \frac{e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{6} d + c^{4} e\right)} \sqrt{c^{2} d + e} c} + \frac{2 \, \sqrt{e x^{2} + d}}{c^{4} e}\right)}}{e} - 18 \, \int \frac{\sqrt{e x^{2} + d} x^{5} \log\left(x\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}\right)} \sqrt{e x^{2} + d} e^{3} + 2 \, {\left(e^{2} x^{4} - 4 \, d e x^{2} - 8 \, d^{2}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b}{3 \, \sqrt{e x^{2} + d} e^{3}}"," ",0,"1/3*(x^4/(sqrt(e*x^2 + d)*e) - 4*d*x^2/(sqrt(e*x^2 + d)*e^2) - 8*d^2/(sqrt(e*x^2 + d)*e^3))*a - 1/3*(3*sqrt(e*x^2 + d)*e^3*integrate((3*c^2*e^3*x^7*log(c) - 3*e^3*x^5*log(c) + ((3*c^2*log(c) + c^2)*e^3*x^7 - 12*c^2*d^2*e*x^3 - 8*c^2*d^3*x - 3*(c^2*d*e^2 + e^3*log(c))*x^5)*e^(log(c*x + 1) + log(c*x - 1)) + 3*(c^2*e^3*x^7 - e^3*x^5 + (c^2*e^3*x^7 - e^3*x^5)*e^(log(c*x + 1) + log(c*x - 1)))*log(x))/((c^2*e^4*x^4 - d*e^3 + (c^2*d*e^3 - e^4)*x^2 + (c^2*e^4*x^4 - d*e^3 + (c^2*d*e^3 - e^4)*x^2)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)), x) - (e^2*x^4 - 4*d*e*x^2 - 8*d^2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/(sqrt(e*x^2 + d)*e^3)","F",0
142,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","a {\left(\frac{x^{2}}{\sqrt{e x^{2} + d} e} + \frac{2 \, d}{\sqrt{e x^{2} + d} e^{2}}\right)} + \frac{\frac{1}{2} \, {\left(2 \, {\left(e x^{2} + 2 \, d\right)} \sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - {\left(e^{3} x^{2} + d e^{2}\right)} {\left(\frac{2 \, c^{4} d^{2} {\left(\frac{2}{{\left(c^{4} d + c^{2} e\right)} \sqrt{e x^{2} + d}} + \frac{\log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{2} d + e\right)}^{\frac{3}{2}} c}\right)}}{e^{2}} - \frac{2 \, c^{2} d^{2} {\left(\frac{c \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{2} d e + e^{2}\right)} \sqrt{c^{2} d + e}} - \frac{2}{{\left(c^{4} d^{2} + c^{2} d e\right)} \sqrt{e x^{2} + d}} - \frac{\log\left(\frac{\sqrt{e x^{2} + d} - \sqrt{d}}{\sqrt{e x^{2} + d} + \sqrt{d}}\right)}{c^{2} d^{\frac{3}{2}} e}\right)}}{e} - \frac{3 \, c^{4} d {\left(\frac{2 \, d}{{\left(c^{4} d + c^{2} e\right)} \sqrt{e x^{2} + d}} - \frac{e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{4} d + c^{2} e\right)} \sqrt{c^{2} d + e} c}\right)}}{e^{2}} + \frac{c^{4} {\left(\frac{2 \, d^{2}}{{\left(c^{4} d + c^{2} e\right)} \sqrt{e x^{2} + d}} + \frac{e^{2} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{6} d + c^{4} e\right)} \sqrt{c^{2} d + e} c} + \frac{2 \, \sqrt{e x^{2} + d}}{c^{4}}\right)} \log\left(c\right)}{e^{2}} + \frac{c^{4} {\left(\frac{2 \, d^{2}}{{\left(c^{4} d + c^{2} e\right)} \sqrt{e x^{2} + d}} + \frac{e^{2} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{6} d + c^{4} e\right)} \sqrt{c^{2} d + e} c} + \frac{2 \, \sqrt{e x^{2} + d}}{c^{4}}\right)}}{e^{2}} - \frac{3 \, c^{2} d {\left(\frac{2}{{\left(c^{4} d + c^{2} e\right)} \sqrt{e x^{2} + d}} + \frac{\log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{2} d + e\right)}^{\frac{3}{2}} c}\right)}}{e} + \frac{c^{2} {\left(\frac{2 \, d}{{\left(c^{4} d + c^{2} e\right)} \sqrt{e x^{2} + d}} - \frac{e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{4} d + c^{2} e\right)} \sqrt{c^{2} d + e} c}\right)} \log\left(c\right)}{e} + \frac{c^{2} {\left(\frac{2 \, d}{{\left(c^{4} d + c^{2} e\right)} \sqrt{e x^{2} + d}} - \frac{e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{4} d + c^{2} e\right)} \sqrt{c^{2} d + e} c}\right)}}{e} + 2 \, \int \frac{\sqrt{e x^{2} + d} x^{3} \log\left(x\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}\right)}\right)} b}{e^{3} x^{2} + d e^{2}}"," ",0,"a*(x^2/(sqrt(e*x^2 + d)*e) + 2*d/(sqrt(e*x^2 + d)*e^2)) + ((e*x^2 + 2*d)*sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - (e^3*x^2 + d*e^2)*integrate((c^2*e^2*x^5*log(c) - e^2*x^3*log(c) + ((c^2*log(c) + c^2)*e^2*x^5 + 2*c^2*d^2*x + (3*c^2*d*e - e^2*log(c))*x^3)*e^(log(c*x + 1) + log(c*x - 1)) + (c^2*e^2*x^5 - e^2*x^3 + (c^2*e^2*x^5 - e^2*x^3)*e^(log(c*x + 1) + log(c*x - 1)))*log(x))/((c^2*e^3*x^4 - d*e^2 + (c^2*d*e^2 - e^3)*x^2 + (c^2*e^3*x^4 - d*e^2 + (c^2*d*e^2 - e^3)*x^2)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)), x))*b/(e^3*x^2 + d*e^2)","F",0
143,0,0,0,0.000000," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","-\frac{-\frac{1}{2} \, {\left({\left(\frac{c^{4} d {\left(\frac{2 \, e}{{\left(c^{4} d + c^{2} e\right)} \sqrt{e x^{2} + d}} + \frac{e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{2} d + e\right)}^{\frac{3}{2}} c}\right)}}{e^{2}} + \frac{c^{4} {\left(\frac{2 \, d e}{{\left(c^{4} d + c^{2} e\right)} \sqrt{e x^{2} + d}} - \frac{e^{2} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{4} d + c^{2} e\right)} \sqrt{c^{2} d + e} c}\right)} \log\left(c\right)}{e^{2}} - \frac{c^{4} {\left(\frac{2 \, d e}{{\left(c^{4} d + c^{2} e\right)} \sqrt{e x^{2} + d}} - \frac{e^{2} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{4} d + c^{2} e\right)} \sqrt{c^{2} d + e} c}\right)}}{e^{2}} - \frac{c^{2} d {\left(\frac{c \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{2} d + e\right)}^{\frac{3}{2}}} - \frac{2 \, e}{{\left(c^{4} d^{2} + c^{2} d e\right)} \sqrt{e x^{2} + d}} - \frac{\log\left(\frac{\sqrt{e x^{2} + d} - \sqrt{d}}{\sqrt{e x^{2} + d} + \sqrt{d}}\right)}{c^{2} d^{\frac{3}{2}}}\right)}}{e} + \frac{c^{2} {\left(\frac{2 \, e}{{\left(c^{4} d + c^{2} e\right)} \sqrt{e x^{2} + d}} + \frac{e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{2} d + e\right)}^{\frac{3}{2}} c}\right)} \log\left(c\right)}{e} - \frac{c^{2} {\left(\frac{2 \, e}{{\left(c^{4} d + c^{2} e\right)} \sqrt{e x^{2} + d}} + \frac{e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{2} d + e\right)}^{\frac{3}{2}} c}\right)}}{e} - 2 \, \int \frac{\sqrt{e x^{2} + d} x \log\left(x\right)}{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}\,{d x}\right)} \sqrt{e x^{2} + d} e - 2 \, \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b}{\sqrt{e x^{2} + d} e} - \frac{a}{\sqrt{e x^{2} + d} e}"," ",0,"-(sqrt(e*x^2 + d)*e*integrate((c^2*e*x^3*log(c) - e*x*log(c) + ((c^2*log(c) - c^2)*e*x^3 - (c^2*d + e*log(c))*x)*e^(log(c*x + 1) + log(c*x - 1)) + (c^2*e*x^3 - e*x + (c^2*e*x^3 - e*x)*e^(log(c*x + 1) + log(c*x - 1)))*log(x))/((c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e + (c^2*e^2*x^4 + (c^2*d*e - e^2)*x^2 - d*e)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)), x) + arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/(sqrt(e*x^2 + d)*e) - a/(sqrt(e*x^2 + d)*e)","F",0
144,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{\operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{d^{\frac{3}{2}}} - \frac{1}{\sqrt{e x^{2} + d} d}\right)} + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(e x^{3} + d x\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"-a*(arcsinh(d/(sqrt(d*e)*abs(x)))/d^(3/2) - 1/(sqrt(e*x^2 + d)*d)) + b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/((e*x^3 + d*x)*sqrt(e*x^2 + d)), x)","F",0
145,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^3/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{3 \, e \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{3 \, e}{\sqrt{e x^{2} + d} d^{2}} - \frac{1}{\sqrt{e x^{2} + d} d x^{2}}\right)} + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(e x^{5} + d x^{3}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"1/2*a*(3*e*arcsinh(d/(sqrt(d*e)*abs(x)))/d^(5/2) - 3*e/(sqrt(e*x^2 + d)*d^2) - 1/(sqrt(e*x^2 + d)*d*x^2)) + b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/((e*x^5 + d*x^3)*sqrt(e*x^2 + d)), x)","F",0
146,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{x^{3}}{\sqrt{e x^{2} + d} e} + \frac{3 \, d x}{\sqrt{e x^{2} + d} e^{2}} - \frac{3 \, d \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{e^{\frac{5}{2}}}\right)} a + b \int \frac{x^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"1/2*(x^3/(sqrt(e*x^2 + d)*e) + 3*d*x/(sqrt(e*x^2 + d)*e^2) - 3*d*arcsinh(e*x/sqrt(d*e))/e^(5/2))*a + b*integrate(x^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^2 + d)^(3/2), x)","F",0
147,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{x}{\sqrt{e x^{2} + d} e} - \frac{\operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{e^{\frac{3}{2}}}\right)} + b \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"-a*(x/(sqrt(e*x^2 + d)*e) - arcsinh(e*x/sqrt(d*e))/e^(3/2)) + b*integrate(x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^2 + d)^(3/2), x)","F",0
148,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x} + \frac{a x}{\sqrt{e x^{2} + d} d}"," ",0,"b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(e*x^2 + d)^(3/2), x) + a*x/(sqrt(e*x^2 + d)*d)","F",0
149,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^2/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","-a {\left(\frac{2 \, e x}{\sqrt{e x^{2} + d} d^{2}} + \frac{1}{\sqrt{e x^{2} + d} d x}\right)} - \frac{{\left({\left(2 \, e x^{2} + d\right)} \sqrt{e x^{2} + d} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) - {\left(2 \, e x^{2} \log\left(c\right) + d \log\left(c\right) + {\left(2 \, e x^{2} + d\right)} \log\left(x\right)\right)} \sqrt{e x^{2} + d}\right)} b}{d^{2} e x^{3} + d^{3} x}"," ",0,"-a*(2*e*x/(sqrt(e*x^2 + d)*d^2) + 1/(sqrt(e*x^2 + d)*d*x)) - ((2*e*x^2 + d)*sqrt(e*x^2 + d)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) + (d^2*e*x^3 + d^3*x)*integrate((c^2*d^2*x^2*log(c) - d^2*log(c) - (2*c^2*e^2*x^6 + 3*c^2*d*e*x^4 - (c^2*log(c) - c^2)*d^2*x^2 + d^2*log(c))*e^(log(c*x + 1) + log(c*x - 1)) + (c^2*d^2*x^2 - d^2 + (c^2*d^2*x^2 - d^2)*e^(log(c*x + 1) + log(c*x - 1)))*log(x))/((c^2*d^2*e*x^6 - d^3*x^2 + (c^2*d^3 - d^2*e)*x^4 + (c^2*d^2*e*x^6 - d^3*x^2 + (c^2*d^3 - d^2*e)*x^4)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)), x))*b/(d^2*e*x^3 + d^3*x)","F",0
150,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^4/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{8 \, e^{2} x}{\sqrt{e x^{2} + d} d^{3}} + \frac{4 \, e}{\sqrt{e x^{2} + d} d^{2} x} - \frac{1}{\sqrt{e x^{2} + d} d x^{3}}\right)} - \frac{{\left(\frac{3 \, {\left(8 \, e^{2} x^{4} \log\left(c\right) + 4 \, d e x^{2} \log\left(c\right) - d^{2} \log\left(c\right) + {\left(8 \, e^{2} x^{4} + 4 \, d e x^{2} - d^{2}\right)} \log\left(x\right)\right)} {\left(e x^{2} + d\right)} d^{3} x^{3}}{d^{3} e x^{5} + d^{4} x^{3}} - {\left(8 \, e^{2} x^{4} + 4 \, d e x^{2} - d^{2}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b}{3 \, \sqrt{e x^{2} + d} d^{3} x^{3}}"," ",0,"1/3*a*(8*e^2*x/(sqrt(e*x^2 + d)*d^3) + 4*e/(sqrt(e*x^2 + d)*d^2*x) - 1/(sqrt(e*x^2 + d)*d*x^3)) - 1/3*(3*sqrt(e*x^2 + d)*d^3*x^3*integrate((3*c^2*d^3*x^2*log(c) - 3*d^3*log(c) + (8*c^2*e^3*x^8 + 12*c^2*d*e^2*x^6 + 3*c^2*d^2*e*x^4 + (3*c^2*log(c) - c^2)*d^3*x^2 - 3*d^3*log(c))*e^(log(c*x + 1) + log(c*x - 1)) + 3*(c^2*d^3*x^2 - d^3 + (c^2*d^3*x^2 - d^3)*e^(log(c*x + 1) + log(c*x - 1)))*log(x))/((c^2*d^3*e*x^8 - d^4*x^4 + (c^2*d^4 - d^3*e)*x^6 + (c^2*d^3*e*x^8 - d^4*x^4 + (c^2*d^4 - d^3*e)*x^6)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)), x) - (8*e^2*x^4 + 4*d*e*x^2 - d^2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/(sqrt(e*x^2 + d)*d^3*x^3)","F",0
151,0,0,0,0.000000," ","integrate(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{3 \, x^{4}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e} + \frac{12 \, d x^{2}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e^{2}} + \frac{8 \, d^{2}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e^{3}}\right)} a - \frac{\frac{1}{2} \, {\left({\left(e^{4} x^{2} + d e^{3}\right)} {\left(\frac{8 \, c^{4} d^{3} {\left(\frac{3 \, c \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{4} d^{2} e + 2 \, c^{2} d e^{2} + e^{3}\right)} \sqrt{c^{2} d + e}} + \frac{2 \, {\left(3 \, {\left(e x^{2} + d\right)} c^{2} + c^{2} d + e\right)}}{{\left(c^{6} d^{2} e + 2 \, c^{4} d e^{2} + c^{2} e^{3}\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}}}\right)}}{e^{2}} - \frac{8 \, {\left(\frac{3 \, c^{3} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{4} d^{2} e^{2} + 2 \, c^{2} d e^{3} + e^{4}\right)} \sqrt{c^{2} d + e}} - \frac{2 \, {\left(c^{2} d^{2} + 3 \, {\left(2 \, c^{2} d + e\right)} {\left(e x^{2} + d\right)} + d e\right)}}{{\left(c^{6} d^{4} e + 2 \, c^{4} d^{3} e^{2} + c^{2} d^{2} e^{3}\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}}} - \frac{3 \, \log\left(\frac{\sqrt{e x^{2} + d} - \sqrt{d}}{\sqrt{e x^{2} + d} + \sqrt{d}}\right)}{c^{2} d^{\frac{5}{2}} e^{2}}\right)} c^{2} d^{3}}{e} - \frac{20 \, c^{4} d^{2} {\left(\frac{2 \, {\left(c^{2} d^{2} - 3 \, {\left(e x^{2} + d\right)} e + d e\right)}}{{\left(c^{6} d^{2} e + 2 \, c^{4} d e^{2} + c^{2} e^{3}\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}}} - \frac{3 \, \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{4} d^{2} + 2 \, c^{2} d e + e^{2}\right)} \sqrt{c^{2} d + e} c}\right)}}{e^{2}} - \frac{20 \, c^{2} d^{2} {\left(\frac{3 \, c \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{4} d^{2} e + 2 \, c^{2} d e^{2} + e^{3}\right)} \sqrt{c^{2} d + e}} + \frac{2 \, {\left(3 \, {\left(e x^{2} + d\right)} c^{2} + c^{2} d + e\right)}}{{\left(c^{6} d^{2} e + 2 \, c^{4} d e^{2} + c^{2} e^{3}\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}}}\right)}}{e} + \frac{15 \, c^{4} d {\left(\frac{3 \, e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{6} d^{2} + 2 \, c^{4} d e + c^{2} e^{2}\right)} \sqrt{c^{2} d + e} c} + \frac{2 \, {\left(c^{2} d^{3} + d^{2} e - 3 \, {\left(c^{2} d^{2} + 2 \, d e\right)} {\left(e x^{2} + d\right)}\right)}}{{\left(c^{6} d^{2} e + 2 \, c^{4} d e^{2} + c^{2} e^{3}\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}}}\right)}}{e^{2}} + \frac{3 \, c^{4} {\left(\frac{3 \, e^{2} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{8} d^{2} + 2 \, c^{6} d e + c^{4} e^{2}\right)} \sqrt{c^{2} d + e} c} - \frac{2 \, {\left(c^{2} d^{4} + d^{3} e - 3 \, {\left(2 \, c^{2} d^{3} + 3 \, d^{2} e\right)} {\left(e x^{2} + d\right)}\right)}}{{\left(c^{6} d^{2} e + 2 \, c^{4} d e^{2} + c^{2} e^{3}\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}}} + \frac{6 \, \sqrt{e x^{2} + d}}{c^{4} e}\right)} \log\left(c\right)}{e^{2}} + \frac{3 \, c^{4} {\left(\frac{3 \, e^{2} \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{8} d^{2} + 2 \, c^{6} d e + c^{4} e^{2}\right)} \sqrt{c^{2} d + e} c} - \frac{2 \, {\left(c^{2} d^{4} + d^{3} e - 3 \, {\left(2 \, c^{2} d^{3} + 3 \, d^{2} e\right)} {\left(e x^{2} + d\right)}\right)}}{{\left(c^{6} d^{2} e + 2 \, c^{4} d e^{2} + c^{2} e^{3}\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}}} + \frac{6 \, \sqrt{e x^{2} + d}}{c^{4} e}\right)}}{e^{2}} + \frac{15 \, c^{2} d {\left(\frac{2 \, {\left(c^{2} d^{2} - 3 \, {\left(e x^{2} + d\right)} e + d e\right)}}{{\left(c^{6} d^{2} e + 2 \, c^{4} d e^{2} + c^{2} e^{3}\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}}} - \frac{3 \, \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{4} d^{2} + 2 \, c^{2} d e + e^{2}\right)} \sqrt{c^{2} d + e} c}\right)}}{e} - \frac{3 \, c^{2} {\left(\frac{3 \, e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{6} d^{2} + 2 \, c^{4} d e + c^{2} e^{2}\right)} \sqrt{c^{2} d + e} c} + \frac{2 \, {\left(c^{2} d^{3} + d^{2} e - 3 \, {\left(c^{2} d^{2} + 2 \, d e\right)} {\left(e x^{2} + d\right)}\right)}}{{\left(c^{6} d^{2} e + 2 \, c^{4} d e^{2} + c^{2} e^{3}\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}}}\right)} \log\left(c\right)}{e} - \frac{3 \, c^{2} {\left(\frac{3 \, e \log\left(\frac{\sqrt{e x^{2} + d} c^{2} - \sqrt{c^{2} d + e} c}{\sqrt{e x^{2} + d} c^{2} + \sqrt{c^{2} d + e} c}\right)}{{\left(c^{6} d^{2} + 2 \, c^{4} d e + c^{2} e^{2}\right)} \sqrt{c^{2} d + e} c} + \frac{2 \, {\left(c^{2} d^{3} + d^{2} e - 3 \, {\left(c^{2} d^{2} + 2 \, d e\right)} {\left(e x^{2} + d\right)}\right)}}{{\left(c^{6} d^{2} e + 2 \, c^{4} d e^{2} + c^{2} e^{3}\right)} {\left(e x^{2} + d\right)}^{\frac{3}{2}}}\right)}}{e} + 18 \, \int \frac{\sqrt{e x^{2} + d} x^{5} \log\left(x\right)}{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}\,{d x}\right)} \sqrt{e x^{2} + d} - 2 \, {\left(3 \, e^{2} x^{4} + 12 \, d e x^{2} + 8 \, d^{2}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b}{3 \, {\left(e^{4} x^{2} + d e^{3}\right)} \sqrt{e x^{2} + d}}"," ",0,"1/3*(3*x^4/((e*x^2 + d)^(3/2)*e) + 12*d*x^2/((e*x^2 + d)^(3/2)*e^2) + 8*d^2/((e*x^2 + d)^(3/2)*e^3))*a - 1/3*(3*(e^4*x^2 + d*e^3)*sqrt(e*x^2 + d)*integrate((3*c^2*e^3*x^7*log(c) - 3*e^3*x^5*log(c) + (3*(c^2*log(c) + c^2)*e^3*x^7 + 20*c^2*d^2*e*x^3 + 8*c^2*d^3*x + 3*(5*c^2*d*e^2 - e^3*log(c))*x^5)*e^(log(c*x + 1) + log(c*x - 1)) + 3*(c^2*e^3*x^7 - e^3*x^5 + (c^2*e^3*x^7 - e^3*x^5)*e^(log(c*x + 1) + log(c*x - 1)))*log(x))/((c^2*e^5*x^6 - d^2*e^3 + (2*c^2*d*e^4 - e^5)*x^4 + (c^2*d^2*e^3 - 2*d*e^4)*x^2 + (c^2*e^5*x^6 - d^2*e^3 + (2*c^2*d*e^4 - e^5)*x^4 + (c^2*d^2*e^3 - 2*d*e^4)*x^2)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)), x) - (3*e^2*x^4 + 12*d*e*x^2 + 8*d^2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/((e^4*x^2 + d*e^3)*sqrt(e*x^2 + d))","F",0
152,0,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{3 \, x^{2}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e} + \frac{2 \, d}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e^{2}}\right)} + b \int \frac{x^{3} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"-1/3*a*(3*x^2/((e*x^2 + d)^(3/2)*e) + 2*d/((e*x^2 + d)^(3/2)*e^2)) + b*integrate(x^3*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/((e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(e*x^2 + d)), x)","F",0
153,0,0,0,0.000000," ","integrate(x*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","b \int \frac{x \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{e x^{2} + d}}\,{d x} - \frac{a}{3 \, {\left(e x^{2} + d\right)}^{\frac{3}{2}} e}"," ",0,"b*integrate(x*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/((e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(e*x^2 + d)), x) - 1/3*a/((e*x^2 + d)^(3/2)*e)","F",0
154,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{3 \, \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{d^{\frac{5}{2}}} - \frac{3}{\sqrt{e x^{2} + d} d^{2}} - \frac{1}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(e^{2} x^{5} + 2 \, d e x^{3} + d^{2} x\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"-1/3*a*(3*arcsinh(d/(sqrt(d*e)*abs(x)))/d^(5/2) - 3/(sqrt(e*x^2 + d)*d^2) - 1/((e*x^2 + d)^(3/2)*d)) + b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/((e^2*x^5 + 2*d*e*x^3 + d^2*x)*sqrt(e*x^2 + d)), x)","F",0
155,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^3/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{15 \, e \operatorname{arsinh}\left(\frac{d}{\sqrt{d e} {\left| x \right|}}\right)}{d^{\frac{7}{2}}} - \frac{15 \, e}{\sqrt{e x^{2} + d} d^{3}} - \frac{5 \, e}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d^{2}} - \frac{3}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d x^{2}}\right)} + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(e^{2} x^{7} + 2 \, d e x^{5} + d^{2} x^{3}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"1/6*a*(15*e*arcsinh(d/(sqrt(d*e)*abs(x)))/d^(7/2) - 15*e/(sqrt(e*x^2 + d)*d^3) - 5*e/((e*x^2 + d)^(3/2)*d^2) - 3/((e*x^2 + d)^(3/2)*d*x^2)) + b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/((e^2*x^7 + 2*d*e*x^5 + d^2*x^3)*sqrt(e*x^2 + d)), x)","F",0
156,0,0,0,0.000000," ","integrate(x^6*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{3 \, x^{5}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e} + \frac{5 \, d x {\left(\frac{3 \, x^{2}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e} + \frac{2 \, d}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e^{2}}\right)}}{e} + \frac{5 \, d x}{\sqrt{e x^{2} + d} e^{3}} - \frac{15 \, d \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{e^{\frac{7}{2}}}\right)} a + b \int \frac{x^{6} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"1/6*(3*x^5/((e*x^2 + d)^(3/2)*e) + 5*d*x*(3*x^2/((e*x^2 + d)^(3/2)*e) + 2*d/((e*x^2 + d)^(3/2)*e^2))/e + 5*d*x/(sqrt(e*x^2 + d)*e^3) - 15*d*arcsinh(e*x/sqrt(d*e))/e^(7/2))*a + b*integrate(x^6*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/((e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(e*x^2 + d)), x)","F",0
157,0,0,0,0.000000," ","integrate(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(x {\left(\frac{3 \, x^{2}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e} + \frac{2 \, d}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e^{2}}\right)} + \frac{x}{\sqrt{e x^{2} + d} e^{2}} - \frac{3 \, \operatorname{arsinh}\left(\frac{e x}{\sqrt{d e}}\right)}{e^{\frac{5}{2}}}\right)} a + b \int \frac{x^{4} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"-1/3*(x*(3*x^2/((e*x^2 + d)^(3/2)*e) + 2*d/((e*x^2 + d)^(3/2)*e^2)) + x/(sqrt(e*x^2 + d)*e^2) - 3*arcsinh(e*x/sqrt(d*e))/e^(5/2))*a + b*integrate(x^4*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/((e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(e*x^2 + d)), x)","F",0
158,0,0,0,0.000000," ","integrate(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} e} - \frac{x}{\sqrt{e x^{2} + d} d e}\right)} + b \int \frac{x^{2} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"-1/3*a*(x/((e*x^2 + d)^(3/2)*e) - x/(sqrt(e*x^2 + d)*d*e)) + b*integrate(x^2*arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/((e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(e*x^2 + d)), x)","F",0
159,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, a {\left(\frac{2 \, x}{\sqrt{e x^{2} + d} d^{2}} + \frac{x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d}\right)} + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{{\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{e x^{2} + d}}\,{d x}"," ",0,"1/3*a*(2*x/(sqrt(e*x^2 + d)*d^2) + x/((e*x^2 + d)^(3/2)*d)) + b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/((e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(e*x^2 + d)), x)","F",0
160,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^2/(e*x^2+d)^(5/2),x, algorithm=""maxima"")","-\frac{1}{3} \, a {\left(\frac{8 \, e x}{\sqrt{e x^{2} + d} d^{3}} + \frac{4 \, e x}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d^{2}} + \frac{3}{{\left(e x^{2} + d\right)}^{\frac{3}{2}} d x}\right)} - \frac{-{\left(\frac{3 \, {\left(d^{3} e x^{3} + d^{4} x\right)} {\left(8 \, e^{2} x^{4} \log\left(c\right) + 12 \, d e x^{2} \log\left(c\right) + 3 \, d^{2} \log\left(c\right) + {\left(8 \, e^{2} x^{4} + 12 \, d e x^{2} + 3 \, d^{2}\right)} \log\left(x\right)\right)} {\left(e x^{2} + d\right)}}{d^{3} e^{2} x^{5} + 2 \, d^{4} e x^{3} + d^{5} x} - {\left(8 \, e^{2} x^{4} + 12 \, d e x^{2} + 3 \, d^{2}\right)} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)\right)} b}{3 \, {\left(d^{3} e x^{3} + d^{4} x\right)} \sqrt{e x^{2} + d}}"," ",0,"-1/3*a*(8*e*x/(sqrt(e*x^2 + d)*d^3) + 4*e*x/((e*x^2 + d)^(3/2)*d^2) + 3/((e*x^2 + d)^(3/2)*d*x)) - 1/3*(3*(d^3*e*x^3 + d^4*x)*sqrt(e*x^2 + d)*integrate((3*c^2*d^3*x^2*log(c) - 3*d^3*log(c) - (8*c^2*e^3*x^8 + 20*c^2*d*e^2*x^6 + 15*c^2*d^2*e*x^4 - 3*(c^2*log(c) - c^2)*d^3*x^2 + 3*d^3*log(c))*e^(log(c*x + 1) + log(c*x - 1)) + 3*(c^2*d^3*x^2 - d^3 + (c^2*d^3*x^2 - d^3)*e^(log(c*x + 1) + log(c*x - 1)))*log(x))/((c^2*d^3*e^2*x^8 - d^5*x^2 + (2*c^2*d^4*e - d^3*e^2)*x^6 + (c^2*d^5 - 2*d^4*e)*x^4 + (c^2*d^3*e^2*x^8 - d^5*x^2 + (2*c^2*d^4*e - d^3*e^2)*x^6 + (c^2*d^5 - 2*d^4*e)*x^4)*e^(log(c*x + 1) + log(c*x - 1)))*sqrt(e*x^2 + d)), x) + (8*e^2*x^4 + 12*d*e*x^2 + 3*d^2)*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)))*b/((d^3*e*x^3 + d^4*x)*sqrt(e*x^2 + d))","F",0
161,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^3*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{a e^{3} f^{m} x^{7} x^{m}}{m + 7} + \frac{3 \, a d e^{2} f^{m} x^{5} x^{m}}{m + 5} + \frac{3 \, a d^{2} e f^{m} x^{3} x^{m}}{m + 3} + \frac{\left(f x\right)^{m + 1} a d^{3}}{f {\left(m + 1\right)}} + \frac{{\left({\left(b e^{3} f^{m} m^{3} + 9 \, b e^{3} f^{m} m^{2} + 23 \, b e^{3} f^{m} m + 15 \, b e^{3} f^{m}\right)} x^{7} + 3 \, {\left(b d e^{2} f^{m} m^{3} + 11 \, b d e^{2} f^{m} m^{2} + 31 \, b d e^{2} f^{m} m + 21 \, b d e^{2} f^{m}\right)} x^{5} + 3 \, {\left(b d^{2} e f^{m} m^{3} + 13 \, b d^{2} e f^{m} m^{2} + 47 \, b d^{2} e f^{m} m + 35 \, b d^{2} e f^{m}\right)} x^{3} + {\left(b d^{3} f^{m} m^{3} + 15 \, b d^{3} f^{m} m^{2} + 71 \, b d^{3} f^{m} m + 105 \, b d^{3} f^{m}\right)} x\right)} x^{m} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105\right)} \int \frac{{\left(b d^{3} f^{m} m^{3} + 15 \, b d^{3} f^{m} m^{2} + {\left(b e^{3} f^{m} m^{3} + 9 \, b e^{3} f^{m} m^{2} + 23 \, b e^{3} f^{m} m + 15 \, b e^{3} f^{m}\right)} x^{6} + 71 \, b d^{3} f^{m} m + 105 \, b d^{3} f^{m} + 3 \, {\left(b d e^{2} f^{m} m^{3} + 11 \, b d e^{2} f^{m} m^{2} + 31 \, b d e^{2} f^{m} m + 21 \, b d e^{2} f^{m}\right)} x^{4} + 3 \, {\left(b d^{2} e f^{m} m^{3} + 13 \, b d^{2} e f^{m} m^{2} + 47 \, b d^{2} e f^{m} m + 35 \, b d^{2} e f^{m}\right)} x^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1} x^{m}}{m^{4} + 16 \, m^{3} - {\left(c^{2} m^{4} + 16 \, c^{2} m^{3} + 86 \, c^{2} m^{2} + 176 \, c^{2} m + 105 \, c^{2}\right)} x^{2} + 86 \, m^{2} + 176 \, m + 105}\,{d x}}{m^{4} + 16 \, m^{3} + 86 \, m^{2} + 176 \, m + 105}"," ",0,"a*e^3*f^m*x^7*x^m/(m + 7) + 3*a*d*e^2*f^m*x^5*x^m/(m + 5) + 3*a*d^2*e*f^m*x^3*x^m/(m + 3) + (f*x)^(m + 1)*a*d^3/(f*(m + 1)) + (((b*e^3*f^m*m^3 + 9*b*e^3*f^m*m^2 + 23*b*e^3*f^m*m + 15*b*e^3*f^m)*x^7 + 3*(b*d*e^2*f^m*m^3 + 11*b*d*e^2*f^m*m^2 + 31*b*d*e^2*f^m*m + 21*b*d*e^2*f^m)*x^5 + 3*(b*d^2*e*f^m*m^3 + 13*b*d^2*e*f^m*m^2 + 47*b*d^2*e*f^m*m + 35*b*d^2*e*f^m)*x^3 + (b*d^3*f^m*m^3 + 15*b*d^3*f^m*m^2 + 71*b*d^3*f^m*m + 105*b*d^3*f^m)*x)*x^m*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - (m^4 + 16*m^3 + 86*m^2 + 176*m + 105)*integrate(-(b*d^3*f^m*m^3 + 15*b*d^3*f^m*m^2 + (b*e^3*f^m*m^3 + 9*b*e^3*f^m*m^2 + 23*b*e^3*f^m*m + 15*b*e^3*f^m)*x^6 + 71*b*d^3*f^m*m + 105*b*d^3*f^m + 3*(b*d*e^2*f^m*m^3 + 11*b*d*e^2*f^m*m^2 + 31*b*d*e^2*f^m*m + 21*b*d*e^2*f^m)*x^4 + 3*(b*d^2*e*f^m*m^3 + 13*b*d^2*e*f^m*m^2 + 47*b*d^2*e*f^m*m + 35*b*d^2*e*f^m)*x^2)*sqrt(c*x + 1)*sqrt(c*x - 1)*x^m/(m^4 + 16*m^3 - (c^2*m^4 + 16*c^2*m^3 + 86*c^2*m^2 + 176*c^2*m + 105*c^2)*x^2 + 86*m^2 + 176*m + 105), x))/(m^4 + 16*m^3 + 86*m^2 + 176*m + 105)","F",0
162,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^2*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\frac{a e^{2} f^{m} x^{5} x^{m}}{m + 5} + \frac{2 \, a d e f^{m} x^{3} x^{m}}{m + 3} + \frac{\left(f x\right)^{m + 1} a d^{2}}{f {\left(m + 1\right)}} + \frac{{\left({\left(b e^{2} f^{m} m^{2} + 4 \, b e^{2} f^{m} m + 3 \, b e^{2} f^{m}\right)} x^{5} + 2 \, {\left(b d e f^{m} m^{2} + 6 \, b d e f^{m} m + 5 \, b d e f^{m}\right)} x^{3} + {\left(b d^{2} f^{m} m^{2} + 8 \, b d^{2} f^{m} m + 15 \, b d^{2} f^{m}\right)} x\right)} x^{m} \arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right) + {\left(m^{3} + 9 \, m^{2} + 23 \, m + 15\right)} \int \frac{{\left(b d^{2} f^{m} m^{2} + 8 \, b d^{2} f^{m} m + {\left(b e^{2} f^{m} m^{2} + 4 \, b e^{2} f^{m} m + 3 \, b e^{2} f^{m}\right)} x^{4} + 15 \, b d^{2} f^{m} + 2 \, {\left(b d e f^{m} m^{2} + 6 \, b d e f^{m} m + 5 \, b d e f^{m}\right)} x^{2}\right)} \sqrt{c x + 1} \sqrt{c x - 1} x^{m}}{m^{3} - {\left(c^{2} m^{3} + 9 \, c^{2} m^{2} + 23 \, c^{2} m + 15 \, c^{2}\right)} x^{2} + 9 \, m^{2} + 23 \, m + 15}\,{d x}}{m^{3} + 9 \, m^{2} + 23 \, m + 15}"," ",0,"a*e^2*f^m*x^5*x^m/(m + 5) + 2*a*d*e*f^m*x^3*x^m/(m + 3) + (f*x)^(m + 1)*a*d^2/(f*(m + 1)) + (((b*e^2*f^m*m^2 + 4*b*e^2*f^m*m + 3*b*e^2*f^m)*x^5 + 2*(b*d*e*f^m*m^2 + 6*b*d*e*f^m*m + 5*b*d*e*f^m)*x^3 + (b*d^2*f^m*m^2 + 8*b*d^2*f^m*m + 15*b*d^2*f^m)*x)*x^m*arctan(sqrt(c*x + 1)*sqrt(c*x - 1)) - (m^3 + 9*m^2 + 23*m + 15)*integrate(-(b*d^2*f^m*m^2 + 8*b*d^2*f^m*m + (b*e^2*f^m*m^2 + 4*b*e^2*f^m*m + 3*b*e^2*f^m)*x^4 + 15*b*d^2*f^m + 2*(b*d*e*f^m*m^2 + 6*b*d*e*f^m*m + 5*b*d*e*f^m)*x^2)*sqrt(c*x + 1)*sqrt(c*x - 1)*x^m/(m^3 - (c^2*m^3 + 9*c^2*m^2 + 23*c^2*m + 15*c^2)*x^2 + 9*m^2 + 23*m + 15), x))/(m^3 + 9*m^2 + 23*m + 15)","F",0
163,-1,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}}{e x^{2} + d}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*(f*x)^m/(e*x^2 + d), x)","F",0
165,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d)^2,x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(e x^{2} + d\right)}^{2}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*(f*x)^m/(e*x^2 + d)^2, x)","F",0
166,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\int {\left(e x^{2} + d\right)}^{\frac{3}{2}} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate((e*x^2 + d)^(3/2)*(b*arcsec(c*x) + a)*(f*x)^m, x)","F",0
167,0,0,0,0.000000," ","integrate((f*x)^m*(e*x^2+d)^(1/2)*(a+b*arcsec(c*x)),x, algorithm=""maxima"")","\int \sqrt{e x^{2} + d} {\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}\,{d x}"," ",0,"integrate(sqrt(e*x^2 + d)*(b*arcsec(c*x) + a)*(f*x)^m, x)","F",0
168,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}}{\sqrt{e x^{2} + d}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*(f*x)^m/sqrt(e*x^2 + d), x)","F",0
169,0,0,0,0.000000," ","integrate((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \operatorname{arcsec}\left(c x\right) + a\right)} \left(f x\right)^{m}}{{\left(e x^{2} + d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arcsec(c*x) + a)*(f*x)^m/(e*x^2 + d)^(3/2), x)","F",0
170,-1,0,0,0.000000," ","integrate(x^11*(a+b*arcsec(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,-1,0,0,0.000000," ","integrate(x^7*(a+b*arcsec(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate(x^3*(a+b*arcsec(c*x))/(-c^4*x^4+1)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x/(-c^4*x^4+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\log\left(\sqrt{-c^{4} x^{4} + 1} + 1\right) - \log\left(\sqrt{-c^{4} x^{4} + 1} - 1\right)\right)} + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{c^{2} x^{2} + 1} \sqrt{c x + 1} \sqrt{-c x + 1} x}\,{d x}"," ",0,"-1/4*a*(log(sqrt(-c^4*x^4 + 1) + 1) - log(sqrt(-c^4*x^4 + 1) - 1)) + b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(sqrt(c^2*x^2 + 1)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x), x)","F",0
174,0,0,0,0.000000," ","integrate((a+b*arcsec(c*x))/x^5/(-c^4*x^4+1)^(1/2),x, algorithm=""maxima"")","-\frac{1}{8} \, {\left(c^{4} \log\left(\sqrt{-c^{4} x^{4} + 1} + 1\right) - c^{4} \log\left(\sqrt{-c^{4} x^{4} + 1} - 1\right) + \frac{2 \, \sqrt{-c^{4} x^{4} + 1}}{x^{4}}\right)} a + b \int \frac{\arctan\left(\sqrt{c x + 1} \sqrt{c x - 1}\right)}{\sqrt{c^{2} x^{2} + 1} \sqrt{c x + 1} \sqrt{-c x + 1} x^{5}}\,{d x}"," ",0,"-1/8*(c^4*log(sqrt(-c^4*x^4 + 1) + 1) - c^4*log(sqrt(-c^4*x^4 + 1) - 1) + 2*sqrt(-c^4*x^4 + 1)/x^4)*a + b*integrate(arctan(sqrt(c*x + 1)*sqrt(c*x - 1))/(sqrt(c^2*x^2 + 1)*sqrt(c*x + 1)*sqrt(-c*x + 1)*x^5), x)","F",0
