1,1,177,96,0.075000," ","int(x^6*(a+b*arcsec(c*x)),x)","\frac{x^{7} a}{7}+\frac{b \,x^{7} \mathrm{arcsec}\left(c x \right)}{7}-\frac{b \,x^{6}}{42 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,x^{4}}{168 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{5 b \,x^{2}}{336 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{5 b}{112 c^{7} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{5 b \sqrt{c^{2} x^{2}-1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{112 c^{8} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/7*x^7*a+1/7*b*x^7*arcsec(c*x)-1/42/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^6-1/168/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^4-5/336/c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2+5/112/c^7*b/((c^2*x^2-1)/c^2/x^2)^(1/2)-5/112/c^8*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*ln(c*x+(c^2*x^2-1)^(1/2))","A"
2,1,83,75,0.048000," ","int(x^5*(a+b*arcsec(c*x)),x)","\frac{\frac{c^{6} x^{6} a}{6}+b \left(\frac{c^{6} x^{6} \mathrm{arcsec}\left(c x \right)}{6}-\frac{\left(c^{2} x^{2}-1\right) \left(3 c^{4} x^{4}+4 c^{2} x^{2}+8\right)}{90 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c x}\right)}{c^{6}}"," ",0,"1/c^6*(1/6*c^6*x^6*a+b*(1/6*c^6*x^6*arcsec(c*x)-1/90*(c^2*x^2-1)*(3*c^4*x^4+4*c^2*x^2+8)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c/x))","A"
3,1,150,75,0.049000," ","int(x^4*(a+b*arcsec(c*x)),x)","\frac{a \,x^{5}}{5}+\frac{x^{5} b \,\mathrm{arcsec}\left(c x \right)}{5}-\frac{b \,x^{4}}{20 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,x^{2}}{40 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{3 b}{40 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{3 b \sqrt{c^{2} x^{2}-1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{40 c^{6} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/5*a*x^5+1/5*x^5*b*arcsec(c*x)-1/20/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^4-1/40/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2+3/40/c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)-3/40/c^6*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*ln(c*x+(c^2*x^2-1)^(1/2))","A"
4,1,74,54,0.050000," ","int(x^3*(a+b*arcsec(c*x)),x)","\frac{\frac{c^{4} x^{4} a}{4}+b \left(\frac{c^{4} x^{4} \mathrm{arcsec}\left(c x \right)}{4}-\frac{\left(c^{2} x^{2}-1\right) \left(c^{2} x^{2}+2\right)}{12 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c x}\right)}{c^{4}}"," ",0,"1/c^4*(1/4*c^4*x^4*a+b*(1/4*c^4*x^4*arcsec(c*x)-1/12*(c^2*x^2-1)*(c^2*x^2+2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c/x))","A"
5,1,123,54,0.048000," ","int(x^2*(a+b*arcsec(c*x)),x)","\frac{x^{3} a}{3}+\frac{x^{3} b \,\mathrm{arcsec}\left(c x \right)}{3}-\frac{b \,x^{2}}{6 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b}{6 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \sqrt{c^{2} x^{2}-1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{6 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/3*x^3*a+1/3*x^3*b*arcsec(c*x)-1/6/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2+1/6/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)-1/6/c^4*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*ln(c*x+(c^2*x^2-1)^(1/2))","B"
6,1,65,33,0.046000," ","int(x*(a+b*arcsec(c*x)),x)","\frac{\frac{c^{2} x^{2} a}{2}+b \left(\frac{c^{2} x^{2} \mathrm{arcsec}\left(c x \right)}{2}-\frac{c^{2} x^{2}-1}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c x}\right)}{c^{2}}"," ",0,"1/c^2*(1/2*c^2*x^2*a+b*(1/2*c^2*x^2*arcsec(c*x)-1/2/((c^2*x^2-1)/c^2/x^2)^(1/2)/c/x*(c^2*x^2-1)))","A"
7,1,38,30,0.043000," ","int(a+b*arcsec(c*x),x)","a x +b x \,\mathrm{arcsec}\left(c x \right)-\frac{b \ln \left(c x +c x \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c}"," ",0,"a*x+b*x*arcsec(c*x)-b/c*ln(c*x+c*x*(1-1/c^2/x^2)^(1/2))","A"
8,1,86,88,0.186000," ","int((a+b*arcsec(c*x))/x,x)","a \ln \left(c x \right)+\frac{i b \mathrm{arcsec}\left(c x \right)^{2}}{2}-b \,\mathrm{arcsec}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)+\frac{i b \polylog \left(2, -\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)}{2}"," ",0,"a*ln(c*x)+1/2*I*b*arcsec(c*x)^2-b*arcsec(c*x)*ln(1+(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)+1/2*I*b*polylog(2,-(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)","A"
9,1,62,31,0.047000," ","int((a+b*arcsec(c*x))/x^2,x)","c \left(-\frac{a}{c x}+b \left(-\frac{\mathrm{arcsec}\left(c x \right)}{c x}+\frac{c^{2} x^{2}-1}{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{2} x^{2}}\right)\right)"," ",0,"c*(-a/c/x+b*(-1/c/x*arcsec(c*x)+1/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^2/x^2*(c^2*x^2-1)))","A"
10,1,118,46,0.049000," ","int((a+b*arcsec(c*x))/x^3,x)","-\frac{a}{2 x^{2}}-\frac{b \,\mathrm{arcsec}\left(c x \right)}{2 x^{2}}-\frac{c b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{c b}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{b}{4 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}"," ",0,"-1/2*a/x^2-1/2*b/x^2*arcsec(c*x)-1/4*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*arctan(1/(c^2*x^2-1)^(1/2))+1/4*c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x-1/4/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^3","B"
11,1,75,53,0.048000," ","int((a+b*arcsec(c*x))/x^4,x)","c^{3} \left(-\frac{a}{3 c^{3} x^{3}}+b \left(-\frac{\mathrm{arcsec}\left(c x \right)}{3 c^{3} x^{3}}+\frac{\left(c^{2} x^{2}-1\right) \left(2 c^{2} x^{2}+1\right)}{9 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{4} x^{4}}\right)\right)"," ",0,"c^3*(-1/3*a/c^3/x^3+b*(-1/3/c^3/x^3*arcsec(c*x)+1/9*(c^2*x^2-1)*(2*c^2*x^2+1)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^4/x^4))","A"
12,1,147,67,0.048000," ","int((a+b*arcsec(c*x))/x^5,x)","-\frac{a}{4 x^{4}}-\frac{b \,\mathrm{arcsec}\left(c x \right)}{4 x^{4}}-\frac{3 c^{3} b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{32 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{3 c^{3} b}{32 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{c b}{32 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}-\frac{b}{16 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{5}}"," ",0,"-1/4*a/x^4-1/4*b/x^4*arcsec(c*x)-3/32*c^3*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*arctan(1/(c^2*x^2-1)^(1/2))+3/32*c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x-1/32*c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^3-1/16/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^5","B"
13,1,83,71,0.049000," ","int((a+b*arcsec(c*x))/x^6,x)","c^{5} \left(-\frac{a}{5 c^{5} x^{5}}+b \left(-\frac{\mathrm{arcsec}\left(c x \right)}{5 c^{5} x^{5}}+\frac{\left(c^{2} x^{2}-1\right) \left(8 c^{4} x^{4}+4 c^{2} x^{2}+3\right)}{75 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{6} x^{6}}\right)\right)"," ",0,"c^5*(-1/5*a/c^5/x^5+b*(-1/5/c^5/x^5*arcsec(c*x)+1/75*(c^2*x^2-1)*(8*c^4*x^4+4*c^2*x^2+3)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^6/x^6))","A"
14,1,174,88,0.051000," ","int((a+b*arcsec(c*x))/x^7,x)","-\frac{a}{6 x^{6}}-\frac{b \,\mathrm{arcsec}\left(c x \right)}{6 x^{6}}-\frac{5 c^{5} b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{96 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{5 c^{5} b}{96 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{5 c^{3} b}{288 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}-\frac{c b}{144 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{5}}-\frac{b}{36 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{7}}"," ",0,"-1/6*a/x^6-1/6*b/x^6*arcsec(c*x)-5/96*c^5*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*arctan(1/(c^2*x^2-1)^(1/2))+5/96*c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x-5/288*c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^3-1/144*c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^5-1/36/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^7","A"
15,1,208,93,0.229000," ","int(x^3*(a+b*arcsec(c*x))^2,x)","\frac{a^{2} x^{4}}{4}+\frac{b^{2} \mathrm{arcsec}\left(c x \right)^{2} x^{4}}{4}-\frac{b^{2} \mathrm{arcsec}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}{6 c}+\frac{b^{2} x^{2}}{12 c^{2}}-\frac{b^{2} \mathrm{arcsec}\left(c x \right) x \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{3 c^{3}}-\frac{b^{2} \ln \left(\frac{1}{c x}\right)}{3 c^{4}}+\frac{a b \,x^{4} \mathrm{arcsec}\left(c x \right)}{2}-\frac{a b \,x^{3}}{6 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{a b x}{6 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{a b}{3 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/4*a^2*x^4+1/4*b^2*arcsec(c*x)^2*x^4-1/6/c*b^2*arcsec(c*x)*((c^2*x^2-1)/c^2/x^2)^(1/2)*x^3+1/12*b^2*x^2/c^2-1/3/c^3*b^2*arcsec(c*x)*x*((c^2*x^2-1)/c^2/x^2)^(1/2)-1/3/c^4*b^2*ln(1/c/x)+1/2*a*b*x^4*arcsec(c*x)-1/6/c*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^3-1/6/c^3*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x+1/3/c^5*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x","B"
16,1,343,167,0.906000," ","int(x^2*(a+b*arcsec(c*x))^2,x)","\frac{x^{3} a^{2}}{3}+\frac{b^{2} x^{3} \mathrm{arcsec}\left(c x \right)^{2}}{3}-\frac{b^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \mathrm{arcsec}\left(c x \right) x^{2}}{3 c}+\frac{b^{2} x}{3 c^{2}}+\frac{b^{2} \mathrm{arcsec}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{3 c^{3}}-\frac{b^{2} \mathrm{arcsec}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{3 c^{3}}-\frac{i b^{2} \dilog \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{3 c^{3}}+\frac{i b^{2} \dilog \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{3 c^{3}}+\frac{2 x^{3} a b \,\mathrm{arcsec}\left(c x \right)}{3}-\frac{a b \,x^{2}}{3 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{a b}{3 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{a b \sqrt{c^{2} x^{2}-1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{3 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/3*x^3*a^2+1/3*b^2*x^3*arcsec(c*x)^2-1/3/c*b^2*((c^2*x^2-1)/c^2/x^2)^(1/2)*arcsec(c*x)*x^2+1/3*b^2*x/c^2+1/3/c^3*b^2*arcsec(c*x)*ln(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))-1/3/c^3*b^2*arcsec(c*x)*ln(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))-1/3*I/c^3*b^2*dilog(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+1/3*I/c^3*b^2*dilog(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+2/3*x^3*a*b*arcsec(c*x)-1/3/c*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2+1/3/c^3*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)-1/3/c^4*a*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*ln(c*x+(c^2*x^2-1)^(1/2))","B"
17,1,134,52,0.257000," ","int(x*(a+b*arcsec(c*x))^2,x)","\frac{a^{2} x^{2}}{2}+\frac{x^{2} b^{2} \mathrm{arcsec}\left(c x \right)^{2}}{2}-\frac{b^{2} \mathrm{arcsec}\left(c x \right) x \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{c}-\frac{b^{2} \ln \left(\frac{1}{c x}\right)}{c^{2}}+a b \,x^{2} \mathrm{arcsec}\left(c x \right)-\frac{a b x}{c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{a b}{c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/2*a^2*x^2+1/2*x^2*b^2*arcsec(c*x)^2-1/c*b^2*arcsec(c*x)*x*((c^2*x^2-1)/c^2/x^2)^(1/2)-1/c^2*b^2*ln(1/c/x)+a*b*x^2*arcsec(c*x)-1/c*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x+1/c^3*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x","B"
18,1,212,126,0.255000," ","int((a+b*arcsec(c*x))^2,x)","x \,b^{2} \mathrm{arcsec}\left(c x \right)^{2}+2 x a b \,\mathrm{arcsec}\left(c x \right)-\frac{2 b^{2} \mathrm{arcsec}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{c}+\frac{2 b^{2} \mathrm{arcsec}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{c}-\frac{2 i \dilog \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right) b^{2}}{c}+\frac{2 i \dilog \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right) b^{2}}{c}+a^{2} x -\frac{2 \ln \left(c x +c x \sqrt{1-\frac{1}{c^{2} x^{2}}}\right) a b}{c}"," ",0,"x*b^2*arcsec(c*x)^2+2*x*a*b*arcsec(c*x)-2/c*b^2*arcsec(c*x)*ln(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+2/c*b^2*arcsec(c*x)*ln(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))-2*I/c*dilog(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))*b^2+2*I/c*dilog(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))*b^2+a^2*x-2/c*ln(c*x+c*x*(1-1/c^2/x^2)^(1/2))*a*b","A"
19,1,215,132,0.215000," ","int((a+b*arcsec(c*x))^2/x,x)","a^{2} \ln \left(c x \right)+\frac{i b^{2} \mathrm{arcsec}\left(c x \right)^{3}}{3}-b^{2} \mathrm{arcsec}\left(c x \right)^{2} \ln \left(1+\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)+i b^{2} \mathrm{arcsec}\left(c x \right) \polylog \left(2, -\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)-\frac{b^{2} \polylog \left(3, -\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)}{2}+i a b \mathrm{arcsec}\left(c x \right)^{2}-2 a b \,\mathrm{arcsec}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)+i a b \polylog \left(2, -\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)"," ",0,"a^2*ln(c*x)+1/3*I*b^2*arcsec(c*x)^3-b^2*arcsec(c*x)^2*ln(1+(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)+I*b^2*arcsec(c*x)*polylog(2,-(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)-1/2*b^2*polylog(3,-(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)+I*a*b*arcsec(c*x)^2-2*a*b*arcsec(c*x)*ln(1+(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)+I*a*b*polylog(2,-(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)","A"
20,1,117,48,0.143000," ","int((a+b*arcsec(c*x))^2/x^2,x)","c \left(-\frac{a^{2}}{c x}+b^{2} \left(-\frac{\mathrm{arcsec}\left(c x \right)^{2}}{c x}+\frac{2}{c x}+2 \,\mathrm{arcsec}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\right)+2 a b \left(-\frac{\mathrm{arcsec}\left(c x \right)}{c x}+\frac{c^{2} x^{2}-1}{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{2} x^{2}}\right)\right)"," ",0,"c*(-a^2/c/x+b^2*(-1/c/x*arcsec(c*x)^2+2/c/x+2*arcsec(c*x)*((c^2*x^2-1)/c^2/x^2)^(1/2))+2*a*b*(-1/c/x*arcsec(c*x)+1/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^2/x^2*(c^2*x^2-1)))","B"
21,1,199,82,0.149000," ","int((a+b*arcsec(c*x))^2/x^3,x)","-\frac{a^{2}}{2 x^{2}}-\frac{b^{2} \mathrm{arcsec}\left(c x \right)^{2}}{2 x^{2}}+\frac{b^{2} c^{2} \mathrm{arcsec}\left(c x \right)^{2}}{4}+\frac{c \,b^{2} \mathrm{arcsec}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{2 x}-\frac{b^{2} c^{2}}{4}+\frac{b^{2}}{4 x^{2}}-\frac{a b \,\mathrm{arcsec}\left(c x \right)}{x^{2}}-\frac{c a b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{c a b}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{a b}{2 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}"," ",0,"-1/2*a^2/x^2-1/2*b^2/x^2*arcsec(c*x)^2+1/4*b^2*c^2*arcsec(c*x)^2+1/2*c*b^2*arcsec(c*x)/x*((c^2*x^2-1)/c^2/x^2)^(1/2)-1/4*b^2*c^2+1/4*b^2/x^2-a*b/x^2*arcsec(c*x)-1/2*c*a*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*arctan(1/(c^2*x^2-1)^(1/2))+1/2*c*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x-1/2/c*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^3","B"
22,1,154,88,0.485000," ","int((a+b*arcsec(c*x))^2/x^4,x)","c^{3} \left(-\frac{a^{2}}{3 c^{3} x^{3}}+b^{2} \left(-\frac{\mathrm{arcsec}\left(c x \right)^{2}}{3 c^{3} x^{3}}+\frac{2 \,\mathrm{arcsec}\left(c x \right) \left(2 c^{2} x^{2}+1\right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{9 c^{2} x^{2}}+\frac{2}{27 c^{3} x^{3}}+\frac{4}{9 c x}\right)+2 a b \left(-\frac{\mathrm{arcsec}\left(c x \right)}{3 c^{3} x^{3}}+\frac{\left(c^{2} x^{2}-1\right) \left(2 c^{2} x^{2}+1\right)}{9 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{4} x^{4}}\right)\right)"," ",0,"c^3*(-1/3*a^2/c^3/x^3+b^2*(-1/3/c^3/x^3*arcsec(c*x)^2+2/9*arcsec(c*x)*(2*c^2*x^2+1)/c^2/x^2*((c^2*x^2-1)/c^2/x^2)^(1/2)+2/27/c^3/x^3+4/9/c/x)+2*a*b*(-1/3/c^3/x^3*arcsec(c*x)+1/9*(c^2*x^2-1)*(2*c^2*x^2+1)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^4/x^4))","A"
23,1,265,116,0.430000," ","int((a+b*arcsec(c*x))^2/x^5,x)","-\frac{a^{2}}{4 x^{4}}-\frac{b^{2} \mathrm{arcsec}\left(c x \right)^{2}}{4 x^{4}}+\frac{3 b^{2} c^{4} \mathrm{arcsec}\left(c x \right)^{2}}{32}+\frac{3 c^{3} b^{2} \mathrm{arcsec}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{16 x}+\frac{c \,b^{2} \mathrm{arcsec}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{8 x^{3}}+\frac{b^{2}}{32 x^{4}}+\frac{3 b^{2} c^{2}}{32 x^{2}}-\frac{a b \,\mathrm{arcsec}\left(c x \right)}{2 x^{4}}-\frac{3 c^{3} a b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{3 c^{3} a b}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{c a b}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}-\frac{a b}{8 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{5}}"," ",0,"-1/4*a^2/x^4-1/4*b^2/x^4*arcsec(c*x)^2+3/32*b^2*c^4*arcsec(c*x)^2+3/16*c^3*b^2*arcsec(c*x)/x*((c^2*x^2-1)/c^2/x^2)^(1/2)+1/8*c*b^2*arcsec(c*x)/x^3*((c^2*x^2-1)/c^2/x^2)^(1/2)+1/32*b^2/x^4+3/32*b^2*c^2/x^2-1/2*a*b/x^4*arcsec(c*x)-3/16*c^3*a*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*arctan(1/(c^2*x^2-1)^(1/2))+3/16*c^3*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x-1/16*c*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^3-1/8/c*a*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^5","B"
24,1,447,215,1.019000," ","int(x^3*(a+b*arcsec(c*x))^3,x)","\frac{x^{4} a^{3}}{4}+\frac{b^{3} \mathrm{arcsec}\left(c x \right)^{3} x^{4}}{4}-\frac{b^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \mathrm{arcsec}\left(c x \right)^{2} x^{3}}{4 c}-\frac{b^{3} \mathrm{arcsec}\left(c x \right)^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}{2 c^{3}}+\frac{i b^{3} \mathrm{arcsec}\left(c x \right)^{2}}{2 c^{4}}+\frac{b^{3} \mathrm{arcsec}\left(c x \right) x^{2}}{4 c^{2}}-\frac{b^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}{4 c^{3}}+\frac{i b^{3} \polylog \left(2, -\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)}{2 c^{4}}-\frac{b^{3} \mathrm{arcsec}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)}{c^{4}}-\frac{i b^{3}}{4 c^{4}}+\frac{3 a^{2} b \,x^{4} \mathrm{arcsec}\left(c x \right)}{4}-\frac{a^{2} b \,x^{3}}{4 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{a^{2} b x}{4 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{a^{2} b}{2 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{3 a \,b^{2} \mathrm{arcsec}\left(c x \right)^{2} x^{4}}{4}-\frac{a \,b^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \mathrm{arcsec}\left(c x \right) x^{3}}{2 c}+\frac{x^{2} a \,b^{2}}{4 c^{2}}-\frac{a \,b^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \mathrm{arcsec}\left(c x \right) x}{c^{3}}-\frac{a \,b^{2} \ln \left(\frac{1}{c x}\right)}{c^{4}}"," ",0,"1/4*x^4*a^3+1/4*b^3*arcsec(c*x)^3*x^4-1/4/c*b^3*((c^2*x^2-1)/c^2/x^2)^(1/2)*arcsec(c*x)^2*x^3-1/2/c^3*b^3*arcsec(c*x)^2*((c^2*x^2-1)/c^2/x^2)^(1/2)*x+1/2*I/c^4*b^3*arcsec(c*x)^2+1/4/c^2*b^3*arcsec(c*x)*x^2-1/4/c^3*b^3*((c^2*x^2-1)/c^2/x^2)^(1/2)*x-1/4*I/c^4*b^3-1/c^4*b^3*arcsec(c*x)*ln(1+(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)+1/2*I*b^3*polylog(2,-(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)/c^4+3/4*a^2*b*x^4*arcsec(c*x)-1/4/c*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^3-1/4/c^3*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x+1/2/c^5*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x+3/4*a*b^2*arcsec(c*x)^2*x^4-1/2/c*a*b^2*((c^2*x^2-1)/c^2/x^2)^(1/2)*arcsec(c*x)*x^3+1/4/c^2*x^2*a*b^2-1/c^3*a*b^2*((c^2*x^2-1)/c^2/x^2)^(1/2)*arcsec(c*x)*x-1/c^4*a*b^2*ln(1/c/x)","B"
25,1,687,286,1.047000," ","int(x^2*(a+b*arcsec(c*x))^3,x)","\frac{a^{3} x^{3}}{3}+\frac{x^{3} b^{3} \mathrm{arcsec}\left(c x \right)^{3}}{3}-\frac{b^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \mathrm{arcsec}\left(c x \right)^{2} x^{2}}{2 c}+\frac{b^{3} \mathrm{arcsec}\left(c x \right) x}{c^{2}}-\frac{b^{3} \mathrm{arcsec}\left(c x \right)^{2} \ln \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{2 c^{3}}-\frac{i a \,b^{2} \dilog \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{c^{3}}-\frac{b^{3} \polylog \left(3, i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{c^{3}}+\frac{b^{3} \mathrm{arcsec}\left(c x \right)^{2} \ln \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{2 c^{3}}-\frac{i b^{3} \mathrm{arcsec}\left(c x \right) \polylog \left(2, -i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{c^{3}}+\frac{b^{3} \polylog \left(3, -i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{c^{3}}+\frac{i b^{3} \mathrm{arcsec}\left(c x \right) \polylog \left(2, i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{c^{3}}+b^{2} x^{3} a \mathrm{arcsec}\left(c x \right)^{2}-\frac{a \,b^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \mathrm{arcsec}\left(c x \right) x^{2}}{c}-\frac{a \,b^{2} \mathrm{arcsec}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{c^{3}}+\frac{a \,b^{2} \mathrm{arcsec}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{c^{3}}+\frac{i a \,b^{2} \dilog \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{c^{3}}+\frac{2 i b^{3} \arctan \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c^{3}}+\frac{a \,b^{2} x}{c^{2}}+x^{3} a^{2} b \,\mathrm{arcsec}\left(c x \right)-\frac{a^{2} b \,x^{2}}{2 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{a^{2} b}{2 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{a^{2} b \sqrt{c^{2} x^{2}-1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{2 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/3*a^3*x^3+1/3*x^3*b^3*arcsec(c*x)^3-1/2/c*b^3*((c^2*x^2-1)/c^2/x^2)^(1/2)*arcsec(c*x)^2*x^2+1/c^2*b^3*arcsec(c*x)*x-1/2/c^3*b^3*arcsec(c*x)^2*ln(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))-I/c^3*a*b^2*dilog(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))-b^3*polylog(3,I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))/c^3+1/2/c^3*b^3*arcsec(c*x)^2*ln(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))-I/c^3*b^3*arcsec(c*x)*polylog(2,-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+b^3*polylog(3,-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))/c^3+I/c^3*b^3*arcsec(c*x)*polylog(2,I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+b^2*x^3*a*arcsec(c*x)^2-1/c*a*b^2*((c^2*x^2-1)/c^2/x^2)^(1/2)*arcsec(c*x)*x^2-1/c^3*a*b^2*arcsec(c*x)*ln(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+1/c^3*a*b^2*arcsec(c*x)*ln(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+2*I/c^3*b^3*arctan(1/c/x+I*(1-1/c^2/x^2)^(1/2))+I/c^3*a*b^2*dilog(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+a*b^2*x/c^2+x^3*a^2*b*arcsec(c*x)-1/2/c*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2+1/2/c^3*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)-1/2/c^4*a^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*ln(c*x+(c^2*x^2-1)^(1/2))","B"
26,1,285,144,0.796000," ","int(x*(a+b*arcsec(c*x))^3,x)","\frac{x^{2} a^{3}}{2}+\frac{x^{2} b^{3} \mathrm{arcsec}\left(c x \right)^{3}}{2}-\frac{3 b^{3} \mathrm{arcsec}\left(c x \right)^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}{2 c}+\frac{3 i b^{3} \mathrm{arcsec}\left(c x \right)^{2}}{2 c^{2}}-\frac{3 b^{3} \mathrm{arcsec}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)}{c^{2}}+\frac{3 i b^{3} \polylog \left(2, -\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)}{2 c^{2}}+\frac{3 x^{2} a \,b^{2} \mathrm{arcsec}\left(c x \right)^{2}}{2}-\frac{3 a \,b^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \mathrm{arcsec}\left(c x \right) x}{c}-\frac{3 a \,b^{2} \ln \left(\frac{1}{c x}\right)}{c^{2}}+\frac{3 a^{2} b \,x^{2} \mathrm{arcsec}\left(c x \right)}{2}-\frac{3 a^{2} b x}{2 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{3 a^{2} b}{2 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/2*x^2*a^3+1/2*x^2*b^3*arcsec(c*x)^3-3/2/c*b^3*arcsec(c*x)^2*((c^2*x^2-1)/c^2/x^2)^(1/2)*x+3/2*I/c^2*b^3*arcsec(c*x)^2-3/c^2*b^3*arcsec(c*x)*ln(1+(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)+3/2*I*b^3*polylog(2,-(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)/c^2+3/2*x^2*a*b^2*arcsec(c*x)^2-3/c*a*b^2*((c^2*x^2-1)/c^2/x^2)^(1/2)*arcsec(c*x)*x-3/c^2*a*b^2*ln(1/c/x)+3/2*a^2*b*x^2*arcsec(c*x)-3/2/c*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x+3/2/c^3*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x","A"
27,0,0,216,0.622000," ","int((a+b*arcsec(c*x))^3,x)","\int \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)^{3}\, dx"," ",0,"int((a+b*arcsec(c*x))^3,x)","F"
28,1,390,177,0.263000," ","int((a+b*arcsec(c*x))^3/x,x)","a^{3} \ln \left(c x \right)+\frac{i b^{3} \mathrm{arcsec}\left(c x \right)^{4}}{4}-b^{3} \mathrm{arcsec}\left(c x \right)^{3} \ln \left(1+\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)+\frac{3 i b^{3} \mathrm{arcsec}\left(c x \right)^{2} \polylog \left(2, -\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)}{2}-\frac{3 b^{3} \mathrm{arcsec}\left(c x \right) \polylog \left(3, -\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)}{2}-\frac{3 i b^{3} \polylog \left(4, -\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)}{4}+i a \,b^{2} \mathrm{arcsec}\left(c x \right)^{3}-3 a \,b^{2} \mathrm{arcsec}\left(c x \right)^{2} \ln \left(1+\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)+3 i a \,b^{2} \mathrm{arcsec}\left(c x \right) \polylog \left(2, -\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)-\frac{3 a \,b^{2} \polylog \left(3, -\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)}{2}+\frac{3 i a^{2} b \mathrm{arcsec}\left(c x \right)^{2}}{2}-3 a^{2} b \,\mathrm{arcsec}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)+\frac{3 i a^{2} b \polylog \left(2, -\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)}{2}"," ",0,"a^3*ln(c*x)+1/4*I*b^3*arcsec(c*x)^4-b^3*arcsec(c*x)^3*ln(1+(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)+3/2*I*b^3*arcsec(c*x)^2*polylog(2,-(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)-3/2*b^3*arcsec(c*x)*polylog(3,-(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)-3/4*I*b^3*polylog(4,-(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)+I*a*b^2*arcsec(c*x)^3-3*a*b^2*arcsec(c*x)^2*ln(1+(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)+3*I*a*b^2*arcsec(c*x)*polylog(2,-(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)-3/2*a*b^2*polylog(3,-(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)+3/2*I*a^2*b*arcsec(c*x)^2-3*a^2*b*arcsec(c*x)*ln(1+(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)+3/2*I*a^2*b*polylog(2,-(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)","B"
29,1,198,76,0.181000," ","int((a+b*arcsec(c*x))^3/x^2,x)","c \left(-\frac{a^{3}}{c x}+b^{3} \left(-\frac{\mathrm{arcsec}\left(c x \right)^{3}}{c x}+3 \mathrm{arcsec}\left(c x \right)^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}-6 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}+\frac{6 \,\mathrm{arcsec}\left(c x \right)}{c x}\right)+3 a \,b^{2} \left(-\frac{\mathrm{arcsec}\left(c x \right)^{2}}{c x}+\frac{2}{c x}+2 \,\mathrm{arcsec}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\right)+3 a^{2} b \left(-\frac{\mathrm{arcsec}\left(c x \right)}{c x}+\frac{c^{2} x^{2}-1}{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{2} x^{2}}\right)\right)"," ",0,"c*(-a^3/c/x+b^3*(-1/c/x*arcsec(c*x)^3+3*arcsec(c*x)^2*((c^2*x^2-1)/c^2/x^2)^(1/2)-6*((c^2*x^2-1)/c^2/x^2)^(1/2)+6/c/x*arcsec(c*x))+3*a*b^2*(-1/c/x*arcsec(c*x)^2+2/c/x+2*arcsec(c*x)*((c^2*x^2-1)/c^2/x^2)^(1/2))+3*a^2*b*(-1/c/x*arcsec(c*x)+1/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^2/x^2*(c^2*x^2-1)))","B"
30,1,324,121,0.374000," ","int((a+b*arcsec(c*x))^3/x^3,x)","-\frac{a^{3}}{2 x^{2}}-\frac{b^{3} \mathrm{arcsec}\left(c x \right)^{3}}{2 x^{2}}+\frac{c^{2} b^{3} \mathrm{arcsec}\left(c x \right)^{3}}{4}+\frac{3 c \,b^{3} \mathrm{arcsec}\left(c x \right)^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{4 x}+\frac{3 b^{3} \mathrm{arcsec}\left(c x \right)}{4 x^{2}}-\frac{3 c \,b^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{8 x}-\frac{3 b^{3} c^{2} \mathrm{arcsec}\left(c x \right)}{8}-\frac{3 a \,b^{2} \mathrm{arcsec}\left(c x \right)^{2}}{2 x^{2}}+\frac{3 c^{2} a \,b^{2} \mathrm{arcsec}\left(c x \right)^{2}}{4}+\frac{3 c a \,b^{2} \mathrm{arcsec}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{2 x}-\frac{3 c^{2} a \,b^{2}}{4}+\frac{3 a \,b^{2}}{4 x^{2}}-\frac{3 a^{2} b \,\mathrm{arcsec}\left(c x \right)}{2 x^{2}}-\frac{3 c \,a^{2} b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{3 c \,a^{2} b}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{3 a^{2} b}{4 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}"," ",0,"-1/2*a^3/x^2-1/2*b^3/x^2*arcsec(c*x)^3+1/4*c^2*b^3*arcsec(c*x)^3+3/4*c*b^3*arcsec(c*x)^2/x*((c^2*x^2-1)/c^2/x^2)^(1/2)+3/4*b^3/x^2*arcsec(c*x)-3/8*c*b^3*((c^2*x^2-1)/c^2/x^2)^(1/2)/x-3/8*b^3*c^2*arcsec(c*x)-3/2*a*b^2/x^2*arcsec(c*x)^2+3/4*c^2*a*b^2*arcsec(c*x)^2+3/2*c*a*b^2*arcsec(c*x)/x*((c^2*x^2-1)/c^2/x^2)^(1/2)-3/4*c^2*a*b^2+3/4*a*b^2/x^2-3/2*a^2*b/x^2*arcsec(c*x)-3/4*c*a^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*arctan(1/(c^2*x^2-1)^(1/2))+3/4*c*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x-3/4/c*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^3","B"
31,1,299,148,0.594000," ","int((a+b*arcsec(c*x))^3/x^4,x)","c^{3} \left(-\frac{a^{3}}{3 c^{3} x^{3}}+b^{3} \left(-\frac{\mathrm{arcsec}\left(c x \right)^{3}}{3 c^{3} x^{3}}+\frac{\mathrm{arcsec}\left(c x \right)^{2} \left(2 c^{2} x^{2}+1\right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{3 c^{2} x^{2}}-\frac{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{3}+\frac{4 \,\mathrm{arcsec}\left(c x \right)}{3 c x}+\frac{2 \,\mathrm{arcsec}\left(c x \right)}{9 c^{3} x^{3}}-\frac{2 \left(2 c^{2} x^{2}+1\right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{27 c^{2} x^{2}}\right)+3 a \,b^{2} \left(-\frac{\mathrm{arcsec}\left(c x \right)^{2}}{3 c^{3} x^{3}}+\frac{2 \,\mathrm{arcsec}\left(c x \right) \left(2 c^{2} x^{2}+1\right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{9 c^{2} x^{2}}+\frac{2}{27 c^{3} x^{3}}+\frac{4}{9 c x}\right)+3 a^{2} b \left(-\frac{\mathrm{arcsec}\left(c x \right)}{3 c^{3} x^{3}}+\frac{\left(c^{2} x^{2}-1\right) \left(2 c^{2} x^{2}+1\right)}{9 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{4} x^{4}}\right)\right)"," ",0,"c^3*(-1/3*a^3/c^3/x^3+b^3*(-1/3/c^3/x^3*arcsec(c*x)^3+1/3*arcsec(c*x)^2*(2*c^2*x^2+1)/c^2/x^2*((c^2*x^2-1)/c^2/x^2)^(1/2)-4/3*((c^2*x^2-1)/c^2/x^2)^(1/2)+4/3/c/x*arcsec(c*x)+2/9/c^3/x^3*arcsec(c*x)-2/27*(2*c^2*x^2+1)/c^2/x^2*((c^2*x^2-1)/c^2/x^2)^(1/2))+3*a*b^2*(-1/3/c^3/x^3*arcsec(c*x)^2+2/9*arcsec(c*x)*(2*c^2*x^2+1)/c^2/x^2*((c^2*x^2-1)/c^2/x^2)^(1/2)+2/27/c^3/x^3+4/9/c/x)+3*a^2*b*(-1/3/c^3/x^3*arcsec(c*x)+1/9*(c^2*x^2-1)*(2*c^2*x^2+1)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^4/x^4))","B"
32,1,472,182,0.641000," ","int((a+b*arcsec(c*x))^3/x^5,x)","-\frac{a^{3}}{4 x^{4}}-\frac{b^{3} \mathrm{arcsec}\left(c x \right)^{3}}{4 x^{4}}+\frac{3 c^{4} b^{3} \mathrm{arcsec}\left(c x \right)^{3}}{32}+\frac{9 c^{3} b^{3} \mathrm{arcsec}\left(c x \right)^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{32 x}+\frac{3 c \,b^{3} \mathrm{arcsec}\left(c x \right)^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{16 x^{3}}+\frac{3 b^{3} \mathrm{arcsec}\left(c x \right)}{32 x^{4}}-\frac{45 c^{3} b^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{256 x}-\frac{3 c \,b^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{128 x^{3}}-\frac{45 b^{3} c^{4} \mathrm{arcsec}\left(c x \right)}{256}+\frac{9 c^{2} b^{3} \mathrm{arcsec}\left(c x \right)}{32 x^{2}}-\frac{3 a \,b^{2} \mathrm{arcsec}\left(c x \right)^{2}}{4 x^{4}}+\frac{9 c^{4} a \,b^{2} \mathrm{arcsec}\left(c x \right)^{2}}{32}+\frac{9 c^{3} a \,b^{2} \mathrm{arcsec}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{16 x}+\frac{3 c a \,b^{2} \mathrm{arcsec}\left(c x \right) \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{8 x^{3}}+\frac{3 a \,b^{2}}{32 x^{4}}+\frac{9 c^{2} a \,b^{2}}{32 x^{2}}-\frac{3 a^{2} b \,\mathrm{arcsec}\left(c x \right)}{4 x^{4}}-\frac{9 c^{3} a^{2} b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{32 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{9 c^{3} a^{2} b}{32 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{3 c \,a^{2} b}{32 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}-\frac{3 a^{2} b}{16 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{5}}"," ",0,"-1/4*a^3/x^4-1/4*b^3/x^4*arcsec(c*x)^3+3/32*c^4*b^3*arcsec(c*x)^3+9/32*c^3*b^3*arcsec(c*x)^2/x*((c^2*x^2-1)/c^2/x^2)^(1/2)+3/16*c*b^3*arcsec(c*x)^2/x^3*((c^2*x^2-1)/c^2/x^2)^(1/2)+3/32*b^3/x^4*arcsec(c*x)-45/256*c^3*b^3*((c^2*x^2-1)/c^2/x^2)^(1/2)/x-3/128*c*b^3/x^3*((c^2*x^2-1)/c^2/x^2)^(1/2)-45/256*b^3*c^4*arcsec(c*x)+9/32*c^2*b^3/x^2*arcsec(c*x)-3/4*a*b^2/x^4*arcsec(c*x)^2+9/32*c^4*a*b^2*arcsec(c*x)^2+9/16*c^3*a*b^2*arcsec(c*x)/x*((c^2*x^2-1)/c^2/x^2)^(1/2)+3/8*c*a*b^2*arcsec(c*x)/x^3*((c^2*x^2-1)/c^2/x^2)^(1/2)+3/32*a*b^2/x^4+9/32*c^2*a*b^2/x^2-3/4*a^2*b/x^4*arcsec(c*x)-9/32*c^3*a^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*arctan(1/(c^2*x^2-1)^(1/2))+9/32*c^3*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x-3/32*c*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^3-3/16/c*a^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^5","B"
33,0,0,14,2.017000," ","int(x/(a+b*arcsec(c*x)),x)","\int \frac{x}{a +b \,\mathrm{arcsec}\left(c x \right)}\, dx"," ",0,"int(x/(a+b*arcsec(c*x)),x)","F"
34,0,0,12,0.611000," ","int(1/(a+b*arcsec(c*x)),x)","\int \frac{1}{a +b \,\mathrm{arcsec}\left(c x \right)}\, dx"," ",0,"int(1/(a+b*arcsec(c*x)),x)","F"
35,0,0,16,0.924000," ","int(1/x/(a+b*arcsec(c*x)),x)","\int \frac{1}{x \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}\, dx"," ",0,"int(1/x/(a+b*arcsec(c*x)),x)","F"
36,1,47,46,0.140000," ","int(1/x^2/(a+b*arcsec(c*x)),x)","c \left(\frac{\Si \left(\frac{a}{b}+\mathrm{arcsec}\left(c x \right)\right) \cos \left(\frac{a}{b}\right)}{b}-\frac{\Ci \left(\frac{a}{b}+\mathrm{arcsec}\left(c x \right)\right) \sin \left(\frac{a}{b}\right)}{b}\right)"," ",0,"c*(Si(a/b+arcsec(c*x))*cos(a/b)/b-Ci(a/b+arcsec(c*x))*sin(a/b)/b)","A"
37,1,58,59,0.103000," ","int(1/x^3/(a+b*arcsec(c*x)),x)","c^{2} \left(\frac{\Si \left(\frac{2 a}{b}+2 \,\mathrm{arcsec}\left(c x \right)\right) \cos \left(\frac{2 a}{b}\right)}{2 b}-\frac{\Ci \left(\frac{2 a}{b}+2 \,\mathrm{arcsec}\left(c x \right)\right) \sin \left(\frac{2 a}{b}\right)}{2 b}\right)"," ",0,"c^2*(1/2*Si(2*a/b+2*arcsec(c*x))*cos(2*a/b)/b-1/2*Ci(2*a/b+2*arcsec(c*x))*sin(2*a/b)/b)","A"
38,1,102,109,0.106000," ","int(1/x^4/(a+b*arcsec(c*x)),x)","c^{3} \left(\frac{\Si \left(\frac{3 a}{b}+3 \,\mathrm{arcsec}\left(c x \right)\right) \cos \left(\frac{3 a}{b}\right)}{4 b}-\frac{\Ci \left(\frac{3 a}{b}+3 \,\mathrm{arcsec}\left(c x \right)\right) \sin \left(\frac{3 a}{b}\right)}{4 b}+\frac{\Si \left(\frac{a}{b}+\mathrm{arcsec}\left(c x \right)\right) \cos \left(\frac{a}{b}\right)}{4 b}-\frac{\Ci \left(\frac{a}{b}+\mathrm{arcsec}\left(c x \right)\right) \sin \left(\frac{a}{b}\right)}{4 b}\right)"," ",0,"c^3*(1/4*Si(3*a/b+3*arcsec(c*x))*cos(3*a/b)/b-1/4*Ci(3*a/b+3*arcsec(c*x))*sin(3*a/b)/b+1/4*Si(a/b+arcsec(c*x))*cos(a/b)/b-1/4*Ci(a/b+arcsec(c*x))*sin(a/b)/b)","A"
39,0,0,14,2.241000," ","int(x/(a+b*arcsec(c*x))^2,x)","\int \frac{x}{\left(a +b \,\mathrm{arcsec}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(x/(a+b*arcsec(c*x))^2,x)","F"
40,0,0,12,0.593000," ","int(1/(a+b*arcsec(c*x))^2,x)","\int \frac{1}{\left(a +b \,\mathrm{arcsec}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(a+b*arcsec(c*x))^2,x)","F"
41,0,0,16,1.003000," ","int(1/x/(a+b*arcsec(c*x))^2,x)","\int \frac{1}{x \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/x/(a+b*arcsec(c*x))^2,x)","F"
42,1,78,73,0.150000," ","int(1/x^2/(a+b*arcsec(c*x))^2,x)","c \left(-\frac{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{\left(a +b \,\mathrm{arcsec}\left(c x \right)\right) b}+\frac{\Si \left(\frac{a}{b}+\mathrm{arcsec}\left(c x \right)\right) \sin \left(\frac{a}{b}\right)+\Ci \left(\frac{a}{b}+\mathrm{arcsec}\left(c x \right)\right) \cos \left(\frac{a}{b}\right)}{b^{2}}\right)"," ",0,"c*(-((c^2*x^2-1)/c^2/x^2)^(1/2)/(a+b*arcsec(c*x))/b+(Si(a/b+arcsec(c*x))*sin(a/b)+Ci(a/b+arcsec(c*x))*cos(a/b))/b^2)","A"
43,1,77,82,0.105000," ","int(1/x^3/(a+b*arcsec(c*x))^2,x)","c^{2} \left(-\frac{\sin \left(2 \,\mathrm{arcsec}\left(c x \right)\right)}{2 \left(a +b \,\mathrm{arcsec}\left(c x \right)\right) b}+\frac{\Si \left(\frac{2 a}{b}+2 \,\mathrm{arcsec}\left(c x \right)\right) \sin \left(\frac{2 a}{b}\right)+\Ci \left(\frac{2 a}{b}+2 \,\mathrm{arcsec}\left(c x \right)\right) \cos \left(\frac{2 a}{b}\right)}{b^{2}}\right)"," ",0,"c^2*(-1/2*sin(2*arcsec(c*x))/(a+b*arcsec(c*x))/b+(Si(2*a/b+2*arcsec(c*x))*sin(2*a/b)+Ci(2*a/b+2*arcsec(c*x))*cos(2*a/b))/b^2)","A"
44,1,153,164,0.114000," ","int(1/x^4/(a+b*arcsec(c*x))^2,x)","c^{3} \left(-\frac{\sin \left(3 \,\mathrm{arcsec}\left(c x \right)\right)}{4 \left(a +b \,\mathrm{arcsec}\left(c x \right)\right) b}+\frac{\frac{3 \Si \left(\frac{3 a}{b}+3 \,\mathrm{arcsec}\left(c x \right)\right) \sin \left(\frac{3 a}{b}\right)}{4}+\frac{3 \Ci \left(\frac{3 a}{b}+3 \,\mathrm{arcsec}\left(c x \right)\right) \cos \left(\frac{3 a}{b}\right)}{4}}{b^{2}}-\frac{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{4 \left(a +b \,\mathrm{arcsec}\left(c x \right)\right) b}+\frac{\Si \left(\frac{a}{b}+\mathrm{arcsec}\left(c x \right)\right) \sin \left(\frac{a}{b}\right)+\Ci \left(\frac{a}{b}+\mathrm{arcsec}\left(c x \right)\right) \cos \left(\frac{a}{b}\right)}{4 b^{2}}\right)"," ",0,"c^3*(-1/4*sin(3*arcsec(c*x))/(a+b*arcsec(c*x))/b+3/4*(Si(3*a/b+3*arcsec(c*x))*sin(3*a/b)+Ci(3*a/b+3*arcsec(c*x))*cos(3*a/b))/b^2-1/4*((c^2*x^2-1)/c^2/x^2)^(1/2)/(a+b*arcsec(c*x))/b+1/4*(Si(a/b+arcsec(c*x))*sin(a/b)+Ci(a/b+arcsec(c*x))*cos(a/b))/b^2)","A"
45,0,0,14,2.550000," ","int(x/(a+b*arcsec(c*x))^3,x)","\int \frac{x}{\left(a +b \,\mathrm{arcsec}\left(c x \right)\right)^{3}}\, dx"," ",0,"int(x/(a+b*arcsec(c*x))^3,x)","F"
46,0,0,12,0.689000," ","int(1/(a+b*arcsec(c*x))^3,x)","\int \frac{1}{\left(a +b \,\mathrm{arcsec}\left(c x \right)\right)^{3}}\, dx"," ",0,"int(1/(a+b*arcsec(c*x))^3,x)","F"
47,0,0,16,1.183000," ","int(1/x/(a+b*arcsec(c*x))^3,x)","\int \frac{1}{x \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)^{3}}\, dx"," ",0,"int(1/x/(a+b*arcsec(c*x))^3,x)","F"
48,1,154,93,0.156000," ","int(1/x^2/(a+b*arcsec(c*x))^3,x)","c \left(-\frac{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{2 \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)^{2} b}-\frac{\mathrm{arcsec}\left(c x \right) \Si \left(\frac{a}{b}+\mathrm{arcsec}\left(c x \right)\right) \cos \left(\frac{a}{b}\right) c x b -\mathrm{arcsec}\left(c x \right) \Ci \left(\frac{a}{b}+\mathrm{arcsec}\left(c x \right)\right) \sin \left(\frac{a}{b}\right) c x b +\Si \left(\frac{a}{b}+\mathrm{arcsec}\left(c x \right)\right) \cos \left(\frac{a}{b}\right) c x a -\Ci \left(\frac{a}{b}+\mathrm{arcsec}\left(c x \right)\right) \sin \left(\frac{a}{b}\right) c x a +b}{2 c x \left(a +b \,\mathrm{arcsec}\left(c x \right)\right) b^{3}}\right)"," ",0,"c*(-1/2*((c^2*x^2-1)/c^2/x^2)^(1/2)/(a+b*arcsec(c*x))^2/b-1/2*(arcsec(c*x)*Si(a/b+arcsec(c*x))*cos(a/b)*c*x*b-arcsec(c*x)*Ci(a/b+arcsec(c*x))*sin(a/b)*c*x*b+Si(a/b+arcsec(c*x))*cos(a/b)*c*x*a-Ci(a/b+arcsec(c*x))*sin(a/b)*c*x*a+b)/c/x/(a+b*arcsec(c*x))/b^3)","A"
49,1,157,108,0.107000," ","int(1/x^3/(a+b*arcsec(c*x))^3,x)","c^{2} \left(-\frac{\sin \left(2 \,\mathrm{arcsec}\left(c x \right)\right)}{4 \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)^{2} b}-\frac{2 \,\mathrm{arcsec}\left(c x \right) \Si \left(\frac{2 a}{b}+2 \,\mathrm{arcsec}\left(c x \right)\right) \cos \left(\frac{2 a}{b}\right) b -2 \,\mathrm{arcsec}\left(c x \right) \Ci \left(\frac{2 a}{b}+2 \,\mathrm{arcsec}\left(c x \right)\right) \sin \left(\frac{2 a}{b}\right) b +2 \Si \left(\frac{2 a}{b}+2 \,\mathrm{arcsec}\left(c x \right)\right) \cos \left(\frac{2 a}{b}\right) a -2 \Ci \left(\frac{2 a}{b}+2 \,\mathrm{arcsec}\left(c x \right)\right) \sin \left(\frac{2 a}{b}\right) a +\cos \left(2 \,\mathrm{arcsec}\left(c x \right)\right) b}{2 \left(a +b \,\mathrm{arcsec}\left(c x \right)\right) b^{3}}\right)"," ",0,"c^2*(-1/4*sin(2*arcsec(c*x))/(a+b*arcsec(c*x))^2/b-1/2*(2*arcsec(c*x)*Si(2*a/b+2*arcsec(c*x))*cos(2*a/b)*b-2*arcsec(c*x)*Ci(2*a/b+2*arcsec(c*x))*sin(2*a/b)*b+2*Si(2*a/b+2*arcsec(c*x))*cos(2*a/b)*a-2*Ci(2*a/b+2*arcsec(c*x))*sin(2*a/b)*a+cos(2*arcsec(c*x))*b)/(a+b*arcsec(c*x))/b^3)","A"
50,1,307,210,0.121000," ","int(1/x^4/(a+b*arcsec(c*x))^3,x)","c^{3} \left(-\frac{\sin \left(3 \,\mathrm{arcsec}\left(c x \right)\right)}{8 \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)^{2} b}-\frac{3 \left(3 \,\mathrm{arcsec}\left(c x \right) \Si \left(\frac{3 a}{b}+3 \,\mathrm{arcsec}\left(c x \right)\right) \cos \left(\frac{3 a}{b}\right) b -3 \,\mathrm{arcsec}\left(c x \right) \Ci \left(\frac{3 a}{b}+3 \,\mathrm{arcsec}\left(c x \right)\right) \sin \left(\frac{3 a}{b}\right) b +3 \Si \left(\frac{3 a}{b}+3 \,\mathrm{arcsec}\left(c x \right)\right) \cos \left(\frac{3 a}{b}\right) a -3 \Ci \left(\frac{3 a}{b}+3 \,\mathrm{arcsec}\left(c x \right)\right) \sin \left(\frac{3 a}{b}\right) a +\cos \left(3 \,\mathrm{arcsec}\left(c x \right)\right) b \right)}{8 \left(a +b \,\mathrm{arcsec}\left(c x \right)\right) b^{3}}-\frac{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{8 \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)^{2} b}-\frac{\mathrm{arcsec}\left(c x \right) \Si \left(\frac{a}{b}+\mathrm{arcsec}\left(c x \right)\right) \cos \left(\frac{a}{b}\right) c x b -\mathrm{arcsec}\left(c x \right) \Ci \left(\frac{a}{b}+\mathrm{arcsec}\left(c x \right)\right) \sin \left(\frac{a}{b}\right) c x b +\Si \left(\frac{a}{b}+\mathrm{arcsec}\left(c x \right)\right) \cos \left(\frac{a}{b}\right) c x a -\Ci \left(\frac{a}{b}+\mathrm{arcsec}\left(c x \right)\right) \sin \left(\frac{a}{b}\right) c x a +b}{8 c x \left(a +b \,\mathrm{arcsec}\left(c x \right)\right) b^{3}}\right)"," ",0,"c^3*(-1/8*sin(3*arcsec(c*x))/(a+b*arcsec(c*x))^2/b-3/8*(3*arcsec(c*x)*Si(3*a/b+3*arcsec(c*x))*cos(3*a/b)*b-3*arcsec(c*x)*Ci(3*a/b+3*arcsec(c*x))*sin(3*a/b)*b+3*Si(3*a/b+3*arcsec(c*x))*cos(3*a/b)*a-3*Ci(3*a/b+3*arcsec(c*x))*sin(3*a/b)*a+cos(3*arcsec(c*x))*b)/(a+b*arcsec(c*x))/b^3-1/8*((c^2*x^2-1)/c^2/x^2)^(1/2)/(a+b*arcsec(c*x))^2/b-1/8*(arcsec(c*x)*Si(a/b+arcsec(c*x))*cos(a/b)*c*x*b-arcsec(c*x)*Ci(a/b+arcsec(c*x))*sin(a/b)*c*x*b+Si(a/b+arcsec(c*x))*cos(a/b)*c*x*a-Ci(a/b+arcsec(c*x))*sin(a/b)*c*x*a+b)/c/x/(a+b*arcsec(c*x))/b^3)","A"
51,0,0,18,3.314000," ","int((d*x)^m*(a+b*arcsec(c*x))^3,x)","\int \left(d x \right)^{m} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)^{3}\, dx"," ",0,"int((d*x)^m*(a+b*arcsec(c*x))^3,x)","F"
52,0,0,18,3.118000," ","int((d*x)^m*(a+b*arcsec(c*x))^2,x)","\int \left(d x \right)^{m} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)^{2}\, dx"," ",0,"int((d*x)^m*(a+b*arcsec(c*x))^2,x)","F"
53,0,0,63,4.371000," ","int((d*x)^m*(a+b*arcsec(c*x)),x)","\int \left(d x \right)^{m} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)\, dx"," ",0,"int((d*x)^m*(a+b*arcsec(c*x)),x)","F"
54,0,0,18,3.829000," ","int((d*x)^m/(a+b*arcsec(c*x)),x)","\int \frac{\left(d x \right)^{m}}{a +b \,\mathrm{arcsec}\left(c x \right)}\, dx"," ",0,"int((d*x)^m/(a+b*arcsec(c*x)),x)","F"
55,0,0,18,2.131000," ","int((d*x)^m/(a+b*arcsec(c*x))^2,x)","\int \frac{\left(d x \right)^{m}}{\left(a +b \,\mathrm{arcsec}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((d*x)^m/(a+b*arcsec(c*x))^2,x)","F"
56,1,486,147,0.056000," ","int((e*x+d)^3*(a+b*arcsec(c*x)),x)","\frac{a \,e^{3} x^{4}}{4}+a \,e^{2} x^{3} d +\frac{3 a e \,x^{2} d^{2}}{2}+a x \,d^{3}+\frac{a \,d^{4}}{4 e}+\frac{b \,e^{3} \mathrm{arcsec}\left(c x \right) x^{4}}{4}+b \,e^{2} \mathrm{arcsec}\left(c x \right) x^{3} d +\frac{3 b e \,\mathrm{arcsec}\left(c x \right) x^{2} d^{2}}{2}+b \,\mathrm{arcsec}\left(c x \right) x \,d^{3}+\frac{b \,\mathrm{arcsec}\left(c x \right) d^{4}}{4 e}+\frac{b \sqrt{c^{2} x^{2}-1}\, d^{4} \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 c e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{b \sqrt{c^{2} x^{2}-1}\, d^{3} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{b \,e^{3} x^{3}}{12 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,e^{3} x}{12 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,e^{2} d \,x^{2}}{2 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,e^{2} d}{2 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{3 b e x \,d^{2}}{2 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{3 b e \,d^{2}}{2 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{b \,e^{2} \sqrt{c^{2} x^{2}-1}\, d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{2 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{b \,e^{3}}{6 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/4*a*e^3*x^4+a*e^2*x^3*d+3/2*a*e*x^2*d^2+a*x*d^3+1/4*a/e*d^4+1/4*b*e^3*arcsec(c*x)*x^4+b*e^2*arcsec(c*x)*x^3*d+3/2*b*e*arcsec(c*x)*x^2*d^2+b*arcsec(c*x)*x*d^3+1/4*b/e*arcsec(c*x)*d^4+1/4/c*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d^4*arctan(1/(c^2*x^2-1)^(1/2))-1/c^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d^3*ln(c*x+(c^2*x^2-1)^(1/2))-1/12/c*b*e^3/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^3-1/12/c^3*b*e^3/((c^2*x^2-1)/c^2/x^2)^(1/2)*x-1/2/c*b*e^2/((c^2*x^2-1)/c^2/x^2)^(1/2)*d*x^2+1/2/c^3*b*e^2/((c^2*x^2-1)/c^2/x^2)^(1/2)*d-3/2/c*b*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x*d^2+3/2/c^3*b*e/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d^2-1/2/c^4*b*e^2*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d*ln(c*x+(c^2*x^2-1)^(1/2))+1/6/c^5*b*e^3/((c^2*x^2-1)/c^2/x^2)^(1/2)/x","B"
57,1,362,110,0.054000," ","int((e*x+d)^2*(a+b*arcsec(c*x)),x)","\frac{a \,e^{2} x^{3}}{3}+a e d \,x^{2}+a x \,d^{2}+\frac{a \,d^{3}}{3 e}+\frac{b \,e^{2} \mathrm{arcsec}\left(c x \right) x^{3}}{3}+b e \,\mathrm{arcsec}\left(c x \right) x^{2} d +b \,\mathrm{arcsec}\left(c x \right) x \,d^{2}+\frac{b \,\mathrm{arcsec}\left(c x \right) d^{3}}{3 e}+\frac{b \sqrt{c^{2} x^{2}-1}\, d^{3} \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{3 c e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{b \sqrt{c^{2} x^{2}-1}\, d^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{b \,e^{2} x^{2}}{6 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,e^{2}}{6 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b e x d}{c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b e d}{c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{b \,e^{2} \sqrt{c^{2} x^{2}-1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{6 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/3*a*e^2*x^3+a*e*d*x^2+a*x*d^2+1/3*a/e*d^3+1/3*b*e^2*arcsec(c*x)*x^3+b*e*arcsec(c*x)*x^2*d+b*arcsec(c*x)*x*d^2+1/3*b/e*arcsec(c*x)*d^3+1/3/c*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d^3*arctan(1/(c^2*x^2-1)^(1/2))-1/c^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d^2*ln(c*x+(c^2*x^2-1)^(1/2))-1/6/c*b*e^2/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2+1/6/c^3*b*e^2/((c^2*x^2-1)/c^2/x^2)^(1/2)-1/c*b*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x*d+1/c^3*b*e/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d-1/6/c^4*b*e^2*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*ln(c*x+(c^2*x^2-1)^(1/2))","B"
58,1,141,74,0.051000," ","int((e*x+d)*(a+b*arcsec(c*x)),x)","\frac{a \,x^{2} e}{2}+a d x +\frac{b \,\mathrm{arcsec}\left(c x \right) x^{2} e}{2}+b \,\mathrm{arcsec}\left(c x \right) x d -\frac{b \sqrt{c^{2} x^{2}-1}\, d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{b x e}{2 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b e}{2 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/2*a*x^2*e+a*d*x+1/2*b*arcsec(c*x)*x^2*e+b*arcsec(c*x)*x*d-1/c^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*(c^2*x^2-1)^(1/2)*d*ln(c*x+(c^2*x^2-1)^(1/2))-1/2/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x*e+1/2/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e","A"
59,1,38,30,0.044000," ","int(a+b*arcsec(c*x),x)","a x +b x \,\mathrm{arcsec}\left(c x \right)-\frac{b \ln \left(c x +c x \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c}"," ",0,"a*x+b*x*arcsec(c*x)-b/c*ln(c*x+c*x*(1-1/c^2/x^2)^(1/2))","A"
60,1,456,316,0.820000," ","int((a+b*arcsec(c*x))/(e*x+d),x)","\frac{a \ln \left(c e x +d c \right)}{e}-\frac{b \,\mathrm{arcsec}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e}-\frac{b \,\mathrm{arcsec}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e}+\frac{i b \dilog \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e}+\frac{i b \dilog \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e}+\frac{b \,\mathrm{arcsec}\left(c x \right) \ln \left(\frac{-d c \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+\sqrt{-c^{2} d^{2}+e^{2}}-e}{-e +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e}+\frac{b \,\mathrm{arcsec}\left(c x \right) \ln \left(\frac{d c \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+\sqrt{-c^{2} d^{2}+e^{2}}+e}{e +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e}-\frac{i b \dilog \left(\frac{-d c \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+\sqrt{-c^{2} d^{2}+e^{2}}-e}{-e +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e}-\frac{i b \dilog \left(\frac{d c \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)+\sqrt{-c^{2} d^{2}+e^{2}}+e}{e +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e}"," ",0,"a*ln(c*e*x+c*d)/e-b/e*arcsec(c*x)*ln(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))-b/e*arcsec(c*x)*ln(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+I*b/e*dilog(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+I*b/e*dilog(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+b/e*arcsec(c*x)*ln((-d*c*(1/c/x+I*(1-1/c^2/x^2)^(1/2))+(-c^2*d^2+e^2)^(1/2)-e)/(-e+(-c^2*d^2+e^2)^(1/2)))+b/e*arcsec(c*x)*ln((d*c*(1/c/x+I*(1-1/c^2/x^2)^(1/2))+(-c^2*d^2+e^2)^(1/2)+e)/(e+(-c^2*d^2+e^2)^(1/2)))-I*b/e*dilog((-d*c*(1/c/x+I*(1-1/c^2/x^2)^(1/2))+(-c^2*d^2+e^2)^(1/2)-e)/(-e+(-c^2*d^2+e^2)^(1/2)))-I*b/e*dilog((d*c*(1/c/x+I*(1-1/c^2/x^2)^(1/2))+(-c^2*d^2+e^2)^(1/2)+e)/(e+(-c^2*d^2+e^2)^(1/2)))","A"
61,1,214,100,0.060000," ","int((a+b*arcsec(c*x))/(e*x+d)^2,x)","-\frac{c a}{\left(c e x +d c \right) e}-\frac{c b \,\mathrm{arcsec}\left(c x \right)}{\left(c e x +d c \right) e}-\frac{b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{c e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d}+\frac{b \sqrt{c^{2} x^{2}-1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e -2 c^{2} d x -2 e}{c e x +d c}\right)}{c e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}"," ",0,"-c*a/(c*e*x+c*d)/e-c*b/(c*e*x+c*d)/e*arcsec(c*x)-1/c*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d*arctan(1/(c^2*x^2-1)^(1/2))+1/c*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/((c^2*d^2-e^2)/e^2)^(1/2)*ln(2*((c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e-c^2*d*x-e)/(c*e*x+c*d))","B"
62,1,1005,159,0.067000," ","int((a+b*arcsec(c*x))/(e*x+d)^3,x)","-\frac{c^{2} a}{2 \left(c e x +d c \right)^{2} e}-\frac{c^{2} b \,\mathrm{arcsec}\left(c x \right)}{2 \left(c e x +d c \right)^{2} e}-\frac{c^{2} b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}-\frac{c^{2} b \sqrt{c^{2} x^{2}-1}\, d \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{2 e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}+\frac{c^{2} b \sqrt{c^{2} x^{2}-1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e -2 c^{2} d x -2 e}{c e x +d c}\right)}{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}+\frac{c^{2} b \sqrt{c^{2} x^{2}-1}\, d \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e -2 c^{2} d x -2 e}{c e x +d c}\right)}{e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}+\frac{c^{2} b e x}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}-\frac{b e}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}+\frac{b \,e^{2} \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d^{2} \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}+\frac{b e \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}-\frac{b \,e^{2} \sqrt{c^{2} x^{2}-1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e -2 c^{2} d x -2 e}{c e x +d c}\right)}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d^{2} \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}-\frac{b e \sqrt{c^{2} x^{2}-1}\, \ln \left(\frac{2 \sqrt{c^{2} x^{2}-1}\, \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, e -2 c^{2} d x -2 e}{c e x +d c}\right)}{2 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \sqrt{\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)}"," ",0,"-1/2*c^2*a/(c*e*x+c*d)^2/e-1/2*c^2*b/(c*e*x+c*d)^2/e*arcsec(c*x)-1/2*c^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/(c^2*d^2-e^2)/(c*e*x+c*d)*arctan(1/(c^2*x^2-1)^(1/2))-1/2*c^2*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d/(c^2*d^2-e^2)/(c*e*x+c*d)*arctan(1/(c^2*x^2-1)^(1/2))+c^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/((c^2*d^2-e^2)/e^2)^(1/2)/(c^2*d^2-e^2)/(c*e*x+c*d)*ln(2*((c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e-c^2*d*x-e)/(c*e*x+c*d))+c^2*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d/((c^2*d^2-e^2)/e^2)^(1/2)/(c^2*d^2-e^2)/(c*e*x+c*d)*ln(2*((c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e-c^2*d*x-e)/(c*e*x+c*d))+1/2*c^2*b*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d/(c^2*d^2-e^2)/(c*e*x+c*d)-1/2*b*e/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/(c^2*d^2-e^2)/(c*e*x+c*d)+1/2*b*e^2*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/d^2/(c^2*d^2-e^2)/(c*e*x+c*d)*arctan(1/(c^2*x^2-1)^(1/2))+1/2*b*e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/(c^2*d^2-e^2)/(c*e*x+c*d)*arctan(1/(c^2*x^2-1)^(1/2))-1/2*b*e^2*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/d^2/((c^2*d^2-e^2)/e^2)^(1/2)/(c^2*d^2-e^2)/(c*e*x+c*d)*ln(2*((c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e-c^2*d*x-e)/(c*e*x+c*d))-1/2*b*e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/((c^2*d^2-e^2)/e^2)^(1/2)/(c^2*d^2-e^2)/(c*e*x+c*d)*ln(2*((c^2*x^2-1)^(1/2)*((c^2*d^2-e^2)/e^2)^(1/2)*e-c^2*d*x-e)/(c*e*x+c*d))","B"
63,1,810,335,0.204000," ","int((e*x+d)^(3/2)*(a+b*arcsec(c*x)),x)","\frac{\frac{2 \left(e x +d \right)^{\frac{5}{2}} a}{5}+2 b \left(\frac{\left(e x +d \right)^{\frac{5}{2}} \mathrm{arcsec}\left(c x \right)}{5}-\frac{2 \left(\sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{5}{2}} c^{2}+9 d^{2} \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{2}-7 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c^{2} d^{2}-3 d^{2} \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) c^{2}-2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{3}{2}} c^{2} d +7 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d e -7 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d e +\sqrt{\frac{c}{d c -e}}\, \sqrt{e x +d}\, c^{2} d^{2}+\sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e^{2}-\sqrt{\frac{c}{d c -e}}\, \sqrt{e x +d}\, e^{2}\right)}{15 c^{3} \sqrt{\frac{c}{d c -e}}\, x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e}"," ",0,"2/e*(1/5*(e*x+d)^(5/2)*a+b*(1/5*(e*x+d)^(5/2)*arcsec(c*x)-2/15/c^3*((c/(c*d-e))^(1/2)*(e*x+d)^(5/2)*c^2+9*d^2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^2-7*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c^2*d^2-3*d^2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*c^2-2*(c/(c*d-e))^(1/2)*(e*x+d)^(3/2)*c^2*d+7*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d*e-7*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d*e+(c/(c*d-e))^(1/2)*(e*x+d)^(1/2)*c^2*d^2+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e^2-(c/(c*d-e))^(1/2)*(e*x+d)^(1/2)*e^2)/(c/(c*d-e))^(1/2)/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","B"
64,1,388,284,0.069000," ","int((e*x+d)^(1/2)*(a+b*arcsec(c*x)),x)","\frac{\frac{2 \left(e x +d \right)^{\frac{3}{2}} a}{3}+2 b \left(\frac{\left(e x +d \right)^{\frac{3}{2}} \mathrm{arcsec}\left(c x \right)}{3}-\frac{2 \left(2 d \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c -\EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) c d -d \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) c +\EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e -\EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) e \right) \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}}{3 c^{2} \sqrt{\frac{c}{d c -e}}\, x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e}"," ",0,"2/e*(1/3*(e*x+d)^(3/2)*a+b*(1/3*(e*x+d)^(3/2)*arcsec(c*x)-2/3/c^2*(2*d*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c-EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*c*d-d*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*c+EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e-EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*e)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)/(c/(c*d-e))^(1/2)/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","A"
65,1,254,196,0.066000," ","int((a+b*arcsec(c*x))/(e*x+d)^(1/2),x)","\frac{2 a \sqrt{e x +d}+2 b \left(\sqrt{e x +d}\, \mathrm{arcsec}\left(c x \right)-\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \left(\EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right)-\EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right)\right)}{c \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}\, x \sqrt{\frac{c}{d c -e}}}\right)}{e}"," ",0,"2/e*(a*(e*x+d)^(1/2)+b*((e*x+d)^(1/2)*arcsec(c*x)-2/c*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*(EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))-EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2)))/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)/x/(c/(c*d-e))^(1/2)))","A"
66,1,217,110,0.066000," ","int((a+b*arcsec(c*x))/(e*x+d)^(3/2),x)","\frac{-\frac{2 a}{\sqrt{e x +d}}+2 b \left(-\frac{\mathrm{arcsec}\left(c x \right)}{\sqrt{e x +d}}-\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right)}{c \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}\, x d \sqrt{\frac{c}{d c -e}}}\right)}{e}"," ",0,"2/e*(-1/(e*x+d)^(1/2)*a+b*(-1/(e*x+d)^(1/2)*arcsec(c*x)-2/c/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)/x/d/(c/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))))","A"
67,1,886,270,0.082000," ","int((a+b*arcsec(c*x))/(e*x+d)^(5/2),x)","\frac{-\frac{2 a}{3 \left(e x +d \right)^{\frac{3}{2}}}+2 b \left(-\frac{\mathrm{arcsec}\left(c x \right)}{3 \left(e x +d \right)^{\frac{3}{2}}}+\frac{\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{2} c^{2} d}{3}-\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) \sqrt{e x +d}\, c^{2} d^{2}}{3}-\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c^{2} d^{2}}{3}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c^{2} d^{2}}{3}-\frac{4 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right) c^{2} d^{2}}{3}-\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c d e}{3}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \sqrt{e x +d}\, c d e}{3}+\frac{2 \sqrt{\frac{c}{d c -e}}\, c^{2} d^{3}}{3}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) \sqrt{e x +d}\, e^{2}}{3}-\frac{2 \sqrt{\frac{c}{d c -e}}\, d \,e^{2}}{3}}{c \left(d c -e \right) \sqrt{e x +d}\, \left(d c +e \right) \sqrt{\frac{c}{d c -e}}\, d^{2} x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e}"," ",0,"2/e*(-1/3*a/(e*x+d)^(3/2)+b*(-1/3/(e*x+d)^(3/2)*arcsec(c*x)+2/3/c*((c/(c*d-e))^(1/2)*(e*x+d)^2*c^2*d-(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*(e*x+d)^(1/2)*c^2*d^2-(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c^2*d^2+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c^2*d^2-2*(c/(c*d-e))^(1/2)*(e*x+d)*c^2*d^2-(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c*d*e+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(1/2)*c*d*e+(c/(c*d-e))^(1/2)*c^2*d^3+(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*(e*x+d)^(1/2)*e^2-(c/(c*d-e))^(1/2)*d*e^2)/(c*d-e)/(e*x+d)^(1/2)/(c*d+e)/(c/(c*d-e))^(1/2)/d^2/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","B"
68,1,1640,491,0.088000," ","int((a+b*arcsec(c*x))/(e*x+d)^(7/2),x)","\frac{-\frac{2 a}{5 \left(e x +d \right)^{\frac{5}{2}}}+2 b \left(-\frac{\mathrm{arcsec}\left(c x \right)}{5 \left(e x +d \right)^{\frac{5}{2}}}+\frac{\frac{14 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{3} c^{4} d^{3}}{15}-\frac{4 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{4} d^{4}}{5}+\frac{14 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{4} d^{4}}{15}-\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{4} d^{4}}{5}-\frac{26 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{2} c^{4} d^{4}}{15}-\frac{14 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{3} e}{15}+\frac{14 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{3} e}{15}-\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{3} c^{2} d \,e^{2}}{5}+\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right) c^{4} d^{5}}{3}+\frac{4 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{2} d^{2} e^{2}}{15}-\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{2} d^{2} e^{2}}{5}+\frac{4 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{2} d^{2} e^{2}}{5}+\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{2} c^{2} d^{2} e^{2}}{3}+\frac{2 \sqrt{\frac{c}{d c -e}}\, c^{4} d^{6}}{15}+\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \left(e x +d \right)^{\frac{3}{2}} c d \,e^{3}}{5}-\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \sqrt{\frac{d c -e}{d c +e}}\right) \left(e x +d \right)^{\frac{3}{2}} c d \,e^{3}}{5}-\frac{16 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right) c^{2} d^{3} e^{2}}{15}-\frac{2 \sqrt{-\frac{\left(e x +d \right) c -d c +e}{d c -e}}\, \sqrt{-\frac{\left(e x +d \right) c -d c -e}{d c +e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{d c -e}}, \frac{d c -e}{c d}, \frac{\sqrt{\frac{c}{d c +e}}}{\sqrt{\frac{c}{d c -e}}}\right) \left(e x +d \right)^{\frac{3}{2}} e^{4}}{5}-\frac{4 \sqrt{\frac{c}{d c -e}}\, c^{2} d^{4} e^{2}}{15}+\frac{2 \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right) d \,e^{4}}{5}+\frac{2 \sqrt{\frac{c}{d c -e}}\, d^{2} e^{4}}{15}}{c \left(d c -e \right) \sqrt{\frac{c}{d c -e}}\, \left(e x +d \right)^{\frac{3}{2}} \left(d c +e \right) \left(c^{2} d^{2}-e^{2}\right) d^{3} x \sqrt{\frac{c^{2} \left(e x +d \right)^{2}-2 c^{2} d \left(e x +d \right)+c^{2} d^{2}-e^{2}}{c^{2} e^{2} x^{2}}}}\right)}{e}"," ",0,"2/e*(-1/5*a/(e*x+d)^(5/2)+b*(-1/5/(e*x+d)^(5/2)*arcsec(c*x)+2/15/c*(7*(c/(c*d-e))^(1/2)*(e*x+d)^3*c^4*d^3-6*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(3/2)*c^4*d^4+7*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(3/2)*c^4*d^4-3*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*(e*x+d)^(3/2)*c^4*d^4-13*(c/(c*d-e))^(1/2)*(e*x+d)^2*c^4*d^4-7*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(3/2)*c^3*d^3*e+7*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(3/2)*c^3*d^3*e-3*(c/(c*d-e))^(1/2)*(e*x+d)^3*c^2*d*e^2+5*(c/(c*d-e))^(1/2)*(e*x+d)*c^4*d^5+2*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(3/2)*c^2*d^2*e^2-3*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(3/2)*c^2*d^2*e^2+6*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*(e*x+d)^(3/2)*c^2*d^2*e^2+5*(c/(c*d-e))^(1/2)*(e*x+d)^2*c^2*d^2*e^2+(c/(c*d-e))^(1/2)*c^4*d^6+3*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticF((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(3/2)*c*d*e^3-3*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticE((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),((c*d-e)/(c*d+e))^(1/2))*(e*x+d)^(3/2)*c*d*e^3-8*(c/(c*d-e))^(1/2)*(e*x+d)*c^2*d^3*e^2-3*(-((e*x+d)*c-d*c+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-d*c-e)/(c*d+e))^(1/2)*EllipticPi((e*x+d)^(1/2)*(c/(c*d-e))^(1/2),1/c*(c*d-e)/d,(c/(c*d+e))^(1/2)/(c/(c*d-e))^(1/2))*(e*x+d)^(3/2)*e^4-2*(c/(c*d-e))^(1/2)*c^2*d^4*e^2+3*(c/(c*d-e))^(1/2)*(e*x+d)*d*e^4+(c/(c*d-e))^(1/2)*d^2*e^4)/(c*d-e)/(c/(c*d-e))^(1/2)/(e*x+d)^(3/2)/(c*d+e)/(c^2*d^2-e^2)/d^3/x/((c^2*(e*x+d)^2-2*c^2*d*(e*x+d)+c^2*d^2-e^2)/c^2/e^2/x^2)^(1/2)))","B"
69,1,338,178,0.055000," ","int(x^4*(e*x^2+d)*(a+b*arcsec(c*x)),x)","\frac{a e \,x^{7}}{7}+\frac{a \,x^{5} d}{5}+\frac{b \,\mathrm{arcsec}\left(c x \right) e \,x^{7}}{7}+\frac{b \,\mathrm{arcsec}\left(c x \right) x^{5} d}{5}-\frac{b \,x^{6} e}{42 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,x^{4} e}{168 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,x^{4} d}{20 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,x^{2} d}{40 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{5 b \,x^{2} e}{336 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{3 b d}{40 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{3 b \sqrt{c^{2} x^{2}-1}\, d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{40 c^{6} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{5 b e}{112 c^{7} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{5 b \sqrt{c^{2} x^{2}-1}\, e \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{112 c^{8} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/7*a*e*x^7+1/5*a*x^5*d+1/7*b*arcsec(c*x)*e*x^7+1/5*b*arcsec(c*x)*x^5*d-1/42/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^6*e-1/168/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^4*e-1/20/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^4*d-1/40/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2*d-5/336/c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2*e+3/40/c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*d-3/40/c^6*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*(c^2*x^2-1)^(1/2)*d*ln(c*x+(c^2*x^2-1)^(1/2))+5/112/c^7*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e-5/112/c^8*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e*ln(c*x+(c^2*x^2-1)^(1/2))","A"
70,1,282,139,0.053000," ","int(x^2*(e*x^2+d)*(a+b*arcsec(c*x)),x)","\frac{a e \,x^{5}}{5}+\frac{a d \,x^{3}}{3}+\frac{b \,\mathrm{arcsec}\left(c x \right) e \,x^{5}}{5}+\frac{b \,\mathrm{arcsec}\left(c x \right) d \,x^{3}}{3}-\frac{b \,x^{4} e}{20 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,x^{2} e}{40 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b d \,x^{2}}{6 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b d}{6 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \sqrt{c^{2} x^{2}-1}\, d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{6 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{3 b e}{40 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{3 b \sqrt{c^{2} x^{2}-1}\, e \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{40 c^{6} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/5*a*e*x^5+1/3*a*d*x^3+1/5*b*arcsec(c*x)*e*x^5+1/3*b*arcsec(c*x)*d*x^3-1/20/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^4*e-1/40/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2*e-1/6/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*d*x^2+1/6/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*d-1/6/c^4*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*(c^2*x^2-1)^(1/2)*d*ln(c*x+(c^2*x^2-1)^(1/2))+3/40/c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e-3/40/c^6*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e*ln(c*x+(c^2*x^2-1)^(1/2))","B"
71,1,195,95,0.052000," ","int((e*x^2+d)*(a+b*arcsec(c*x)),x)","\frac{a e \,x^{3}}{3}+a d x +\frac{b \,\mathrm{arcsec}\left(c x \right) x^{3} e}{3}+b \,\mathrm{arcsec}\left(c x \right) x d -\frac{b \sqrt{c^{2} x^{2}-1}\, d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{b e \,x^{2}}{6 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b e}{6 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \sqrt{c^{2} x^{2}-1}\, e \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{6 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/3*a*e*x^3+a*d*x+1/3*b*arcsec(c*x)*x^3*e+b*arcsec(c*x)*x*d-1/c^2*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*(c^2*x^2-1)^(1/2)*d*ln(c*x+(c^2*x^2-1)^(1/2))-1/6/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e*x^2+1/6/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e-1/6/c^4*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e*ln(c*x+(c^2*x^2-1)^(1/2))","B"
72,1,137,79,0.058000," ","int((e*x^2+d)*(a+b*arcsec(c*x))/x^2,x)","a e x -\frac{a d}{x}+b \,\mathrm{arcsec}\left(c x \right) e x -\frac{b \,\mathrm{arcsec}\left(c x \right) d}{x}+\frac{c b d}{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b d}{c \,x^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \sqrt{c^{2} x^{2}-1}\, e \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"a*e*x-a*d/x+b*arcsec(c*x)*e*x-b*arcsec(c*x)*d/x+c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*d-b/c/x^2/((c^2*x^2-1)/c^2/x^2)^(1/2)*d-b/c^2*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e*ln(c*x+(c^2*x^2-1)^(1/2))","A"
73,1,121,91,0.059000," ","int((e*x^2+d)*(a+b*arcsec(c*x))/x^4,x)","c^{3} \left(\frac{a \left(-\frac{d}{3 c \,x^{3}}-\frac{e}{c x}\right)}{c^{2}}+\frac{b \left(-\frac{\mathrm{arcsec}\left(c x \right) d}{3 c \,x^{3}}-\frac{\mathrm{arcsec}\left(c x \right) e}{c x}+\frac{\left(c^{2} x^{2}-1\right) \left(2 c^{4} d \,x^{2}+9 c^{2} e \,x^{2}+c^{2} d \right)}{9 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{4} x^{4}}\right)}{c^{2}}\right)"," ",0,"c^3*(a/c^2*(-1/3/c*d/x^3-e/c/x)+b/c^2*(-1/3*arcsec(c*x)/c*d/x^3-arcsec(c*x)*e/c/x+1/9*(c^2*x^2-1)*(2*c^4*d*x^2+9*c^2*e*x^2+c^2*d)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^4/x^4))","A"
74,1,140,130,0.059000," ","int((e*x^2+d)*(a+b*arcsec(c*x))/x^6,x)","c^{5} \left(\frac{a \left(-\frac{e}{3 c^{3} x^{3}}-\frac{d}{5 c^{3} x^{5}}\right)}{c^{2}}+\frac{b \left(-\frac{\mathrm{arcsec}\left(c x \right) e}{3 c^{3} x^{3}}-\frac{\mathrm{arcsec}\left(c x \right) d}{5 c^{3} x^{5}}+\frac{\left(c^{2} x^{2}-1\right) \left(24 x^{4} c^{6} d +50 c^{4} e \,x^{4}+12 c^{4} d \,x^{2}+25 c^{2} e \,x^{2}+9 c^{2} d \right)}{225 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{6} x^{6}}\right)}{c^{2}}\right)"," ",0,"c^5*(a/c^2*(-1/3*e/c^3/x^3-1/5/c^3*d/x^5)+b/c^2*(-1/3*arcsec(c*x)*e/c^3/x^3-1/5*arcsec(c*x)/c^3*d/x^5+1/225*(c^2*x^2-1)*(24*c^6*d*x^4+50*c^4*e*x^4+12*c^4*d*x^2+25*c^2*e*x^2+9*c^2*d)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^6/x^6))","A"
75,1,158,169,0.062000," ","int((e*x^2+d)*(a+b*arcsec(c*x))/x^8,x)","c^{7} \left(\frac{a \left(-\frac{d}{7 c^{5} x^{7}}-\frac{e}{5 c^{5} x^{5}}\right)}{c^{2}}+\frac{b \left(-\frac{\mathrm{arcsec}\left(c x \right) d}{7 c^{5} x^{7}}-\frac{\mathrm{arcsec}\left(c x \right) e}{5 c^{5} x^{5}}+\frac{\left(c^{2} x^{2}-1\right) \left(240 c^{8} d \,x^{6}+392 e \,c^{6} x^{6}+120 x^{4} c^{6} d +196 c^{4} e \,x^{4}+90 c^{4} d \,x^{2}+147 c^{2} e \,x^{2}+75 c^{2} d \right)}{3675 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{8} x^{8}}\right)}{c^{2}}\right)"," ",0,"c^7*(a/c^2*(-1/7/c^5*d/x^7-1/5*e/c^5/x^5)+b/c^2*(-1/7*arcsec(c*x)/c^5*d/x^7-1/5*arcsec(c*x)*e/c^5/x^5+1/3675*(c^2*x^2-1)*(240*c^8*d*x^6+392*c^6*e*x^6+120*c^6*d*x^4+196*c^4*e*x^4+90*c^4*d*x^2+147*c^2*e*x^2+75*c^2*d)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^8/x^8))","A"
76,1,152,168,0.054000," ","int(x^5*(e*x^2+d)*(a+b*arcsec(c*x)),x)","\frac{\frac{a \left(\frac{1}{8} e \,c^{8} x^{8}+\frac{1}{6} c^{8} d \,x^{6}\right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arcsec}\left(c x \right) e \,c^{8} x^{8}}{8}+\frac{\mathrm{arcsec}\left(c x \right) c^{8} x^{6} d}{6}-\frac{\left(c^{2} x^{2}-1\right) \left(45 e \,c^{6} x^{6}+84 x^{4} c^{6} d +54 c^{4} e \,x^{4}+112 c^{4} d \,x^{2}+72 c^{2} e \,x^{2}+224 c^{2} d +144 e \right)}{2520 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c x}\right)}{c^{2}}}{c^{6}}"," ",0,"1/c^6*(a/c^2*(1/8*e*c^8*x^8+1/6*c^8*d*x^6)+b/c^2*(1/8*arcsec(c*x)*e*c^8*x^8+1/6*arcsec(c*x)*c^8*x^6*d-1/2520*(c^2*x^2-1)*(45*c^6*e*x^6+84*c^6*d*x^4+54*c^4*e*x^4+112*c^4*d*x^2+72*c^2*e*x^2+224*c^2*d+144*e)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c/x))","A"
77,1,134,131,0.052000," ","int(x^3*(e*x^2+d)*(a+b*arcsec(c*x)),x)","\frac{\frac{a \left(\frac{1}{6} e \,c^{6} x^{6}+\frac{1}{4} x^{4} c^{6} d \right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arcsec}\left(c x \right) e \,c^{6} x^{6}}{6}+\frac{\mathrm{arcsec}\left(c x \right) c^{6} x^{4} d}{4}-\frac{\left(c^{2} x^{2}-1\right) \left(6 c^{4} e \,x^{4}+15 c^{4} d \,x^{2}+8 c^{2} e \,x^{2}+30 c^{2} d +16 e \right)}{180 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c x}\right)}{c^{2}}}{c^{4}}"," ",0,"1/c^4*(a/c^2*(1/6*e*c^6*x^6+1/4*x^4*c^6*d)+b/c^2*(1/6*arcsec(c*x)*e*c^6*x^6+1/4*arcsec(c*x)*c^6*x^4*d-1/180*(c^2*x^2-1)*(6*c^4*e*x^4+15*c^4*d*x^2+8*c^2*e*x^2+30*c^2*d+16*e)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c/x))","A"
78,1,115,118,0.052000," ","int(x*(e*x^2+d)*(a+b*arcsec(c*x)),x)","\frac{\frac{a \left(\frac{1}{4} c^{4} e \,x^{4}+\frac{1}{2} c^{4} d \,x^{2}\right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arcsec}\left(c x \right) e \,c^{4} x^{4}}{4}+\frac{\mathrm{arcsec}\left(c x \right) c^{4} d \,x^{2}}{2}-\frac{\left(c^{2} x^{2}-1\right) \left(c^{2} e \,x^{2}+6 c^{2} d +2 e \right)}{12 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c x}\right)}{c^{2}}}{c^{2}}"," ",0,"1/c^2*(a/c^2*(1/4*c^4*e*x^4+1/2*c^4*d*x^2)+b/c^2*(1/4*arcsec(c*x)*e*c^4*x^4+1/2*arcsec(c*x)*c^4*d*x^2-1/12*(c^2*x^2-1)*(c^2*e*x^2+6*c^2*d+2*e)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c/x))","A"
79,1,142,140,2.625000," ","int((e*x^2+d)*(a+b*arcsec(c*x))/x,x)","\frac{a \,x^{2} e}{2}+d a \ln \left(c x \right)+\frac{i b d \mathrm{arcsec}\left(c x \right)^{2}}{2}+\frac{b \,\mathrm{arcsec}\left(c x \right) x^{2} e}{2}-\frac{b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x e}{2 c}-\frac{i b e}{2 c^{2}}-b d \,\mathrm{arcsec}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)+\frac{i b d \polylog \left(2, -\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)}{2}"," ",0,"1/2*a*x^2*e+d*a*ln(c*x)+1/2*I*b*d*arcsec(c*x)^2+1/2*b*arcsec(c*x)*x^2*e-1/2*b/c*((c^2*x^2-1)/c^2/x^2)^(1/2)*x*e-1/2*I*b/c^2*e-b*d*arcsec(c*x)*ln(1+(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)+1/2*I*b*d*polylog(2,-(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)","A"
80,1,145,151,0.851000," ","int((e*x^2+d)*(a+b*arcsec(c*x))/x^3,x)","a e \ln \left(c x \right)-\frac{d a}{2 x^{2}}+\frac{i b \mathrm{arcsec}\left(c x \right)^{2} e}{2}+\frac{c b d \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{4 x}+\frac{c^{2} b d \,\mathrm{arcsec}\left(c x \right)}{4}-\frac{b \,\mathrm{arcsec}\left(c x \right) d}{2 x^{2}}-b e \,\mathrm{arcsec}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)+\frac{i b e \polylog \left(2, -\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)}{2}"," ",0,"a*e*ln(c*x)-1/2*d*a/x^2+1/2*I*b*arcsec(c*x)^2*e+1/4*c*b*d/x*((c^2*x^2-1)/c^2/x^2)^(1/2)+1/4*c^2*b*d*arcsec(c*x)-1/2*b*arcsec(c*x)*d/x^2-b*e*arcsec(c*x)*ln(1+(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)+1/2*I*b*e*polylog(2,-(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)","A"
81,1,494,222,0.054000," ","int(x^2*(e*x^2+d)^2*(a+b*arcsec(c*x)),x)","\frac{a \,e^{2} x^{7}}{7}+\frac{2 a e d \,x^{5}}{5}+\frac{a \,x^{3} d^{2}}{3}+\frac{b \,\mathrm{arcsec}\left(c x \right) e^{2} x^{7}}{7}+\frac{2 b \,\mathrm{arcsec}\left(c x \right) e d \,x^{5}}{5}+\frac{b \,\mathrm{arcsec}\left(c x \right) x^{3} d^{2}}{3}-\frac{b \,x^{6} e^{2}}{42 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,x^{4} e^{2}}{168 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,x^{4} e d}{10 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,x^{2} e d}{20 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,d^{2} x^{2}}{6 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,d^{2}}{6 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \sqrt{c^{2} x^{2}-1}\, d^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{6 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{5 b \,x^{2} e^{2}}{336 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{3 b e d}{20 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{3 b \sqrt{c^{2} x^{2}-1}\, e d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{20 c^{6} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{5 b \,e^{2}}{112 c^{7} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{5 b \sqrt{c^{2} x^{2}-1}\, e^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{112 c^{8} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/7*a*e^2*x^7+2/5*a*e*d*x^5+1/3*a*x^3*d^2+1/7*b*arcsec(c*x)*e^2*x^7+2/5*b*arcsec(c*x)*e*d*x^5+1/3*b*arcsec(c*x)*x^3*d^2-1/42/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^6*e^2-1/168/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^4*e^2-1/10/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^4*e*d-1/20/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2*e*d-1/6/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*d^2*x^2+1/6/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*d^2-1/6/c^4*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d^2*ln(c*x+(c^2*x^2-1)^(1/2))-5/336/c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2*e^2+3/20/c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e*d-3/20/c^6*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e*d*ln(c*x+(c^2*x^2-1)^(1/2))+5/112/c^7*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e^2-5/112/c^8*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e^2*ln(c*x+(c^2*x^2-1)^(1/2))","B"
82,1,372,169,0.053000," ","int((e*x^2+d)^2*(a+b*arcsec(c*x)),x)","\frac{a \,e^{2} x^{5}}{5}+\frac{2 a \,x^{3} d e}{3}+a x \,d^{2}+\frac{b \,\mathrm{arcsec}\left(c x \right) e^{2} x^{5}}{5}+\frac{2 b \,\mathrm{arcsec}\left(c x \right) x^{3} d e}{3}+b \,\mathrm{arcsec}\left(c x \right) x \,d^{2}-\frac{b \sqrt{c^{2} x^{2}-1}\, d^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{b \,x^{4} e^{2}}{20 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,x^{2} e^{2}}{40 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b e d \,x^{2}}{3 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b e d}{3 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \sqrt{c^{2} x^{2}-1}\, e d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{3 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}+\frac{3 b \,e^{2}}{40 c^{5} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{3 b \sqrt{c^{2} x^{2}-1}\, e^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{40 c^{6} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/5*a*e^2*x^5+2/3*a*x^3*d*e+a*x*d^2+1/5*b*arcsec(c*x)*e^2*x^5+2/3*b*arcsec(c*x)*x^3*d*e+b*arcsec(c*x)*x*d^2-1/c^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d^2*ln(c*x+(c^2*x^2-1)^(1/2))-1/20/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^4*e^2-1/40/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2*e^2-1/3/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e*d*x^2+1/3/c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e*d-1/3/c^4*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e*d*ln(c*x+(c^2*x^2-1)^(1/2))+3/40/c^5*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e^2-3/40/c^6*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e^2*ln(c*x+(c^2*x^2-1)^(1/2))","B"
83,1,286,144,0.060000," ","int((e*x^2+d)^2*(a+b*arcsec(c*x))/x^2,x)","\frac{a \,e^{2} x^{3}}{3}+2 a e d x -\frac{a \,d^{2}}{x}+\frac{b \,e^{2} \mathrm{arcsec}\left(c x \right) x^{3}}{3}+2 b \,\mathrm{arcsec}\left(c x \right) e d x -\frac{b \,\mathrm{arcsec}\left(c x \right) d^{2}}{x}+\frac{c b \,d^{2}}{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,d^{2}}{c \,x^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{2 b \sqrt{c^{2} x^{2}-1}\, e d \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}-\frac{b \,e^{2} x^{2}}{6 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{b \,e^{2}}{6 c^{3} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{b \,e^{2} \sqrt{c^{2} x^{2}-1}\, \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{6 c^{4} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"1/3*a*e^2*x^3+2*a*e*d*x-a*d^2/x+1/3*b*e^2*arcsec(c*x)*x^3+2*b*arcsec(c*x)*e*d*x-b*arcsec(c*x)*d^2/x+c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*d^2-b/c/x^2/((c^2*x^2-1)/c^2/x^2)^(1/2)*d^2-2*b/c^2*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e*d*ln(c*x+(c^2*x^2-1)^(1/2))-1/6/c*b*e^2/((c^2*x^2-1)/c^2/x^2)^(1/2)*x^2+1/6/c^3*b*e^2/((c^2*x^2-1)/c^2/x^2)^(1/2)-1/6/c^4*b*e^2*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*ln(c*x+(c^2*x^2-1)^(1/2))","A"
84,1,255,140,0.063000," ","int((e*x^2+d)^2*(a+b*arcsec(c*x))/x^4,x)","a x \,e^{2}-\frac{a \,d^{2}}{3 x^{3}}-\frac{2 a e d}{x}+b \,\mathrm{arcsec}\left(c x \right) x \,e^{2}-\frac{b \,\mathrm{arcsec}\left(c x \right) d^{2}}{3 x^{3}}-\frac{2 b \,\mathrm{arcsec}\left(c x \right) e d}{x}+\frac{2 c^{3} b \,d^{2}}{9 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{c b \,d^{2}}{9 x^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}+\frac{2 c b e d}{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}-\frac{2 b e d}{c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{2}}-\frac{b \,d^{2}}{9 c \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{4}}-\frac{b \sqrt{c^{2} x^{2}-1}\, e^{2} \ln \left(c x +\sqrt{c^{2} x^{2}-1}\right)}{c^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x}"," ",0,"a*x*e^2-1/3*a*d^2/x^3-2*a*e*d/x+b*arcsec(c*x)*x*e^2-1/3*b*arcsec(c*x)*d^2/x^3-2*b*arcsec(c*x)*e*d/x+2/9*c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*d^2-1/9*c*b/x^2/((c^2*x^2-1)/c^2/x^2)^(1/2)*d^2+2*c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*e*d-2/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^2*e*d-1/9/c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x^4*d^2-1/c^2*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*e^2*ln(c*x+(c^2*x^2-1)^(1/2))","A"
85,1,191,161,0.063000," ","int((e*x^2+d)^2*(a+b*arcsec(c*x))/x^6,x)","c^{5} \left(\frac{a \left(-\frac{2 e d}{3 c \,x^{3}}-\frac{e^{2}}{c x}-\frac{d^{2}}{5 c \,x^{5}}\right)}{c^{4}}+\frac{b \left(-\frac{2 \,\mathrm{arcsec}\left(c x \right) e d}{3 c \,x^{3}}-\frac{\mathrm{arcsec}\left(c x \right) e^{2}}{c x}-\frac{\mathrm{arcsec}\left(c x \right) d^{2}}{5 c \,x^{5}}+\frac{\left(c^{2} x^{2}-1\right) \left(24 x^{4} c^{8} d^{2}+100 c^{6} e d \,x^{4}+12 x^{2} c^{6} d^{2}+225 c^{4} e^{2} x^{4}+50 c^{4} d e \,x^{2}+9 d^{2} c^{4}\right)}{225 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{6} x^{6}}\right)}{c^{4}}\right)"," ",0,"c^5*(a/c^4*(-2/3/c*e*d/x^3-e^2/c/x-1/5*d^2/c/x^5)+b/c^4*(-2/3*arcsec(c*x)/c*e*d/x^3-arcsec(c*x)*e^2/c/x-1/5*arcsec(c*x)*d^2/c/x^5+1/225*(c^2*x^2-1)*(24*c^8*d^2*x^4+100*c^6*d*e*x^4+12*c^6*d^2*x^2+225*c^4*e^2*x^4+50*c^4*d*e*x^2+9*c^4*d^2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^6/x^6))","A"
86,1,223,211,0.065000," ","int((e*x^2+d)^2*(a+b*arcsec(c*x))/x^8,x)","c^{7} \left(\frac{a \left(-\frac{d^{2}}{7 c^{3} x^{7}}-\frac{e^{2}}{3 c^{3} x^{3}}-\frac{2 e d}{5 c^{3} x^{5}}\right)}{c^{4}}+\frac{b \left(-\frac{\mathrm{arcsec}\left(c x \right) d^{2}}{7 c^{3} x^{7}}-\frac{\mathrm{arcsec}\left(c x \right) e^{2}}{3 c^{3} x^{3}}-\frac{2 \,\mathrm{arcsec}\left(c x \right) e d}{5 c^{3} x^{5}}+\frac{\left(c^{2} x^{2}-1\right) \left(720 c^{10} d^{2} x^{6}+2352 c^{8} e d \,x^{6}+360 x^{4} c^{8} d^{2}+2450 e^{2} c^{6} x^{6}+1176 c^{6} e d \,x^{4}+270 x^{2} c^{6} d^{2}+1225 c^{4} e^{2} x^{4}+882 c^{4} d e \,x^{2}+225 d^{2} c^{4}\right)}{11025 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c^{8} x^{8}}\right)}{c^{4}}\right)"," ",0,"c^7*(a/c^4*(-1/7*d^2/c^3/x^7-1/3*e^2/c^3/x^3-2/5/c^3*e*d/x^5)+b/c^4*(-1/7*arcsec(c*x)*d^2/c^3/x^7-1/3*arcsec(c*x)*e^2/c^3/x^3-2/5*arcsec(c*x)/c^3*e*d/x^5+1/11025*(c^2*x^2-1)*(720*c^10*d^2*x^6+2352*c^8*d*e*x^6+360*c^8*d^2*x^4+2450*c^6*e^2*x^6+1176*c^6*d*e*x^4+270*c^6*d^2*x^2+1225*c^4*e^2*x^4+882*c^4*d*e*x^2+225*c^4*d^2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c^8/x^8))","A"
87,1,214,212,0.054000," ","int(x^3*(e*x^2+d)^2*(a+b*arcsec(c*x)),x)","\frac{\frac{a \left(\frac{1}{8} e^{2} c^{8} x^{8}+\frac{1}{3} c^{8} e d \,x^{6}+\frac{1}{4} x^{4} c^{8} d^{2}\right)}{c^{4}}+\frac{b \left(\frac{\mathrm{arcsec}\left(c x \right) e^{2} c^{8} x^{8}}{8}+\frac{\mathrm{arcsec}\left(c x \right) c^{8} e d \,x^{6}}{3}+\frac{\mathrm{arcsec}\left(c x \right) c^{8} x^{4} d^{2}}{4}-\frac{\left(c^{2} x^{2}-1\right) \left(45 e^{2} c^{6} x^{6}+168 c^{6} e d \,x^{4}+210 x^{2} c^{6} d^{2}+54 c^{4} e^{2} x^{4}+224 c^{4} d e \,x^{2}+420 d^{2} c^{4}+72 c^{2} e^{2} x^{2}+448 c^{2} e d +144 e^{2}\right)}{2520 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c x}\right)}{c^{4}}}{c^{4}}"," ",0,"1/c^4*(a/c^4*(1/8*e^2*c^8*x^8+1/3*c^8*e*d*x^6+1/4*x^4*c^8*d^2)+b/c^4*(1/8*arcsec(c*x)*e^2*c^8*x^8+1/3*arcsec(c*x)*c^8*e*d*x^6+1/4*arcsec(c*x)*c^8*x^4*d^2-1/2520*(c^2*x^2-1)*(45*c^6*e^2*x^6+168*c^6*d*e*x^4+210*c^6*d^2*x^2+54*c^4*e^2*x^4+224*c^4*d*e*x^2+420*c^4*d^2+72*c^2*e^2*x^2+448*c^2*d*e+144*e^2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c/x))","A"
88,1,182,169,0.052000," ","int(x*(e*x^2+d)^2*(a+b*arcsec(c*x)),x)","\frac{\frac{a \left(\frac{1}{6} e^{2} c^{6} x^{6}+\frac{1}{2} c^{6} e d \,x^{4}+\frac{1}{2} x^{2} c^{6} d^{2}\right)}{c^{4}}+\frac{b \left(\frac{\mathrm{arcsec}\left(c x \right) e^{2} c^{6} x^{6}}{6}+\frac{\mathrm{arcsec}\left(c x \right) c^{6} x^{4} d e}{2}+\frac{\mathrm{arcsec}\left(c x \right) c^{6} x^{2} d^{2}}{2}-\frac{\left(c^{2} x^{2}-1\right) \left(3 c^{4} e^{2} x^{4}+15 c^{4} d e \,x^{2}+45 d^{2} c^{4}+4 c^{2} e^{2} x^{2}+30 c^{2} e d +8 e^{2}\right)}{90 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, c x}\right)}{c^{4}}}{c^{2}}"," ",0,"1/c^2*(a/c^4*(1/6*e^2*c^6*x^6+1/2*c^6*e*d*x^4+1/2*x^2*c^6*d^2)+b/c^4*(1/6*arcsec(c*x)*e^2*c^6*x^6+1/2*arcsec(c*x)*c^6*x^4*d*e+1/2*arcsec(c*x)*c^6*x^2*d^2-1/90*(c^2*x^2-1)*(3*c^4*e^2*x^4+15*c^4*d*e*x^2+45*c^4*d^2+4*c^2*e^2*x^2+30*c^2*d*e+8*e^2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/c/x))","A"
89,1,242,198,3.521000," ","int((e*x^2+d)^2*(a+b*arcsec(c*x))/x,x)","\frac{a \,x^{4} e^{2}}{4}+a e d \,x^{2}+a \,d^{2} \ln \left(c x \right)+\frac{i b \,d^{2} \mathrm{arcsec}\left(c x \right)^{2}}{2}+\frac{b \,\mathrm{arcsec}\left(c x \right) x^{4} e^{2}}{4}+b e \,\mathrm{arcsec}\left(c x \right) x^{2} d -\frac{b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3} e^{2}}{12 c}-\frac{b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d e}{c}-\frac{i b d e}{c^{2}}-\frac{b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \,e^{2}}{6 c^{3}}-\frac{i b \,e^{2}}{6 c^{4}}-b \,d^{2} \mathrm{arcsec}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)+\frac{i b \,d^{2} \polylog \left(2, -\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)}{2}"," ",0,"1/4*a*x^4*e^2+a*e*d*x^2+a*d^2*ln(c*x)+1/2*I*b*d^2*arcsec(c*x)^2+1/4*b*arcsec(c*x)*x^4*e^2+b*e*arcsec(c*x)*x^2*d-1/12*b/c*((c^2*x^2-1)/c^2/x^2)^(1/2)*x^3*e^2-b/c*((c^2*x^2-1)/c^2/x^2)^(1/2)*x*d*e-I*b/c^2*d*e-1/6*b/c^3*((c^2*x^2-1)/c^2/x^2)^(1/2)*x*e^2-1/6*I*b/c^4*e^2-b*d^2*arcsec(c*x)*ln(1+(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)+1/2*I*b*d^2*polylog(2,-(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)","A"
90,1,218,201,2.877000," ","int((e*x^2+d)^2*(a+b*arcsec(c*x))/x^3,x)","\frac{a \,x^{2} e^{2}}{2}+2 a e d \ln \left(c x \right)-\frac{a \,d^{2}}{2 x^{2}}+i b e d \mathrm{arcsec}\left(c x \right)^{2}+\frac{c b \,d^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{4 x}+\frac{c^{2} b \,d^{2} \mathrm{arcsec}\left(c x \right)}{4}-\frac{b \,\mathrm{arcsec}\left(c x \right) d^{2}}{2 x^{2}}+\frac{b \,\mathrm{arcsec}\left(c x \right) x^{2} e^{2}}{2}-\frac{b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \,e^{2}}{2 c}-\frac{i b \,e^{2}}{2 c^{2}}-2 b e d \,\mathrm{arcsec}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)+i b e d \polylog \left(2, -\left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}\right)"," ",0,"1/2*a*x^2*e^2+2*a*e*d*ln(c*x)-1/2*a*d^2/x^2+I*b*e*d*arcsec(c*x)^2+1/4*c*b*d^2/x*((c^2*x^2-1)/c^2/x^2)^(1/2)+1/4*c^2*b*d^2*arcsec(c*x)-1/2*b*arcsec(c*x)*d^2/x^2+1/2*b*arcsec(c*x)*x^2*e^2-1/2/c*b*((c^2*x^2-1)/c^2/x^2)^(1/2)*x*e^2-1/2*I/c^2*b*e^2-2*b*e*d*arcsec(c*x)*ln(1+(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)+I*b*e*d*polylog(2,-(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2)","A"
91,1,374,548,3.800000," ","int(x^2*(a+b*arcsec(c*x))/(e*x^2+d),x)","\frac{a x}{e}-\frac{a d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{e \sqrt{d e}}+\frac{b \,\mathrm{arcsec}\left(c x \right) x}{e}+\frac{i c b d \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d +c^{2} d +4 e \right) \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{8 e^{2}}+\frac{2 i b \arctan \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c e}-\frac{i c b d \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d +4 \textit{\_R1}^{2} e +c^{2} d \right) \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{8 e^{2}}"," ",0,"a*x/e-a*d/e/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+b*arcsec(c*x)/e*x+1/8*I*c*b/e^2*d*sum((_R1^2*c^2*d+c^2*d+4*e)/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+2*I/c*b/e*arctan(1/c/x+I*(1-1/c^2/x^2)^(1/2))-1/8*I*c*b/e^2*d*sum((_R1^2*c^2*d+4*_R1^2*e+c^2*d)/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))","C"
92,1,453,550,1.041000," ","int(x*(a+b*arcsec(c*x))/(e*x^2+d),x)","\frac{a \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 e}-\frac{i c^{2} b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2}+1\right) \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right) d}{4 e}-\frac{b \,\mathrm{arcsec}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e}-\frac{b \,\mathrm{arcsec}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e}+\frac{i b \dilog \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e}+\frac{i b \dilog \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e}-\frac{i b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d +c^{2} d +4 e \right) \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{4 e}"," ",0,"1/2*a/e*ln(c^2*e*x^2+c^2*d)-1/4*I*c^2*b*sum((_R1^2+1)/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))*d/e-b/e*arcsec(c*x)*ln(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))-b/e*arcsec(c*x)*ln(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+I*b/e*dilog(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+I*b/e*dilog(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))-1/4*I*b*sum((_R1^2*c^2*d+c^2*d+4*e)/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))/e","C"
93,1,272,513,1.893000," ","int((a+b*arcsec(c*x))/(e*x^2+d),x)","\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}+\frac{i c b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\textit{\_R1} \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{2}-\frac{i c b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{2}"," ",0,"a/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+1/2*I*c*b*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-1/2*I*c*b*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))","C"
94,1,2933,492,1.028000," ","int((a+b*arcsec(c*x))/x/(e*x^2+d),x)","\text{output too large to display}"," ",0,"I*b/c^4*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*e^2/d^3+1/2*b*(e*(c^2*d+e))^(1/2)/d/(c^2*d+e)*arcsec(c*x)*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e))+5/2*b*e/d/(c^2*d+e)*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)+I*b*(e*(c^2*d+e))^(1/2)/d/(c^2*d+e)*arcsec(c*x)^2+3/4*I*b*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/d/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-5/4*I*b*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/d/(c^2*d+e)*e-1/4*I*b*(e*(c^2*d+e))^(1/2)/d/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e))-1/2*I*b/c^2*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/d^2*(e*(c^2*d+e))^(1/2)-I*b/c^2*arcsec(c*x)^2/d^2*(e*(c^2*d+e))^(1/2)+2*I*b/c^2*arcsec(c*x)^2*e/d^2+2*I*b/c^4*arcsec(c*x)^2*e^2/d^3-5/2*I*b*arcsec(c*x)^2*e/d/(c^2*d+e)-3/2*b/d/(c^2*d+e)*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)*(e*(c^2*d+e))^(1/2)+b/c^2/d^2*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)*(e*(c^2*d+e))^(1/2)-2*b/c^2/d^2*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)*e-2*b/c^4/d^3*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)*e^2+I*b/c^2*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/d^2*e-1/2*I*b*c^2*arcsec(c*x)^2/(c^2*d+e)-1/4*I*b*c^2*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/(c^2*d+e)+4*b/c^2*e^2/d^2/(c^2*d+e)*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)-1/4*b*c^2/e/(c^2*d+e)*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)*(e*(c^2*d+e))^(1/2)-4*I*b/c^2*e^2*arcsec(c*x)^2/d^2/(c^2*d+e)+1/8*I*b*c^2*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/e/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-2*I*b/c^4*arcsec(c*x)^2*e/d^3*(e*(c^2*d+e))^(1/2)-2*I*b/c^4*e^3*arcsec(c*x)^2/d^3/(c^2*d+e)-2*I*b/c^2*e^2*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/d^2/(c^2*d+e)-I*b/c^4*e^3*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/d^3/(c^2*d+e)-I*b/c^4*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*e/d^3*(e*(c^2*d+e))^(1/2)-1/8*I*b*c^2*(e*(c^2*d+e))^(1/2)/e/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e))+2*b/c^4*e^3/d^3/(c^2*d+e)*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)+2*b/c^4/d^3*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)*e*(e*(c^2*d+e))^(1/2)+1/4*b*c^2*(e*(c^2*d+e))^(1/2)/e/(c^2*d+e)*arcsec(c*x)*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e))+1/2*b*c^2/(c^2*d+e)*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)+1/4*I*b*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/d+1/2*I*b/d*sum((_R1^2*c^2*d+2*c^2*d+4*e)/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-1/2*b/d*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)+I*b*arcsec(c*x)^2/d-1/2*a/d*ln(c^2*e*x^2+c^2*d)+a/d*ln(c*x)-2*b/c^4*e^2/d^3/(c^2*d+e)*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)*(e*(c^2*d+e))^(1/2)+3*I*b/c^2*e*arcsec(c*x)^2/d^2/(c^2*d+e)*(e*(c^2*d+e))^(1/2)+I*b/c^4*e^2*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/d^3/(c^2*d+e)*(e*(c^2*d+e))^(1/2)+2*I*b/c^4*e^2*arcsec(c*x)^2/d^3/(c^2*d+e)*(e*(c^2*d+e))^(1/2)+3/2*I*b/c^2*e*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/d^2/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-3*b/c^2*e/d^2/(c^2*d+e)*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)*(e*(c^2*d+e))^(1/2)","C"
95,1,331,553,3.666000," ","int((a+b*arcsec(c*x))/x^2/(e*x^2+d),x)","-\frac{a e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{d \sqrt{d e}}-\frac{a}{d x}+\frac{c b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{d}-\frac{b \,\mathrm{arcsec}\left(c x \right)}{d x}-\frac{i c b e \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\textit{\_R1} \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{2 d}+\frac{i c b e \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{2 d}"," ",0,"-a*e/d/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-a/d/x+c*b/d*((c^2*x^2-1)/c^2/x^2)^(1/2)-b*arcsec(c*x)/d/x-1/2*I*c*b*e/d*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+1/2*I*c*b*e/d*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))","C"
96,1,783,669,1.668000," ","int(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^2,x)","\frac{a \,x^{2}}{2 e^{2}}-\frac{a d \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{e^{3}}-\frac{c^{2} a \,d^{2}}{2 e^{3} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c^{2} b \,\mathrm{arcsec}\left(c x \right) x^{4}}{2 \left(c^{2} e \,x^{2}+c^{2} d \right) e}+\frac{c^{2} b \,\mathrm{arcsec}\left(c x \right) d \,x^{2}}{\left(c^{2} e \,x^{2}+c^{2} d \right) e^{2}}-\frac{c b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3}}{2 \left(c^{2} e \,x^{2}+c^{2} d \right) e}-\frac{c b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d}{2 \left(c^{2} e \,x^{2}+c^{2} d \right) e^{2}}-\frac{i b d}{2 \left(c^{2} e \,x^{2}+c^{2} d \right) e^{2}}+\frac{i c^{2} b \,d^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2}+1\right) \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{2 e^{3}}+\frac{i b d \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d +c^{2} d +4 e \right) \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{2 e^{3}}-\frac{2 i b d \dilog \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e^{3}}+\frac{2 b d \,\mathrm{arcsec}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e^{3}}+\frac{2 b d \,\mathrm{arcsec}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e^{3}}-\frac{2 i b d \dilog \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e^{3}}-\frac{i b \,x^{2}}{2 \left(c^{2} e \,x^{2}+c^{2} d \right) e}-\frac{i b \sqrt{e \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 c^{2} d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}+2 c^{2} d +4 e}{4 \sqrt{c^{2} e d +e^{2}}}\right) d}{2 \left(c^{2} d +e \right) e^{3}}"," ",0,"1/2*a*x^2/e^2-a/e^3*d*ln(c^2*e*x^2+c^2*d)-1/2*c^2*a/e^3*d^2/(c^2*e*x^2+c^2*d)+1/2*c^2*b/(c^2*e*x^2+c^2*d)/e*arcsec(c*x)*x^4+c^2*b/(c^2*e*x^2+c^2*d)/e^2*arcsec(c*x)*d*x^2-1/2*c*b/(c^2*e*x^2+c^2*d)/e*((c^2*x^2-1)/c^2/x^2)^(1/2)*x^3-1/2*c*b/(c^2*e*x^2+c^2*d)/e^2*((c^2*x^2-1)/c^2/x^2)^(1/2)*x*d-1/2*I*b/(c^2*e*x^2+c^2*d)/e^2*d-2*I*b/e^3*d*dilog(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+1/2*I*c^2*b/e^3*d^2*sum((_R1^2+1)/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+1/2*I*b/e^3*d*sum((_R1^2*c^2*d+c^2*d+4*e)/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+2*b/e^3*d*arcsec(c*x)*ln(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+2*b/e^3*d*arcsec(c*x)*ln(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))-1/2*I*b/(c^2*e*x^2+c^2*d)/e*x^2-1/2*I*b*(e*(c^2*d+e))^(1/2)/(c^2*d+e)/e^3*arctanh(1/4*(2*c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2+2*c^2*d+4*e)/(c^2*d*e+e^2)^(1/2))*d-2*I*b/e^3*d*dilog(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))","C"
97,1,594,622,1.369000," ","int(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^2,x)","\frac{a \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 e^{2}}+\frac{c^{2} a d}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{2} b \,x^{2} \mathrm{arcsec}\left(c x \right)}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{i b \sqrt{e \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 c^{2} d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}+2 c^{2} d +4 e}{4 \sqrt{c^{2} e d +e^{2}}}\right)}{2 \left(c^{2} d +e \right) e^{2}}-\frac{i b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d +c^{2} d +4 e \right) \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{4 e^{2}}-\frac{b \,\mathrm{arcsec}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e^{2}}-\frac{b \,\mathrm{arcsec}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e^{2}}+\frac{i b \dilog \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e^{2}}+\frac{i b \dilog \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e^{2}}-\frac{i c^{2} b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2}+1\right) \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right) d}{4 e^{2}}"," ",0,"1/2*a/e^2*ln(c^2*e*x^2+c^2*d)+1/2*c^2*a/e^2*d/(c^2*e*x^2+c^2*d)-1/2*c^2*b*x^2*arcsec(c*x)/e/(c^2*e*x^2+c^2*d)+1/2*I*b*(e*(c^2*d+e))^(1/2)/(c^2*d+e)/e^2*arctanh(1/4*(2*c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2+2*c^2*d+4*e)/(c^2*d*e+e^2)^(1/2))-1/4*I*b/e^2*sum((_R1^2*c^2*d+c^2*d+4*e)/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-b/e^2*arcsec(c*x)*ln(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))-b/e^2*arcsec(c*x)*ln(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+I*b/e^2*dilog(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+I*b/e^2*dilog(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))-1/4*I*c^2*b/e^2*sum((_R1^2+1)/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))*d","C"
98,1,354,112,0.076000," ","int(x*(a+b*arcsec(c*x))/(e*x^2+d)^2,x)","-\frac{c^{2} a}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{c^{2} b \,\mathrm{arcsec}\left(c x \right)}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{2 c e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d}+\frac{b \sqrt{c^{2} x^{2}-1}\, \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right)}{4 c e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \sqrt{-\frac{c^{2} d +e}{e}}}+\frac{b \sqrt{c^{2} x^{2}-1}\, \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right)}{4 c e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \sqrt{-\frac{c^{2} d +e}{e}}}"," ",0,"-1/2*c^2*a/e/(c^2*e*x^2+c^2*d)-1/2*c^2*b/e/(c^2*e*x^2+c^2*d)*arcsec(c*x)-1/2/c*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d*arctan(1/(c^2*x^2-1)^(1/2))+1/4/c*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/(-(c^2*d+e)/e)^(1/2)*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))+1/4/c*b/e*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/(-(c^2*d+e)/e)^(1/2)*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))","B"
99,1,3095,565,2.679000," ","int((a+b*arcsec(c*x))/x/(e*x^2+d)^2,x)","\text{output too large to display}"," ",0,"-1/2*a/d^2*ln(c^2*e*x^2+c^2*d)+a/d^2*ln(c*x)+1/2*a*c^2/d/(c^2*e*x^2+c^2*d)-1/2*I*b/c^2*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/d^3*(e*(c^2*d+e))^(1/2)-1/4*I*b*c^2*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/d/(c^2*d+e)-2*b/c^4/d^4*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)*e^2+1/2*b*c^2/d/(c^2*d+e)*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)+I*b*arcsec(c*x)^2/d^2-1/2*b/d^2*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)+1/4*I*b*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/d^2+1/2*I*b/d^2*sum((_R1^2*c^2*d+2*c^2*d+4*e)/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-5/4*I*b*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/d^2/(c^2*d+e)*e-1/4*I*b*(e*(c^2*d+e))^(1/2)/d^2/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e))-5/2*I*b*arcsec(c*x)^2/d^2/(c^2*d+e)*e+I*b/c^4*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*e^2/d^4+2*I*b/c^4*arcsec(c*x)^2*e^2/d^4+I*b/c^2*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*e/d^3+1/2*I*b*(e*(c^2*d+e))^(1/2)/d^2/(c^2*d+e)*arctanh(1/4*(2*c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2+2*c^2*d+4*e)/(c^2*d*e+e^2)^(1/2))+3/4*I*b*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/d^2/(c^2*d+e)*(e*(c^2*d+e))^(1/2)+4*b/c^2*e^2/(c^2*d+e)/d^3*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)+2*b/c^4*e^3/(c^2*d+e)/d^4*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)+2*b/c^4/d^4*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)*e*(e*(c^2*d+e))^(1/2)-2*I*b/c^2*e^2*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/(c^2*d+e)/d^3-I*b/c^4*e^3*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/(c^2*d+e)/d^4-3/2*b/d^2/(c^2*d+e)*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)*(e*(c^2*d+e))^(1/2)+1/2*b*(e*(c^2*d+e))^(1/2)/d^2/(c^2*d+e)*arcsec(c*x)*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e))+5/2*b/d^2*e/(c^2*d+e)*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)+b/c^2/d^3*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)*(e*(c^2*d+e))^(1/2)-2*b/c^2/d^3*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)*e-1/2*I*b*c^2*arcsec(c*x)^2/d/(c^2*d+e)-2*I*b/c^4*arcsec(c*x)^2*e/d^4*(e*(c^2*d+e))^(1/2)-2*I*b/c^4*e^3*arcsec(c*x)^2/(c^2*d+e)/d^4-I*b/c^4*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*e/d^4*(e*(c^2*d+e))^(1/2)-4*I*b/c^2*arcsec(c*x)^2/d^3/(c^2*d+e)*e^2-1/2*b*c^2*x^2*arcsec(c*x)*e/(c^2*e*x^2+c^2*d)/d^2+2*I*b/c^2*arcsec(c*x)^2*e/d^3-I*b/c^2*arcsec(c*x)^2/d^3*(e*(c^2*d+e))^(1/2)+I*b*(e*(c^2*d+e))^(1/2)/d^2/(c^2*d+e)*arcsec(c*x)^2+2*I*b/c^4*e^2*arcsec(c*x)^2/(c^2*d+e)/d^4*(e*(c^2*d+e))^(1/2)+1/8*I*b*c^2*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/d/e/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-3*b/c^2*e/(c^2*d+e)/d^3*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)*(e*(c^2*d+e))^(1/2)-1/8*I*b*c^2*(e*(c^2*d+e))^(1/2)/e/(c^2*d+e)/d*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e))+I*b/c^4*e^2*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/(c^2*d+e)/d^4*(e*(c^2*d+e))^(1/2)-2*b/c^4*e^2/(c^2*d+e)/d^4*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)*(e*(c^2*d+e))^(1/2)-1/4*b*c^2/d/e/(c^2*d+e)*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsec(c*x)*(e*(c^2*d+e))^(1/2)+1/4*b*c^2*(e*(c^2*d+e))^(1/2)/e/(c^2*d+e)/d*arcsec(c*x)*ln(1-c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e))+3*I*b/c^2*arcsec(c*x)^2/d^3/(c^2*d+e)*(e*(c^2*d+e))^(1/2)*e+3/2*I*b/c^2*e*polylog(2,c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))/(c^2*d+e)/d^3*(e*(c^2*d+e))^(1/2)","C"
100,1,1887,742,16.500000," ","int(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^2,x)","\frac{a x}{e^{2}}+\frac{c^{2} a d x}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{3 a d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 e^{2} \sqrt{d e}}+\frac{c^{2} b \,x^{3} \mathrm{arcsec}\left(c x \right)}{e \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{3 c^{2} b \,\mathrm{arcsec}\left(c x \right) d x}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{2 c^{2} e^{2} \left(c^{2} d +e \right) d}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{2 c^{2} e^{2} d}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} e^{2} d^{2}}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} e^{2} d^{2}}+\frac{2 i b \arctan \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{c \,e^{2}}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{2 c^{2} e^{2} \left(c^{2} d +e \right) d}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{c^{4} \left(c^{2} d +e \right) d^{2}}+\frac{3 i c b d \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d +c^{2} d +4 e \right) \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{16 e^{3}}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{c^{4} e \,d^{2}}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{c^{4} \left(c^{2} d +e \right) d^{2}}-\frac{3 i c b d \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d +4 \textit{\_R1}^{2} e +c^{2} d \right) \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{16 e^{3}}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} e \left(c^{2} d +e \right) d^{2}}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{c^{2} e \left(c^{2} d +e \right) d}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{c^{2} e \left(c^{2} d +e \right) d}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} e \left(c^{2} d +e \right) d^{2}}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{2 c^{2} e^{2} d}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{c^{4} e \,d^{2}}"," ",0,"a*x/e^2+1/2*c^2*a/e^2*d*x/(c^2*e*x^2+c^2*d)-3/2*a/e^2*d/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+c^2*b*x^3*arcsec(c*x)/e/(c^2*e*x^2+c^2*d)+3/2*c^2*b*arcsec(c*x)/e^2*d*x/(c^2*e*x^2+c^2*d)+1/2*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e^2/(c^2*d+e)/d*(e*(c^2*d+e))^(1/2)+1/2*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e^2/d-I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e^2/d^2*(e*(c^2*d+e))^(1/2)-3/16*I*c*b/e^3*d*sum((_R1^2*c^2*d+4*_R1^2*e+c^2*d)/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-1/2*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e^2/(c^2*d+e)/d*(e*(c^2*d+e))^(1/2)+2*I/c*b/e^2*arctan(1/c/x+I*(1-1/c^2/x^2)^(1/2))+I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e^2/d^2*(e*(c^2*d+e))^(1/2)-I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^2-I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)/d^2*(e*(c^2*d+e))^(1/2)+I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/d^2-I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)/d+3/16*I*c*b/e^3*d*sum((_R1^2*c^2*d+c^2*d+4*e)/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+1/2*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e^2/d+I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)/d^2*(e*(c^2*d+e))^(1/2)-I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)/d+I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/d^2-I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^2","C"
101,1,1756,708,3.780000," ","int(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^2,x)","-\frac{c^{2} a x}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 e \sqrt{d e}}-\frac{c^{2} b \,\mathrm{arcsec}\left(c x \right) x}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} e \,d^{3}}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{2 c^{2} e \left(c^{2} d +e \right) d^{2}}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} e \,d^{3}}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) e}{c^{4} \left(c^{2} d +e \right) d^{3}}+\frac{i c b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\textit{\_R1} \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{4 e}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{2 c^{2} e \,d^{2}}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{c^{4} d^{3}}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} \left(c^{2} d +e \right) d^{3}}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{2 c^{2} e \left(c^{2} d +e \right) d^{2}}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{c^{2} \left(c^{2} d +e \right) d^{2}}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} \left(c^{2} d +e \right) d^{3}}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{2 c^{2} e \,d^{2}}-\frac{i c b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{4 e}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{c^{4} d^{3}}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{c^{2} \left(c^{2} d +e \right) d^{2}}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) e}{c^{4} \left(c^{2} d +e \right) d^{3}}"," ",0,"-1/2*c^2*a/e*x/(c^2*e*x^2+c^2*d)+1/2*a/e/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-1/2*c^2*b*arcsec(c*x)/e*x/(c^2*e*x^2+c^2*d)+I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/d^3*(e*(c^2*d+e))^(1/2)-1/2*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)/d^2*(e*(c^2*d+e))^(1/2)+I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))*e/(c^2*d+e)/d^3+I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^3*(e*(c^2*d+e))^(1/2)-1/2*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/d^2-I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^3+I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^2-I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/d^3*(e*(c^2*d+e))^(1/2)-1/4*I*c*b/e*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^3*(e*(c^2*d+e))^(1/2)+1/2*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)/d^2*(e*(c^2*d+e))^(1/2)+1/4*I*c*b/e*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-1/2*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/d^2+I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))*e/(c^2*d+e)/d^3+I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^2-I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^3","C"
102,1,1748,702,4.343000," ","int((a+b*arcsec(c*x))/(e*x^2+d)^2,x)","\frac{c^{2} a x}{2 d \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 d \sqrt{d e}}+\frac{c^{2} b \,\mathrm{arcsec}\left(c x \right) x}{2 d \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}\, e}{c^{4} d^{4} \left(c^{2} d +e \right)}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} d^{4}}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) e^{2}}{c^{4} d^{4} \left(c^{2} d +e \right)}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{2 c^{2} d^{3} \left(c^{2} d +e \right)}+\frac{i c b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\textit{\_R1} \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{4 d}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) e}{c^{2} \left(c^{2} d +e \right) d^{3}}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) e}{c^{4} d^{4}}-\frac{i c b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{4 d}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{2 c^{2} \left(c^{2} d +e \right) d^{3}}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{2 c^{2} d^{3}}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) e}{c^{2} \left(c^{2} d +e \right) d^{3}}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) e^{2}}{c^{4} d^{4} \left(c^{2} d +e \right)}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}\, e}{c^{4} d^{4} \left(c^{2} d +e \right)}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} d^{4}}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) e}{c^{4} d^{4}}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{2 c^{2} d^{3}}"," ",0,"1/2*c^2*a*x/d/(c^2*e*x^2+c^2*d)+1/2*a/d/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))+1/2*c^2*b*arcsec(c*x)*x/d/(c^2*e*x^2+c^2*d)-I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))*e/(c^2*d+e)/d^3-I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4/(c^2*d+e)*e^2+1/4*I*c*b/d*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+1/2*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^3+1/2*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^3/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))*e/(c^2*d+e)/d^3+I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4*e-I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4/(c^2*d+e)*(e*(c^2*d+e))^(1/2)*e-1/4*I*c*b/d*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-1/2*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^3*(e*(c^2*d+e))^(1/2)+I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4*(e*(c^2*d+e))^(1/2)-I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4/(c^2*d+e)*e^2+I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4/(c^2*d+e)*(e*(c^2*d+e))^(1/2)*e-I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4*(e*(c^2*d+e))^(1/2)+I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4*e+1/2*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^3","C"
103,1,1817,743,15.836000," ","int((a+b*arcsec(c*x))/x^2/(e*x^2+d)^2,x)","-\frac{a e \,c^{2} x}{2 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{3 a e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 d^{2} \sqrt{d e}}-\frac{a}{d^{2} x}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, e^{3} \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{c^{4} d^{5} \left(c^{2} d +e \right)}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, e^{3} \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{c^{4} d^{5} \left(c^{2} d +e \right)}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, e^{2} \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} d^{5} \left(c^{2} d +e \right)}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) e^{2}}{c^{4} d^{5}}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}\, e}{2 c^{2} d^{4} \left(c^{2} d +e \right)}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, e \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{2 c^{2} d^{4} \left(c^{2} d +e \right)}-\frac{3 i c b e \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\textit{\_R1} \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{4 d^{2}}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, e^{2} \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{c^{2} d^{4} \left(c^{2} d +e \right)}+\frac{c b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{d^{2}}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) e \sqrt{e \left(c^{2} d +e \right)}}{c^{4} d^{5}}+\frac{3 i c b e \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{4 d^{2}}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, e^{2} \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{c^{2} d^{4} \left(c^{2} d +e \right)}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, e^{2} \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{c^{4} d^{5} \left(c^{2} d +e \right)}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) e}{2 c^{2} d^{4}}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) e^{2}}{c^{4} d^{5}}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) e \sqrt{e \left(c^{2} d +e \right)}}{c^{4} d^{5}}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) e}{2 c^{2} d^{4}}-\frac{b \,\mathrm{arcsec}\left(c x \right) e \,c^{2} x}{2 d^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}-\frac{b \,\mathrm{arcsec}\left(c x \right)}{d^{2} x}"," ",0,"-1/2*a/d^2*e*c^2*x/(c^2*e*x^2+c^2*d)-3/2*a/d^2*e/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-a/d^2/x-I*b/c^4*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))*e^2/d^5+I*b/c^4*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^3*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^5/(c^2*d+e)+3/4*I*c*b/d^2*e*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-I*b/c^4*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^5/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-I*b/c^4*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))*e^2/d^5-1/2*I*b/c^2*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4/(c^2*d+e)*(e*(c^2*d+e))^(1/2)*e+I*b/c^4*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^5/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-I*b/c^4*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))*e/d^5*(e*(c^2*d+e))^(1/2)+c*b/d^2*((c^2*x^2-1)/c^2/x^2)^(1/2)+I*b/c^4*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))*e/d^5*(e*(c^2*d+e))^(1/2)-3/4*I*c*b/d^2*e*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+I*b/c^2*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4/(c^2*d+e)+I*b/c^4*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^3*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^5/(c^2*d+e)-1/2*I*b/c^2*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4*e-1/2*I*b/c^2*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4*e+I*b/c^2*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4/(c^2*d+e)+1/2*I*b/c^2*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-1/2*b*arcsec(c*x)/d^2*e*c^2*x/(c^2*e*x^2+c^2*d)-b*arcsec(c*x)/d^2/x","C"
104,1,1626,744,1.964000," ","int(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^3,x)","\frac{c^{2} a d}{e^{3} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{5 i c^{2} b \sqrt{e \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 c^{2} d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}+2 c^{2} d +4 e}{4 \sqrt{c^{2} e d +e^{2}}}\right) d}{8 e^{3} \left(c^{2} d +e \right)^{2}}-\frac{i c^{4} b \,x^{2} d}{4 e \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{4} b \,\mathrm{arcsec}\left(c x \right) d \,x^{2}}{2 e \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{5} b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x^{3} d}{8 e \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{5} b \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \,d^{2}}{8 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{3 c^{6} b \,\mathrm{arcsec}\left(c x \right) d \,x^{4}}{4 e \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{6} b \,\mathrm{arcsec}\left(c x \right) d^{2} x^{2}}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{a \ln \left(c^{2} e \,x^{2}+c^{2} d \right)}{2 e^{3}}-\frac{i b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d +c^{2} d +4 e \right) \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{4 e^{2} \left(c^{2} d +e \right)}+\frac{i b \dilog \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e^{2} \left(c^{2} d +e \right)}+\frac{i b \dilog \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e^{2} \left(c^{2} d +e \right)}-\frac{b \,\mathrm{arcsec}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e^{2} \left(c^{2} d +e \right)}-\frac{b \,\mathrm{arcsec}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e^{2} \left(c^{2} d +e \right)}+\frac{3 i b \sqrt{e \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 c^{2} d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)^{2}+2 c^{2} d +4 e}{4 \sqrt{c^{2} e d +e^{2}}}\right)}{4 e^{2} \left(c^{2} d +e \right)^{2}}-\frac{i c^{4} b \,x^{4}}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{4} a \,d^{2}}{4 e^{3} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{2} b d \,\mathrm{arcsec}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e^{3} \left(c^{2} d +e \right)}-\frac{c^{2} b d \,\mathrm{arcsec}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e^{3} \left(c^{2} d +e \right)}-\frac{i c^{4} b \,d^{2}}{8 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{i c^{2} b d \dilog \left(1+i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e^{3} \left(c^{2} d +e \right)}+\frac{i c^{2} b d \dilog \left(1-i \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)\right)}{e^{3} \left(c^{2} d +e \right)}-\frac{i c^{2} b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2}+1\right) \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right) d}{4 e^{2} \left(c^{2} d +e \right)}-\frac{i c^{2} b d \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2} c^{2} d +c^{2} d +4 e \right) \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{4 e^{3} \left(c^{2} d +e \right)}-\frac{i c^{4} b \,d^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\left(\textit{\_R1}^{2}+1\right) \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{4 e^{3} \left(c^{2} d +e \right)}-\frac{3 c^{4} b \,\mathrm{arcsec}\left(c x \right) x^{4}}{4 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}"," ",0,"c^2*a/e^3*d/(c^2*e*x^2+c^2*d)-1/4*I*c^4*b/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*x^2*d+5/8*I*c^2*b*(e*(c^2*d+e))^(1/2)/e^3/(c^2*d+e)^2*arctanh(1/4*(2*c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2+2*c^2*d+4*e)/(c^2*d*e+e^2)^(1/2))*d-1/2*c^4*b/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsec(c*x)*d*x^2-1/8*c^5*b/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*((c^2*x^2-1)/c^2/x^2)^(1/2)*x^3*d-1/8*c^5*b/e^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*((c^2*x^2-1)/c^2/x^2)^(1/2)*x*d^2-3/4*c^6*b/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsec(c*x)*d*x^4-1/2*c^6*b/e^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsec(c*x)*d^2*x^2-c^2*b/e^3/(c^2*d+e)*d*arcsec(c*x)*ln(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))-c^2*b/e^3/(c^2*d+e)*d*arcsec(c*x)*ln(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+I*c^2*b/e^3/(c^2*d+e)*d*dilog(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+I*c^2*b/e^3/(c^2*d+e)*d*dilog(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))-1/8*I*c^4*b/e^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*d^2-1/4*I*c^2*b/e^2/(c^2*d+e)*sum((_R1^2+1)/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))*d-1/4*I*c^2*b/e^3/(c^2*d+e)*d*sum((_R1^2*c^2*d+c^2*d+4*e)/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-1/4*I*c^4*b/e^3/(c^2*d+e)*d^2*sum((_R1^2+1)/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+1/2*a/e^3*ln(c^2*e*x^2+c^2*d)-1/4*I*b/e^2/(c^2*d+e)*sum((_R1^2*c^2*d+c^2*d+4*e)/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-1/4*c^4*a*d^2/e^3/(c^2*e*x^2+c^2*d)^2-3/4*c^4*b/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsec(c*x)*x^4+3/4*I*b*(e*(c^2*d+e))^(1/2)/e^2/(c^2*d+e)^2*arctanh(1/4*(2*c^2*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))^2+2*c^2*d+4*e)/(c^2*d*e+e^2)^(1/2))-1/8*I*c^4*b/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*x^4+I*b/e^2/(c^2*d+e)*dilog(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))+I*b/e^2/(c^2*d+e)*dilog(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))-b/e^2/(c^2*d+e)*arcsec(c*x)*ln(1+I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))-b/e^2/(c^2*d+e)*arcsec(c*x)*ln(1-I*(1/c/x+I*(1-1/c^2/x^2)^(1/2)))","C"
105,1,1870,135,0.082000," ","int(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^3,x)","-\frac{c^{2} a}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c^{4} a d}{4 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{2} b \,\mathrm{arcsec}\left(c x \right)}{2 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)}+\frac{c^{4} b \,\mathrm{arcsec}\left(c x \right) d}{4 e^{2} \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}+\frac{c^{3} b \sqrt{c^{2} x^{2}-1}\, x \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{c^{3} b \sqrt{c^{2} x^{2}-1}\, d \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c^{3} b \sqrt{c^{2} x^{2}-1}\, x \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right)}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c^{3} b \sqrt{c^{2} x^{2}-1}\, d \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right)}{16 e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c^{3} b \sqrt{c^{2} x^{2}-1}\, x \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right)}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c^{3} b \sqrt{c^{2} x^{2}-1}\, d \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right)}{16 e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{c b \sqrt{c^{2} x^{2}-1}\, e x \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{c b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c^{3} b x}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{c b}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c b \sqrt{c^{2} x^{2}-1}\, e x \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right)}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c b \sqrt{c^{2} x^{2}-1}\, \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right)}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c b \sqrt{c^{2} x^{2}-1}\, e x \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right)}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c b \sqrt{c^{2} x^{2}-1}\, \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right)}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}"," ",0,"-1/2*c^2*a/e^2/(c^2*e*x^2+c^2*d)+1/4*c^4*a/e^2*d/(c^2*e*x^2+c^2*d)^2-1/2*c^2*b*arcsec(c*x)/e^2/(c^2*e*x^2+c^2*d)+1/4*c^4*b*arcsec(c*x)/e^2*d/(c^2*e*x^2+c^2*d)^2+1/4*c^3*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*arctan(1/(c^2*x^2-1)^(1/2))+1/4*c^3*b*(c^2*x^2-1)^(1/2)/e/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*arctan(1/(c^2*x^2-1)^(1/2))-1/16*c^3*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))-1/16*c^3*b*(c^2*x^2-1)^(1/2)/e/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))-1/16*c^3*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))-1/16*c^3*b*(c^2*x^2-1)^(1/2)/e/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*d/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))+1/4*c*b*(c^2*x^2-1)^(1/2)*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*arctan(1/(c^2*x^2-1)^(1/2))+1/4*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*arctan(1/(c^2*x^2-1)^(1/2))-1/8*c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))+1/8*c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))-1/8*c*b*(c^2*x^2-1)^(1/2)*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))-1/8*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))-1/8*c*b*(c^2*x^2-1)^(1/2)*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))-1/8*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))","B"
106,1,1840,168,0.074000," ","int(x*(a+b*arcsec(c*x))/(e*x^2+d)^3,x)","-\frac{c^{4} a}{4 e \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}-\frac{c^{4} b \,\mathrm{arcsec}\left(c x \right)}{4 e \left(c^{2} e \,x^{2}+c^{2} d \right)^{2}}+\frac{c^{3} b \sqrt{c^{2} x^{2}-1}\, e x \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{c^{3} b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{3 c^{3} b \sqrt{c^{2} x^{2}-1}\, e x \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right)}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{3 c^{3} b \sqrt{c^{2} x^{2}-1}\, \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right)}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{3 c^{3} b \sqrt{c^{2} x^{2}-1}\, e x \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right)}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{3 c^{3} b \sqrt{c^{2} x^{2}-1}\, \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right)}{16 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{c b \sqrt{c^{2} x^{2}-1}\, x \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right) e^{2}}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d^{2} \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{c b \sqrt{c^{2} x^{2}-1}\, \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right) e}{4 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}+\frac{c^{3} b x e}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c b e}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c b \sqrt{c^{2} x^{2}-1}\, x \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right) e^{2}}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d^{2} \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c b \sqrt{c^{2} x^{2}-1}\, \ln \left(\frac{2 \sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e -2 \sqrt{-c^{2} e d}\, c x -2 e}{c e x +\sqrt{-c^{2} e d}}\right) e}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c b \sqrt{c^{2} x^{2}-1}\, x \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right) e^{2}}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, d^{2} \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}-\frac{c b \sqrt{c^{2} x^{2}-1}\, \ln \left(-\frac{2 \left(\sqrt{-\frac{c^{2} d +e}{e}}\, \sqrt{c^{2} x^{2}-1}\, e +\sqrt{-c^{2} e d}\, c x -e \right)}{-c e x +\sqrt{-c^{2} e d}}\right) e}{8 \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, x d \sqrt{-\frac{c^{2} d +e}{e}}\, \left(c^{2} d +e \right) \left(-c e x +\sqrt{-c^{2} e d}\right) \left(c e x +\sqrt{-c^{2} e d}\right)}"," ",0,"-1/4*c^4*a/e/(c^2*e*x^2+c^2*d)^2-1/4*c^4*b/e/(c^2*e*x^2+c^2*d)^2*arcsec(c*x)+1/4*c^3*b*(c^2*x^2-1)^(1/2)*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*arctan(1/(c^2*x^2-1)^(1/2))+1/4*c^3*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*arctan(1/(c^2*x^2-1)^(1/2))-3/16*c^3*b*(c^2*x^2-1)^(1/2)*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))-3/16*c^3*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))-3/16*c^3*b*(c^2*x^2-1)^(1/2)*e/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))-3/16*c^3*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))+1/4*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d^2/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*arctan(1/(c^2*x^2-1)^(1/2))*e^2+1/4*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*arctan(1/(c^2*x^2-1)^(1/2))*e+1/8*c^3*b/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*e-1/8*c*b/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*e-1/8*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d^2/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))*e^2-1/8*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e-(-c^2*e*d)^(1/2)*c*x-e)/(c*e*x+(-c^2*e*d)^(1/2)))*e-1/8*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)*x/d^2/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))*e^2-1/8*c*b*(c^2*x^2-1)^(1/2)/((c^2*x^2-1)/c^2/x^2)^(1/2)/x/d/(-(c^2*d+e)/e)^(1/2)/(c^2*d+e)/(-c*e*x+(-c^2*e*d)^(1/2))/(c*e*x+(-c^2*e*d)^(1/2))*ln(-2*((-(c^2*d+e)/e)^(1/2)*(c^2*x^2-1)^(1/2)*e+(-c^2*e*d)^(1/2)*c*x-e)/(-c*e*x+(-c^2*e*d)^(1/2)))*e","B"
107,1,5373,690,6.522000," ","int((a+b*arcsec(c*x))/x/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
108,1,3223,1008,4.414000," ","int(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"-3/8*I*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e^2/(c^2*d+e)^2/d*(e*(c^2*d+e))^(1/2)-I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/d^3*(e*(c^2*d+e))^(1/2)+3/8*I*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e^2/(c^2*d+e)^2/d*(e*(c^2*d+e))^(1/2)-5/4*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)/d^2-5/4*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)/d^2+I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/d^3*(e*(c^2*d+e))^(1/2)-5/8*c^6*b*x^3/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)/e*arcsec(c*x)*d-3/8*c^6*b*x/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)/e^2*arcsec(c*x)*d^2+1/8*c^5*b*x^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)/e*((c^2*x^2-1)/c^2/x^2)^(1/2)*d-3/8*c^4*b*x/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)/e*arcsec(c*x)*d+I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2*e/d^3+I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2*e/d^3+I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)/d^3*(e*(c^2*d+e))^(1/2)+3/4*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e^2/(c^2*d+e)/d^2*(e*(c^2*d+e))^(1/2)+5/4*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/e/d^2*(e*(c^2*d+e))^(1/2)-5/4*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/e/d^2*(e*(c^2*d+e))^(1/2)-3/4*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e^2/(c^2*d+e)/d^2*(e*(c^2*d+e))^(1/2)-I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)/d^3*(e*(c^2*d+e))^(1/2)+3/8*a/e^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-5/8*c^4*a/(c^2*e*x^2+c^2*d)^2/e*x^3-I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^3+3/16*I*c^3*b/e^2/(c^2*d+e)*d*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-3/16*I*c^3*b/e^2/(c^2*d+e)*d*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+7/4*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/d^2-I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^3+7/4*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/d^2+3/4*I*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)^2/d-3/8*I*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e^2/(c^2*d+e)/d-3/8*I*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e^2/(c^2*d+e)/d+3/4*I*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)^2/d-5/8*c^4*b*x^3/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsec(c*x)+1/8*c^5*b*x^4/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*((c^2*x^2-1)/c^2/x^2)^(1/2)+3/16*I*c*b/e/(c^2*d+e)*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-3/16*I*c*b/e/(c^2*d+e)*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-3/8*c^4*a/(c^2*e*x^2+c^2*d)^2/e^2*d*x","C"
109,1,2357,1014,6.712000," ","int(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^3,x)","-\frac{c^{6} b x \,\mathrm{arcsec}\left(c x \right) d}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right) e}-\frac{c^{5} b \,x^{4} e \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right) d}+\frac{c^{4} b \,x^{3} e \,\mathrm{arcsec}\left(c x \right)}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right) d}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{4 c^{2} \left(c^{2} d +e \right)^{2} d^{3}}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{4 c^{2} \left(c^{2} d +e \right)^{2} d^{3}}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{8 \left(c^{2} d +e \right)^{2} e \,d^{2}}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) e}{4 c^{2} \left(c^{2} d +e \right)^{2} d^{3}}-\frac{i c b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{16 d \left(c^{2} d +e \right)}+\frac{i c^{3} b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\textit{\_R1} \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{16 e \left(c^{2} d +e \right)}+\frac{c^{6} b \,x^{3} \mathrm{arcsec}\left(c x \right)}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{5} b \,x^{2} \sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{4} b x \,\mathrm{arcsec}\left(c x \right)}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{4 \left(c^{2} d +e \right)^{2} d^{2}}+\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{4 \left(c^{2} d +e \right)^{2} d^{2}}-\frac{i c^{3} b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{16 e \left(c^{2} d +e \right)}+\frac{i c b \left(\munderset{\textit{\_R1} =\RootOf \left(c^{2} d \,\textit{\_Z}^{4}+\left(2 c^{2} d +4 e \right) \textit{\_Z}^{2}+c^{2} d \right)}{\sum}\frac{\textit{\_R1} \left(i \mathrm{arcsec}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-i \sqrt{1-\frac{1}{c^{2} x^{2}}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{16 d \left(c^{2} d +e \right)}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{4 c^{2} e \left(c^{2} d +e \right) d^{3}}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{4 c^{2} e \left(c^{2} d +e \right) d^{3}}+\frac{c^{4} a \,x^{3}}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} d}-\frac{c^{4} a x}{8 \left(c^{2} e \,x^{2}+c^{2} d \right)^{2} e}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 d e \sqrt{d e}}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{8 e \left(c^{2} d +e \right) d^{2}}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{4 c^{2} \left(c^{2} d +e \right) d^{3}}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{4 c^{2} \left(c^{2} d +e \right) d^{3}}-\frac{i b \sqrt{-\left(c^{2} d -2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctanh \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{8 e \left(c^{2} d +e \right) d^{2}}+\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) e}{4 c^{2} \left(c^{2} d +e \right)^{2} d^{3}}-\frac{i b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, \arctan \left(\frac{c d \left(\frac{1}{c x}+i \sqrt{1-\frac{1}{c^{2} x^{2}}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right) \sqrt{e \left(c^{2} d +e \right)}}{8 \left(c^{2} d +e \right)^{2} e \,d^{2}}"," ",0,"-1/8*c^6*b*x/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)/e*arcsec(c*x)*d-1/8*c^5*b*x^4/(c^2*e*x^2+c^2*d)^2*e/(c^2*d+e)/d*((c^2*x^2-1)/c^2/x^2)^(1/2)+1/8*c^4*b*x^3/(c^2*e*x^2+c^2*d)^2*e/(c^2*d+e)/d*arcsec(c*x)+1/4*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2*e/d^3+1/4*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/d^3*(e*(c^2*d+e))^(1/2)-1/8*I*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/e/d^2*(e*(c^2*d+e))^(1/2)+1/8*I*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/e/d^2*(e*(c^2*d+e))^(1/2)-1/4*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/d^3*(e*(c^2*d+e))^(1/2)+1/4*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2*e/d^3+1/8*c^6*b*x^3/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsec(c*x)-1/8*c^5*b*x^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*((c^2*x^2-1)/c^2/x^2)^(1/2)-1/8*c^4*b*x/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsec(c*x)+1/4*I*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/d^2+1/4*I*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/d^2-1/16*I*c^3*b/e/(c^2*d+e)*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+1/16*I*c*b/d/(c^2*d+e)*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-1/16*I*c*b/d/(c^2*d+e)*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+1/16*I*c^3*b/e/(c^2*d+e)*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-1/8*I*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)/d^2-1/4*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^3-1/4*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^3-1/8*I*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)/d^2+1/4*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)/d^3*(e*(c^2*d+e))^(1/2)-1/4*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)/d^3*(e*(c^2*d+e))^(1/2)+1/8*c^4*a/(c^2*e*x^2+c^2*d)^2/d*x^3-1/8*c^4*a/(c^2*e*x^2+c^2*d)^2/e*x+1/8*a/d/e/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))","C"
110,1,3214,998,7.829000," ","int((a+b*arcsec(c*x))/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"-9/4*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4/(c^2*d+e)^2+5/4*I/c^2*b*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)/d^4/(c^2*d+e)*(e*(c^2*d+e))^(1/2)-9/4*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4/(c^2*d+e)^2-I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^3*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^5/(c^2*d+e)^2+7/4*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))*e/d^4/(c^2*d+e)-I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^3*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^5/(c^2*d+e)^2+7/4*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))*e/d^4/(c^2*d+e)-5/4*I/c^2*b*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)/d^4/(c^2*d+e)*(e*(c^2*d+e))^(1/2)+5/8*c^6*b*x/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsec(c*x)+5/8*I*b*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)/d^3/(c^2*d+e)+5/8*I*b*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)/d^3/(c^2*d+e)+3/16*I*c^3*b/d/(c^2*d+e)*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-3/16*I*c^3*b/d/(c^2*d+e)*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+3/16*I*c*b/d^2/(c^2*d+e)*e*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-3/16*I*c*b/d^2/(c^2*d+e)*e*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(I*arcsec(c*x)*ln((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)+dilog((_R1-1/c/x-I*(1-1/c^2/x^2)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-5/8*I*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/d^3*(e*(c^2*d+e))^(1/2)+5/8*I*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^3/(c^2*d+e)^2*(e*(c^2*d+e))^(1/2)-5/4*I*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2*e/d^3-5/4*I*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2*e/d^3+I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))*e/d^5/(c^2*d+e)*(e*(c^2*d+e))^(1/2)+I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^5/(c^2*d+e)^2*(e*(c^2*d+e))^(1/2)+1/4*c^4*a*x/d/(c^2*e*x^2+c^2*d)^2+3/8*c^2*a/d^2*x/(c^2*e*x^2+c^2*d)+3/8*a/d^2/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))-I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e^2*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^5/(c^2*d+e)^2*(e*(c^2*d+e))^(1/2)-I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))*e/d^5/(c^2*d+e)*(e*(c^2*d+e))^(1/2)+7/4*I/c^2*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4/(c^2*d+e)^2*(e*(c^2*d+e))^(1/2)-7/4*I/c^2*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4/(c^2*d+e)^2*(e*(c^2*d+e))^(1/2)+3/8*c^6*b*x^3/(c^2*e*x^2+c^2*d)^2*e/(c^2*d+e)/d*arcsec(c*x)+1/8*c^5*b*x^4/(c^2*e*x^2+c^2*d)^2/d^2/(c^2*d+e)*((c^2*x^2-1)/c^2/x^2)^(1/2)*e^2+1/8*c^5*b*x^2/(c^2*e*x^2+c^2*d)^2/d/(c^2*d+e)*((c^2*x^2-1)/c^2/x^2)^(1/2)*e+3/8*c^4*b*x^3/(c^2*e*x^2+c^2*d)^2/d^2/(c^2*d+e)*arcsec(c*x)*e^2+5/8*c^4*b*x/(c^2*e*x^2+c^2*d)^2/d/(c^2*d+e)*arcsec(c*x)*e+I/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))*e^2/d^5/(c^2*d+e)+I/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+I*(1-1/c^2/x^2)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))*e^2/d^5/(c^2*d+e)","C"
111,0,0,343,4.859000," ","int(x^5*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x)","\int x^{5} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int(x^5*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x)","F"
112,0,0,246,4.493000," ","int(x^3*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x)","\int x^{3} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int(x^3*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x)","F"
113,0,0,159,3.336000," ","int(x*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x)","\int x \left(a +b \,\mathrm{arcsec}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int(x*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x)","F"
114,0,0,23,2.209000," ","int((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x,x)","\int \frac{\left(a +b \,\mathrm{arcsec}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x}\, dx"," ",0,"int((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x,x)","F"
115,0,0,23,0.947000," ","int((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x^3,x)","\int \frac{\left(a +b \,\mathrm{arcsec}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x^{3}}\, dx"," ",0,"int((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x^3,x)","F"
116,0,0,23,3.904000," ","int(x^2*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x)","\int x^{2} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int(x^2*(a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x)","F"
117,0,0,20,2.306000," ","int((a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x)","\int \left(a +b \,\mathrm{arcsec}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arcsec(c*x))*(e*x^2+d)^(1/2),x)","F"
118,0,0,23,1.748000," ","int((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x^2,x)","\int \frac{\left(a +b \,\mathrm{arcsec}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x^{2}}\, dx"," ",0,"int((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x^2,x)","F"
119,0,0,286,3.297000," ","int((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x^4,x)","\int \frac{\left(a +b \,\mathrm{arcsec}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x^{4}}\, dx"," ",0,"int((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x^4,x)","F"
120,0,0,849,4.681000," ","int((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x^6,x)","\int \frac{\left(a +b \,\mathrm{arcsec}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x^{6}}\, dx"," ",0,"int((a+b*arcsec(c*x))*(e*x^2+d)^(1/2)/x^6,x)","F"
121,0,0,318,4.330000," ","int(x^3*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x)","\int x^{3} \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)\, dx"," ",0,"int(x^3*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x)","F"
122,0,0,218,3.270000," ","int(x*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x)","\int x \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)\, dx"," ",0,"int(x*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x)","F"
123,0,0,23,2.196000," ","int((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{x}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x,x)","F"
124,0,0,23,0.834000," ","int((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^3,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{x^{3}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^3,x)","F"
125,0,0,23,3.938000," ","int(x^2*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x)","\int x^{2} \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)\, dx"," ",0,"int(x^2*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x)","F"
126,0,0,20,2.263000," ","int((e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x)","\int \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x)","F"
127,0,0,23,1.678000," ","int((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^2,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{x^{2}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^2,x)","F"
128,0,0,23,3.175000," ","int((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^4,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{x^{4}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^4,x)","F"
129,0,0,366,4.555000," ","int((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^6,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{x^{6}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^6,x)","F"
130,0,0,492,5.489000," ","int((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^8,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{x^{8}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arcsec(c*x))/x^8,x)","F"
131,0,0,271,5.363000," ","int(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x^{5} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x)","F"
132,0,0,187,4.820000," ","int(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x)","F"
133,0,0,110,3.495000," ","int(x*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x)","F"
134,0,0,23,2.375000," ","int((a+b*arcsec(c*x))/x/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{x \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsec(c*x))/x/(e*x^2+d)^(1/2),x)","F"
135,0,0,23,1.442000," ","int((a+b*arcsec(c*x))/x^3/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{x^{3} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsec(c*x))/x^3/(e*x^2+d)^(1/2),x)","F"
136,0,0,23,3.167000," ","int(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x^{2} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x)","F"
137,0,0,20,2.528000," ","int((a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x)","F"
138,0,0,220,2.226000," ","int((a+b*arcsec(c*x))/x^2/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{x^{2} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsec(c*x))/x^2/(e*x^2+d)^(1/2),x)","F"
139,0,0,316,4.688000," ","int((a+b*arcsec(c*x))/x^4/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{x^{4} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsec(c*x))/x^4/(e*x^2+d)^(1/2),x)","F"
140,0,0,880,6.309000," ","int((a+b*arcsec(c*x))/x^6/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{x^{6} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsec(c*x))/x^6/(e*x^2+d)^(1/2),x)","F"
141,0,0,212,5.162000," ","int(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{5} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x)","F"
142,0,0,133,4.655000," ","int(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x)","F"
143,0,0,70,3.364000," ","int(x*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x)","F"
144,0,0,23,2.135000," ","int((a+b*arcsec(c*x))/x/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{x \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsec(c*x))/x/(e*x^2+d)^(3/2),x)","F"
145,0,0,23,1.276000," ","int((a+b*arcsec(c*x))/x^3/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{x^{3} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsec(c*x))/x^3/(e*x^2+d)^(3/2),x)","F"
146,0,0,23,3.350000," ","int(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{4} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x)","F"
147,0,0,23,3.146000," ","int(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{2} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x)","F"
148,0,0,98,2.310000," ","int((a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x)","F"
149,0,0,248,2.118000," ","int((a+b*arcsec(c*x))/x^2/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{x^{2} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsec(c*x))/x^2/(e*x^2+d)^(3/2),x)","F"
150,0,0,613,4.457000," ","int((a+b*arcsec(c*x))/x^4/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{x^{4} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsec(c*x))/x^4/(e*x^2+d)^(3/2),x)","F"
151,0,0,206,5.329000," ","int(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{5} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^5*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x)","F"
152,0,0,139,4.628000," ","int(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^3*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x)","F"
153,0,0,117,3.471000," ","int(x*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x)","F"
154,0,0,23,2.136000," ","int((a+b*arcsec(c*x))/x/(e*x^2+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{x \left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsec(c*x))/x/(e*x^2+d)^(5/2),x)","F"
155,0,0,23,1.258000," ","int((a+b*arcsec(c*x))/x^3/(e*x^2+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{x^{3} \left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsec(c*x))/x^3/(e*x^2+d)^(5/2),x)","F"
156,0,0,23,3.691000," ","int(x^6*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{6} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^6*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x)","F"
157,0,0,23,3.365000," ","int(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{4} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^4*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x)","F"
158,0,0,242,3.151000," ","int(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{2} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^2*(a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x)","F"
159,0,0,258,2.311000," ","int((a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsec(c*x))/(e*x^2+d)^(5/2),x)","F"
160,0,0,563,2.075000," ","int((a+b*arcsec(c*x))/x^2/(e*x^2+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{x^{2} \left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsec(c*x))/x^2/(e*x^2+d)^(5/2),x)","F"
161,0,0,567,9.227000," ","int((f*x)^m*(e*x^2+d)^3*(a+b*arcsec(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right)^{3} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^3*(a+b*arcsec(c*x)),x)","F"
162,0,0,356,7.521000," ","int((f*x)^m*(e*x^2+d)^2*(a+b*arcsec(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right)^{2} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^2*(a+b*arcsec(c*x)),x)","F"
163,0,0,168,6.105000," ","int((f*x)^m*(e*x^2+d)*(a+b*arcsec(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right) \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)*(a+b*arcsec(c*x)),x)","F"
164,0,0,25,3.145000," ","int((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{e \,x^{2}+d}\, dx"," ",0,"int((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d),x)","F"
165,0,0,25,5.103000," ","int((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d)^2,x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d)^2,x)","F"
166,0,0,25,2.835000," ","int((f*x)^m*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^(3/2)*(a+b*arcsec(c*x)),x)","F"
167,0,0,25,2.798000," ","int((f*x)^m*(e*x^2+d)^(1/2)*(a+b*arcsec(c*x)),x)","\int \left(f x \right)^{m} \sqrt{e \,x^{2}+d}\, \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^(1/2)*(a+b*arcsec(c*x)),x)","F"
168,0,0,25,3.767000," ","int((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d)^(1/2),x)","F"
169,0,0,25,3.786000," ","int((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((f*x)^m*(a+b*arcsec(c*x))/(e*x^2+d)^(3/2),x)","F"
170,0,0,341,10.870000," ","int(x^11*(a+b*arcsec(c*x))/(-c^4*x^4+1)^(1/2),x)","\int \frac{x^{11} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int(x^11*(a+b*arcsec(c*x))/(-c^4*x^4+1)^(1/2),x)","F"
171,0,0,228,7.001000," ","int(x^7*(a+b*arcsec(c*x))/(-c^4*x^4+1)^(1/2),x)","\int \frac{x^{7} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int(x^7*(a+b*arcsec(c*x))/(-c^4*x^4+1)^(1/2),x)","F"
172,0,0,106,4.447000," ","int(x^3*(a+b*arcsec(c*x))/(-c^4*x^4+1)^(1/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arcsec}\left(c x \right)\right)}{\sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int(x^3*(a+b*arcsec(c*x))/(-c^4*x^4+1)^(1/2),x)","F"
173,0,0,26,4.082000," ","int((a+b*arcsec(c*x))/x/(-c^4*x^4+1)^(1/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{x \sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int((a+b*arcsec(c*x))/x/(-c^4*x^4+1)^(1/2),x)","F"
174,0,0,26,4.770000," ","int((a+b*arcsec(c*x))/x^5/(-c^4*x^4+1)^(1/2),x)","\int \frac{a +b \,\mathrm{arcsec}\left(c x \right)}{x^{5} \sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int((a+b*arcsec(c*x))/x^5/(-c^4*x^4+1)^(1/2),x)","F"