1,1,289,215,0.946000," ","int(x^4*arcsech(a*x)^2,x)","\frac{x^{5} \mathrm{arcsech}\left(a x \right)^{2}}{5}-\frac{\mathrm{arcsech}\left(a x \right) \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, x^{4}}{10 a}-\frac{3 \,\mathrm{arcsech}\left(a x \right) \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, x^{2}}{20 a^{3}}-\frac{x^{3}}{30 a^{2}}-\frac{3 x}{20 a^{4}}+\frac{3 i \mathrm{arcsech}\left(a x \right) \ln \left(1+i \left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)\right)}{20 a^{5}}-\frac{3 i \mathrm{arcsech}\left(a x \right) \ln \left(1-i \left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)\right)}{20 a^{5}}+\frac{3 i \dilog \left(1+i \left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)\right)}{20 a^{5}}-\frac{3 i \dilog \left(1-i \left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)\right)}{20 a^{5}}"," ",0,"1/5*x^5*arcsech(a*x)^2-1/10/a*arcsech(a*x)*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)*x^4-3/20/a^3*arcsech(a*x)*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)*x^2-1/30*x^3/a^2-3/20*x/a^4+3/20*I/a^5*arcsech(a*x)*ln(1+I*(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)))-3/20*I/a^5*arcsech(a*x)*ln(1-I*(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)))+3/20*I/a^5*dilog(1+I*(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)))-3/20*I/a^5*dilog(1-I*(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)))","A"
2,1,151,90,0.798000," ","int(x^3*arcsech(a*x)^2,x)","-\frac{\mathrm{arcsech}\left(a x \right)}{3 a^{4}}+\frac{x^{4} \mathrm{arcsech}\left(a x \right)^{2}}{4}-\frac{\sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \mathrm{arcsech}\left(a x \right) x^{3}}{6 a}-\frac{\sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \mathrm{arcsech}\left(a x \right) x}{3 a^{3}}-\frac{x^{2}}{12 a^{2}}+\frac{\ln \left(1+\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)^{2}\right)}{3 a^{4}}"," ",0,"-1/3/a^4*arcsech(a*x)+1/4*x^4*arcsech(a*x)^2-1/6/a*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)*arcsech(a*x)*x^3-1/3/a^3*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)*arcsech(a*x)*x-1/12*x^2/a^2+1/3/a^4*ln(1+(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2)","A"
3,1,240,174,0.715000," ","int(x^2*arcsech(a*x)^2,x)","\frac{x^{3} \mathrm{arcsech}\left(a x \right)^{2}}{3}-\frac{\mathrm{arcsech}\left(a x \right) \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, x^{2}}{3 a}-\frac{x}{3 a^{2}}+\frac{i \mathrm{arcsech}\left(a x \right) \ln \left(1+i \left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)\right)}{3 a^{3}}-\frac{i \mathrm{arcsech}\left(a x \right) \ln \left(1-i \left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)\right)}{3 a^{3}}+\frac{i \dilog \left(1+i \left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)\right)}{3 a^{3}}-\frac{i \dilog \left(1-i \left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)\right)}{3 a^{3}}"," ",0,"1/3*x^3*arcsech(a*x)^2-1/3/a*arcsech(a*x)*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)*x^2-1/3*x/a^2+1/3*I/a^3*arcsech(a*x)*ln(1+I*(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)))-1/3*I/a^3*arcsech(a*x)*ln(1-I*(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)))+1/3*I/a^3*dilog(1+I*(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)))-1/3*I/a^3*dilog(1-I*(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)))","A"
4,1,101,49,0.612000," ","int(x*arcsech(a*x)^2,x)","-\frac{\mathrm{arcsech}\left(a x \right)}{a^{2}}+\frac{x^{2} \mathrm{arcsech}\left(a x \right)^{2}}{2}-\frac{\sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \mathrm{arcsech}\left(a x \right) x}{a}+\frac{\ln \left(1+\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)^{2}\right)}{a^{2}}"," ",0,"-1/a^2*arcsech(a*x)+1/2*x^2*arcsech(a*x)^2-1/a*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)*arcsech(a*x)*x+1/a^2*ln(1+(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2)","B"
5,1,190,134,0.336000," ","int(arcsech(a*x)^2,x)","x \mathrm{arcsech}\left(a x \right)^{2}+\frac{2 i \mathrm{arcsech}\left(a x \right) \ln \left(1+i \left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)\right)}{a}-\frac{2 i \mathrm{arcsech}\left(a x \right) \ln \left(1-i \left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)\right)}{a}+\frac{2 i \dilog \left(1+i \left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)\right)}{a}-\frac{2 i \dilog \left(1-i \left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)\right)}{a}"," ",0,"x*arcsech(a*x)^2+2*I/a*arcsech(a*x)*ln(1+I*(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)))-2*I/a*arcsech(a*x)*ln(1-I*(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)))+2*I/a*dilog(1+I*(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)))-2*I/a*dilog(1-I*(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)))","A"
6,1,136,135,0.141000," ","int(arcsech(a*x)^2/x,x)","\frac{\mathrm{arcsech}\left(a x \right)^{3}}{3}-\mathrm{arcsech}\left(a x \right)^{2} \ln \left(1+\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)^{2}\right)-\mathrm{arcsech}\left(a x \right) \polylog \left(2, -\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)^{2}\right)+\frac{\polylog \left(3, -\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)^{2}\right)}{2}"," ",0,"1/3*arcsech(a*x)^3-arcsech(a*x)^2*ln(1+(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2)-arcsech(a*x)*polylog(2,-(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2)+1/2*polylog(3,-(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2)","A"
7,1,61,47,0.119000," ","int(arcsech(a*x)^2/x^2,x)","a \left(-\frac{\mathrm{arcsech}\left(a x \right)^{2}}{a x}+2 \,\mathrm{arcsech}\left(a x \right) \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}-\frac{2}{a x}\right)"," ",0,"a*(-arcsech(a*x)^2/a/x+2*arcsech(a*x)*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)-2/a/x)","A"
8,1,77,80,0.123000," ","int(arcsech(a*x)^2/x^3,x)","a^{2} \left(-\frac{\mathrm{arcsech}\left(a x \right)^{2}}{2 a^{2} x^{2}}+\frac{\mathrm{arcsech}\left(a x \right) \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}}{2 a x}+\frac{\mathrm{arcsech}\left(a x \right)^{2}}{4}-\frac{1}{4 x^{2} a^{2}}\right)"," ",0,"a^2*(-1/2*arcsech(a*x)^2/a^2/x^2+1/2*arcsech(a*x)/a/x*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)+1/4*arcsech(a*x)^2-1/4/x^2/a^2)","A"
9,1,112,88,0.421000," ","int(arcsech(a*x)^2/x^4,x)","a^{3} \left(-\frac{\mathrm{arcsech}\left(a x \right)^{2}}{3 a^{3} x^{3}}+\frac{4 \,\mathrm{arcsech}\left(a x \right) \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}}{9}+\frac{2 \,\mathrm{arcsech}\left(a x \right) \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}}{9 a^{2} x^{2}}-\frac{4}{9 a x}-\frac{2}{27 a^{3} x^{3}}\right)"," ",0,"a^3*(-1/3*arcsech(a*x)^2/a^3/x^3+4/9*arcsech(a*x)*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)+2/9*arcsech(a*x)/a^2/x^2*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)-4/9/a/x-2/27/a^3/x^3)","A"
10,0,0,382,1.342000," ","int(x^4*arcsech(a*x)^3,x)","\int x^{4} \mathrm{arcsech}\left(a x \right)^{3}\, dx"," ",0,"int(x^4*arcsech(a*x)^3,x)","F"
11,1,246,214,0.857000," ","int(x^3*arcsech(a*x)^3,x)","\frac{x^{4} \mathrm{arcsech}\left(a x \right)^{3}}{4}-\frac{\mathrm{arcsech}\left(a x \right)^{2} \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, x^{3}}{4 a}-\frac{\mathrm{arcsech}\left(a x \right)^{2} \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, x}{2 a^{3}}-\frac{x^{2} \mathrm{arcsech}\left(a x \right)}{4 a^{2}}+\frac{\sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, x}{4 a^{3}}-\frac{\mathrm{arcsech}\left(a x \right)^{2}}{2 a^{4}}-\frac{1}{4 a^{4}}+\frac{\mathrm{arcsech}\left(a x \right) \ln \left(1+\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)^{2}\right)}{a^{4}}+\frac{\polylog \left(2, -\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)^{2}\right)}{2 a^{4}}"," ",0,"1/4*x^4*arcsech(a*x)^3-1/4/a*arcsech(a*x)^2*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)*x^3-1/2/a^3*arcsech(a*x)^2*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)*x-1/4*x^2*arcsech(a*x)/a^2+1/4/a^3*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)*x-1/2*arcsech(a*x)^2/a^4-1/4/a^4+arcsech(a*x)*ln(1+(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2)/a^4+1/2*polylog(2,-(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2)/a^4","A"
12,0,0,307,0.916000," ","int(x^2*arcsech(a*x)^3,x)","\int x^{2} \mathrm{arcsech}\left(a x \right)^{3}\, dx"," ",0,"int(x^2*arcsech(a*x)^3,x)","F"
13,1,152,142,0.645000," ","int(x*arcsech(a*x)^3,x)","\frac{x^{2} \mathrm{arcsech}\left(a x \right)^{3}}{2}-\frac{3 \mathrm{arcsech}\left(a x \right)^{2} \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, x}{2 a}-\frac{3 \mathrm{arcsech}\left(a x \right)^{2}}{2 a^{2}}+\frac{3 \,\mathrm{arcsech}\left(a x \right) \ln \left(1+\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)^{2}\right)}{a^{2}}+\frac{3 \polylog \left(2, -\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)^{2}\right)}{2 a^{2}}"," ",0,"1/2*x^2*arcsech(a*x)^3-3/2/a*arcsech(a*x)^2*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)*x-3/2*arcsech(a*x)^2/a^2+3*arcsech(a*x)*ln(1+(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2)/a^2+3/2*polylog(2,-(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2)/a^2","A"
14,0,0,228,0.398000," ","int(arcsech(a*x)^3,x)","\int \mathrm{arcsech}\left(a x \right)^{3}\, dx"," ",0,"int(arcsech(a*x)^3,x)","F"
15,1,181,180,0.148000," ","int(arcsech(a*x)^3/x,x)","\frac{\mathrm{arcsech}\left(a x \right)^{4}}{4}-\mathrm{arcsech}\left(a x \right)^{3} \ln \left(1+\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)^{2}\right)-\frac{3 \mathrm{arcsech}\left(a x \right)^{2} \polylog \left(2, -\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)^{2}\right)}{2}+\frac{3 \,\mathrm{arcsech}\left(a x \right) \polylog \left(3, -\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)^{2}\right)}{2}-\frac{3 \polylog \left(4, -\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right)^{2}\right)}{4}"," ",0,"1/4*arcsech(a*x)^4-arcsech(a*x)^3*ln(1+(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2)-3/2*arcsech(a*x)^2*polylog(2,-(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2)+3/2*arcsech(a*x)*polylog(3,-(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2)-3/4*polylog(4,-(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2)","A"
16,1,98,79,0.127000," ","int(arcsech(a*x)^3/x^2,x)","a \left(-\frac{\mathrm{arcsech}\left(a x \right)^{3}}{a x}+3 \mathrm{arcsech}\left(a x \right)^{2} \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}-\frac{6 \,\mathrm{arcsech}\left(a x \right)}{a x}+6 \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\right)"," ",0,"a*(-arcsech(a*x)^3/a/x+3*arcsech(a*x)^2*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)-6/a/x*arcsech(a*x)+6*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2))","A"
17,1,126,121,0.129000," ","int(arcsech(a*x)^3/x^3,x)","a^{2} \left(-\frac{\mathrm{arcsech}\left(a x \right)^{3}}{2 a^{2} x^{2}}+\frac{3 \mathrm{arcsech}\left(a x \right)^{2} \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}}{4 a x}+\frac{\mathrm{arcsech}\left(a x \right)^{3}}{4}-\frac{3 \,\mathrm{arcsech}\left(a x \right)}{4 a^{2} x^{2}}+\frac{3 \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}}{8 a x}+\frac{3 \,\mathrm{arcsech}\left(a x \right)}{8}\right)"," ",0,"a^2*(-1/2*arcsech(a*x)^3/a^2/x^2+3/4*arcsech(a*x)^2/a/x*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)+1/4*arcsech(a*x)^3-3/4/a^2/x^2*arcsech(a*x)+3/8/a/x*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)+3/8*arcsech(a*x))","A"
18,1,192,157,0.427000," ","int(arcsech(a*x)^3/x^4,x)","a^{3} \left(-\frac{\mathrm{arcsech}\left(a x \right)^{3}}{3 a^{3} x^{3}}+\frac{2 \mathrm{arcsech}\left(a x \right)^{2} \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}}{3}+\frac{\mathrm{arcsech}\left(a x \right)^{2} \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}}{3 a^{2} x^{2}}-\frac{4 \,\mathrm{arcsech}\left(a x \right)}{3 a x}+\frac{40 \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}}{27}-\frac{2 \,\mathrm{arcsech}\left(a x \right)}{9 a^{3} x^{3}}+\frac{2 \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}}{27 a^{2} x^{2}}\right)"," ",0,"a^3*(-1/3*arcsech(a*x)^3/a^3/x^3+2/3*arcsech(a*x)^2*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)+1/3*arcsech(a*x)^2/a^2/x^2*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)-4/3/a/x*arcsech(a*x)+40/27*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)-2/9*arcsech(a*x)/a^3/x^3+2/27/a^2/x^2*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2))","A"
19,1,138,116,0.087000," ","int(x^6*(a+b*arcsech(c*x)),x)","\frac{\frac{c^{7} x^{7} a}{7}+b \left(\frac{c^{7} x^{7} \mathrm{arcsech}\left(c x \right)}{7}-\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(8 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}+10 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}+15 c x \sqrt{-c^{2} x^{2}+1}-15 \arcsin \left(c x \right)\right)}{336 \sqrt{-c^{2} x^{2}+1}}\right)}{c^{7}}"," ",0,"1/c^7*(1/7*c^7*x^7*a+b*(1/7*c^7*x^7*arcsech(c*x)-1/336*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(8*c^5*x^5*(-c^2*x^2+1)^(1/2)+10*c^3*x^3*(-c^2*x^2+1)^(1/2)+15*c*x*(-c^2*x^2+1)^(1/2)-15*arcsin(c*x))/(-c^2*x^2+1)^(1/2)))","A"
20,1,81,89,0.065000," ","int(x^5*(a+b*arcsech(c*x)),x)","\frac{\frac{c^{6} x^{6} a}{6}+b \left(\frac{c^{6} x^{6} \mathrm{arcsech}\left(c x \right)}{6}-\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(3 c^{4} x^{4}+4 c^{2} x^{2}+8\right)}{90}\right)}{c^{6}}"," ",0,"1/c^6*(1/6*c^6*x^6*a+b*(1/6*c^6*x^6*arcsech(c*x)-1/90*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(3*c^4*x^4+4*c^2*x^2+8)))","A"
21,1,118,90,0.064000," ","int(x^4*(a+b*arcsech(c*x)),x)","\frac{\frac{c^{5} x^{5} a}{5}+b \left(\frac{c^{5} x^{5} \mathrm{arcsech}\left(c x \right)}{5}+\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(-2 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}-3 c x \sqrt{-c^{2} x^{2}+1}+3 \arcsin \left(c x \right)\right)}{40 \sqrt{-c^{2} x^{2}+1}}\right)}{c^{5}}"," ",0,"1/c^5*(1/5*c^5*x^5*a+b*(1/5*c^5*x^5*arcsech(c*x)+1/40*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(-2*c^3*x^3*(-c^2*x^2+1)^(1/2)-3*c*x*(-c^2*x^2+1)^(1/2)+3*arcsin(c*x))/(-c^2*x^2+1)^(1/2)))","A"
22,1,72,63,0.060000," ","int(x^3*(a+b*arcsech(c*x)),x)","\frac{\frac{c^{4} x^{4} a}{4}+b \left(\frac{c^{4} x^{4} \mathrm{arcsech}\left(c x \right)}{4}-\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(c^{2} x^{2}+2\right)}{12}\right)}{c^{4}}"," ",0,"1/c^4*(1/4*c^4*x^4*a+b*(1/4*c^4*x^4*arcsech(c*x)-1/12*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(c^2*x^2+2)))","A"
23,1,96,64,0.062000," ","int(x^2*(a+b*arcsech(c*x)),x)","\frac{\frac{c^{3} x^{3} a}{3}+b \left(\frac{c^{3} x^{3} \mathrm{arcsech}\left(c x \right)}{3}+\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(-c x \sqrt{-c^{2} x^{2}+1}+\arcsin \left(c x \right)\right)}{6 \sqrt{-c^{2} x^{2}+1}}\right)}{c^{3}}"," ",0,"1/c^3*(1/3*c^3*x^3*a+b*(1/3*c^3*x^3*arcsech(c*x)+1/6*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(-c*x*(-c^2*x^2+1)^(1/2)+arcsin(c*x))/(-c^2*x^2+1)^(1/2)))","A"
24,1,63,37,0.061000," ","int(x*(a+b*arcsech(c*x)),x)","\frac{\frac{c^{2} x^{2} a}{2}+b \left(\frac{\mathrm{arcsech}\left(c x \right) c^{2} x^{2}}{2}-\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x}{2}\right)}{c^{2}}"," ",0,"1/c^2*(1/2*c^2*x^2*a+b*(1/2*arcsech(c*x)*c^2*x^2-1/2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x))","A"
25,1,42,36,0.042000," ","int(a+b*arcsech(c*x),x)","a x +b x \,\mathrm{arcsech}\left(c x \right)-\frac{b \arctan \left(\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)}{c}"," ",0,"a*x+b*x*arcsech(c*x)-b/c*arctan((-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))","A"
26,1,100,102,0.155000," ","int((a+b*arcsech(c*x))/x,x)","a \ln \left(c x \right)+\frac{b \mathrm{arcsech}\left(c x \right)^{2}}{2}-b \,\mathrm{arcsech}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)-\frac{b \polylog \left(2, -\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{2}"," ",0,"a*ln(c*x)+1/2*b*arcsech(c*x)^2-b*arcsech(c*x)*ln(1+(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)-1/2*b*polylog(2,-(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)","A"
27,1,58,38,0.061000," ","int((a+b*arcsech(c*x))/x^2,x)","c \left(-\frac{a}{c x}+b \left(-\frac{\mathrm{arcsech}\left(c x \right)}{c x}+\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\right)\right)"," ",0,"c*(-a/c/x+b*(-1/c/x*arcsech(c*x)+(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)))","A"
28,1,112,79,0.072000," ","int((a+b*arcsech(c*x))/x^3,x)","c^{2} \left(-\frac{a}{2 c^{2} x^{2}}+b \left(-\frac{\mathrm{arcsech}\left(c x \right)}{2 c^{2} x^{2}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(\arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right) c^{2} x^{2}+\sqrt{-c^{2} x^{2}+1}\right)}{4 c x \sqrt{-c^{2} x^{2}+1}}\right)\right)"," ",0,"c^2*(-1/2*a/c^2/x^2+b*(-1/2/c^2/x^2*arcsech(c*x)+1/4*(-(c*x-1)/c/x)^(1/2)/c/x*((c*x+1)/c/x)^(1/2)*(arctanh(1/(-c^2*x^2+1)^(1/2))*c^2*x^2+(-c^2*x^2+1)^(1/2))/(-c^2*x^2+1)^(1/2)))","A"
29,1,77,66,0.065000," ","int((a+b*arcsech(c*x))/x^4,x)","c^{3} \left(-\frac{a}{3 c^{3} x^{3}}+b \left(-\frac{\mathrm{arcsech}\left(c x \right)}{3 c^{3} x^{3}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(2 c^{2} x^{2}+1\right)}{9 c^{2} x^{2}}\right)\right)"," ",0,"c^3*(-1/3/c^3/x^3*a+b*(-1/3*arcsech(c*x)/c^3/x^3+1/9*(-(c*x-1)/c/x)^(1/2)/c^2/x^2*((c*x+1)/c/x)^(1/2)*(2*c^2*x^2+1)))","A"
30,1,135,105,0.066000," ","int((a+b*arcsech(c*x))/x^5,x)","c^{4} \left(-\frac{a}{4 c^{4} x^{4}}+b \left(-\frac{\mathrm{arcsech}\left(c x \right)}{4 c^{4} x^{4}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(3 \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right) c^{4} x^{4}+3 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}+2 \sqrt{-c^{2} x^{2}+1}\right)}{32 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}\right)\right)"," ",0,"c^4*(-1/4*a/c^4/x^4+b*(-1/4/c^4/x^4*arcsech(c*x)+1/32*(-(c*x-1)/c/x)^(1/2)/c^3/x^3*((c*x+1)/c/x)^(1/2)*(3*arctanh(1/(-c^2*x^2+1)^(1/2))*c^4*x^4+3*c^2*x^2*(-c^2*x^2+1)^(1/2)+2*(-c^2*x^2+1)^(1/2))/(-c^2*x^2+1)^(1/2)))","A"
31,1,85,92,0.066000," ","int((a+b*arcsech(c*x))/x^6,x)","c^{5} \left(-\frac{a}{5 c^{5} x^{5}}+b \left(-\frac{\mathrm{arcsech}\left(c x \right)}{5 c^{5} x^{5}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(8 c^{4} x^{4}+4 c^{2} x^{2}+3\right)}{75 c^{4} x^{4}}\right)\right)"," ",0,"c^5*(-1/5*a/c^5/x^5+b*(-1/5/c^5/x^5*arcsech(c*x)+1/75*(-(c*x-1)/c/x)^(1/2)/c^4/x^4*((c*x+1)/c/x)^(1/2)*(8*c^4*x^4+4*c^2*x^2+3)))","A"
32,1,155,131,0.074000," ","int((a+b*arcsech(c*x))/x^7,x)","c^{6} \left(-\frac{a}{6 c^{6} x^{6}}+b \left(-\frac{\mathrm{arcsech}\left(c x \right)}{6 c^{6} x^{6}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(15 \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right) c^{6} x^{6}+15 \sqrt{-c^{2} x^{2}+1}\, c^{4} x^{4}+10 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}+8 \sqrt{-c^{2} x^{2}+1}\right)}{288 c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}\right)\right)"," ",0,"c^6*(-1/6*a/c^6/x^6+b*(-1/6/c^6/x^6*arcsech(c*x)+1/288*(-(c*x-1)/c/x)^(1/2)/c^5/x^5*((c*x+1)/c/x)^(1/2)*(15*arctanh(1/(-c^2*x^2+1)^(1/2))*c^6*x^6+15*(-c^2*x^2+1)^(1/2)*c^4*x^4+10*c^2*x^2*(-c^2*x^2+1)^(1/2)+8*(-c^2*x^2+1)^(1/2))/(-c^2*x^2+1)^(1/2)))","A"
33,1,264,110,0.721000," ","int(x^3*(a+b*arcsech(c*x))^2,x)","\frac{a^{2} x^{4}}{4}-\frac{b^{2} \mathrm{arcsech}\left(c x \right)}{3 c^{4}}+\frac{b^{2} \mathrm{arcsech}\left(c x \right)^{2} x^{4}}{4}-\frac{b^{2} \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \mathrm{arcsech}\left(c x \right) x^{3}}{6 c}-\frac{b^{2} \mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x}{3 c^{3}}-\frac{b^{2} x^{2}}{12 c^{2}}+\frac{b^{2} \ln \left(1+\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{3 c^{4}}+\frac{a b \,x^{4} \mathrm{arcsech}\left(c x \right)}{2}-\frac{a b \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x^{3}}{6 c}-\frac{a b \sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}}{3 c^{3}}"," ",0,"1/4*a^2*x^4-1/3/c^4*b^2*arcsech(c*x)+1/4*b^2*arcsech(c*x)^2*x^4-1/6/c*b^2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*arcsech(c*x)*x^3-1/3/c^3*b^2*arcsech(c*x)*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x-1/12*b^2*x^2/c^2+1/3/c^4*b^2*ln(1+(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)+1/2*a*b*x^4*arcsech(c*x)-1/6/c*a*b*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x^3-1/3/c^3*a*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)","B"
34,1,372,197,0.642000," ","int(x^2*(a+b*arcsech(c*x))^2,x)","\frac{x^{3} a^{2}}{3}+\frac{x^{3} b^{2} \mathrm{arcsech}\left(c x \right)^{2}}{3}-\frac{b^{2} \mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x^{2}}{3 c}-\frac{b^{2} x}{3 c^{2}}+\frac{i b^{2} \mathrm{arcsech}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{3 c^{3}}-\frac{i b^{2} \mathrm{arcsech}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{3 c^{3}}+\frac{i b^{2} \dilog \left(1+i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{3 c^{3}}-\frac{i b^{2} \dilog \left(1-i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{3 c^{3}}+\frac{2 a b \,x^{3} \mathrm{arcsech}\left(c x \right)}{3}-\frac{a b \sqrt{-\frac{c x -1}{c x}}\, x^{2} \sqrt{\frac{c x +1}{c x}}}{3 c}+\frac{a b \sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, \arcsin \left(c x \right)}{3 c^{2} \sqrt{-c^{2} x^{2}+1}}"," ",0,"1/3*x^3*a^2+1/3*x^3*b^2*arcsech(c*x)^2-1/3/c*b^2*arcsech(c*x)*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x^2-1/3*b^2*x/c^2+1/3*I/c^3*b^2*arcsech(c*x)*ln(1+I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-1/3*I/c^3*b^2*arcsech(c*x)*ln(1-I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))+1/3*I/c^3*b^2*dilog(1+I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-1/3*I/c^3*b^2*dilog(1-I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))+2/3*a*b*x^3*arcsech(c*x)-1/3/c*a*b*(-(c*x-1)/c/x)^(1/2)*x^2*((c*x+1)/c/x)^(1/2)+1/3/c^2*a*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/(-c^2*x^2+1)^(1/2)*arcsin(c*x)","A"
35,1,168,61,0.579000," ","int(x*(a+b*arcsech(c*x))^2,x)","\frac{a^{2} x^{2}}{2}-\frac{b^{2} \mathrm{arcsech}\left(c x \right)}{c^{2}}+\frac{x^{2} b^{2} \mathrm{arcsech}\left(c x \right)^{2}}{2}-\frac{b^{2} \mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x}{c}+\frac{b^{2} \ln \left(1+\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{c^{2}}+a b \,\mathrm{arcsech}\left(c x \right) x^{2}-\frac{a b \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x}{c}"," ",0,"1/2*a^2*x^2-1/c^2*b^2*arcsech(c*x)+1/2*x^2*b^2*arcsech(c*x)^2-1/c*b^2*arcsech(c*x)*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x+1/c^2*b^2*ln(1+(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)+a*b*arcsech(c*x)*x^2-1/c*a*b*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x","B"
36,1,250,149,0.297000," ","int((a+b*arcsech(c*x))^2,x)","x \,b^{2} \mathrm{arcsech}\left(c x \right)^{2}-\frac{2 i \mathrm{arcsech}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right) b^{2}}{c}+\frac{2 i \mathrm{arcsech}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right) b^{2}}{c}+2 x a b \,\mathrm{arcsech}\left(c x \right)+\frac{2 i \dilog \left(1+i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right) b^{2}}{c}-\frac{2 i \dilog \left(1-i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right) b^{2}}{c}+a^{2} x -\frac{2 \arctan \left(\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right) a b}{c}"," ",0,"x*b^2*arcsech(c*x)^2-2*I/c*arcsech(c*x)*ln(1-I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))*b^2+2*I/c*arcsech(c*x)*ln(1+I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))*b^2+2*x*a*b*arcsech(c*x)+2*I/c*dilog(1+I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))*b^2-2*I/c*dilog(1-I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))*b^2+a^2*x-2/c*arctan((-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))*a*b","A"
37,1,250,154,0.128000," ","int((a+b*arcsech(c*x))^2/x,x)","a^{2} \ln \left(c x \right)+\frac{b^{2} \mathrm{arcsech}\left(c x \right)^{3}}{3}-b^{2} \mathrm{arcsech}\left(c x \right)^{2} \ln \left(1+\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)-b^{2} \mathrm{arcsech}\left(c x \right) \polylog \left(2, -\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)+\frac{b^{2} \polylog \left(3, -\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{2}+a b \mathrm{arcsech}\left(c x \right)^{2}-2 a b \,\mathrm{arcsech}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)-a b \polylog \left(2, -\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)"," ",0,"a^2*ln(c*x)+1/3*b^2*arcsech(c*x)^3-b^2*arcsech(c*x)^2*ln(1+(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)-b^2*arcsech(c*x)*polylog(2,-(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)+1/2*b^2*polylog(3,-(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)+a*b*arcsech(c*x)^2-2*a*b*arcsech(c*x)*ln(1+(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)-a*b*polylog(2,-(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)","A"
38,1,124,59,0.139000," ","int((a+b*arcsech(c*x))^2/x^2,x)","c \left(-\frac{a^{2}}{c x}+b^{2} \left(-\frac{\mathrm{arcsech}\left(c x \right)^{2}}{c x}+2 \,\mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}-\frac{2}{c x}\right)+2 a b \left(-\frac{\mathrm{arcsech}\left(c x \right)}{c x}+\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\right)\right)"," ",0,"c*(-a^2/c/x+b^2*(-1/c/x*arcsech(c*x)^2+2*arcsech(c*x)*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)-2/c/x)+2*a*b*(-1/c/x*arcsech(c*x)+(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)))","B"
39,1,192,106,0.141000," ","int((a+b*arcsech(c*x))^2/x^3,x)","c^{2} \left(-\frac{a^{2}}{2 c^{2} x^{2}}+b^{2} \left(-\frac{\mathrm{arcsech}\left(c x \right)^{2}}{2 c^{2} x^{2}}+\frac{\mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{2 c x}+\frac{\mathrm{arcsech}\left(c x \right)^{2}}{4}-\frac{1}{4 c^{2} x^{2}}\right)+2 a b \left(-\frac{\mathrm{arcsech}\left(c x \right)}{2 c^{2} x^{2}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(\arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right) c^{2} x^{2}+\sqrt{-c^{2} x^{2}+1}\right)}{4 c x \sqrt{-c^{2} x^{2}+1}}\right)\right)"," ",0,"c^2*(-1/2*a^2/c^2/x^2+b^2*(-1/2/c^2/x^2*arcsech(c*x)^2+1/2*arcsech(c*x)/c/x*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+1/4*arcsech(c*x)^2-1/4/c^2/x^2)+2*a*b*(-1/2/c^2/x^2*arcsech(c*x)+1/4*(-(c*x-1)/c/x)^(1/2)/c/x*((c*x+1)/c/x)^(1/2)*(arctanh(1/(-c^2*x^2+1)^(1/2))*c^2*x^2+(-c^2*x^2+1)^(1/2))/(-c^2*x^2+1)^(1/2)))","A"
40,1,192,108,0.440000," ","int((a+b*arcsech(c*x))^2/x^4,x)","c^{3} \left(-\frac{a^{2}}{3 c^{3} x^{3}}+b^{2} \left(-\frac{\mathrm{arcsech}\left(c x \right)^{2}}{3 c^{3} x^{3}}+\frac{4 \,\mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{9}+\frac{2 \,\mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{9 c^{2} x^{2}}-\frac{4}{9 c x}-\frac{2}{27 c^{3} x^{3}}\right)+2 a b \left(-\frac{\mathrm{arcsech}\left(c x \right)}{3 c^{3} x^{3}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(2 c^{2} x^{2}+1\right)}{9 c^{2} x^{2}}\right)\right)"," ",0,"c^3*(-1/3*a^2/c^3/x^3+b^2*(-1/3/c^3/x^3*arcsech(c*x)^2+4/9*arcsech(c*x)*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+2/9*arcsech(c*x)/c^2/x^2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)-4/9/c/x-2/27/c^3/x^3)+2*a*b*(-1/3*arcsech(c*x)/c^3/x^3+1/9*(-(c*x-1)/c/x)^(1/2)/c^2/x^2*((c*x+1)/c/x)^(1/2)*(2*c^2*x^2+1)))","A"
41,1,264,133,0.473000," ","int((a+b*arcsech(c*x))^2/x^5,x)","c^{4} \left(-\frac{a^{2}}{4 c^{4} x^{4}}+b^{2} \left(-\frac{\mathrm{arcsech}\left(c x \right)^{2}}{4 c^{4} x^{4}}+\frac{\mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{8 c^{3} x^{3}}+\frac{3 \,\mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{16 c x}+\frac{3 \mathrm{arcsech}\left(c x \right)^{2}}{32}-\frac{1}{32 c^{4} x^{4}}-\frac{3}{32 c^{2} x^{2}}\right)+2 a b \left(-\frac{\mathrm{arcsech}\left(c x \right)}{4 c^{4} x^{4}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(3 \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right) c^{4} x^{4}+3 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}+2 \sqrt{-c^{2} x^{2}+1}\right)}{32 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}\right)\right)"," ",0,"c^4*(-1/4*a^2/c^4/x^4+b^2*(-1/4/c^4/x^4*arcsech(c*x)^2+1/8*arcsech(c*x)/c^3/x^3*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+3/16*arcsech(c*x)/c/x*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+3/32*arcsech(c*x)^2-1/32/c^4/x^4-3/32/c^2/x^2)+2*a*b*(-1/4/c^4/x^4*arcsech(c*x)+1/32*(-(c*x-1)/c/x)^(1/2)/c^3/x^3*((c*x+1)/c/x)^(1/2)*(3*arctanh(1/(-c^2*x^2+1)^(1/2))*c^4*x^4+3*c^2*x^2*(-c^2*x^2+1)^(1/2)+2*(-c^2*x^2+1)^(1/2))/(-c^2*x^2+1)^(1/2)))","A"
42,1,546,253,0.955000," ","int(x^3*(a+b*arcsech(c*x))^3,x)","\frac{x^{4} a^{3}}{4}+\frac{b^{3} \mathrm{arcsech}\left(c x \right)^{3} x^{4}}{4}-\frac{b^{3} \mathrm{arcsech}\left(c x \right)^{2} \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x^{3}}{4 c}-\frac{b^{3} \mathrm{arcsech}\left(c x \right)^{2} \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x}{2 c^{3}}-\frac{b^{3} \mathrm{arcsech}\left(c x \right) x^{2}}{4 c^{2}}+\frac{b^{3} \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x}{4 c^{3}}-\frac{b^{3} \mathrm{arcsech}\left(c x \right)^{2}}{2 c^{4}}-\frac{b^{3}}{4 c^{4}}+\frac{b^{3} \mathrm{arcsech}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{c^{4}}+\frac{b^{3} \polylog \left(2, -\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{2 c^{4}}-\frac{a \,b^{2} \mathrm{arcsech}\left(c x \right)}{c^{4}}+\frac{3 a \,b^{2} \mathrm{arcsech}\left(c x \right)^{2} x^{4}}{4}-\frac{a \,b^{2} \mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x^{3}}{2 c}-\frac{a \,b^{2} \mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x}{c^{3}}-\frac{x^{2} a \,b^{2}}{4 c^{2}}+\frac{a \,b^{2} \ln \left(1+\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{c^{4}}+\frac{3 a^{2} b \,x^{4} \mathrm{arcsech}\left(c x \right)}{4}-\frac{a^{2} b \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x^{3}}{4 c}-\frac{a^{2} b \sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}}{2 c^{3}}"," ",0,"1/4*x^4*a^3+1/4*b^3*arcsech(c*x)^3*x^4-1/4/c*b^3*arcsech(c*x)^2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x^3-1/2/c^3*b^3*arcsech(c*x)^2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x-1/4/c^2*b^3*arcsech(c*x)*x^2+1/4/c^3*b^3*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x-1/2/c^4*b^3*arcsech(c*x)^2-1/4/c^4*b^3+1/c^4*b^3*arcsech(c*x)*ln(1+(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)+1/2*b^3*polylog(2,-(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)/c^4-1/c^4*a*b^2*arcsech(c*x)+3/4*a*b^2*arcsech(c*x)^2*x^4-1/2/c*a*b^2*arcsech(c*x)*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x^3-1/c^3*a*b^2*arcsech(c*x)*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x-1/4/c^2*x^2*a*b^2+1/c^4*a*b^2*ln(1+(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)+3/4*a^2*b*x^4*arcsech(c*x)-1/4/c*a^2*b*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x^3-1/2/c^3*a^2*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)","B"
43,0,0,351,1.017000," ","int(x^2*(a+b*arcsech(c*x))^3,x)","\int x^{2} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)^{3}\, dx"," ",0,"int(x^2*(a+b*arcsech(c*x))^3,x)","F"
44,1,343,166,0.715000," ","int(x*(a+b*arcsech(c*x))^3,x)","\frac{x^{2} a^{3}}{2}+\frac{x^{2} b^{3} \mathrm{arcsech}\left(c x \right)^{3}}{2}-\frac{3 b^{3} \mathrm{arcsech}\left(c x \right)^{2} \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x}{2 c}-\frac{3 b^{3} \mathrm{arcsech}\left(c x \right)^{2}}{2 c^{2}}+\frac{3 b^{3} \mathrm{arcsech}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{c^{2}}+\frac{3 b^{3} \polylog \left(2, -\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{2 c^{2}}-\frac{3 a \,b^{2} \mathrm{arcsech}\left(c x \right)}{c^{2}}+\frac{3 x^{2} a \,b^{2} \mathrm{arcsech}\left(c x \right)^{2}}{2}-\frac{3 a \,b^{2} \mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x}{c}+\frac{3 a \,b^{2} \ln \left(1+\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{c^{2}}+\frac{3 x^{2} a^{2} b \,\mathrm{arcsech}\left(c x \right)}{2}-\frac{3 a^{2} b \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x}{2 c}"," ",0,"1/2*x^2*a^3+1/2*x^2*b^3*arcsech(c*x)^3-3/2/c*b^3*arcsech(c*x)^2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x-3/2/c^2*b^3*arcsech(c*x)^2+3/c^2*b^3*arcsech(c*x)*ln(1+(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)+3/2*b^3*polylog(2,-(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)/c^2-3/c^2*a*b^2*arcsech(c*x)+3/2*x^2*a*b^2*arcsech(c*x)^2-3/c*a*b^2*arcsech(c*x)*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x+3/c^2*a*b^2*ln(1+(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)+3/2*x^2*a^2*b*arcsech(c*x)-3/2/c*a^2*b*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x","B"
45,0,0,257,0.417000," ","int((a+b*arcsech(c*x))^3,x)","\int \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)^{3}\, dx"," ",0,"int((a+b*arcsech(c*x))^3,x)","F"
46,1,454,206,0.151000," ","int((a+b*arcsech(c*x))^3/x,x)","a^{3} \ln \left(c x \right)+\frac{b^{3} \mathrm{arcsech}\left(c x \right)^{4}}{4}-b^{3} \mathrm{arcsech}\left(c x \right)^{3} \ln \left(1+\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)-\frac{3 b^{3} \mathrm{arcsech}\left(c x \right)^{2} \polylog \left(2, -\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{2}+\frac{3 b^{3} \mathrm{arcsech}\left(c x \right) \polylog \left(3, -\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{2}-\frac{3 b^{3} \polylog \left(4, -\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{4}+a \,b^{2} \mathrm{arcsech}\left(c x \right)^{3}-3 a \,b^{2} \mathrm{arcsech}\left(c x \right)^{2} \ln \left(1+\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)-3 a \,b^{2} \mathrm{arcsech}\left(c x \right) \polylog \left(2, -\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)+\frac{3 a \,b^{2} \polylog \left(3, -\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{2}+\frac{3 a^{2} b \mathrm{arcsech}\left(c x \right)^{2}}{2}-3 a^{2} b \,\mathrm{arcsech}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)-\frac{3 a^{2} b \polylog \left(2, -\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{2}"," ",0,"a^3*ln(c*x)+1/4*b^3*arcsech(c*x)^4-b^3*arcsech(c*x)^3*ln(1+(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)-3/2*b^3*arcsech(c*x)^2*polylog(2,-(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)+3/2*b^3*arcsech(c*x)*polylog(3,-(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)-3/4*b^3*polylog(4,-(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)+a*b^2*arcsech(c*x)^3-3*a*b^2*arcsech(c*x)^2*ln(1+(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)-3*a*b^2*arcsech(c*x)*polylog(2,-(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)+3/2*a*b^2*polylog(3,-(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)+3/2*a^2*b*arcsech(c*x)^2-3*a^2*b*arcsech(c*x)*ln(1+(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)-3/2*a^2*b*polylog(2,-(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)","B"
47,1,227,98,0.171000," ","int((a+b*arcsech(c*x))^3/x^2,x)","c \left(-\frac{a^{3}}{c x}+b^{3} \left(-\frac{\mathrm{arcsech}\left(c x \right)^{3}}{c x}+3 \mathrm{arcsech}\left(c x \right)^{2} \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}-\frac{6 \,\mathrm{arcsech}\left(c x \right)}{c x}+6 \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\right)+3 a \,b^{2} \left(-\frac{\mathrm{arcsech}\left(c x \right)^{2}}{c x}+2 \,\mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}-\frac{2}{c x}\right)+3 a^{2} b \left(-\frac{\mathrm{arcsech}\left(c x \right)}{c x}+\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\right)\right)"," ",0,"c*(-a^3/c/x+b^3*(-1/c/x*arcsech(c*x)^3+3*arcsech(c*x)^2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)-6/c/x*arcsech(c*x)+6*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2))+3*a*b^2*(-1/c/x*arcsech(c*x)^2+2*arcsech(c*x)*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)-2/c/x)+3*a^2*b*(-1/c/x*arcsech(c*x)+(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)))","B"
48,1,321,147,0.174000," ","int((a+b*arcsech(c*x))^3/x^3,x)","c^{2} \left(-\frac{a^{3}}{2 c^{2} x^{2}}+b^{3} \left(-\frac{\mathrm{arcsech}\left(c x \right)^{3}}{2 c^{2} x^{2}}+\frac{3 \mathrm{arcsech}\left(c x \right)^{2} \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{4 c x}+\frac{\mathrm{arcsech}\left(c x \right)^{3}}{4}-\frac{3 \,\mathrm{arcsech}\left(c x \right)}{4 c^{2} x^{2}}+\frac{3 \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{8 c x}+\frac{3 \,\mathrm{arcsech}\left(c x \right)}{8}\right)+3 a \,b^{2} \left(-\frac{\mathrm{arcsech}\left(c x \right)^{2}}{2 c^{2} x^{2}}+\frac{\mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{2 c x}+\frac{\mathrm{arcsech}\left(c x \right)^{2}}{4}-\frac{1}{4 c^{2} x^{2}}\right)+3 a^{2} b \left(-\frac{\mathrm{arcsech}\left(c x \right)}{2 c^{2} x^{2}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(\arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right) c^{2} x^{2}+\sqrt{-c^{2} x^{2}+1}\right)}{4 c x \sqrt{-c^{2} x^{2}+1}}\right)\right)"," ",0,"c^2*(-1/2*a^3/c^2/x^2+b^3*(-1/2/c^2/x^2*arcsech(c*x)^3+3/4*arcsech(c*x)^2/c/x*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+1/4*arcsech(c*x)^3-3/4/c^2/x^2*arcsech(c*x)+3/8/c/x*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+3/8*arcsech(c*x))+3*a*b^2*(-1/2/c^2/x^2*arcsech(c*x)^2+1/2*arcsech(c*x)/c/x*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+1/4*arcsech(c*x)^2-1/4/c^2/x^2)+3*a^2*b*(-1/2/c^2/x^2*arcsech(c*x)+1/4*(-(c*x-1)/c/x)^(1/2)/c/x*((c*x+1)/c/x)^(1/2)*(arctanh(1/(-c^2*x^2+1)^(1/2))*c^2*x^2+(-c^2*x^2+1)^(1/2))/(-c^2*x^2+1)^(1/2)))","B"
49,1,387,191,0.506000," ","int((a+b*arcsech(c*x))^3/x^4,x)","c^{3} \left(-\frac{a^{3}}{3 c^{3} x^{3}}+b^{3} \left(-\frac{\mathrm{arcsech}\left(c x \right)^{3}}{3 c^{3} x^{3}}+\frac{2 \mathrm{arcsech}\left(c x \right)^{2} \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{3}+\frac{\mathrm{arcsech}\left(c x \right)^{2} \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{3 c^{2} x^{2}}-\frac{4 \,\mathrm{arcsech}\left(c x \right)}{3 c x}+\frac{40 \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{27}-\frac{2 \,\mathrm{arcsech}\left(c x \right)}{9 c^{3} x^{3}}+\frac{2 \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{27 c^{2} x^{2}}\right)+3 a \,b^{2} \left(-\frac{\mathrm{arcsech}\left(c x \right)^{2}}{3 c^{3} x^{3}}+\frac{4 \,\mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{9}+\frac{2 \,\mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{9 c^{2} x^{2}}-\frac{4}{9 c x}-\frac{2}{27 c^{3} x^{3}}\right)+3 a^{2} b \left(-\frac{\mathrm{arcsech}\left(c x \right)}{3 c^{3} x^{3}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(2 c^{2} x^{2}+1\right)}{9 c^{2} x^{2}}\right)\right)"," ",0,"c^3*(-1/3*a^3/c^3/x^3+b^3*(-1/3/c^3/x^3*arcsech(c*x)^3+2/3*arcsech(c*x)^2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+1/3*arcsech(c*x)^2/c^2/x^2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)-4/3/c/x*arcsech(c*x)+40/27*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)-2/9*arcsech(c*x)/c^3/x^3+2/27/c^2/x^2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2))+3*a*b^2*(-1/3/c^3/x^3*arcsech(c*x)^2+4/9*arcsech(c*x)*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+2/9*arcsech(c*x)/c^2/x^2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)-4/9/c/x-2/27/c^3/x^3)+3*a^2*b*(-1/3*arcsech(c*x)/c^3/x^3+1/9*(-(c*x-1)/c/x)^(1/2)/c^2/x^2*((c*x+1)/c/x)^(1/2)*(2*c^2*x^2+1)))","B"
50,1,485,216,0.481000," ","int((a+b*arcsech(c*x))^3/x^5,x)","c^{4} \left(-\frac{a^{3}}{4 c^{4} x^{4}}+b^{3} \left(-\frac{\mathrm{arcsech}\left(c x \right)^{3}}{4 c^{4} x^{4}}+\frac{3 \mathrm{arcsech}\left(c x \right)^{2} \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{16 c^{3} x^{3}}+\frac{9 \mathrm{arcsech}\left(c x \right)^{2} \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{32 c x}+\frac{3 \mathrm{arcsech}\left(c x \right)^{3}}{32}-\frac{3 \,\mathrm{arcsech}\left(c x \right)}{32 c^{4} x^{4}}+\frac{3 \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{128 c^{3} x^{3}}+\frac{45 \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{256 c x}+\frac{45 \,\mathrm{arcsech}\left(c x \right)}{256}-\frac{9 \,\mathrm{arcsech}\left(c x \right)}{32 c^{2} x^{2}}\right)+3 a \,b^{2} \left(-\frac{\mathrm{arcsech}\left(c x \right)^{2}}{4 c^{4} x^{4}}+\frac{\mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{8 c^{3} x^{3}}+\frac{3 \,\mathrm{arcsech}\left(c x \right) \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{16 c x}+\frac{3 \mathrm{arcsech}\left(c x \right)^{2}}{32}-\frac{1}{32 c^{4} x^{4}}-\frac{3}{32 c^{2} x^{2}}\right)+3 a^{2} b \left(-\frac{\mathrm{arcsech}\left(c x \right)}{4 c^{4} x^{4}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(3 \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right) c^{4} x^{4}+3 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}+2 \sqrt{-c^{2} x^{2}+1}\right)}{32 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}\right)\right)"," ",0,"c^4*(-1/4*a^3/c^4/x^4+b^3*(-1/4/c^4/x^4*arcsech(c*x)^3+3/16*arcsech(c*x)^2/c^3/x^3*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+9/32*arcsech(c*x)^2/c/x*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+3/32*arcsech(c*x)^3-3/32/c^4/x^4*arcsech(c*x)+3/128/c^3/x^3*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+45/256/c/x*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+45/256*arcsech(c*x)-9/32/c^2/x^2*arcsech(c*x))+3*a*b^2*(-1/4/c^4/x^4*arcsech(c*x)^2+1/8*arcsech(c*x)/c^3/x^3*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+3/16*arcsech(c*x)/c/x*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+3/32*arcsech(c*x)^2-1/32/c^4/x^4-3/32/c^2/x^2)+3*a^2*b*(-1/4/c^4/x^4*arcsech(c*x)+1/32*(-(c*x-1)/c/x)^(1/2)/c^3/x^3*((c*x+1)/c/x)^(1/2)*(3*arctanh(1/(-c^2*x^2+1)^(1/2))*c^4*x^4+3*c^2*x^2*(-c^2*x^2+1)^(1/2)+2*(-c^2*x^2+1)^(1/2))/(-c^2*x^2+1)^(1/2)))","B"
51,0,0,14,1.069000," ","int(x/(a+b*arcsech(c*x)),x)","\int \frac{x}{a +b \,\mathrm{arcsech}\left(c x \right)}\, dx"," ",0,"int(x/(a+b*arcsech(c*x)),x)","F"
52,0,0,12,0.486000," ","int(1/(a+b*arcsech(c*x)),x)","\int \frac{1}{a +b \,\mathrm{arcsech}\left(c x \right)}\, dx"," ",0,"int(1/(a+b*arcsech(c*x)),x)","F"
53,0,0,16,0.257000," ","int(1/x/(a+b*arcsech(c*x)),x)","\int \frac{1}{x \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}\, dx"," ",0,"int(1/x/(a+b*arcsech(c*x)),x)","F"
54,1,54,46,0.132000," ","int(1/x^2/(a+b*arcsech(c*x)),x)","c \left(-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \frac{a}{b}+\mathrm{arcsech}\left(c x \right)\right)}{2 b}+\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arcsech}\left(c x \right)-\frac{a}{b}\right)}{2 b}\right)"," ",0,"c*(-1/2/b*exp(a/b)*Ei(1,a/b+arcsech(c*x))+1/2/b*exp(-a/b)*Ei(1,-arcsech(c*x)-a/b))","A"
55,1,60,59,0.242000," ","int(1/x^3/(a+b*arcsech(c*x)),x)","c^{2} \left(-\frac{{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, \frac{2 a}{b}+2 \,\mathrm{arcsech}\left(c x \right)\right)}{4 b}+\frac{{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arcsech}\left(c x \right)-\frac{2 a}{b}\right)}{4 b}\right)"," ",0,"c^2*(-1/4/b*exp(2*a/b)*Ei(1,2*a/b+2*arcsech(c*x))+1/4/b*exp(-2*a/b)*Ei(1,-2*arcsech(c*x)-2*a/b))","A"
56,1,110,109,0.402000," ","int(1/x^4/(a+b*arcsech(c*x)),x)","c^{3} \left(-\frac{{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, \frac{3 a}{b}+3 \,\mathrm{arcsech}\left(c x \right)\right)}{8 b}-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \frac{a}{b}+\mathrm{arcsech}\left(c x \right)\right)}{8 b}+\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arcsech}\left(c x \right)-\frac{a}{b}\right)}{8 b}+\frac{{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arcsech}\left(c x \right)-\frac{3 a}{b}\right)}{8 b}\right)"," ",0,"c^3*(-1/8/b*exp(3*a/b)*Ei(1,3*a/b+3*arcsech(c*x))-1/8/b*exp(a/b)*Ei(1,a/b+arcsech(c*x))+1/8/b*exp(-a/b)*Ei(1,-arcsech(c*x)-a/b)+1/8/b*exp(-3*a/b)*Ei(1,-3*arcsech(c*x)-3*a/b))","A"
57,0,0,14,1.076000," ","int(x/(a+b*arcsech(c*x))^2,x)","\int \frac{x}{\left(a +b \,\mathrm{arcsech}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(x/(a+b*arcsech(c*x))^2,x)","F"
58,0,0,12,0.474000," ","int(1/(a+b*arcsech(c*x))^2,x)","\int \frac{1}{\left(a +b \,\mathrm{arcsech}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(a+b*arcsech(c*x))^2,x)","F"
59,0,0,16,0.263000," ","int(1/x/(a+b*arcsech(c*x))^2,x)","\int \frac{1}{x \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/x/(a+b*arcsech(c*x))^2,x)","F"
60,1,164,84,0.194000," ","int(1/x^2/(a+b*arcsech(c*x))^2,x)","c \left(\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x +1}{2 b c x \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}+\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arcsech}\left(c x \right)-\frac{a}{b}\right)}{2 b^{2}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x -1}{2 b c x \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}+\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \frac{a}{b}+\mathrm{arcsech}\left(c x \right)\right)}{2 b^{2}}\right)"," ",0,"c*(1/2/b*((-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x+1)/c/x/(a+b*arcsech(c*x))+1/2/b^2*exp(-a/b)*Ei(1,-arcsech(c*x)-a/b)+1/2*((-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x-1)/b/c/x/(a+b*arcsech(c*x))+1/2/b^2*exp(a/b)*Ei(1,a/b+arcsech(c*x)))","A"
61,1,186,83,0.260000," ","int(1/x^3/(a+b*arcsech(c*x))^2,x)","c^{2} \left(\frac{2 \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x +c^{2} x^{2}-2}{4 c^{2} x^{2} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right) b}+\frac{{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, \frac{2 a}{b}+2 \,\mathrm{arcsech}\left(c x \right)\right)}{2 b^{2}}-\frac{c^{2} x^{2}-2-2 \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x}{4 b \,c^{2} x^{2} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}+\frac{{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arcsech}\left(c x \right)-\frac{2 a}{b}\right)}{2 b^{2}}\right)"," ",0,"c^2*(1/4*(2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x+c^2*x^2-2)/c^2/x^2/(a+b*arcsech(c*x))/b+1/2/b^2*exp(2*a/b)*Ei(1,2*a/b+2*arcsech(c*x))-1/4/b*(c^2*x^2-2-2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x)/c^2/x^2/(a+b*arcsech(c*x))+1/2/b^2*exp(-2*a/b)*Ei(1,-2*arcsech(c*x)-2*a/b))","B"
62,1,420,176,0.435000," ","int(1/x^4/(a+b*arcsech(c*x))^2,x)","c^{3} \left(-\frac{\sqrt{\frac{c x +1}{c x}}\, \sqrt{-\frac{c x -1}{c x}}\, c^{3} x^{3}-4 \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x -3 c^{2} x^{2}+4}{8 c^{3} x^{3} b \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}+\frac{3 \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, \frac{3 a}{b}+3 \,\mathrm{arcsech}\left(c x \right)\right)}{8 b^{2}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x -1}{8 b c x \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}+\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \frac{a}{b}+\mathrm{arcsech}\left(c x \right)\right)}{8 b^{2}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x +1}{8 b c x \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}+\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arcsech}\left(c x \right)-\frac{a}{b}\right)}{8 b^{2}}-\frac{\sqrt{\frac{c x +1}{c x}}\, \sqrt{-\frac{c x -1}{c x}}\, c^{3} x^{3}-4 \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x +3 c^{2} x^{2}-4}{8 b \,c^{3} x^{3} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}+\frac{3 \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arcsech}\left(c x \right)-\frac{3 a}{b}\right)}{8 b^{2}}\right)"," ",0,"c^3*(-1/8*(((c*x+1)/c/x)^(1/2)*(-(c*x-1)/c/x)^(1/2)*c^3*x^3-4*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x-3*c^2*x^2+4)/c^3/x^3/b/(a+b*arcsech(c*x))+3/8/b^2*exp(3*a/b)*Ei(1,3*a/b+3*arcsech(c*x))+1/8*((-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x-1)/b/c/x/(a+b*arcsech(c*x))+1/8/b^2*exp(a/b)*Ei(1,a/b+arcsech(c*x))+1/8/b*((-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x+1)/c/x/(a+b*arcsech(c*x))+1/8/b^2*exp(-a/b)*Ei(1,-arcsech(c*x)-a/b)-1/8/b*(((c*x+1)/c/x)^(1/2)*(-(c*x-1)/c/x)^(1/2)*c^3*x^3-4*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x+3*c^2*x^2-4)/c^3/x^3/(a+b*arcsech(c*x))+3/8/b^2*exp(-3*a/b)*Ei(1,-3*arcsech(c*x)-3*a/b))","B"
63,0,0,14,1.030000," ","int(x/(a+b*arcsech(c*x))^3,x)","\int \frac{x}{\left(a +b \,\mathrm{arcsech}\left(c x \right)\right)^{3}}\, dx"," ",0,"int(x/(a+b*arcsech(c*x))^3,x)","F"
64,0,0,12,0.678000," ","int(1/(a+b*arcsech(c*x))^3,x)","\int \frac{1}{\left(a +b \,\mathrm{arcsech}\left(c x \right)\right)^{3}}\, dx"," ",0,"int(1/(a+b*arcsech(c*x))^3,x)","F"
65,0,0,16,0.237000," ","int(1/x/(a+b*arcsech(c*x))^3,x)","\int \frac{1}{x \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)^{3}}\, dx"," ",0,"int(1/x/(a+b*arcsech(c*x))^3,x)","F"
66,1,244,104,0.171000," ","int(1/x^2/(a+b*arcsech(c*x))^3,x)","c \left(-\frac{\left(\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x -1\right) \left(b \,\mathrm{arcsech}\left(c x \right)+a -b \right)}{4 c x \,b^{2} \left(\mathrm{arcsech}\left(c x \right)^{2} b^{2}+2 \,\mathrm{arcsech}\left(c x \right) a b +a^{2}\right)}-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \frac{a}{b}+\mathrm{arcsech}\left(c x \right)\right)}{4 b^{3}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x +1}{4 b c x \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)^{2}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x +1}{4 b^{2} c x \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}+\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arcsech}\left(c x \right)-\frac{a}{b}\right)}{4 b^{3}}\right)"," ",0,"c*(-1/4*((-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x-1)*(b*arcsech(c*x)+a-b)/c/x/b^2/(arcsech(c*x)^2*b^2+2*arcsech(c*x)*a*b+a^2)-1/4/b^3*exp(a/b)*Ei(1,a/b+arcsech(c*x))+1/4/b*((-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x+1)/c/x/(a+b*arcsech(c*x))^2+1/4/b^2*((-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x+1)/c/x/(a+b*arcsech(c*x))+1/4/b^3*exp(-a/b)*Ei(1,-arcsech(c*x)-a/b))","B"
67,1,277,108,0.287000," ","int(1/x^3/(a+b*arcsech(c*x))^3,x)","c^{2} \left(-\frac{\left(2 \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x +c^{2} x^{2}-2\right) \left(2 b \,\mathrm{arcsech}\left(c x \right)+2 a -b \right)}{8 c^{2} x^{2} b^{2} \left(\mathrm{arcsech}\left(c x \right)^{2} b^{2}+2 \,\mathrm{arcsech}\left(c x \right) a b +a^{2}\right)}-\frac{{\mathrm e}^{\frac{2 a}{b}} \Ei \left(1, \frac{2 a}{b}+2 \,\mathrm{arcsech}\left(c x \right)\right)}{2 b^{3}}-\frac{c^{2} x^{2}-2-2 \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x}{8 b \,c^{2} x^{2} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)^{2}}-\frac{c^{2} x^{2}-2-2 \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x}{4 b^{2} c^{2} x^{2} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}+\frac{{\mathrm e}^{-\frac{2 a}{b}} \Ei \left(1, -2 \,\mathrm{arcsech}\left(c x \right)-\frac{2 a}{b}\right)}{2 b^{3}}\right)"," ",0,"c^2*(-1/8*(2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x+c^2*x^2-2)*(2*b*arcsech(c*x)+2*a-b)/c^2/x^2/b^2/(arcsech(c*x)^2*b^2+2*arcsech(c*x)*a*b+a^2)-1/2/b^3*exp(2*a/b)*Ei(1,2*a/b+2*arcsech(c*x))-1/8/b*(c^2*x^2-2-2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x)/c^2/x^2/(a+b*arcsech(c*x))^2-1/4/b^2*(c^2*x^2-2-2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x)/c^2/x^2/(a+b*arcsech(c*x))+1/2/b^3*exp(-2*a/b)*Ei(1,-2*arcsech(c*x)-2*a/b))","B"
68,1,628,222,0.469000," ","int(1/x^4/(a+b*arcsech(c*x))^3,x)","c^{3} \left(\frac{\left(\sqrt{\frac{c x +1}{c x}}\, \sqrt{-\frac{c x -1}{c x}}\, c^{3} x^{3}-4 \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x -3 c^{2} x^{2}+4\right) \left(3 b \,\mathrm{arcsech}\left(c x \right)+3 a -b \right)}{16 c^{3} x^{3} b^{2} \left(\mathrm{arcsech}\left(c x \right)^{2} b^{2}+2 \,\mathrm{arcsech}\left(c x \right) a b +a^{2}\right)}-\frac{9 \,{\mathrm e}^{\frac{3 a}{b}} \Ei \left(1, \frac{3 a}{b}+3 \,\mathrm{arcsech}\left(c x \right)\right)}{16 b^{3}}-\frac{\left(\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x -1\right) \left(b \,\mathrm{arcsech}\left(c x \right)+a -b \right)}{16 c x \,b^{2} \left(\mathrm{arcsech}\left(c x \right)^{2} b^{2}+2 \,\mathrm{arcsech}\left(c x \right) a b +a^{2}\right)}-\frac{{\mathrm e}^{\frac{a}{b}} \Ei \left(1, \frac{a}{b}+\mathrm{arcsech}\left(c x \right)\right)}{16 b^{3}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x +1}{16 b c x \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)^{2}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x +1}{16 b^{2} c x \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}+\frac{{\mathrm e}^{-\frac{a}{b}} \Ei \left(1, -\mathrm{arcsech}\left(c x \right)-\frac{a}{b}\right)}{16 b^{3}}-\frac{\sqrt{\frac{c x +1}{c x}}\, \sqrt{-\frac{c x -1}{c x}}\, c^{3} x^{3}-4 \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x +3 c^{2} x^{2}-4}{16 b \,c^{3} x^{3} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)^{2}}-\frac{3 \left(\sqrt{\frac{c x +1}{c x}}\, \sqrt{-\frac{c x -1}{c x}}\, c^{3} x^{3}-4 \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, c x +3 c^{2} x^{2}-4\right)}{16 b^{2} c^{3} x^{3} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}+\frac{9 \,{\mathrm e}^{-\frac{3 a}{b}} \Ei \left(1, -3 \,\mathrm{arcsech}\left(c x \right)-\frac{3 a}{b}\right)}{16 b^{3}}\right)"," ",0,"c^3*(1/16*(((c*x+1)/c/x)^(1/2)*(-(c*x-1)/c/x)^(1/2)*c^3*x^3-4*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x-3*c^2*x^2+4)*(3*b*arcsech(c*x)+3*a-b)/c^3/x^3/b^2/(arcsech(c*x)^2*b^2+2*arcsech(c*x)*a*b+a^2)-9/16/b^3*exp(3*a/b)*Ei(1,3*a/b+3*arcsech(c*x))-1/16*((-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x-1)*(b*arcsech(c*x)+a-b)/c/x/b^2/(arcsech(c*x)^2*b^2+2*arcsech(c*x)*a*b+a^2)-1/16/b^3*exp(a/b)*Ei(1,a/b+arcsech(c*x))+1/16/b*((-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x+1)/c/x/(a+b*arcsech(c*x))^2+1/16/b^2*((-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x+1)/c/x/(a+b*arcsech(c*x))+1/16/b^3*exp(-a/b)*Ei(1,-arcsech(c*x)-a/b)-1/16/b*(((c*x+1)/c/x)^(1/2)*(-(c*x-1)/c/x)^(1/2)*c^3*x^3-4*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x+3*c^2*x^2-4)/c^3/x^3/(a+b*arcsech(c*x))^2-3/16/b^2*(((c*x+1)/c/x)^(1/2)*(-(c*x-1)/c/x)^(1/2)*c^3*x^3-4*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*c*x+3*c^2*x^2-4)/c^3/x^3/(a+b*arcsech(c*x))+9/16/b^3*exp(-3*a/b)*Ei(1,-3*arcsech(c*x)-3*a/b))","B"
69,0,0,18,2.891000," ","int((d*x)^m*(a+b*arcsech(c*x))^3,x)","\int \left(d x \right)^{m} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)^{3}\, dx"," ",0,"int((d*x)^m*(a+b*arcsech(c*x))^3,x)","F"
70,0,0,18,2.683000," ","int((d*x)^m*(a+b*arcsech(c*x))^2,x)","\int \left(d x \right)^{m} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)^{2}\, dx"," ",0,"int((d*x)^m*(a+b*arcsech(c*x))^2,x)","F"
71,0,0,79,2.598000," ","int((d*x)^m*(a+b*arcsech(c*x)),x)","\int \left(d x \right)^{m} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)\, dx"," ",0,"int((d*x)^m*(a+b*arcsech(c*x)),x)","F"
72,0,0,18,1.846000," ","int((d*x)^m/(a+b*arcsech(c*x)),x)","\int \frac{\left(d x \right)^{m}}{a +b \,\mathrm{arcsech}\left(c x \right)}\, dx"," ",0,"int((d*x)^m/(a+b*arcsech(c*x)),x)","F"
73,0,0,18,1.718000," ","int((d*x)^m/(a+b*arcsech(c*x))^2,x)","\int \frac{\left(d x \right)^{m}}{\left(a +b \,\mathrm{arcsech}\left(c x \right)\right)^{2}}\, dx"," ",0,"int((d*x)^m/(a+b*arcsech(c*x))^2,x)","F"
74,1,283,224,0.069000," ","int((e*x+d)^3*(a+b*arcsech(c*x)),x)","\frac{\frac{\left(c x e +c d \right)^{4} a}{4 c^{3} e}+\frac{b \left(\frac{e^{3} \mathrm{arcsech}\left(c x \right) c^{4} x^{4}}{4}+e^{2} \mathrm{arcsech}\left(c x \right) c^{4} x^{3} d +\frac{3 e \,\mathrm{arcsech}\left(c x \right) c^{4} x^{2} d^{2}}{2}+\mathrm{arcsech}\left(c x \right) c^{4} x \,d^{3}+\frac{\mathrm{arcsech}\left(c x \right) c^{4} d^{4}}{4 e}+\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(-3 c^{4} d^{4} \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)+12 c^{3} d^{3} e \arcsin \left(c x \right)-c^{2} x^{2} e^{4} \sqrt{-c^{2} x^{2}+1}-6 c^{2} d \,e^{3} x \sqrt{-c^{2} x^{2}+1}-18 c^{2} d^{2} e^{2} \sqrt{-c^{2} x^{2}+1}+6 c d \,e^{3} \arcsin \left(c x \right)-2 e^{4} \sqrt{-c^{2} x^{2}+1}\right)}{12 e \sqrt{-c^{2} x^{2}+1}}\right)}{c^{3}}}{c}"," ",0,"1/c*(1/4*(c*e*x+c*d)^4*a/c^3/e+b/c^3*(1/4*e^3*arcsech(c*x)*c^4*x^4+e^2*arcsech(c*x)*c^4*x^3*d+3/2*e*arcsech(c*x)*c^4*x^2*d^2+arcsech(c*x)*c^4*x*d^3+1/4/e*arcsech(c*x)*c^4*d^4+1/12/e*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(-3*c^4*d^4*arctanh(1/(-c^2*x^2+1)^(1/2))+12*c^3*d^3*e*arcsin(c*x)-c^2*x^2*e^4*(-c^2*x^2+1)^(1/2)-6*c^2*d*e^3*x*(-c^2*x^2+1)^(1/2)-18*c^2*d^2*e^2*(-c^2*x^2+1)^(1/2)+6*c*d*e^3*arcsin(c*x)-2*e^4*(-c^2*x^2+1)^(1/2))/(-c^2*x^2+1)^(1/2)))","A"
75,1,215,171,0.066000," ","int((e*x+d)^2*(a+b*arcsech(c*x)),x)","\frac{\frac{\left(c x e +c d \right)^{3} a}{3 c^{2} e}+\frac{b \left(\frac{e^{2} \mathrm{arcsech}\left(c x \right) c^{3} x^{3}}{3}+e \,\mathrm{arcsech}\left(c x \right) c^{3} x^{2} d +\mathrm{arcsech}\left(c x \right) c^{3} x \,d^{2}+\frac{\mathrm{arcsech}\left(c x \right) c^{3} d^{3}}{3 e}+\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(-2 c^{3} d^{3} \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)+6 c^{2} d^{2} e \arcsin \left(c x \right)-e^{3} c x \sqrt{-c^{2} x^{2}+1}-6 c d \,e^{2} \sqrt{-c^{2} x^{2}+1}+e^{3} \arcsin \left(c x \right)\right)}{6 e \sqrt{-c^{2} x^{2}+1}}\right)}{c^{2}}}{c}"," ",0,"1/c*(1/3*(c*e*x+c*d)^3*a/c^2/e+b/c^2*(1/3*e^2*arcsech(c*x)*c^3*x^3+e*arcsech(c*x)*c^3*x^2*d+arcsech(c*x)*c^3*x*d^2+1/3/e*arcsech(c*x)*c^3*d^3+1/6/e*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(-2*c^3*d^3*arctanh(1/(-c^2*x^2+1)^(1/2))+6*c^2*d^2*e*arcsin(c*x)-e^3*c*x*(-c^2*x^2+1)^(1/2)-6*c*d*e^2*(-c^2*x^2+1)^(1/2)+e^3*arcsin(c*x))/(-c^2*x^2+1)^(1/2)))","A"
76,1,125,120,0.063000," ","int((e*x+d)*(a+b*arcsech(c*x)),x)","\frac{\frac{a \left(\frac{1}{2} c^{2} x^{2} e +c^{2} d x \right)}{c}+\frac{b \left(\frac{\mathrm{arcsech}\left(c x \right) c^{2} x^{2} e}{2}+\mathrm{arcsech}\left(c x \right) c^{2} x d +\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(2 c d \arcsin \left(c x \right)-e \sqrt{-c^{2} x^{2}+1}\right)}{2 \sqrt{-c^{2} x^{2}+1}}\right)}{c}}{c}"," ",0,"1/c*(a/c*(1/2*c^2*x^2*e+c^2*d*x)+b/c*(1/2*arcsech(c*x)*c^2*x^2*e+arcsech(c*x)*c^2*x*d+1/2*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(2*c*d*arcsin(c*x)-e*(-c^2*x^2+1)^(1/2))/(-c^2*x^2+1)^(1/2)))","A"
77,1,42,36,0.040000," ","int(a+b*arcsech(c*x),x)","a x +b x \,\mathrm{arcsech}\left(c x \right)-\frac{b \arctan \left(\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)}{c}"," ",0,"a*x+b*x*arcsech(c*x)-b/c*arctan((-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))","A"
78,1,514,371,0.679000," ","int((a+b*arcsech(c*x))/(e*x+d),x)","\frac{a \ln \left(c x e +c d \right)}{e}+\frac{b \,\mathrm{arcsech}\left(c x \right) \ln \left(\frac{-c d \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)+\sqrt{-c^{2} d^{2}+e^{2}}-e}{-e +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e}+\frac{b \,\mathrm{arcsech}\left(c x \right) \ln \left(\frac{c d \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)+\sqrt{-c^{2} d^{2}+e^{2}}+e}{e +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e}+\frac{b \dilog \left(\frac{c d \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)+\sqrt{-c^{2} d^{2}+e^{2}}+e}{e +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e}+\frac{b \dilog \left(\frac{-c d \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)+\sqrt{-c^{2} d^{2}+e^{2}}-e}{-e +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e}-\frac{b \,\mathrm{arcsech}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e}-\frac{b \,\mathrm{arcsech}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e}-\frac{b \dilog \left(1+i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e}-\frac{b \dilog \left(1-i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e}"," ",0,"a*ln(c*e*x+c*d)/e+b/e*arcsech(c*x)*ln((-c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))+(-c^2*d^2+e^2)^(1/2)-e)/(-e+(-c^2*d^2+e^2)^(1/2)))+b/e*arcsech(c*x)*ln((c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))+(-c^2*d^2+e^2)^(1/2)+e)/(e+(-c^2*d^2+e^2)^(1/2)))+b/e*dilog((c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))+(-c^2*d^2+e^2)^(1/2)+e)/(e+(-c^2*d^2+e^2)^(1/2)))+b/e*dilog((-c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))+(-c^2*d^2+e^2)^(1/2)-e)/(-e+(-c^2*d^2+e^2)^(1/2)))-b/e*arcsech(c*x)*ln(1+I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-b/e*arcsech(c*x)*ln(1-I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-b/e*dilog(1+I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-b/e*dilog(1-I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))","C"
79,1,231,133,0.122000," ","int((a+b*arcsech(c*x))/(e*x+d)^2,x)","-\frac{c a}{\left(c x e +c d \right) e}-\frac{c b \,\mathrm{arcsech}\left(c x \right)}{\left(c x e +c d \right) e}+\frac{c b \sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{e d \sqrt{-c^{2} x^{2}+1}}-\frac{c b \sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, \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 x e +c d}\right)}{e \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, d \sqrt{-c^{2} x^{2}+1}}"," ",0,"-c*a/(c*e*x+c*d)/e-c*b/(c*e*x+c*d)/e*arcsech(c*x)+c*b/e*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/d/(-c^2*x^2+1)^(1/2)*arctanh(1/(-c^2*x^2+1)^(1/2))-c*b/e*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/(-(c^2*d^2-e^2)/e^2)^(1/2)/d/(-c^2*x^2+1)^(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))","A"
80,1,1090,267,0.087000," ","int((a+b*arcsech(c*x))/(e*x+d)^3,x)","-\frac{c^{2} a}{2 \left(c x e +c d \right)^{2} e}-\frac{c^{2} b \,\mathrm{arcsech}\left(c x \right)}{2 \left(c x e +c d \right)^{2} e}+\frac{c^{4} b \sqrt{-\frac{c x -1}{c x}}\, x^{2} \sqrt{\frac{c x +1}{c x}}\, \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{2 \sqrt{-c^{2} x^{2}+1}\, \left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right)}+\frac{c^{4} b \sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, d \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{2 e \sqrt{-c^{2} x^{2}+1}\, \left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right)}-\frac{c^{4} b \sqrt{-\frac{c x -1}{c x}}\, x^{2} \sqrt{\frac{c x +1}{c x}}\, \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 x e +c d}\right)}{\sqrt{-c^{2} x^{2}+1}\, \left(c d +e \right) \left(c d -e \right) \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \left(c x e +c d \right)}-\frac{c^{4} b \sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, 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 x e +c d}\right)}{e \sqrt{-c^{2} x^{2}+1}\, \left(c d +e \right) \left(c d -e \right) \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \left(c x e +c d \right)}+\frac{c^{2} b e \sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}}{2 d \left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right)}-\frac{c^{2} b \,e^{2} \sqrt{-\frac{c x -1}{c x}}\, x^{2} \sqrt{\frac{c x +1}{c x}}\, \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{2 \sqrt{-c^{2} x^{2}+1}\, d^{2} \left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right)}-\frac{c^{2} b e \sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{2 \sqrt{-c^{2} x^{2}+1}\, d \left(c d +e \right) \left(c d -e \right) \left(c x e +c d \right)}+\frac{c^{2} b \,e^{2} \sqrt{-\frac{c x -1}{c x}}\, x^{2} \sqrt{\frac{c x +1}{c x}}\, \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 x e +c d}\right)}{2 \sqrt{-c^{2} x^{2}+1}\, d^{2} \left(c d +e \right) \left(c d -e \right) \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \left(c x e +c d \right)}+\frac{c^{2} b e \sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, \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 x e +c d}\right)}{2 \sqrt{-c^{2} x^{2}+1}\, d \left(c d +e \right) \left(c d -e \right) \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \left(c x e +c d \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*arcsech(c*x)+1/2*c^4*b*(-(c*x-1)/c/x)^(1/2)*x^2*((c*x+1)/c/x)^(1/2)/(-c^2*x^2+1)^(1/2)/(c*d+e)/(c*d-e)/(c*e*x+c*d)*arctanh(1/(-c^2*x^2+1)^(1/2))+1/2*c^4*b/e*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/(-c^2*x^2+1)^(1/2)*d/(c*d+e)/(c*d-e)/(c*e*x+c*d)*arctanh(1/(-c^2*x^2+1)^(1/2))-c^4*b*(-(c*x-1)/c/x)^(1/2)*x^2*((c*x+1)/c/x)^(1/2)/(-c^2*x^2+1)^(1/2)/(c*d+e)/(c*d-e)/(-(c^2*d^2-e^2)/e^2)^(1/2)/(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^4*b/e*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/(-c^2*x^2+1)^(1/2)*d/(c*d+e)/(c*d-e)/(-(c^2*d^2-e^2)/e^2)^(1/2)/(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*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/d/(c*d+e)/(c*d-e)/(c*e*x+c*d)-1/2*c^2*b*e^2*(-(c*x-1)/c/x)^(1/2)*x^2*((c*x+1)/c/x)^(1/2)/(-c^2*x^2+1)^(1/2)/d^2/(c*d+e)/(c*d-e)/(c*e*x+c*d)*arctanh(1/(-c^2*x^2+1)^(1/2))-1/2*c^2*b*e*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/(-c^2*x^2+1)^(1/2)/d/(c*d+e)/(c*d-e)/(c*e*x+c*d)*arctanh(1/(-c^2*x^2+1)^(1/2))+1/2*c^2*b*e^2*(-(c*x-1)/c/x)^(1/2)*x^2*((c*x+1)/c/x)^(1/2)/(-c^2*x^2+1)^(1/2)/d^2/(c*d+e)/(c*d-e)/(-(c^2*d^2-e^2)/e^2)^(1/2)/(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*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/(-c^2*x^2+1)^(1/2)/d/(c*d+e)/(c*d-e)/(-(c^2*d^2-e^2)/e^2)^(1/2)/(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"
81,1,830,302,0.228000," ","int((e*x+d)^(3/2)*(a+b*arcsech(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{arcsech}\left(c x \right)}{5}-\frac{2 e^{2} \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c x e}}\, x \sqrt{\frac{\left(e x +d \right) c -c d +e}{c x e}}\, \left(\sqrt{\frac{c}{c d +e}}\, \left(e x +d \right)^{\frac{5}{2}} c^{2}+9 \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) c^{2} d^{2}-7 \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) c^{2} d^{2}-3 \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \frac{c d +e}{c d}, \frac{\sqrt{\frac{c}{c d -e}}}{\sqrt{\frac{c}{c d +e}}}\right) c^{2} d^{2}-2 \sqrt{\frac{c}{c d +e}}\, \left(e x +d \right)^{\frac{3}{2}} c^{2} d -7 \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) c d e +7 \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) c d e +\sqrt{\frac{c}{c d +e}}\, \sqrt{e x +d}\, c^{2} d^{2}+\sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) e^{2}-\sqrt{\frac{c}{c d +e}}\, \sqrt{e x +d}\, e^{2}\right)}{15 c \sqrt{\frac{c}{c d +e}}\, \left(\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}-e^{2}\right)}\right)}{e}"," ",0,"2/e*(1/5*(e*x+d)^(5/2)*a+b*(1/5*(e*x+d)^(5/2)*arcsech(c*x)-2/15/c*e^2*(-((e*x+d)*c-c*d-e)/c/x/e)^(1/2)*x*(((e*x+d)*c-c*d+e)/c/x/e)^(1/2)*((c/(c*d+e))^(1/2)*(e*x+d)^(5/2)*c^2+9*(-((e*x+d)*c-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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*d^2-7*(-((e*x+d)*c-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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*(-((e*x+d)*c-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-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*d^2-2*(c/(c*d+e))^(1/2)*(e*x+d)^(3/2)*c^2*d-7*(-((e*x+d)*c-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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)/((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2-e^2)))","B"
82,1,415,248,0.100000," ","int((e*x+d)^(1/2)*(a+b*arcsech(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{arcsech}\left(c x \right)}{3}-\frac{2 e^{2} \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c x e}}\, x \sqrt{\frac{\left(e x +d \right) c -c d +e}{c x e}}\, \left(2 \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) c d -\EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) c d -\EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \frac{c d +e}{c d}, \frac{\sqrt{\frac{c}{c d -e}}}{\sqrt{\frac{c}{c d +e}}}\right) c d -\EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) e +\EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) e \right) \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}}{3 \sqrt{\frac{c}{c d +e}}\, \left(\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}-e^{2}\right)}\right)}{e}"," ",0,"2/e*(1/3*(e*x+d)^(3/2)*a+b*(1/3*(e*x+d)^(3/2)*arcsech(c*x)-2/3*e^2*(-((e*x+d)*c-c*d-e)/c/x/e)^(1/2)*x*(((e*x+d)*c-c*d+e)/c/x/e)^(1/2)*(2*EllipticF((e*x+d)^(1/2)*(c/(c*d+e))^(1/2),((c*d+e)/(c*d-e))^(1/2))*c*d-EllipticE((e*x+d)^(1/2)*(c/(c*d+e))^(1/2),((c*d+e)/(c*d-e))^(1/2))*c*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*d-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-c*d+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-c*d-e)/(c*d+e))^(1/2)/(c/(c*d+e))^(1/2)/((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2-e^2)))","A"
83,1,288,171,0.100000," ","int((a+b*arcsech(c*x))/(e*x+d)^(1/2),x)","\frac{2 a \sqrt{e x +d}+2 b \left(\sqrt{e x +d}\, \mathrm{arcsech}\left(c x \right)-\frac{2 c \,e^{2} \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c x e}}\, x \sqrt{\frac{\left(e x +d \right) c -c d +e}{c x e}}\, \left(\EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right)-\EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \frac{c d +e}{c d}, \frac{\sqrt{\frac{c}{c d -e}}}{\sqrt{\frac{c}{c d +e}}}\right)\right) \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}}{\sqrt{\frac{c}{c d +e}}\, \left(\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}-e^{2}\right)}\right)}{e}"," ",0,"2/e*(a*(e*x+d)^(1/2)+b*((e*x+d)^(1/2)*arcsech(c*x)-2*c*e^2*(-((e*x+d)*c-c*d-e)/c/x/e)^(1/2)*x*(((e*x+d)*c-c*d+e)/c/x/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)))*(-((e*x+d)*c-c*d+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-c*d-e)/(c*d+e))^(1/2)/(c/(c*d+e))^(1/2)/((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2-e^2)))","A"
84,1,253,96,0.094000," ","int((a+b*arcsech(c*x))/(e*x+d)^(3/2),x)","\frac{-\frac{2 a}{\sqrt{e x +d}}+2 b \left(-\frac{\mathrm{arcsech}\left(c x \right)}{\sqrt{e x +d}}-\frac{2 c \,e^{2} \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c x e}}\, x \sqrt{\frac{\left(e x +d \right) c -c d +e}{c x e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \frac{c d +e}{c d}, \frac{\sqrt{\frac{c}{c d -e}}}{\sqrt{\frac{c}{c d +e}}}\right) \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}}{d \sqrt{\frac{c}{c d +e}}\, \left(\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}-e^{2}\right)}\right)}{e}"," ",0,"2/e*(-a/(e*x+d)^(1/2)+b*(-1/(e*x+d)^(1/2)*arcsech(c*x)-2*c*e^2*(-((e*x+d)*c-c*d-e)/c/x/e)^(1/2)*x*(((e*x+d)*c-c*d+e)/c/x/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)*c-c*d+e)/(c*d-e))^(1/2)*(-((e*x+d)*c-c*d-e)/(c*d+e))^(1/2)/d/(c/(c*d+e))^(1/2)/((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2-e^2)))","B"
85,1,902,246,0.117000," ","int((a+b*arcsech(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{arcsech}\left(c x \right)}{3 \left(e x +d \right)^{\frac{3}{2}}}+\frac{2 c \,e^{2} \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c x e}}\, x \sqrt{\frac{\left(e x +d \right) c -c d +e}{c x e}}\, \left(\sqrt{\frac{c}{c d +e}}\, \left(e x +d \right)^{2} c^{2} d -\sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) \sqrt{e x +d}\, c^{2} d^{2}+c^{2} \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) d^{2} \sqrt{e x +d}-\sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \frac{c d +e}{c d}, \frac{\sqrt{\frac{c}{c d -e}}}{\sqrt{\frac{c}{c d +e}}}\right) \sqrt{e x +d}\, c^{2} d^{2}-2 \sqrt{\frac{c}{c d +e}}\, \left(e x +d \right) c^{2} d^{2}+\sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) \sqrt{e x +d}\, c d e -\sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) \sqrt{e x +d}\, c d e +\sqrt{\frac{c}{c d +e}}\, c^{2} d^{3}+\sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \frac{c d +e}{c d}, \frac{\sqrt{\frac{c}{c d -e}}}{\sqrt{\frac{c}{c d +e}}}\right) \sqrt{e x +d}\, e^{2}-\sqrt{\frac{c}{c d +e}}\, d \,e^{2}\right)}{3 \sqrt{e x +d}\, \left(c d -e \right) \left(c d +e \right) \sqrt{\frac{c}{c d +e}}\, d^{2} \left(\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}-e^{2}\right)}\right)}{e}"," ",0,"2/e*(-1/3/(e*x+d)^(3/2)*a+b*(-1/3/(e*x+d)^(3/2)*arcsech(c*x)+2/3*c*e^2*(-((e*x+d)*c-c*d-e)/c/x/e)^(1/2)*x*(((e*x+d)*c-c*d+e)/c/x/e)^(1/2)*((c/(c*d+e))^(1/2)*(e*x+d)^2*c^2*d-(-((e*x+d)*c-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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+c^2*(-((e*x+d)*c-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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))*d^2*(e*x+d)^(1/2)-(-((e*x+d)*c-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-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))*(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-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-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))*(e*x+d)^(1/2)*e^2-(c/(c*d+e))^(1/2)*d*e^2)/(e*x+d)^(1/2)/(c*d-e)/(c*d+e)/(c/(c*d+e))^(1/2)/d^2/((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2-e^2)))","B"
86,1,1632,539,0.129000," ","int((a+b*arcsech(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{arcsech}\left(c x \right)}{5 \left(e x +d \right)^{\frac{5}{2}}}+\frac{2 c \,e^{2} \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c x e}}\, x \sqrt{\frac{\left(e x +d \right) c -c d +e}{c x e}}\, \left(7 \sqrt{\frac{c}{c d +e}}\, \left(e x +d \right)^{3} c^{4} d^{3}-6 \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{4} d^{4}+7 \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{4} d^{4}-3 \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \frac{c d +e}{c d}, \frac{\sqrt{\frac{c}{c d -e}}}{\sqrt{\frac{c}{c d +e}}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{4} d^{4}-13 \sqrt{\frac{c}{c d +e}}\, \left(e x +d \right)^{2} c^{4} d^{4}+7 \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{3} e -7 \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{3} e -3 \sqrt{\frac{c}{c d +e}}\, \left(e x +d \right)^{3} c^{2} d \,e^{2}+5 \sqrt{\frac{c}{c d +e}}\, \left(e x +d \right) c^{4} d^{5}+2 \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{2} d^{2} e^{2}-3 \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{2} d^{2} e^{2}+6 \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \frac{c d +e}{c d}, \frac{\sqrt{\frac{c}{c d -e}}}{\sqrt{\frac{c}{c d +e}}}\right) \left(e x +d \right)^{\frac{3}{2}} c^{2} d^{2} e^{2}+5 \sqrt{\frac{c}{c d +e}}\, \left(e x +d \right)^{2} c^{2} d^{2} e^{2}+\sqrt{\frac{c}{c d +e}}\, c^{4} d^{6}-3 \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticF \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) \left(e x +d \right)^{\frac{3}{2}} c d \,e^{3}+3 \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticE \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \sqrt{\frac{c d +e}{c d -e}}\right) \left(e x +d \right)^{\frac{3}{2}} c d \,e^{3}-8 \sqrt{\frac{c}{c d +e}}\, \left(e x +d \right) c^{2} d^{3} e^{2}-3 \sqrt{-\frac{\left(e x +d \right) c -c d -e}{c d +e}}\, \sqrt{-\frac{\left(e x +d \right) c -c d +e}{c d -e}}\, \EllipticPi \left(\sqrt{e x +d}\, \sqrt{\frac{c}{c d +e}}, \frac{c d +e}{c d}, \frac{\sqrt{\frac{c}{c d -e}}}{\sqrt{\frac{c}{c d +e}}}\right) \left(e x +d \right)^{\frac{3}{2}} e^{4}-2 \sqrt{\frac{c}{c d +e}}\, c^{2} d^{4} e^{2}+3 \sqrt{\frac{c}{c d +e}}\, \left(e x +d \right) d \,e^{4}+\sqrt{\frac{c}{c d +e}}\, d^{2} e^{4}\right)}{15 \left(\left(e x +d \right)^{2} c^{2}-2 \left(e x +d \right) c^{2} d +c^{2} d^{2}-e^{2}\right) d^{3} \sqrt{\frac{c}{c d +e}}\, \left(c d +e \right) \left(c d -e \right) \left(e x +d \right)^{\frac{3}{2}} \left(c^{2} d^{2}-e^{2}\right)}\right)}{e}"," ",0,"2/e*(-1/5*a/(e*x+d)^(5/2)+b*(-1/5/(e*x+d)^(5/2)*arcsech(c*x)+2/15*c*e^2*(-((e*x+d)*c-c*d-e)/c/x/e)^(1/2)*x*(((e*x+d)*c-c*d+e)/c/x/e)^(1/2)*(7*(c/(c*d+e))^(1/2)*(e*x+d)^3*c^4*d^3-6*(-((e*x+d)*c-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-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))*(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-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-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))*(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-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-c*d+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-c*d-e)/(c*d+e))^(1/2)*(-((e*x+d)*c-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))*(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)/((e*x+d)^2*c^2-2*(e*x+d)*c^2*d+c^2*d^2-e^2)/d^3/(c/(c*d+e))^(1/2)/(c*d+e)/(c*d-e)/(e*x+d)^(3/2)/(c^2*d^2-e^2)))","B"
87,0,0,80,2.095000," ","int((e*x+d)^m*(a+b*arcsech(c*x)),x)","\int \left(e x +d \right)^{m} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)\, dx"," ",0,"int((e*x+d)^m*(a+b*arcsech(c*x)),x)","F"
88,1,224,195,0.067000," ","int(x^4*(e*x^2+d)*(a+b*arcsech(c*x)),x)","\frac{\frac{a \left(\frac{1}{7} e \,c^{7} x^{7}+\frac{1}{5} c^{7} x^{5} d \right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arcsech}\left(c x \right) e \,c^{7} x^{7}}{7}+\frac{\mathrm{arcsech}\left(c x \right) c^{7} x^{5} d}{5}+\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(-40 c^{5} x^{5} e \sqrt{-c^{2} x^{2}+1}-84 c^{5} x^{3} d \sqrt{-c^{2} x^{2}+1}-50 e \,c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}-126 \sqrt{-c^{2} x^{2}+1}\, c^{3} x d +126 \arcsin \left(c x \right) c^{2} d -75 e c x \sqrt{-c^{2} x^{2}+1}+75 e \arcsin \left(c x \right)\right)}{1680 \sqrt{-c^{2} x^{2}+1}}\right)}{c^{2}}}{c^{5}}"," ",0,"1/c^5*(a/c^2*(1/7*e*c^7*x^7+1/5*c^7*x^5*d)+b/c^2*(1/7*arcsech(c*x)*e*c^7*x^7+1/5*arcsech(c*x)*c^7*x^5*d+1/1680*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(-40*c^5*x^5*e*(-c^2*x^2+1)^(1/2)-84*c^5*x^3*d*(-c^2*x^2+1)^(1/2)-50*e*c^3*x^3*(-c^2*x^2+1)^(1/2)-126*(-c^2*x^2+1)^(1/2)*c^3*x*d+126*arcsin(c*x)*c^2*d-75*e*c*x*(-c^2*x^2+1)^(1/2)+75*e*arcsin(c*x))/(-c^2*x^2+1)^(1/2)))","A"
89,1,182,148,0.065000," ","int(x^2*(e*x^2+d)*(a+b*arcsech(c*x)),x)","\frac{\frac{a \left(\frac{1}{5} c^{5} x^{5} e +\frac{1}{3} c^{5} x^{3} d \right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arcsech}\left(c x \right) c^{5} x^{5} e}{5}+\frac{\mathrm{arcsech}\left(c x \right) c^{5} x^{3} d}{3}+\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(-6 e \,c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}-20 \sqrt{-c^{2} x^{2}+1}\, c^{3} x d +20 \arcsin \left(c x \right) c^{2} d -9 e c x \sqrt{-c^{2} x^{2}+1}+9 e \arcsin \left(c x \right)\right)}{120 \sqrt{-c^{2} x^{2}+1}}\right)}{c^{2}}}{c^{3}}"," ",0,"1/c^3*(a/c^2*(1/5*c^5*x^5*e+1/3*c^5*x^3*d)+b/c^2*(1/5*arcsech(c*x)*c^5*x^5*e+1/3*arcsech(c*x)*c^5*x^3*d+1/120*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(-6*e*c^3*x^3*(-c^2*x^2+1)^(1/2)-20*(-c^2*x^2+1)^(1/2)*c^3*x*d+20*arcsin(c*x)*c^2*d-9*e*c*x*(-c^2*x^2+1)^(1/2)+9*e*arcsin(c*x))/(-c^2*x^2+1)^(1/2)))","A"
90,1,135,96,0.065000," ","int((e*x^2+d)*(a+b*arcsech(c*x)),x)","\frac{\frac{a \left(\frac{1}{3} e \,c^{3} x^{3}+x \,c^{3} d \right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arcsech}\left(c x \right) e \,c^{3} x^{3}}{3}+\mathrm{arcsech}\left(c x \right) c^{3} d x +\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(6 \arcsin \left(c x \right) c^{2} d -e c x \sqrt{-c^{2} x^{2}+1}+e \arcsin \left(c x \right)\right)}{6 \sqrt{-c^{2} x^{2}+1}}\right)}{c^{2}}}{c}"," ",0,"1/c*(a/c^2*(1/3*e*c^3*x^3+x*c^3*d)+b/c^2*(1/3*arcsech(c*x)*e*c^3*x^3+arcsech(c*x)*c^3*d*x+1/6*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(6*arcsin(c*x)*c^2*d-e*c*x*(-c^2*x^2+1)^(1/2)+e*arcsin(c*x))/(-c^2*x^2+1)^(1/2)))","A"
91,1,114,86,0.067000," ","int((e*x^2+d)*(a+b*arcsech(c*x))/x^2,x)","c \left(\frac{a \left(c x e -\frac{c d}{x}\right)}{c^{2}}+\frac{b \left(\mathrm{arcsech}\left(c x \right) c x e -\frac{\mathrm{arcsech}\left(c x \right) c d}{x}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(\sqrt{-c^{2} x^{2}+1}\, c^{2} d +\arcsin \left(c x \right) c x e \right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{2}}\right)"," ",0,"c*(a/c^2*(c*x*e-c*d/x)+b/c^2*(arcsech(c*x)*c*x*e-arcsech(c*x)*c*d/x+(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*((-c^2*x^2+1)^(1/2)*c^2*d+arcsin(c*x)*c*x*e)/(-c^2*x^2+1)^(1/2)))","A"
92,1,123,108,0.068000," ","int((e*x^2+d)*(a+b*arcsech(c*x))/x^4,x)","c^{3} \left(\frac{a \left(-\frac{e}{c x}-\frac{d}{3 c \,x^{3}}\right)}{c^{2}}+\frac{b \left(-\frac{\mathrm{arcsech}\left(c x \right) e}{c x}-\frac{\mathrm{arcsech}\left(c x \right) d}{3 c \,x^{3}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(2 c^{4} d \,x^{2}+9 c^{2} x^{2} e +c^{2} d \right)}{9 c^{2} x^{2}}\right)}{c^{2}}\right)"," ",0,"c^3*(a/c^2*(-e/c/x-1/3/c*d/x^3)+b/c^2*(-arcsech(c*x)*e/c/x-1/3*arcsech(c*x)/c*d/x^3+1/9*(-(c*x-1)/c/x)^(1/2)/c^2/x^2*((c*x+1)/c/x)^(1/2)*(2*c^4*d*x^2+9*c^2*e*x^2+c^2*d)))","A"
93,1,142,155,0.072000," ","int((e*x^2+d)*(a+b*arcsech(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{arcsech}\left(c x \right) e}{3 c^{3} x^{3}}-\frac{\mathrm{arcsech}\left(c x \right) d}{5 c^{3} x^{5}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(24 c^{6} d \,x^{4}+50 c^{4} e \,x^{4}+12 c^{4} d \,x^{2}+25 c^{2} x^{2} e +9 c^{2} d \right)}{225 c^{4} x^{4}}\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*arcsech(c*x)*e/c^3/x^3-1/5*arcsech(c*x)/c^3*d/x^5+1/225*(-(c*x-1)/c/x)^(1/2)/c^4/x^4*((c*x+1)/c/x)^(1/2)*(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)))","A"
94,1,160,202,0.076000," ","int((e*x^2+d)*(a+b*arcsech(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{arcsech}\left(c x \right) d}{7 c^{5} x^{7}}-\frac{\mathrm{arcsech}\left(c x \right) e}{5 c^{5} x^{5}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(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} x^{2} e +75 c^{2} d \right)}{3675 c^{6} x^{6}}\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*arcsech(c*x)/c^5*d/x^7-1/5*arcsech(c*x)*e/c^5/x^5+1/3675*(-(c*x-1)/c/x)^(1/2)/c^6/x^6*((c*x+1)/c/x)^(1/2)*(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)))","A"
95,1,150,196,0.069000," ","int(x^5*(e*x^2+d)*(a+b*arcsech(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{arcsech}\left(c x \right) e \,c^{8} x^{8}}{8}+\frac{\mathrm{arcsech}\left(c x \right) c^{8} x^{6} d}{6}-\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(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} x^{2} e +224 c^{2} d +144 e \right)}{2520}\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*arcsech(c*x)*e*c^8*x^8+1/6*arcsech(c*x)*c^8*x^6*d-1/2520*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(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)))","A"
96,1,132,152,0.063000," ","int(x^3*(e*x^2+d)*(a+b*arcsech(c*x)),x)","\frac{\frac{a \left(\frac{1}{6} c^{6} e \,x^{6}+\frac{1}{4} c^{6} d \,x^{4}\right)}{c^{2}}+\frac{b \left(\frac{\mathrm{arcsech}\left(c x \right) c^{6} x^{6} e}{6}+\frac{\mathrm{arcsech}\left(c x \right) c^{6} x^{4} d}{4}-\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(6 c^{4} e \,x^{4}+15 c^{4} d \,x^{2}+8 c^{2} x^{2} e +30 c^{2} d +16 e \right)}{180}\right)}{c^{2}}}{c^{4}}"," ",0,"1/c^4*(a/c^2*(1/6*c^6*e*x^6+1/4*c^6*d*x^4)+b/c^2*(1/6*arcsech(c*x)*c^6*x^6*e+1/4*arcsech(c*x)*c^6*x^4*d-1/180*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(6*c^4*e*x^4+15*c^4*d*x^2+8*c^2*e*x^2+30*c^2*d+16*e)))","A"
97,1,113,138,0.066000," ","int(x*(e*x^2+d)*(a+b*arcsech(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{arcsech}\left(c x \right) c^{4} x^{4} e}{4}+\frac{\mathrm{arcsech}\left(c x \right) c^{4} x^{2} d}{2}-\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(c^{2} x^{2} e +6 c^{2} d +2 e \right)}{12}\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*arcsech(c*x)*c^4*x^4*e+1/2*arcsech(c*x)*c^4*x^2*d-1/12*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(c^2*e*x^2+6*c^2*d+2*e)))","A"
98,1,166,286,1.493000," ","int((e*x^2+d)*(a+b*arcsech(c*x))/x,x)","\frac{a \,x^{2} e}{2}+\ln \left(c x \right) a d +\frac{b \mathrm{arcsech}\left(c x \right)^{2} d}{2}-\frac{b \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x e}{2 c}+\frac{b \,\mathrm{arcsech}\left(c x \right) x^{2} e}{2}+\frac{b e}{2 c^{2}}-b d \,\mathrm{arcsech}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)-\frac{b d \polylog \left(2, -\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{2}"," ",0,"1/2*a*x^2*e+ln(c*x)*a*d+1/2*b*arcsech(c*x)^2*d-1/2*b/c*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x*e+1/2*b*arcsech(c*x)*x^2*e+1/2*b/c^2*e-b*d*arcsech(c*x)*ln(1+(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)-1/2*b*d*polylog(2,-(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)","A"
99,1,170,297,0.786000," ","int((e*x^2+d)*(a+b*arcsech(c*x))/x^3,x)","a e \ln \left(c x \right)-\frac{d a}{2 x^{2}}+\frac{b \mathrm{arcsech}\left(c x \right)^{2} e}{2}+\frac{b \,c^{2} d \,\mathrm{arcsech}\left(c x \right)}{4}+\frac{c b d \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{4 x}-\frac{b \,\mathrm{arcsech}\left(c x \right) d}{2 x^{2}}-b e \,\mathrm{arcsech}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)-\frac{b e \polylog \left(2, -\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{2}"," ",0,"a*e*ln(c*x)-1/2/x^2*d*a+1/2*b*arcsech(c*x)^2*e+1/4*b*c^2*d*arcsech(c*x)+1/4*c*b*d/x*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)-1/2*b*arcsech(c*x)*d/x^2-b*e*arcsech(c*x)*ln(1+(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)-1/2*b*e*polylog(2,-(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)","A"
100,1,300,239,0.069000," ","int(x^2*(e*x^2+d)^2*(a+b*arcsech(c*x)),x)","\frac{\frac{a \left(\frac{1}{7} e^{2} c^{7} x^{7}+\frac{2}{5} c^{7} d e \,x^{5}+\frac{1}{3} x^{3} c^{7} d^{2}\right)}{c^{4}}+\frac{b \left(\frac{\mathrm{arcsech}\left(c x \right) e^{2} c^{7} x^{7}}{7}+\frac{2 \,\mathrm{arcsech}\left(c x \right) c^{7} d e \,x^{5}}{5}+\frac{\mathrm{arcsech}\left(c x \right) c^{7} x^{3} d^{2}}{3}+\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(-40 c^{5} x^{5} e^{2} \sqrt{-c^{2} x^{2}+1}-168 c^{5} x^{3} d e \sqrt{-c^{2} x^{2}+1}-280 d^{2} c^{5} x \sqrt{-c^{2} x^{2}+1}+280 d^{2} c^{4} \arcsin \left(c x \right)-50 e^{2} c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}-252 c^{3} d e x \sqrt{-c^{2} x^{2}+1}+252 c^{2} d e \arcsin \left(c x \right)-75 e^{2} c x \sqrt{-c^{2} x^{2}+1}+75 e^{2} \arcsin \left(c x \right)\right)}{1680 \sqrt{-c^{2} x^{2}+1}}\right)}{c^{4}}}{c^{3}}"," ",0,"1/c^3*(a/c^4*(1/7*e^2*c^7*x^7+2/5*c^7*d*e*x^5+1/3*x^3*c^7*d^2)+b/c^4*(1/7*arcsech(c*x)*e^2*c^7*x^7+2/5*arcsech(c*x)*c^7*d*e*x^5+1/3*arcsech(c*x)*c^7*x^3*d^2+1/1680*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(-40*c^5*x^5*e^2*(-c^2*x^2+1)^(1/2)-168*c^5*x^3*d*e*(-c^2*x^2+1)^(1/2)-280*d^2*c^5*x*(-c^2*x^2+1)^(1/2)+280*d^2*c^4*arcsin(c*x)-50*e^2*c^3*x^3*(-c^2*x^2+1)^(1/2)-252*c^3*d*e*x*(-c^2*x^2+1)^(1/2)+252*c^2*d*e*arcsin(c*x)-75*e^2*c*x*(-c^2*x^2+1)^(1/2)+75*e^2*arcsin(c*x))/(-c^2*x^2+1)^(1/2)))","A"
101,1,228,178,0.069000," ","int((e*x^2+d)^2*(a+b*arcsech(c*x)),x)","\frac{\frac{a \left(\frac{1}{5} e^{2} c^{5} x^{5}+\frac{2}{3} c^{5} d e \,x^{3}+x \,c^{5} d^{2}\right)}{c^{4}}+\frac{b \left(\frac{\mathrm{arcsech}\left(c x \right) e^{2} c^{5} x^{5}}{5}+\frac{2 \,\mathrm{arcsech}\left(c x \right) c^{5} d e \,x^{3}}{3}+\mathrm{arcsech}\left(c x \right) c^{5} x \,d^{2}+\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(120 d^{2} c^{4} \arcsin \left(c x \right)-6 e^{2} c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}-40 c^{3} d e x \sqrt{-c^{2} x^{2}+1}+40 c^{2} d e \arcsin \left(c x \right)-9 e^{2} c x \sqrt{-c^{2} x^{2}+1}+9 e^{2} \arcsin \left(c x \right)\right)}{120 \sqrt{-c^{2} x^{2}+1}}\right)}{c^{4}}}{c}"," ",0,"1/c*(a/c^4*(1/5*e^2*c^5*x^5+2/3*c^5*d*e*x^3+x*c^5*d^2)+b/c^4*(1/5*arcsech(c*x)*e^2*c^5*x^5+2/3*arcsech(c*x)*c^5*d*e*x^3+arcsech(c*x)*c^5*x*d^2+1/120*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(120*d^2*c^4*arcsin(c*x)-6*e^2*c^3*x^3*(-c^2*x^2+1)^(1/2)-40*c^3*d*e*x*(-c^2*x^2+1)^(1/2)+40*c^2*d*e*arcsin(c*x)-9*e^2*c*x*(-c^2*x^2+1)^(1/2)+9*e^2*arcsin(c*x))/(-c^2*x^2+1)^(1/2)))","A"
102,1,197,155,0.075000," ","int((e*x^2+d)^2*(a+b*arcsech(c*x))/x^2,x)","c \left(\frac{a \left(\frac{c^{3} x^{3} e^{2}}{3}+2 c^{3} d e x -\frac{d^{2} c^{3}}{x}\right)}{c^{4}}+\frac{b \left(\frac{e^{2} \mathrm{arcsech}\left(c x \right) c^{3} x^{3}}{3}+2 \,\mathrm{arcsech}\left(c x \right) c^{3} d e x -\frac{\mathrm{arcsech}\left(c x \right) d^{2} c^{3}}{x}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(6 \sqrt{-c^{2} x^{2}+1}\, c^{4} d^{2}+12 \arcsin \left(c x \right) c^{3} x d e -c^{2} x^{2} e^{2} \sqrt{-c^{2} x^{2}+1}+\arcsin \left(c x \right) c x \,e^{2}\right)}{6 \sqrt{-c^{2} x^{2}+1}}\right)}{c^{4}}\right)"," ",0,"c*(a/c^4*(1/3*c^3*x^3*e^2+2*c^3*d*e*x-d^2*c^3/x)+b/c^4*(1/3*e^2*arcsech(c*x)*c^3*x^3+2*arcsech(c*x)*c^3*d*e*x-arcsech(c*x)*d^2*c^3/x+1/6*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*(6*(-c^2*x^2+1)^(1/2)*c^4*d^2+12*arcsin(c*x)*c^3*x*d*e-c^2*x^2*e^2*(-c^2*x^2+1)^(1/2)+arcsin(c*x)*c*x*e^2)/(-c^2*x^2+1)^(1/2)))","A"
103,1,205,154,0.073000," ","int((e*x^2+d)^2*(a+b*arcsech(c*x))/x^4,x)","c^{3} \left(\frac{a \left(c x \,e^{2}-\frac{2 c d e}{x}-\frac{d^{2} c}{3 x^{3}}\right)}{c^{4}}+\frac{b \left(\mathrm{arcsech}\left(c x \right) c x \,e^{2}-\frac{2 \,\mathrm{arcsech}\left(c x \right) c d e}{x}-\frac{\mathrm{arcsech}\left(c x \right) d^{2} c}{3 x^{3}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(2 \sqrt{-c^{2} x^{2}+1}\, c^{6} x^{2} d^{2}+18 c^{4} d e \,x^{2} \sqrt{-c^{2} x^{2}+1}+\sqrt{-c^{2} x^{2}+1}\, c^{4} d^{2}+9 \arcsin \left(c x \right) c^{3} x^{3} e^{2}\right)}{9 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}\right)}{c^{4}}\right)"," ",0,"c^3*(a/c^4*(c*x*e^2-2*c*d*e/x-1/3*d^2*c/x^3)+b/c^4*(arcsech(c*x)*c*x*e^2-2*arcsech(c*x)*c*d*e/x-1/3*arcsech(c*x)*d^2*c/x^3+1/9*(-(c*x-1)/c/x)^(1/2)/c^2/x^2*((c*x+1)/c/x)^(1/2)*(2*(-c^2*x^2+1)^(1/2)*c^6*x^2*d^2+18*c^4*d*e*x^2*(-c^2*x^2+1)^(1/2)+(-c^2*x^2+1)^(1/2)*c^4*d^2+9*arcsin(c*x)*c^3*x^3*e^2)/(-c^2*x^2+1)^(1/2)))","A"
104,1,193,185,0.076000," ","int((e*x^2+d)^2*(a+b*arcsech(c*x))/x^6,x)","c^{5} \left(\frac{a \left(-\frac{e^{2}}{c x}-\frac{2 d e}{3 c \,x^{3}}-\frac{d^{2}}{5 c \,x^{5}}\right)}{c^{4}}+\frac{b \left(-\frac{\mathrm{arcsech}\left(c x \right) e^{2}}{c x}-\frac{2 \,\mathrm{arcsech}\left(c x \right) d e}{3 c \,x^{3}}-\frac{\mathrm{arcsech}\left(c x \right) d^{2}}{5 c \,x^{5}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(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 d^{2} c^{4}\right)}{225 c^{4} x^{4}}\right)}{c^{4}}\right)"," ",0,"c^5*(a/c^4*(-e^2/c/x-2/3/c*d*e/x^3-1/5*d^2/c/x^5)+b/c^4*(-arcsech(c*x)*e^2/c/x-2/3*arcsech(c*x)/c*d*e/x^3-1/5*arcsech(c*x)*d^2/c/x^5+1/225*(-(c*x-1)/c/x)^(1/2)/c^4/x^4*((c*x+1)/c/x)^(1/2)*(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)))","A"
105,1,225,243,0.084000," ","int((e*x^2+d)^2*(a+b*arcsech(c*x))/x^8,x)","c^{7} \left(\frac{a \left(-\frac{e^{2}}{3 c^{3} x^{3}}-\frac{d^{2}}{7 c^{3} x^{7}}-\frac{2 d e}{5 c^{3} x^{5}}\right)}{c^{4}}+\frac{b \left(-\frac{\mathrm{arcsech}\left(c x \right) e^{2}}{3 c^{3} x^{3}}-\frac{\mathrm{arcsech}\left(c x \right) d^{2}}{7 c^{3} x^{7}}-\frac{2 \,\mathrm{arcsech}\left(c x \right) d e}{5 c^{3} x^{5}}+\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(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 d^{2} c^{4}\right)}{11025 c^{6} x^{6}}\right)}{c^{4}}\right)"," ",0,"c^7*(a/c^4*(-1/3*e^2/c^3/x^3-1/7*d^2/c^3/x^7-2/5/c^3*d*e/x^5)+b/c^4*(-1/3*arcsech(c*x)*e^2/c^3/x^3-1/7*arcsech(c*x)*d^2/c^3/x^7-2/5*arcsech(c*x)/c^3*d*e/x^5+1/11025*(-(c*x-1)/c/x)^(1/2)/c^6/x^6*((c*x+1)/c/x)^(1/2)*(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)))","A"
106,1,212,240,0.071000," ","int(x^3*(e*x^2+d)^2*(a+b*arcsech(c*x)),x)","\frac{\frac{a \left(\frac{1}{8} e^{2} c^{8} x^{8}+\frac{1}{3} c^{8} d e \,x^{6}+\frac{1}{4} c^{8} d^{2} x^{4}\right)}{c^{4}}+\frac{b \left(\frac{\mathrm{arcsech}\left(c x \right) e^{2} c^{8} x^{8}}{8}+\frac{\mathrm{arcsech}\left(c x \right) c^{8} d e \,x^{6}}{3}+\frac{\mathrm{arcsech}\left(c x \right) c^{8} x^{4} d^{2}}{4}-\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \left(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 d^{2} c^{4}+72 c^{2} e^{2} x^{2}+448 c^{2} d e +144 e^{2}\right)}{2520}\right)}{c^{4}}}{c^{4}}"," ",0,"1/c^4*(a/c^4*(1/8*e^2*c^8*x^8+1/3*c^8*d*e*x^6+1/4*c^8*d^2*x^4)+b/c^4*(1/8*arcsech(c*x)*e^2*c^8*x^8+1/3*arcsech(c*x)*c^8*d*e*x^6+1/4*arcsech(c*x)*c^8*x^4*d^2-1/2520*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(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)))","A"
107,1,180,196,0.069000," ","int(x*(e*x^2+d)^2*(a+b*arcsech(c*x)),x)","\frac{\frac{a \left(\frac{1}{6} c^{6} e^{2} x^{6}+\frac{1}{2} c^{6} d e \,x^{4}+\frac{1}{2} c^{6} d^{2} x^{2}\right)}{c^{4}}+\frac{b \left(\frac{\mathrm{arcsech}\left(c x \right) e^{2} c^{6} x^{6}}{6}+\frac{\mathrm{arcsech}\left(c x \right) c^{6} d e \,x^{4}}{2}+\frac{\mathrm{arcsech}\left(c x \right) c^{6} x^{2} d^{2}}{2}-\frac{\sqrt{-\frac{c x -1}{c x}}\, c x \sqrt{\frac{c x +1}{c x}}\, \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} d e +8 e^{2}\right)}{90}\right)}{c^{4}}}{c^{2}}"," ",0,"1/c^2*(a/c^4*(1/6*c^6*e^2*x^6+1/2*c^6*d*e*x^4+1/2*c^6*d^2*x^2)+b/c^4*(1/6*arcsech(c*x)*e^2*c^6*x^6+1/2*arcsech(c*x)*c^6*d*e*x^4+1/2*arcsech(c*x)*c^6*x^2*d^2-1/90*(-(c*x-1)/c/x)^(1/2)*c*x*((c*x+1)/c/x)^(1/2)*(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)))","A"
108,1,286,354,1.818000," ","int((e*x^2+d)^2*(a+b*arcsech(c*x))/x,x)","\frac{a \,e^{2} x^{4}}{4}+a d e \,x^{2}+a \,d^{2} \ln \left(c x \right)+\frac{b \mathrm{arcsech}\left(c x \right)^{2} d^{2}}{2}-\frac{b \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x^{3} e^{2}}{12 c}-\frac{b \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x d e}{c}+\frac{b \,\mathrm{arcsech}\left(c x \right) e^{2} x^{4}}{4}+b \,\mathrm{arcsech}\left(c x \right) d e \,x^{2}-\frac{b \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x \,e^{2}}{6 c^{3}}+\frac{b d e}{c^{2}}+\frac{b \,e^{2}}{6 c^{4}}-b \,d^{2} \mathrm{arcsech}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)-\frac{b \,d^{2} \polylog \left(2, -\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)}{2}"," ",0,"1/4*a*e^2*x^4+a*d*e*x^2+a*d^2*ln(c*x)+1/2*b*arcsech(c*x)^2*d^2-1/12*b/c*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x^3*e^2-b/c*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x*d*e+1/4*b*arcsech(c*x)*e^2*x^4+b*arcsech(c*x)*d*e*x^2-1/6*b/c^3*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x*e^2+b/c^2*d*e+1/6*b/c^4*e^2-b*d^2*arcsech(c*x)*ln(1+(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)-1/2*b*d^2*polylog(2,-(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)","A"
109,1,252,357,1.602000," ","int((e*x^2+d)^2*(a+b*arcsech(c*x))/x^3,x)","\frac{a \,x^{2} e^{2}}{2}+2 a d e \ln \left(c x \right)-\frac{a \,d^{2}}{2 x^{2}}+b d e \mathrm{arcsech}\left(c x \right)^{2}+\frac{c b \,d^{2} \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{4 x}+\frac{b \,c^{2} d^{2} \mathrm{arcsech}\left(c x \right)}{4}-\frac{b \,\mathrm{arcsech}\left(c x \right) d^{2}}{2 x^{2}}-\frac{b \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x \,e^{2}}{2 c}+\frac{b \,\mathrm{arcsech}\left(c x \right) x^{2} e^{2}}{2}+\frac{b \,e^{2}}{2 c^{2}}-2 b d e \,\mathrm{arcsech}\left(c x \right) \ln \left(1+\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)-b d e \polylog \left(2, -\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}\right)"," ",0,"1/2*a*x^2*e^2+2*a*d*e*ln(c*x)-1/2*a*d^2/x^2+b*d*e*arcsech(c*x)^2+1/4*c*b*d^2/x*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+1/4*b*c^2*d^2*arcsech(c*x)-1/2*b*arcsech(c*x)*d^2/x^2-1/2/c*b*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x*e^2+1/2*b*arcsech(c*x)*x^2*e^2+1/2*b/c^2*e^2-2*b*d*e*arcsech(c*x)*ln(1+(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)-b*d*e*polylog(2,-(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2)","A"
110,1,411,619,6.534000," ","int(x^2*(a+b*arcsech(c*x))/(e*x^2+d),x)","\frac{a x}{e}-\frac{a d \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{e \sqrt{d e}}+\frac{b \,\mathrm{arcsech}\left(c x \right) x}{e}+\frac{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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\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 b \arctan \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)}{c e}-\frac{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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\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(x*e/(d*e)^(1/2))+b*arcsech(c*x)/e*x+1/8*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)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-2/c*b/e*arctan(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))-1/8*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)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))","C"
111,1,513,643,0.893000," ","int(x*(a+b*arcsech(c*x))/(e*x^2+d),x)","\frac{a \ln \left(c^{2} x^{2} e +c^{2} d \right)}{2 e}+\frac{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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right) d}{4 e}-\frac{b \,\mathrm{arcsech}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e}-\frac{b \,\mathrm{arcsech}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e}-\frac{b \dilog \left(1+i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e}-\frac{b \dilog \left(1-i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e}+\frac{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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\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*c^2*b*sum((_R1^2+1)/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(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*arcsech(c*x)*ln(1+I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-b/e*arcsech(c*x)*ln(1-I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-b/e*dilog(1+I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-b/e*dilog(1-I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))+1/4*b*sum((_R1^2*c^2*d+c^2*d+4*e)/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))/e","C"
112,1,302,573,2.693000," ","int((a+b*arcsech(c*x))/(e*x^2+d),x)","\frac{a \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{\sqrt{d e}}-\frac{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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{2}+\frac{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{\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\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(x*e/(d*e)^(1/2))-1/2*c*b*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+1/2*c*b*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))","C"
113,1,3157,551,0.892000," ","int((a+b*arcsech(c*x))/x/(e*x^2+d),x)","\text{output too large to display}"," ",0,"1/4*b*c^2/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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)*arcsech(c*x)^2+a/d*ln(c*x)-b/c^4/d^3*e^2/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*(e*(c^2*d+e))^(1/2)-3*b/c^2/(c^2*d+e)/d^2*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)*(e*(c^2*d+e))^(1/2)*e-2*b/c^4/d^3*e^2/(c^2*d+e)*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)*(e*(c^2*d+e))^(1/2)-b/c^2/d^2*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*e-b/c^4/d^3*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*e^2-b/c^2/d^2*arcsech(c*x)^2*(e*(c^2*d+e))^(1/2)+1/2*b/c^2/d^2*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*(e*(c^2*d+e))^(1/2)+1/2*b*c^2/(c^2*d+e)*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)-5/2*b/(c^2*d+e)/d*arcsech(c*x)^2*e-3/4*b/(c^2*d+e)/d*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*(e*(c^2*d+e))^(1/2)+5/4*b/(c^2*d+e)/d*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*e+1/4*b*(e*(c^2*d+e))^(1/2)/d/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e))+b*(e*(c^2*d+e))^(1/2)/d/(c^2*d+e)*arcsech(c*x)^2+2*b/c^2/d^2*arcsech(c*x)^2*e+2*b/c^4/d^3*arcsech(c*x)^2*e^2-1/2*a/d*ln(c^2*e*x^2+c^2*d)-1/2*b*sum((_R1^2*c^2*d+2*c^2*d+4*e)/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))/d+b*arcsech(c*x)^2/d-1/4*b/d*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))-1/2*b/d*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)-1/8*b*c^2/e/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*(e*(c^2*d+e))^(1/2)+1/2*b*(e*(c^2*d+e))^(1/2)/d/(c^2*d+e)*arcsech(c*x)*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e))-3/2*b/(c^2*d+e)/d*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)*(e*(c^2*d+e))^(1/2)+5/2*b*e/(c^2*d+e)/d*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)-2*b/c^2/d^2*e*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)-2*b/c^4/d^3*e^2*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)+b/c^2/d^2*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)*(e*(c^2*d+e))^(1/2)-4*b/c^2/(c^2*d+e)/d^2*arcsech(c*x)^2*e^2+2*b/c^2/(c^2*d+e)/d^2*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*e^2+1/8*b*c^2*(e*(c^2*d+e))^(1/2)/e/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e))-2*b/c^4/d^3*arcsech(c*x)^2*e*(e*(c^2*d+e))^(1/2)+b/c^4/d^3*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*e*(e*(c^2*d+e))^(1/2)-2*b/c^4/d^3*e^3/(c^2*d+e)*arcsech(c*x)^2+b/c^4/d^3*e^3/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))+1/4*b*c^2*(e*(c^2*d+e))^(1/2)/e/(c^2*d+e)*arcsech(c*x)*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e))-1/4*b*c^2/e/(c^2*d+e)*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)*(e*(c^2*d+e))^(1/2)+2*b/c^4/d^3*e^2/(c^2*d+e)*arcsech(c*x)^2*(e*(c^2*d+e))^(1/2)+3*b/c^2/(c^2*d+e)/d^2*arcsech(c*x)^2*(e*(c^2*d+e))^(1/2)*e-3/2*b/c^2/(c^2*d+e)/d^2*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*(e*(c^2*d+e))^(1/2)*e+2*b/c^4/d^3*e*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)*(e*(c^2*d+e))^(1/2)+4*b/c^2/(c^2*d+e)/d^2*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)*e^2+2*b/c^4/d^3*e^3/(c^2*d+e)*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)","C"
114,1,372,623,6.503000," ","int((a+b*arcsech(c*x))/x^2/(e*x^2+d),x)","-\frac{a}{d x}-\frac{a e \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{d \sqrt{d e}}+\frac{c b \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{d}-\frac{b \,\mathrm{arcsech}\left(c x \right)}{d x}+\frac{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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{2 d}-\frac{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{\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{2 d}"," ",0,"-a/d/x-a*e/d/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))+c*b/d*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)-b*arcsech(c*x)/d/x+1/2*c*b*e/d*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-1/2*c*b*e/d*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))","C"
115,1,870,805,1.628000," ","int(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^2,x)","\frac{a \,x^{2}}{2 e^{2}}-\frac{c^{2} a \,d^{2}}{2 e^{3} \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{a d \ln \left(c^{2} x^{2} e +c^{2} d \right)}{e^{3}}-\frac{c b \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x^{3}}{2 \left(c^{2} x^{2} e +c^{2} d \right) e}-\frac{c b \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x d}{2 \left(c^{2} x^{2} e +c^{2} d \right) e^{2}}+\frac{c^{2} b \,\mathrm{arcsech}\left(c x \right) x^{4}}{2 \left(c^{2} x^{2} e +c^{2} d \right) e}+\frac{c^{2} b \,\mathrm{arcsech}\left(c x \right) d \,x^{2}}{\left(c^{2} x^{2} e +c^{2} d \right) e^{2}}+\frac{b \,x^{2}}{2 \left(c^{2} x^{2} e +c^{2} d \right) e}+\frac{b d}{2 \left(c^{2} x^{2} e +c^{2} d \right) e^{2}}+\frac{b \sqrt{e \left(c^{2} d +e \right)}\, d \arctanh \left(\frac{2 c^{2} d \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}+2 c^{2} d +4 e}{4 \sqrt{c^{2} d e +e^{2}}}\right)}{2 e^{3} \left(c^{2} d +e \right)}-\frac{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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{2 e^{3}}+\frac{2 b d \,\mathrm{arcsech}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e^{3}}+\frac{2 b d \,\mathrm{arcsech}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e^{3}}+\frac{2 b d \dilog \left(1+i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e^{3}}+\frac{2 b d \dilog \left(1-i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e^{3}}-\frac{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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{2 e^{3}}"," ",0,"1/2*a*x^2/e^2-1/2*c^2*a/e^3*d^2/(c^2*e*x^2+c^2*d)-a/e^3*d*ln(c^2*e*x^2+c^2*d)-1/2*c*b/(c^2*e*x^2+c^2*d)/e*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x^3-1/2*c*b/(c^2*e*x^2+c^2*d)/e^2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x*d+1/2*c^2*b/(c^2*e*x^2+c^2*d)/e*arcsech(c*x)*x^4+c^2*b/(c^2*e*x^2+c^2*d)/e^2*arcsech(c*x)*d*x^2+1/2*b/(c^2*e*x^2+c^2*d)/e*x^2+1/2*b/(c^2*e*x^2+c^2*d)/e^2*d+1/2*b*(e*(c^2*d+e))^(1/2)/e^3/(c^2*d+e)*d*arctanh(1/4*(2*c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2+2*c^2*d+4*e)/(c^2*d*e+e^2)^(1/2))-1/2*c^2*b/e^3*d^2*sum((_R1^2+1)/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(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*arcsech(c*x)*ln(1+I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))+2*b/e^3*d*arcsech(c*x)*ln(1-I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))+2*b/e^3*d*dilog(1+I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))+2*b/e^3*d*dilog(1-I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-1/2*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)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))","C"
116,1,661,747,1.107000," ","int(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^2,x)","\frac{c^{2} a d}{2 e^{2} \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{a \ln \left(c^{2} x^{2} e +c^{2} d \right)}{2 e^{2}}-\frac{c^{2} b \,x^{2} \mathrm{arcsech}\left(c x \right)}{2 \left(c^{2} x^{2} e +c^{2} d \right) e}-\frac{b \sqrt{e \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 c^{2} d \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}+2 c^{2} d +4 e}{4 \sqrt{c^{2} d e +e^{2}}}\right)}{2 e^{2} \left(c^{2} d +e \right)}+\frac{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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right) d}{4 e^{2}}-\frac{b \,\mathrm{arcsech}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e^{2}}-\frac{b \,\mathrm{arcsech}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e^{2}}-\frac{b \dilog \left(1+i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e^{2}}-\frac{b \dilog \left(1-i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e^{2}}+\frac{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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{4 e^{2}}"," ",0,"1/2*c^2*a/e^2*d/(c^2*e*x^2+c^2*d)+1/2*a/e^2*ln(c^2*e*x^2+c^2*d)-1/2*c^2*b*x^2*arcsech(c*x)/(c^2*e*x^2+c^2*d)/e-1/2*b*(e*(c^2*d+e))^(1/2)/e^2/(c^2*d+e)*arctanh(1/4*(2*c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2+2*c^2*d+4*e)/(c^2*d*e+e^2)^(1/2))+1/4*c^2*b/e^2*sum((_R1^2+1)/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))*d-b/e^2*arcsech(c*x)*ln(1+I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-b/e^2*arcsech(c*x)*ln(1-I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-b/e^2*dilog(1+I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-b/e^2*dilog(1-I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))+1/4*b/e^2*sum((_R1^2*c^2*d+c^2*d+4*e)/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))","C"
117,1,840,124,0.101000," ","int(x*(a+b*arcsech(c*x))/(e*x^2+d)^2,x)","-\frac{c^{2} a}{2 e \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{c^{2} b \,\mathrm{arcsech}\left(c x \right)}{2 e \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{c^{3} b \sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{2 \sqrt{-c^{2} x^{2}+1}\, \left(\sqrt{-c^{2} d e}+e \right) \left(\sqrt{-c^{2} d e}-e \right)}+\frac{c^{3} b \sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, \ln \left(-\frac{2 \left(\sqrt{-c^{2} x^{2}+1}\, \sqrt{\frac{c^{2} d +e}{e}}\, e -\sqrt{-c^{2} d e}\, c x +e \right)}{-c x e +\sqrt{-c^{2} d e}}\right)}{4 \sqrt{-c^{2} x^{2}+1}\, \left(\sqrt{-c^{2} d e}+e \right) \left(\sqrt{-c^{2} d e}-e \right) \sqrt{\frac{c^{2} d +e}{e}}}+\frac{c^{3} b \sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, \ln \left(\frac{2 \sqrt{-c^{2} x^{2}+1}\, \sqrt{\frac{c^{2} d +e}{e}}\, e +2 \sqrt{-c^{2} d e}\, c x +2 e}{c x e +\sqrt{-c^{2} d e}}\right)}{4 \sqrt{-c^{2} x^{2}+1}\, \left(\sqrt{-c^{2} d e}+e \right) \left(\sqrt{-c^{2} d e}-e \right) \sqrt{\frac{c^{2} d +e}{e}}}-\frac{c b \sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right) e}{2 \sqrt{-c^{2} x^{2}+1}\, d \left(\sqrt{-c^{2} d e}+e \right) \left(\sqrt{-c^{2} d e}-e \right)}+\frac{c b \sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, \ln \left(-\frac{2 \left(\sqrt{-c^{2} x^{2}+1}\, \sqrt{\frac{c^{2} d +e}{e}}\, e -\sqrt{-c^{2} d e}\, c x +e \right)}{-c x e +\sqrt{-c^{2} d e}}\right) e}{4 \sqrt{-c^{2} x^{2}+1}\, d \left(\sqrt{-c^{2} d e}+e \right) \left(\sqrt{-c^{2} d e}-e \right) \sqrt{\frac{c^{2} d +e}{e}}}+\frac{c b \sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, \ln \left(\frac{2 \sqrt{-c^{2} x^{2}+1}\, \sqrt{\frac{c^{2} d +e}{e}}\, e +2 \sqrt{-c^{2} d e}\, c x +2 e}{c x e +\sqrt{-c^{2} d e}}\right) e}{4 \sqrt{-c^{2} x^{2}+1}\, d \left(\sqrt{-c^{2} d e}+e \right) \left(\sqrt{-c^{2} d e}-e \right) \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)*arcsech(c*x)-1/2*c^3*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/(-c^2*x^2+1)^(1/2)/((-c^2*d*e)^(1/2)+e)/((-c^2*d*e)^(1/2)-e)*arctanh(1/(-c^2*x^2+1)^(1/2))+1/4*c^3*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/(-c^2*x^2+1)^(1/2)/((-c^2*d*e)^(1/2)+e)/((-c^2*d*e)^(1/2)-e)/((c^2*d+e)/e)^(1/2)*ln(-2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e-(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))+1/4*c^3*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/(-c^2*x^2+1)^(1/2)/((-c^2*d*e)^(1/2)+e)/((-c^2*d*e)^(1/2)-e)/((c^2*d+e)/e)^(1/2)*ln(2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))-1/2*c*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/(-c^2*x^2+1)^(1/2)/d/((-c^2*d*e)^(1/2)+e)/((-c^2*d*e)^(1/2)-e)*arctanh(1/(-c^2*x^2+1)^(1/2))*e+1/4*c*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/(-c^2*x^2+1)^(1/2)/d/((-c^2*d*e)^(1/2)+e)/((-c^2*d*e)^(1/2)-e)/((c^2*d+e)/e)^(1/2)*ln(-2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e-(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))*e+1/4*c*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/(-c^2*x^2+1)^(1/2)/d/((-c^2*d*e)^(1/2)+e)/((-c^2*d*e)^(1/2)-e)/((c^2*d+e)/e)^(1/2)*ln(2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))*e","B"
118,1,3326,656,2.174000," ","int((a+b*arcsech(c*x))/x/(e*x^2+d)^2,x)","\text{output too large to display}"," ",0,"1/8*b*c^2*(e*(c^2*d+e))^(1/2)/d/e/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e))-1/2*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)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-1/4*b/d^2*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))-b/c^2/d^3*e*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))-b/c^4/d^4*e^2*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))+1/4*b*c^2/d/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))-1/2*b*c^2/d/(c^2*d+e)*arcsech(c*x)^2+1/2*b/c^2/d^3*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*(e*(c^2*d+e))^(1/2)-b/c^2/d^3*arcsech(c*x)^2*(e*(c^2*d+e))^(1/2)+2*b/c^2/d^3*arcsech(c*x)^2*e+2*b/c^4/d^4*e^2*arcsech(c*x)^2-1/2*b*(e*(c^2*d+e))^(1/2)/d^2/(c^2*d+e)*arctanh(1/4*(2*c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2+2*c^2*d+4*e)/(c^2*d*e+e^2)^(1/2))-5/2*b/d^2/(c^2*d+e)*arcsech(c*x)^2*e-3/4*b/d^2/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*(e*(c^2*d+e))^(1/2)+5/4*b/d^2*e/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))+b*(e*(c^2*d+e))^(1/2)/d^2/(c^2*d+e)*arcsech(c*x)^2+1/4*b*(e*(c^2*d+e))^(1/2)/d^2/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e))+1/2*a*c^2/d/(c^2*e*x^2+c^2*d)+a/d^2*ln(c*x)-1/2*a/d^2*ln(c^2*e*x^2+c^2*d)-1/4*b*c^2/d/e/(c^2*d+e)*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)*(e*(c^2*d+e))^(1/2)-3*b/c^2/d^3/(c^2*d+e)*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)*(e*(c^2*d+e))^(1/2)*e+1/4*b*c^2*(e*(c^2*d+e))^(1/2)/d/e/(c^2*d+e)*arcsech(c*x)*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e))-2*b/c^4/d^4*e^2/(c^2*d+e)*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)*(e*(c^2*d+e))^(1/2)-1/2*b/d^2*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)-1/2*b*c^2*x^2*arcsech(c*x)*e/(c^2*e*x^2+c^2*d)/d^2+b*arcsech(c*x)^2/d^2-2*b/c^4/d^4*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)*e^2+b/c^2/d^3*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)*(e*(c^2*d+e))^(1/2)-3/2*b/d^2/(c^2*d+e)*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)*(e*(c^2*d+e))^(1/2)+b/c^4/d^4*e^3/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))-b/c^4/d^4*e^2/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*(e*(c^2*d+e))^(1/2)+3*b/c^2/d^3/(c^2*d+e)*arcsech(c*x)^2*(e*(c^2*d+e))^(1/2)*e-3/2*b/c^2/d^3/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*(e*(c^2*d+e))^(1/2)*e+4*b/c^2/d^3/(c^2*d+e)*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)*e^2-2*b/c^4/d^4*e*arcsech(c*x)^2*(e*(c^2*d+e))^(1/2)+5/2*b/d^2*e/(c^2*d+e)*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)+1/2*b*c^2/d/(c^2*d+e)*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)+2*b/c^2/d^3/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*e^2-2*b/c^4/d^4*e^3/(c^2*d+e)*arcsech(c*x)^2-2*b/c^2/d^3*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)*e+1/2*b*(e*(c^2*d+e))^(1/2)/d^2/(c^2*d+e)*arcsech(c*x)*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e))-4*b/c^2/d^3/(c^2*d+e)*arcsech(c*x)^2*e^2+b/c^4/d^4*e*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*(e*(c^2*d+e))^(1/2)-1/8*b*c^2/d/e/(c^2*d+e)*polylog(2,c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*(e*(c^2*d+e))^(1/2)+2*b/c^4/d^4*e^2/(c^2*d+e)*arcsech(c*x)^2*(e*(c^2*d+e))^(1/2)+2*b/c^4/d^4*e^3/(c^2*d+e)*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)+2*b/c^4/d^4*ln(1-c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2/(-c^2*d-2*(e*(c^2*d+e))^(1/2)-2*e))*arcsech(c*x)*e*(e*(c^2*d+e))^(1/2)","C"
119,1,2016,868,18.231000," ","int(x^4*(a+b*arcsech(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} x^{2} e +c^{2} d \right)}-\frac{3 a d \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{2 e^{2} \sqrt{d e}}+\frac{c^{2} b \,x^{3} \mathrm{arcsech}\left(c x \right)}{e \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{3 c^{2} b \,\mathrm{arcsech}\left(c x \right) d x}{2 e^{2} \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{2 c^{2} d \,e^{2}}-\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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^{2} e^{2}}-\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{c^{4} d^{2} e}+\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{2 c^{2} d \,e^{2}}+\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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^{2} e^{2}}-\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{c^{4} d^{2} e}-\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{2 b \arctan \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)}{c \,e^{2}}-\frac{3 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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{16 e^{3}}+\frac{3 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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{16 e^{3}}"," ",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(x*e/(d*e)^(1/2))+c^2*b*x^3*arcsech(c*x)/e/(c^2*e*x^2+c^2*d)+3/2*c^2*b*arcsech(c*x)/e^2*d*x/(c^2*e*x^2+c^2*d)-1/2/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d/e^2-1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^2/e^2*(e*(c^2*d+e))^(1/2)-1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^2/e+1/2/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/e/(c^2*d+e)/d+1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^2-1/2/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d/e^2+1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^2/e^2*(e*(c^2*d+e))^(1/2)-1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^2/e-1/2/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/e/(c^2*d+e)/d-1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^2-2/c*b/e^2*arctan(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))-3/16*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)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+3/16*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)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))","C"
120,1,1880,821,5.842000," ","int(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^2,x)","-\frac{c^{2} a x}{2 e \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{a \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{2 e \sqrt{d e}}-\frac{c^{2} b \,\mathrm{arcsech}\left(c x \right) x}{2 e \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{4 e}+\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{2 c^{2} d^{2} e}+\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{2 c^{2} d^{2} e}-\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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{\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{4 e}"," ",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(x*e/(d*e)^(1/2))-1/2*c^2*b*arcsech(c*x)/e*x/(c^2*e*x^2+c^2*d)-1/4*c*b/e*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+1/2/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^2/e+1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^3-1/2/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^2-1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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+1/2/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^2/e-1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^3+1/2/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^2+1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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+1/4*c*b/e*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))","C"
121,1,1870,821,6.059000," ","int((a+b*arcsech(c*x))/(e*x^2+d)^2,x)","\frac{c^{2} a x}{2 d \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{a \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{2 d \sqrt{d e}}+\frac{c^{2} b \,\mathrm{arcsech}\left(c x \right) x}{2 d \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{4 d}+\frac{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{\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{4 d}"," ",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(x*e/(d*e)^(1/2))+1/2*c^2*b*arcsech(c*x)*x/d/(c^2*e*x^2+c^2*d)-1/2/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^3-1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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)-1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4*e+1/2/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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+1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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^2-1/2/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^3+1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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)-1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4*e-1/2/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))*e/(c^2*d+e)/d^3-1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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*c*b/d*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+1/4*c*b/d*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))","C"
122,1,1952,872,12.207000," ","int((a+b*arcsech(c*x))/x^2/(e*x^2+d)^2,x)","-\frac{a}{d^{2} x}-\frac{a e \,c^{2} x}{2 d^{2} \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{3 a e \arctan \left(\frac{x e}{\sqrt{d e}}\right)}{2 d^{2} \sqrt{d e}}-\frac{b \,\mathrm{arcsech}\left(c x \right)}{d^{2} x}-\frac{b \,\mathrm{arcsech}\left(c x \right) e \,c^{2} x}{2 d^{2} \left(c^{2} x^{2} e +c^{2} d \right)}+\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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}}-\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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} \left(c^{2} d +e \right)}-\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{b \sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}\, e \arctan \left(\frac{c d \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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}}-\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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} \left(c^{2} d +e \right)}-\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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 \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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)}{\sqrt{\left(-c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}-2 e \right) d}}\right)}{c^{4} d^{5}}+\frac{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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\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 \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}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)}{\sqrt{\left(c^{2} d +2 \sqrt{e \left(c^{2} d +e \right)}+2 e \right) d}}\right)}{c^{4} d^{5}}+\frac{c b \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}}{d^{2}}-\frac{3 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{\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)}{\textit{\_R1} \left(\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e \right)}\right)}{4 d^{2}}+\frac{3 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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)\right)}{\textit{\_R1}^{2} c^{2} d +c^{2} d +2 e}\right)}{4 d^{2}}"," ",0,"-a/d^2/x-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(x*e/(d*e)^(1/2))-b*arcsech(c*x)/d^2/x-1/2*b*arcsech(c*x)/d^2*e*c^2*x/(c^2*e*x^2+c^2*d)+b/c^4*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e*arctanh(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^5*(e*(c^2*d+e))^(1/2)-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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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-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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^5/(c^2*d+e)-b/c^4*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e*arctan(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^5*(e*(c^2*d+e))^(1/2)-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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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-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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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*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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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-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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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)+1/2*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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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+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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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)+1/2*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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^4*e+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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/d^5+1/2*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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^4*e+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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/d^5+c*b/d^2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)-3/4*c*b/d^2*e*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+3/4*c*b/d^2*e*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))","C"
123,1,1779,922,1.580000," ","int(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^3,x)","\frac{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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\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{b \dilog \left(1+i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e^{2} \left(c^{2} d +e \right)}-\frac{b \dilog \left(1-i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e^{2} \left(c^{2} d +e \right)}-\frac{c^{2} b d \dilog \left(1-i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e^{3} \left(c^{2} d +e \right)}-\frac{c^{6} b \,\mathrm{arcsech}\left(c x \right) d^{2} x^{2}}{2 e^{2} \left(c^{2} x^{2} e +c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{4} b \,\mathrm{arcsech}\left(c x \right) d \,x^{2}}{2 e \left(c^{2} x^{2} e +c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{3 c^{6} b \,\mathrm{arcsech}\left(c x \right) d \,x^{4}}{4 e \left(c^{2} x^{2} e +c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{a \ln \left(c^{2} x^{2} e +c^{2} d \right)}{2 e^{3}}+\frac{c^{2} a d}{e^{3} \left(c^{2} x^{2} e +c^{2} d \right)}-\frac{c^{4} a \,d^{2}}{4 e^{3} \left(c^{2} x^{2} e +c^{2} d \right)^{2}}-\frac{5 c^{2} b \sqrt{e \left(c^{2} d +e \right)}\, d \arctanh \left(\frac{2 c^{2} d \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}+2 c^{2} d +4 e}{4 \sqrt{c^{2} d e +e^{2}}}\right)}{8 e^{3} \left(c^{2} d +e \right)^{2}}-\frac{c^{2} b d \,\mathrm{arcsech}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e^{3} \left(c^{2} d +e \right)}-\frac{c^{2} b d \,\mathrm{arcsech}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e^{3} \left(c^{2} d +e \right)}-\frac{c^{2} b d \dilog \left(1+i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e^{3} \left(c^{2} d +e \right)}+\frac{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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\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{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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\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{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(\mathrm{arcsech}\left(c x \right) \ln \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\textit{\_R1}}\right)+\dilog \left(\frac{\textit{\_R1} -\frac{1}{c x}-\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}}{\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{c^{4} b \,d^{2}}{8 e^{2} \left(c^{2} x^{2} e +c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{3 c^{4} b \,\mathrm{arcsech}\left(c x \right) x^{4}}{4 \left(c^{2} x^{2} e +c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{5} b \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x \,d^{2}}{8 e^{2} \left(c^{2} x^{2} e +c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{c^{5} b \sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, x^{3} d}{8 e \left(c^{2} x^{2} e +c^{2} d \right)^{2} \left(c^{2} d +e \right)}+\frac{c^{4} b d \,x^{2}}{4 e \left(c^{2} x^{2} e +c^{2} d \right)^{2} \left(c^{2} d +e \right)}-\frac{3 b \sqrt{e \left(c^{2} d +e \right)}\, \arctanh \left(\frac{2 c^{2} d \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)^{2}+2 c^{2} d +4 e}{4 \sqrt{c^{2} d e +e^{2}}}\right)}{4 e^{2} \left(c^{2} d +e \right)^{2}}-\frac{b \,\mathrm{arcsech}\left(c x \right) \ln \left(1-i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e^{2} \left(c^{2} d +e \right)}-\frac{b \,\mathrm{arcsech}\left(c x \right) \ln \left(1+i \left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right)\right)}{e^{2} \left(c^{2} d +e \right)}+\frac{c^{4} b \,x^{4}}{8 \left(c^{2} x^{2} e +c^{2} d \right)^{2} \left(c^{2} d +e \right)}"," ",0,"1/4*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)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-b/e^2/(c^2*d+e)*dilog(1+I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-b/e^2/(c^2*d+e)*dilog(1-I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-1/2*c^6*b/e^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsech(c*x)*d^2*x^2-1/2*c^4*b/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsech(c*x)*d*x^2-3/4*c^6*b/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsech(c*x)*d*x^4+1/2*a/e^3*ln(c^2*e*x^2+c^2*d)+c^2*a/e^3*d/(c^2*e*x^2+c^2*d)-1/4*c^4*a*d^2/e^3/(c^2*e*x^2+c^2*d)^2-c^2*b/e^3/(c^2*d+e)*d*arcsech(c*x)*ln(1-I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-c^2*b/e^3/(c^2*d+e)*d*arcsech(c*x)*ln(1+I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))+1/4*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)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+1/4*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)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+1/8*c^4*b/e^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*d^2-c^2*b/e^3/(c^2*d+e)*d*dilog(1-I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))+1/4*c^2*b/e^2/(c^2*d+e)*sum((_R1^2+1)/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))*d-c^2*b/e^3/(c^2*d+e)*d*dilog(1+I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-3/4*c^4*b/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsech(c*x)*x^4-1/8*c^5*b/e^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x*d^2-1/8*c^5*b/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*x^3*d+1/4*c^4*b/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*d*x^2-5/8*c^2*b*(e*(c^2*d+e))^(1/2)/e^3/(c^2*d+e)^2*d*arctanh(1/4*(2*c^2*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2+2*c^2*d+4*e)/(c^2*d*e+e^2)^(1/2))+1/8*c^4*b/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*x^4-3/4*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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))^2+2*c^2*d+4*e)/(c^2*d*e+e^2)^(1/2))-b/e^2/(c^2*d+e)*arcsech(c*x)*ln(1-I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))-b/e^2/(c^2*d+e)*arcsech(c*x)*ln(1+I*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2)))","C"
124,1,3331,147,0.112000," ","int(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"1/4*c^4*a/e^2*d/(c^2*e*x^2+c^2*d)^2-1/2*c^2*a/e^2/(c^2*e*x^2+c^2*d)+1/4*c^4*b*arcsech(c*x)/e^2*d/(c^2*e*x^2+c^2*d)^2-1/2*c^2*b*arcsech(c*x)/e^2/(c^2*e*x^2+c^2*d)-1/4*c^7*b*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)*e^2/(-c*x*e+(-c^2*d*e)^(1/2))*d/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*arctanh(1/(-c^2*x^2+1)^(1/2))-1/4*c^7*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e/(-c*x*e+(-c^2*d*e)^(1/2))*d^2/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*arctanh(1/(-c^2*x^2+1)^(1/2))+1/16*c^7*b*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)*e^2/(-c*x*e+(-c^2*d*e)^(1/2))*d/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(-2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e-(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))+1/16*c^7*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e/(-c*x*e+(-c^2*d*e)^(1/2))*d^2/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(-2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e-(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))+1/16*c^7*b*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)*e^2/(-c*x*e+(-c^2*d*e)^(1/2))*d/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))+1/16*c^7*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e/(-c*x*e+(-c^2*d*e)^(1/2))*d^2/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))-1/8*c^5*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e^2/(-c*x*e+(-c^2*d*e)^(1/2))*d/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2-1/2*c^5*b*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)*e^3/(-c*x*e+(-c^2*d*e)^(1/2))/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*arctanh(1/(-c^2*x^2+1)^(1/2))-1/2*c^5*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e^2/(-c*x*e+(-c^2*d*e)^(1/2))*d/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*arctanh(1/(-c^2*x^2+1)^(1/2))+3/16*c^5*b*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)*e^3/(-c*x*e+(-c^2*d*e)^(1/2))/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(-2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e-(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))+3/16*c^5*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e^2/(-c*x*e+(-c^2*d*e)^(1/2))*d/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(-2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e-(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))+3/16*c^5*b*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)*e^3/(-c*x*e+(-c^2*d*e)^(1/2))/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))+3/16*c^5*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e^2/(-c*x*e+(-c^2*d*e)^(1/2))*d/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))-1/8*c^3*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e^3/(-c*x*e+(-c^2*d*e)^(1/2))/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2-1/4*c^3*b*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)*e^4/(-c*x*e+(-c^2*d*e)^(1/2))/d/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*arctanh(1/(-c^2*x^2+1)^(1/2))-1/4*c^3*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e^3/(-c*x*e+(-c^2*d*e)^(1/2))/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*arctanh(1/(-c^2*x^2+1)^(1/2))+1/8*c^3*b*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)*e^4/(-c*x*e+(-c^2*d*e)^(1/2))/d/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(-2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e-(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))+1/8*c^3*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e^3/(-c*x*e+(-c^2*d*e)^(1/2))/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(-2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e-(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))+1/8*c^3*b*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)*e^4/(-c*x*e+(-c^2*d*e)^(1/2))/d/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))+1/8*c^3*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e^3/(-c*x*e+(-c^2*d*e)^(1/2))/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))","B"
125,1,3289,186,0.103000," ","int(x*(a+b*arcsech(c*x))/(e*x^2+d)^3,x)","\text{output too large to display}"," ",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*arcsech(c*x)-1/4*c^7*b*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)*e^3/(-c*x*e+(-c^2*d*e)^(1/2))/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*arctanh(1/(-c^2*x^2+1)^(1/2))-1/4*c^7*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e^2/(-c*x*e+(-c^2*d*e)^(1/2))*d/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*arctanh(1/(-c^2*x^2+1)^(1/2))+3/16*c^7*b*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)*e^3/(-c*x*e+(-c^2*d*e)^(1/2))/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))+3/16*c^7*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e^2/(-c*x*e+(-c^2*d*e)^(1/2))*d/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))+3/16*c^7*b*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)*e^3/(-c*x*e+(-c^2*d*e)^(1/2))/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(-2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e-(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))+3/16*c^7*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e^2/(-c*x*e+(-c^2*d*e)^(1/2))*d/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(-2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e-(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))+1/8*c^5*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e^3/(-c*x*e+(-c^2*d*e)^(1/2))/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2-1/2*c^5*b*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)*e^4/(-c*x*e+(-c^2*d*e)^(1/2))/d/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*arctanh(1/(-c^2*x^2+1)^(1/2))-1/2*c^5*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e^3/(-c*x*e+(-c^2*d*e)^(1/2))/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*arctanh(1/(-c^2*x^2+1)^(1/2))+5/16*c^5*b*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)*e^4/(-c*x*e+(-c^2*d*e)^(1/2))/d/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))+5/16*c^5*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e^3/(-c*x*e+(-c^2*d*e)^(1/2))/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))+5/16*c^5*b*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)*e^4/(-c*x*e+(-c^2*d*e)^(1/2))/d/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(-2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e-(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))+5/16*c^5*b*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*e^3/(-c*x*e+(-c^2*d*e)^(1/2))/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/(-c^2*x^2+1)^(1/2)*ln(-2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e-(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))+1/8*c^3*b*e^4*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/d-1/4*c^3*b*e^5*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/d^2/(-c^2*x^2+1)^(1/2)*arctanh(1/(-c^2*x^2+1)^(1/2))-1/4*c^3*b*e^4*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/d/(-c^2*x^2+1)^(1/2)*arctanh(1/(-c^2*x^2+1)^(1/2))+1/8*c^3*b*e^5*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/d^2/(-c^2*x^2+1)^(1/2)*ln(2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))+1/8*c^3*b*e^4*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/d/(-c^2*x^2+1)^(1/2)*ln(2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e+(-c^2*d*e)^(1/2)*c*x+e)/(c*x*e+(-c^2*d*e)^(1/2)))+1/8*c^3*b*e^5*(-(c*x-1)/c/x)^(1/2)*x^3*((c*x+1)/c/x)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/d^2/(-c^2*x^2+1)^(1/2)*ln(-2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e-(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))+1/8*c^3*b*e^4*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/(-c*x*e+(-c^2*d*e)^(1/2))/((c^2*d+e)/e)^(1/2)/(c*x*e+(-c^2*d*e)^(1/2))/((-c^2*d*e)^(1/2)-e)^2/((-c^2*d*e)^(1/2)+e)^2/d/(-c^2*x^2+1)^(1/2)*ln(-2*((-c^2*x^2+1)^(1/2)*((c^2*d+e)/e)^(1/2)*e-(-c^2*d*e)^(1/2)*c*x+e)/(-c*x*e+(-c^2*d*e)^(1/2)))","B"
126,1,5713,833,2.779000," ","int((a+b*arcsech(c*x))/x/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
127,1,3455,1196,9.406000," ","int(x^4*(a+b*arcsech(c*x))/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"5/4/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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^5*b*x^4/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)-3/8*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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)+3/8*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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)+1/8*c^5*b*x^2/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*d+3/8*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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*c^4*a/(c^2*e*x^2+c^2*d)^2/e^2*d*x+3/16*c^3*b/e^2/(c^2*d+e)*d*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-7/4/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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*c^3*b/e^2/(c^2*d+e)*d*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-5/8*c^4*b*x^3/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsech(c*x)-3/4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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-5/4/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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)+5/4/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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)+1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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)-5/8*c^6*b*x^3/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsech(c*x)*d-3/8*c^6*b*x/e^2/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsech(c*x)*d^2-3/8*c^4*b*x/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*d*arcsech(c*x)-5/8*c^4*a/(c^2*e*x^2+c^2*d)^2*x^3/e-3/16*c*b/e/(c^2*d+e)*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+3/16*c*b/e/(c^2*d+e)*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+3/8*a/e^2/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))","C"
128,1,2537,1206,9.280000," ","int(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^3,x)","\text{Expression too large to display}"," ",0,"-1/8*c^6*b*x/e/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*d*arcsech(c*x)+1/8*c^4*b*x^3/d*e/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsech(c*x)-1/4/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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^5*b*x^2/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)+1/4/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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*c^4*b*x/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsech(c*x)+1/8*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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+1/8*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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+1/8*c^6*b*x^3/(c^2*e*x^2+c^2*d)^2/(c^2*d+e)*arcsech(c*x)-1/8*c^5*b*x^4/d*e/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(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-1/4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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+1/8*a/d/e/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))-1/16*c*b/d/(c^2*d+e)*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+1/16*c*b/d/(c^2*d+e)*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-1/16*c^3*b/e/(c^2*d+e)*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+1/16*c^3*b/e/(c^2*d+e)*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))","C"
129,1,3446,1196,10.821000," ","int((a+b*arcsech(c*x))/(e*x^2+d)^3,x)","\text{output too large to display}"," ",0,"3/8*a/d^2/(d*e)^(1/2)*arctan(x*e/(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)-3/16*c^3*b/d/(c^2*d+e)*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+3/16*c^3*b/d/(c^2*d+e)*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))-5/8*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^3-5/8*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^3+5/8*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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)+5/4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctan(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^4*(e*(c^2*d+e))^(1/2)+1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/d^5-5/4/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^4*(e*(c^2*d+e))^(1/2)-7/4/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^4-1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^5+9/4/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/d^4+1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/d^5-7/4/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^4-1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^5+9/4/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/d^4+5/8*c^6*b*x/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsech(c*x)-3/16*c*b/(c^2*d+e)/d^2*e*sum(_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+3/16*c*b/(c^2*d+e)/d^2*e*sum(1/_R1/(_R1^2*c^2*d+c^2*d+2*e)*(arcsech(c*x)*ln((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)+dilog((_R1-1/c/x-(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/_R1)),_R1=RootOf(c^2*d*_Z^4+(2*c^2*d+4*e)*_Z^2+c^2*d))+5/4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*arctanh(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(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+7/4/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/d^4*(e*(c^2*d+e))^(1/2)+1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)^2/d^5*(e*(c^2*d+e))^(1/2)+3/8*c^4*b*x^3/d^2/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsech(c*x)*e^2+5/8*c^4*b*x/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*e*arcsech(c*x)+3/8*c^6*b*x^3/d*e/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*arcsech(c*x)+1/c^4*b*((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e*arctan(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)/d^5*(e*(c^2*d+e))^(1/2)-7/4/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/d^4*(e*(c^2*d+e))^(1/2)-1/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+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((c^2*d+2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2))/(c^2*d+e)^2/d^5*(e*(c^2*d+e))^(1/2)-1/c^4*b*(-(c^2*d-2*(e*(c^2*d+e))^(1/2)+2*e)*d)^(1/2)*e*arctanh(c*d*(1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/((-c^2*d+2*(e*(c^2*d+e))^(1/2)-2*e)*d)^(1/2))/(c^2*d+e)/d^5*(e*(c^2*d+e))^(1/2)+1/8*c^5*b*x^2/d/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*e+1/8*c^5*b*x^4/d^2/(c^2*d+e)/(c^2*e*x^2+c^2*d)^2*(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*e^2","C"
130,0,0,377,3.720000," ","int(x^5*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x)","\int x^{5} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int(x^5*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x)","F"
131,0,0,273,3.394000," ","int(x^3*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x)","\int x^{3} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int(x^3*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x)","F"
132,0,0,179,2.553000," ","int(x*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x)","\int x \left(a +b \,\mathrm{arcsech}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int(x*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x)","F"
133,0,0,23,1.622000," ","int((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x,x)","\int \frac{\left(a +b \,\mathrm{arcsech}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x}\, dx"," ",0,"int((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x,x)","F"
134,0,0,23,0.870000," ","int((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x^3,x)","\int \frac{\left(a +b \,\mathrm{arcsech}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x^{3}}\, dx"," ",0,"int((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x^3,x)","F"
135,0,0,23,2.839000," ","int(x^2*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x)","\int x^{2} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int(x^2*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x)","F"
136,0,0,20,1.624000," ","int((a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x)","\int \left(a +b \,\mathrm{arcsech}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int((a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x)","F"
137,0,0,23,1.326000," ","int((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x^2,x)","\int \frac{\left(a +b \,\mathrm{arcsech}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x^{2}}\, dx"," ",0,"int((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x^2,x)","F"
138,-2,0,270,180.000000," ","int((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x^4,x)","\int \frac{\left(a +b \,\mathrm{arcsech}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x^{4}}\, dx"," ",0,"int((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x^4,x)","F"
139,-2,0,791,180.000000," ","int((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x^6,x)","\int \frac{\left(a +b \,\mathrm{arcsech}\left(c x \right)\right) \sqrt{e \,x^{2}+d}}{x^{6}}\, dx"," ",0,"int((a+b*arcsech(c*x))*(e*x^2+d)^(1/2)/x^6,x)","F"
140,0,0,352,3.371000," ","int(x^3*(e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x)","\int x^{3} \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)\, dx"," ",0,"int(x^3*(e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x)","F"
141,0,0,245,2.426000," ","int(x*(e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x)","\int x \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)\, dx"," ",0,"int(x*(e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x)","F"
142,0,0,23,1.500000," ","int((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{x}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x,x)","F"
143,0,0,23,0.710000," ","int((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^3,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{x^{3}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^3,x)","F"
144,0,0,23,2.730000," ","int(x^2*(e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x)","\int x^{2} \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)\, dx"," ",0,"int(x^2*(e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x)","F"
145,0,0,20,1.438000," ","int((e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x)","\int \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x)","F"
146,0,0,23,1.137000," ","int((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^2,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{x^{2}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^2,x)","F"
147,-2,0,23,180.000000," ","int((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^4,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{x^{4}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^4,x)","F"
148,-2,0,357,180.000000," ","int((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^6,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{x^{6}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^6,x)","F"
149,-2,0,490,180.000000," ","int((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^8,x)","\int \frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{x^{8}}\, dx"," ",0,"int((e*x^2+d)^(3/2)*(a+b*arcsech(c*x))/x^8,x)","F"
150,0,0,298,4.740000," ","int(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x^{5} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x)","F"
151,0,0,207,4.609000," ","int(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x)","F"
152,0,0,127,2.728000," ","int(x*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x)","F"
153,0,0,23,1.605000," ","int((a+b*arcsech(c*x))/x/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arcsech}\left(c x \right)}{x \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsech(c*x))/x/(e*x^2+d)^(1/2),x)","F"
154,0,0,23,1.147000," ","int((a+b*arcsech(c*x))/x^3/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arcsech}\left(c x \right)}{x^{3} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsech(c*x))/x^3/(e*x^2+d)^(1/2),x)","F"
155,0,0,23,3.518000," ","int(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{x^{2} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x)","F"
156,0,0,20,2.061000," ","int((a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arcsech}\left(c x \right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x)","F"
157,0,0,197,1.540000," ","int((a+b*arcsech(c*x))/x^2/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arcsech}\left(c x \right)}{x^{2} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsech(c*x))/x^2/(e*x^2+d)^(1/2),x)","F"
158,-2,0,300,180.000000," ","int((a+b*arcsech(c*x))/x^4/(e*x^2+d)^(1/2),x)","\int \frac{a +b \,\mathrm{arcsech}\left(c x \right)}{x^{4} \sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsech(c*x))/x^4/(e*x^2+d)^(1/2),x)","F"
159,0,0,232,4.654000," ","int(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{5} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x)","F"
160,0,0,149,4.328000," ","int(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x)","F"
161,0,0,75,2.418000," ","int(x*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x)","F"
162,0,0,23,1.406000," ","int((a+b*arcsech(c*x))/x/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arcsech}\left(c x \right)}{x \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsech(c*x))/x/(e*x^2+d)^(3/2),x)","F"
163,0,0,23,1.102000," ","int((a+b*arcsech(c*x))/x^3/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arcsech}\left(c x \right)}{x^{3} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsech(c*x))/x^3/(e*x^2+d)^(3/2),x)","F"
164,0,0,23,3.915000," ","int(x^4*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{4} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^4*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x)","F"
165,0,0,23,3.768000," ","int(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{x^{2} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x)","F"
166,0,0,83,2.171000," ","int((a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arcsech}\left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x)","F"
167,0,0,225,1.510000," ","int((a+b*arcsech(c*x))/x^2/(e*x^2+d)^(3/2),x)","\int \frac{a +b \,\mathrm{arcsech}\left(c x \right)}{x^{2} \left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsech(c*x))/x^2/(e*x^2+d)^(3/2),x)","F"
168,0,0,228,4.575000," ","int(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{5} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^5*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x)","F"
169,0,0,151,4.483000," ","int(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^3*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x)","F"
170,0,0,129,2.580000," ","int(x*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x)","F"
171,0,0,23,1.476000," ","int((a+b*arcsech(c*x))/x/(e*x^2+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arcsech}\left(c x \right)}{x \left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsech(c*x))/x/(e*x^2+d)^(5/2),x)","F"
172,0,0,23,1.234000," ","int((a+b*arcsech(c*x))/x^3/(e*x^2+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arcsech}\left(c x \right)}{x^{3} \left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsech(c*x))/x^3/(e*x^2+d)^(5/2),x)","F"
173,0,0,23,4.402000," ","int(x^6*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{6} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^6*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x)","F"
174,0,0,23,3.947000," ","int(x^4*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{4} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^4*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x)","F"
175,0,0,214,3.603000," ","int(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{x^{2} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int(x^2*(a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x)","F"
176,0,0,230,2.023000," ","int((a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x)","\int \frac{a +b \,\mathrm{arcsech}\left(c x \right)}{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsech(c*x))/(e*x^2+d)^(5/2),x)","F"
177,-2,0,570,180.000000," ","int((f*x)^m*(e*x^2+d)^3*(a+b*arcsech(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right)^{3} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^3*(a+b*arcsech(c*x)),x)","F"
178,-2,0,352,180.000000," ","int((f*x)^m*(e*x^2+d)^2*(a+b*arcsech(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right)^{2} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^2*(a+b*arcsech(c*x)),x)","F"
179,-2,0,192,180.000000," ","int((f*x)^m*(e*x^2+d)*(a+b*arcsech(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right) \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)*(a+b*arcsech(c*x)),x)","F"
180,0,0,25,2.377000," ","int((f*x)^m*(a+b*arcsech(c*x))/(e*x^2+d),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{e \,x^{2}+d}\, dx"," ",0,"int((f*x)^m*(a+b*arcsech(c*x))/(e*x^2+d),x)","F"
181,-2,0,25,180.000000," ","int((f*x)^m*(a+b*arcsech(c*x))/(e*x^2+d)^2,x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{2}}\, dx"," ",0,"int((f*x)^m*(a+b*arcsech(c*x))/(e*x^2+d)^2,x)","F"
182,0,0,25,1.794000," ","int((f*x)^m*(e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x)","\int \left(f x \right)^{m} \left(e \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^(3/2)*(a+b*arcsech(c*x)),x)","F"
183,0,0,25,1.724000," ","int((f*x)^m*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x)","\int \left(f x \right)^{m} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right) \sqrt{e \,x^{2}+d}\, dx"," ",0,"int((f*x)^m*(a+b*arcsech(c*x))*(e*x^2+d)^(1/2),x)","F"
184,0,0,25,2.583000," ","int((f*x)^m*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\sqrt{e \,x^{2}+d}}\, dx"," ",0,"int((f*x)^m*(a+b*arcsech(c*x))/(e*x^2+d)^(1/2),x)","F"
185,0,0,25,2.456000," ","int((f*x)^m*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x)","\int \frac{\left(f x \right)^{m} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((f*x)^m*(a+b*arcsech(c*x))/(e*x^2+d)^(3/2),x)","F"
186,0,0,401,6.404000," ","int(x^11*(a+b*arcsech(c*x))/(-c^4*x^4+1)^(1/2),x)","\int \frac{x^{11} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int(x^11*(a+b*arcsech(c*x))/(-c^4*x^4+1)^(1/2),x)","F"
187,0,0,268,5.727000," ","int(x^7*(a+b*arcsech(c*x))/(-c^4*x^4+1)^(1/2),x)","\int \frac{x^{7} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int(x^7*(a+b*arcsech(c*x))/(-c^4*x^4+1)^(1/2),x)","F"
188,0,0,135,3.326000," ","int(x^3*(a+b*arcsech(c*x))/(-c^4*x^4+1)^(1/2),x)","\int \frac{x^{3} \left(a +b \,\mathrm{arcsech}\left(c x \right)\right)}{\sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int(x^3*(a+b*arcsech(c*x))/(-c^4*x^4+1)^(1/2),x)","F"
189,0,0,26,3.198000," ","int((a+b*arcsech(c*x))/x/(-c^4*x^4+1)^(1/2),x)","\int \frac{a +b \,\mathrm{arcsech}\left(c x \right)}{x \sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int((a+b*arcsech(c*x))/x/(-c^4*x^4+1)^(1/2),x)","F"
190,-2,0,26,180.000000," ","int((a+b*arcsech(c*x))/x^5/(-c^4*x^4+1)^(1/2),x)","\int \frac{a +b \,\mathrm{arcsech}\left(c x \right)}{x^{5} \sqrt{-c^{4} x^{4}+1}}\, dx"," ",0,"int((a+b*arcsech(c*x))/x^5/(-c^4*x^4+1)^(1/2),x)","F"