1,1,226,127,0.074000," ","int(x^3*arccsch(b*x+a),x)","\frac{\frac{\mathrm{arccsch}\left(b x +a \right) \left(b x +a \right)^{4}}{4}-\mathrm{arccsch}\left(b x +a \right) \left(b x +a \right)^{3} a +\frac{3 \,\mathrm{arccsch}\left(b x +a \right) \left(b x +a \right)^{2} a^{2}}{2}-\mathrm{arccsch}\left(b x +a \right) \left(b x +a \right) a^{3}+\frac{\mathrm{arccsch}\left(b x +a \right) a^{4}}{4}+\frac{\sqrt{1+\left(b x +a \right)^{2}}\, \left(-3 a^{4} \arctanh \left(\frac{1}{\sqrt{1+\left(b x +a \right)^{2}}}\right)-12 \arcsinh \left(b x +a \right) a^{3}+\left(b x +a \right)^{2} \sqrt{1+\left(b x +a \right)^{2}}-6 a \left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}+18 a^{2} \sqrt{1+\left(b x +a \right)^{2}}+6 a \arcsinh \left(b x +a \right)-2 \sqrt{1+\left(b x +a \right)^{2}}\right)}{12 \sqrt{\frac{1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}}{b^{4}}"," ",0,"1/b^4*(1/4*arccsch(b*x+a)*(b*x+a)^4-arccsch(b*x+a)*(b*x+a)^3*a+3/2*arccsch(b*x+a)*(b*x+a)^2*a^2-arccsch(b*x+a)*(b*x+a)*a^3+1/4*arccsch(b*x+a)*a^4+1/12*(1+(b*x+a)^2)^(1/2)*(-3*a^4*arctanh(1/(1+(b*x+a)^2)^(1/2))-12*arcsinh(b*x+a)*a^3+(b*x+a)^2*(1+(b*x+a)^2)^(1/2)-6*a*(b*x+a)*(1+(b*x+a)^2)^(1/2)+18*a^2*(1+(b*x+a)^2)^(1/2)+6*a*arcsinh(b*x+a)-2*(1+(b*x+a)^2)^(1/2))/((1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a))","A"
2,1,170,94,0.056000," ","int(x^2*arccsch(b*x+a),x)","\frac{\frac{\mathrm{arccsch}\left(b x +a \right) \left(b x +a \right)^{3}}{3}-\mathrm{arccsch}\left(b x +a \right) \left(b x +a \right)^{2} a +\mathrm{arccsch}\left(b x +a \right) \left(b x +a \right) a^{2}-\frac{\mathrm{arccsch}\left(b x +a \right) a^{3}}{3}+\frac{\sqrt{1+\left(b x +a \right)^{2}}\, \left(2 a^{3} \arctanh \left(\frac{1}{\sqrt{1+\left(b x +a \right)^{2}}}\right)+6 \arcsinh \left(b x +a \right) a^{2}+\left(b x +a \right) \sqrt{1+\left(b x +a \right)^{2}}-6 a \sqrt{1+\left(b x +a \right)^{2}}-\arcsinh \left(b x +a \right)\right)}{6 \sqrt{\frac{1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}}{b^{3}}"," ",0,"1/b^3*(1/3*arccsch(b*x+a)*(b*x+a)^3-arccsch(b*x+a)*(b*x+a)^2*a+arccsch(b*x+a)*(b*x+a)*a^2-1/3*arccsch(b*x+a)*a^3+1/6*(1+(b*x+a)^2)^(1/2)*(2*a^3*arctanh(1/(1+(b*x+a)^2)^(1/2))+6*arcsinh(b*x+a)*a^2+(b*x+a)*(1+(b*x+a)^2)^(1/2)-6*a*(1+(b*x+a)^2)^(1/2)-arcsinh(b*x+a))/((1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a))","A"
3,1,97,65,0.050000," ","int(x*arccsch(b*x+a),x)","\frac{\frac{\mathrm{arccsch}\left(b x +a \right) \left(b x +a \right)^{2}}{2}-\mathrm{arccsch}\left(b x +a \right) a \left(b x +a \right)-\frac{\sqrt{1+\left(b x +a \right)^{2}}\, \left(2 a \arcsinh \left(b x +a \right)-\sqrt{1+\left(b x +a \right)^{2}}\right)}{2 \sqrt{\frac{1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right)}}{b^{2}}"," ",0,"1/b^2*(1/2*arccsch(b*x+a)*(b*x+a)^2-arccsch(b*x+a)*a*(b*x+a)-1/2*(1+(b*x+a)^2)^(1/2)*(2*a*arcsinh(b*x+a)-(1+(b*x+a)^2)^(1/2))/((1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a))","A"
4,0,0,218,0.069000," ","int(arccsch(b*x+a)/x,x)","\int \frac{\mathrm{arccsch}\left(b x +a \right)}{x}\, dx"," ",0,"int(arccsch(b*x+a)/x,x)","F"
5,1,154,57,0.074000," ","int(arccsch(b*x+a)/x^2,x)","-\frac{\mathrm{arccsch}\left(b x +a \right)}{x}-\frac{b \sqrt{1+\left(b x +a \right)^{2}}\, \arctanh \left(\frac{1}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{\sqrt{\frac{1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a}+\frac{b \sqrt{1+\left(b x +a \right)^{2}}\, \ln \left(\frac{2 \sqrt{a^{2}+1}\, \sqrt{1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)+2}{b x}\right)}{\sqrt{\frac{1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a \sqrt{a^{2}+1}}"," ",0,"-arccsch(b*x+a)/x-b*(1+(b*x+a)^2)^(1/2)/((1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a*arctanh(1/(1+(b*x+a)^2)^(1/2))+b*(1+(b*x+a)^2)^(1/2)/((1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a/(a^2+1)^(1/2)*ln(2*((a^2+1)^(1/2)*(1+(b*x+a)^2)^(1/2)+a*(b*x+a)+1)/b/x)","B"
6,1,453,100,0.061000," ","int(arccsch(b*x+a)/x^3,x)","-\frac{\mathrm{arccsch}\left(b x +a \right)}{2 x^{2}}+\frac{b^{2} \sqrt{1+\left(b x +a \right)^{2}}\, \arctanh \left(\frac{1}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{2 \sqrt{\frac{1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}+1\right)}-\frac{b^{2} \sqrt{1+\left(b x +a \right)^{2}}\, a^{2} \ln \left(\frac{2 \sqrt{a^{2}+1}\, \sqrt{1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)+2}{b x}\right)}{\sqrt{\frac{1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}+1\right)^{\frac{5}{2}}}+\frac{b^{2} \sqrt{1+\left(b x +a \right)^{2}}\, \arctanh \left(\frac{1}{\sqrt{1+\left(b x +a \right)^{2}}}\right)}{2 \sqrt{\frac{1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a^{2} \left(a^{2}+1\right)}+\frac{b \left(1+\left(b x +a \right)^{2}\right)}{2 \sqrt{\frac{1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a \left(a^{2}+1\right) x}-\frac{3 b^{2} \sqrt{1+\left(b x +a \right)^{2}}\, \ln \left(\frac{2 \sqrt{a^{2}+1}\, \sqrt{1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)+2}{b x}\right)}{2 \sqrt{\frac{1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) \left(a^{2}+1\right)^{\frac{5}{2}}}-\frac{b^{2} \sqrt{1+\left(b x +a \right)^{2}}\, \ln \left(\frac{2 \sqrt{a^{2}+1}\, \sqrt{1+\left(b x +a \right)^{2}}+2 a \left(b x +a \right)+2}{b x}\right)}{2 \sqrt{\frac{1+\left(b x +a \right)^{2}}{\left(b x +a \right)^{2}}}\, \left(b x +a \right) a^{2} \left(a^{2}+1\right)^{\frac{5}{2}}}"," ",0,"-1/2*arccsch(b*x+a)/x^2+1/2*b^2*(1+(b*x+a)^2)^(1/2)/((1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/(a^2+1)*arctanh(1/(1+(b*x+a)^2)^(1/2))-b^2*(1+(b*x+a)^2)^(1/2)/((1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)*a^2/(a^2+1)^(5/2)*ln(2*((a^2+1)^(1/2)*(1+(b*x+a)^2)^(1/2)+a*(b*x+a)+1)/b/x)+1/2*b^2*(1+(b*x+a)^2)^(1/2)/((1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a^2/(a^2+1)*arctanh(1/(1+(b*x+a)^2)^(1/2))+1/2*b*(1+(b*x+a)^2)/((1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a/(a^2+1)/x-3/2*b^2*(1+(b*x+a)^2)^(1/2)/((1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/(a^2+1)^(5/2)*ln(2*((a^2+1)^(1/2)*(1+(b*x+a)^2)^(1/2)+a*(b*x+a)+1)/b/x)-1/2*b^2*(1+(b*x+a)^2)^(1/2)/((1+(b*x+a)^2)/(b*x+a)^2)^(1/2)/(b*x+a)/a^2/(a^2+1)^(5/2)*ln(2*((a^2+1)^(1/2)*(1+(b*x+a)^2)^(1/2)+a*(b*x+a)+1)/b/x)","B"
7,0,0,551,0.413000," ","int((f*x+e)^3*(a+b*arccsch(d*x+c))^2,x)","\int \left(f x +e \right)^{3} \left(a +b \,\mathrm{arccsch}\left(d x +c \right)\right)^{2}\, dx"," ",0,"int((f*x+e)^3*(a+b*arccsch(d*x+c))^2,x)","F"
8,0,0,403,0.429000," ","int((f*x+e)^2*(a+b*arccsch(d*x+c))^2,x)","\int \left(f x +e \right)^{2} \left(a +b \,\mathrm{arccsch}\left(d x +c \right)\right)^{2}\, dx"," ",0,"int((f*x+e)^2*(a+b*arccsch(d*x+c))^2,x)","F"
9,0,0,223,0.055000," ","int((f*x+e)*(a+b*arccsch(d*x+c))^2,x)","\int \left(f x +e \right) \left(a +b \,\mathrm{arccsch}\left(d x +c \right)\right)^{2}\, dx"," ",0,"int((f*x+e)*(a+b*arccsch(d*x+c))^2,x)","F"
10,0,0,120,0.054000," ","int((a+b*arccsch(d*x+c))^2,x)","\int \left(a +b \,\mathrm{arccsch}\left(d x +c \right)\right)^{2}\, dx"," ",0,"int((a+b*arccsch(d*x+c))^2,x)","F"
11,0,0,560,0.537000," ","int((a+b*arccsch(d*x+c))^2/(f*x+e),x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(d x +c \right)\right)^{2}}{f x +e}\, dx"," ",0,"int((a+b*arccsch(d*x+c))^2/(f*x+e),x)","F"
12,0,0,476,0.486000," ","int((a+b*arccsch(d*x+c))^2/(f*x+e)^2,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(d x +c \right)\right)^{2}}{\left(f x +e \right)^{2}}\, dx"," ",0,"int((a+b*arccsch(d*x+c))^2/(f*x+e)^2,x)","F"
13,0,0,1074,0.480000," ","int((a+b*arccsch(d*x+c))^2/(f*x+e)^3,x)","\int \frac{\left(a +b \,\mathrm{arccsch}\left(d x +c \right)\right)^{2}}{\left(f x +e \right)^{3}}\, dx"," ",0,"int((a+b*arccsch(d*x+c))^2/(f*x+e)^3,x)","F"
14,1,43,78,0.048000," ","int(x^3*arccsch(x^(1/2)),x)","\frac{x^{4} \mathrm{arccsch}\left(\sqrt{x}\right)}{4}+\frac{\left(1+x \right) \left(5 x^{3}-6 x^{2}+8 x -16\right)}{140 \sqrt{\frac{1+x}{x}}\, \sqrt{x}}"," ",0,"1/4*x^4*arccsch(x^(1/2))+1/140*(1+x)*(5*x^3-6*x^2+8*x-16)/((1+x)/x)^(1/2)/x^(1/2)","A"
15,1,38,61,0.048000," ","int(x^2*arccsch(x^(1/2)),x)","\frac{x^{3} \mathrm{arccsch}\left(\sqrt{x}\right)}{3}+\frac{\left(1+x \right) \left(3 x^{2}-4 x +8\right)}{45 \sqrt{\frac{1+x}{x}}\, \sqrt{x}}"," ",0,"1/3*x^3*arccsch(x^(1/2))+1/45*(1+x)*(3*x^2-4*x+8)/((1+x)/x)^(1/2)/x^(1/2)","A"
16,1,31,44,0.045000," ","int(x*arccsch(x^(1/2)),x)","\frac{x^{2} \mathrm{arccsch}\left(\sqrt{x}\right)}{2}+\frac{\left(1+x \right) \left(x -2\right)}{6 \sqrt{\frac{1+x}{x}}\, \sqrt{x}}"," ",0,"1/2*x^2*arccsch(x^(1/2))+1/6*(1+x)*(x-2)/((1+x)/x)^(1/2)/x^(1/2)","A"
17,1,24,23,0.050000," ","int(arccsch(x^(1/2)),x)","x \,\mathrm{arccsch}\left(\sqrt{x}\right)+\frac{1+x}{\sqrt{\frac{1+x}{x}}\, \sqrt{x}}"," ",0,"x*arccsch(x^(1/2))+1/((1+x)/x)^(1/2)/x^(1/2)*(1+x)","A"
18,0,0,48,0.073000," ","int(arccsch(x^(1/2))/x,x)","\int \frac{\mathrm{arccsch}\left(\sqrt{x}\right)}{x}\, dx"," ",0,"int(arccsch(x^(1/2))/x,x)","F"
19,1,45,45,0.055000," ","int(arccsch(x^(1/2))/x^2,x)","-\frac{\mathrm{arccsch}\left(\sqrt{x}\right)}{x}+\frac{\sqrt{1+x}\, \left(-\arctanh \left(\frac{1}{\sqrt{1+x}}\right) x +\sqrt{1+x}\right)}{2 \sqrt{\frac{1+x}{x}}\, x^{\frac{3}{2}}}"," ",0,"-arccsch(x^(1/2))/x+1/2*(1+x)^(1/2)*(-arctanh(1/(1+x)^(1/2))*x+(1+x)^(1/2))/((1+x)/x)^(1/2)/x^(3/2)","A"
20,1,57,62,0.050000," ","int(arccsch(x^(1/2))/x^3,x)","-\frac{\mathrm{arccsch}\left(\sqrt{x}\right)}{2 x^{2}}-\frac{\sqrt{1+x}\, \left(-3 \arctanh \left(\frac{1}{\sqrt{1+x}}\right) x^{2}+3 x \sqrt{1+x}-2 \sqrt{1+x}\right)}{16 \sqrt{\frac{1+x}{x}}\, x^{\frac{5}{2}}}"," ",0,"-1/2*arccsch(x^(1/2))/x^2-1/16*(1+x)^(1/2)*(-3*arctanh(1/(1+x)^(1/2))*x^2+3*x*(1+x)^(1/2)-2*(1+x)^(1/2))/((1+x)/x)^(1/2)/x^(5/2)","A"
21,1,67,79,0.060000," ","int(arccsch(x^(1/2))/x^4,x)","-\frac{\mathrm{arccsch}\left(\sqrt{x}\right)}{3 x^{3}}+\frac{\sqrt{1+x}\, \left(-15 \arctanh \left(\frac{1}{\sqrt{1+x}}\right) x^{3}+15 x^{2} \sqrt{1+x}-10 x \sqrt{1+x}+8 \sqrt{1+x}\right)}{144 \sqrt{\frac{1+x}{x}}\, x^{\frac{7}{2}}}"," ",0,"-1/3*arccsch(x^(1/2))/x^3+1/144*(1+x)^(1/2)*(-15*arctanh(1/(1+x)^(1/2))*x^3+15*x^2*(1+x)^(1/2)-10*x*(1+x)^(1/2)+8*(1+x)^(1/2))/((1+x)/x)^(1/2)/x^(7/2)","A"
22,1,29,14,0.049000," ","int(arccsch(1/x),x)","x \,\mathrm{arccsch}\left(\frac{1}{x}\right)-\frac{x^{2} \left(1+\frac{1}{x^{2}}\right)}{\sqrt{\left(1+\frac{1}{x^{2}}\right) x^{2}}}"," ",0,"x*arccsch(1/x)-1/((1+1/x^2)*x^2)^(1/2)*x^2*(1+1/x^2)","A"
23,0,0,87,0.238000," ","int(arccsch(a*x^n)/x,x)","\int \frac{\mathrm{arccsch}\left(a \,x^{n}\right)}{x}\, dx"," ",0,"int(arccsch(a*x^n)/x,x)","F"
24,0,0,70,0.089000," ","int(arccsch(a*x^5)/x,x)","\int \frac{\mathrm{arccsch}\left(a \,x^{5}\right)}{x}\, dx"," ",0,"int(arccsch(a*x^5)/x,x)","F"
25,0,0,105,0.269000," ","int(arccsch(c*exp(b*x+a)),x)","\int \mathrm{arccsch}\left(c \,{\mathrm e}^{b x +a}\right)\, dx"," ",0,"int(arccsch(c*exp(b*x+a)),x)","F"
26,0,0,44,0.052000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))*x^m,x)","\int \left(\frac{1}{a x}+\sqrt{1+\frac{1}{x^{2} a^{2}}}\right) x^{m}\, dx"," ",0,"int((1/a/x+(1+1/x^2/a^2)^(1/2))*x^m,x)","F"
27,1,53,44,0.086000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))*x^4,x)","\frac{\sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, x \left(a^{2} x^{2}+1\right) \left(3 a^{2} x^{2}-2\right)}{15 a^{4}}+\frac{x^{4}}{4 a}"," ",0,"1/15*((a^2*x^2+1)/a^2/x^2)^(1/2)*x/a^4*(a^2*x^2+1)*(3*a^2*x^2-2)+1/4*x^4/a","A"
28,1,109,61,0.049000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))*x^3,x)","-\frac{\sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, x \left(-2 x \left(\frac{a^{2} x^{2}+1}{a^{2}}\right)^{\frac{3}{2}} a^{4}+x \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, a^{2}+\ln \left(x +\sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\right)\right)}{8 \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, a^{4}}+\frac{x^{3}}{3 a}"," ",0,"-1/8*((a^2*x^2+1)/a^2/x^2)^(1/2)*x*(-2*x*((a^2*x^2+1)/a^2)^(3/2)*a^4+x*((a^2*x^2+1)/a^2)^(1/2)*a^2+ln(x+((a^2*x^2+1)/a^2)^(1/2)))/((a^2*x^2+1)/a^2)^(1/2)/a^4+1/3*x^3/a","A"
29,1,43,25,0.044000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))*x^2,x)","\frac{\sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, x \left(a^{2} x^{2}+1\right)}{3 a^{2}}+\frac{x^{2}}{2 a}"," ",0,"1/3*((a^2*x^2+1)/a^2/x^2)^(1/2)*x/a^2*(a^2*x^2+1)+1/2*x^2/a","A"
30,1,85,39,0.046000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))*x,x)","\frac{\sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, x \left(x \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, a^{2}+\ln \left(x +\sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\right)\right)}{2 \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, a^{2}}+\frac{x}{a}"," ",0,"1/2*((a^2*x^2+1)/a^2/x^2)^(1/2)*x*(x*((a^2*x^2+1)/a^2)^(1/2)*a^2+ln(x+((a^2*x^2+1)/a^2)^(1/2)))/((a^2*x^2+1)/a^2)^(1/2)/a^2+x/a","B"
31,1,113,37,0.046000," ","int(1/a/x+(1+1/x^2/a^2)^(1/2),x)","-\frac{\sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, x \left(-\sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, a^{2}+\ln \left(\frac{2 \sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, a^{2}+2}{a^{2} x}\right)\right)}{\sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, a^{2}}+\frac{\ln \left(x \right)}{a}"," ",0,"-((a^2*x^2+1)/a^2/x^2)^(1/2)*x*(-(1/a^2)^(1/2)*((a^2*x^2+1)/a^2)^(1/2)*a^2+ln(2*((1/a^2)^(1/2)*((a^2*x^2+1)/a^2)^(1/2)*a^2+1)/a^2/x))/(1/a^2)^(1/2)/((a^2*x^2+1)/a^2)^(1/2)/a^2+ln(x)/a","B"
32,1,107,34,0.045000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))/x,x)","\frac{\sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, \left(-a^{2} \left(\frac{a^{2} x^{2}+1}{a^{2}}\right)^{\frac{3}{2}}+\sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, x^{2} a^{2}+\ln \left(x +\sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\right) x \right)}{\sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}}-\frac{1}{a x}"," ",0,"((a^2*x^2+1)/a^2/x^2)^(1/2)*(-a^2*((a^2*x^2+1)/a^2)^(3/2)+((a^2*x^2+1)/a^2)^(1/2)*x^2*a^2+ln(x+((a^2*x^2+1)/a^2)^(1/2))*x)/((a^2*x^2+1)/a^2)^(1/2)-1/a/x","B"
33,1,145,32,0.046000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))/x^2,x)","-\frac{\sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, \left(a^{2} \left(\frac{a^{2} x^{2}+1}{a^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{a^{2}}}-\sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, x^{2} a^{2}+\ln \left(\frac{2 \sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, a^{2}+2}{a^{2} x}\right) x^{2}\right)}{2 x \sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}}-\frac{1}{2 a \,x^{2}}"," ",0,"-1/2*((a^2*x^2+1)/a^2/x^2)^(1/2)/x*(a^2*((a^2*x^2+1)/a^2)^(3/2)*(1/a^2)^(1/2)-(1/a^2)^(1/2)*((a^2*x^2+1)/a^2)^(1/2)*x^2*a^2+ln(2*((1/a^2)^(1/2)*((a^2*x^2+1)/a^2)^(1/2)*a^2+1)/a^2/x)*x^2)/(1/a^2)^(1/2)/((a^2*x^2+1)/a^2)^(1/2)-1/2/a/x^2","B"
34,1,42,25,0.064000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))/x^3,x)","-\frac{\sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, \left(a^{2} x^{2}+1\right)}{3 x^{2}}-\frac{1}{3 x^{3} a}"," ",0,"-1/3*((a^2*x^2+1)/a^2/x^2)^(1/2)/x^2*(a^2*x^2+1)-1/3/x^3/a","A"
35,1,173,53,0.056000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))/x^4,x)","\frac{\sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, a^{2} \left(\sqrt{\frac{1}{a^{2}}}\, \left(\frac{a^{2} x^{2}+1}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}-\sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, x^{4} a^{2}+\ln \left(\frac{2 \sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, a^{2}+2}{a^{2} x}\right) x^{4}-2 \left(\frac{a^{2} x^{2}+1}{a^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{a^{2}}}\right)}{8 x^{3} \sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}}-\frac{1}{4 x^{4} a}"," ",0,"1/8*((a^2*x^2+1)/a^2/x^2)^(1/2)/x^3*a^2*((1/a^2)^(1/2)*((a^2*x^2+1)/a^2)^(3/2)*x^2*a^2-(1/a^2)^(1/2)*((a^2*x^2+1)/a^2)^(1/2)*x^4*a^2+ln(2*((1/a^2)^(1/2)*((a^2*x^2+1)/a^2)^(1/2)*a^2+1)/a^2/x)*x^4-2*((a^2*x^2+1)/a^2)^(3/2)*(1/a^2)^(1/2))/(1/a^2)^(1/2)/((a^2*x^2+1)/a^2)^(1/2)-1/4/x^4/a","B"
36,1,52,41,0.050000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))/x^5,x)","\frac{\sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, \left(a^{2} x^{2}+1\right) \left(2 a^{2} x^{2}-3\right)}{15 x^{4}}-\frac{1}{5 a \,x^{5}}"," ",0,"1/15*((a^2*x^2+1)/a^2/x^2)^(1/2)/x^4*(a^2*x^2+1)*(2*a^2*x^2-3)-1/5/a/x^5","A"
37,0,0,51,0.072000," ","int((1/a/x^2+(1+1/a^2/x^4)^(1/2))*x^m,x)","\int \left(\frac{1}{a \,x^{2}}+\sqrt{1+\frac{1}{a^{2} x^{4}}}\right) x^{m}\, dx"," ",0,"int((1/a/x^2+(1+1/a^2/x^4)^(1/2))*x^m,x)","F"
38,1,150,222,0.074000," ","int((1/a/x^2+(1+1/a^2/x^4)^(1/2))*x^4,x)","\frac{\sqrt{\frac{a^{2} x^{4}+1}{a^{2} x^{4}}}\, x^{2} \left(\sqrt{i a}\, x^{7} a^{3}+x^{3} a \sqrt{i a}+2 i \sqrt{-i a \,x^{2}+1}\, \sqrt{i a \,x^{2}+1}\, \EllipticF \left(x \sqrt{i a}, i\right)-2 i \sqrt{-i a \,x^{2}+1}\, \sqrt{i a \,x^{2}+1}\, \EllipticE \left(x \sqrt{i a}, i\right)\right)}{5 a \left(a^{2} x^{4}+1\right) \sqrt{i a}}+\frac{x^{3}}{3 a}"," ",0,"1/5*((a^2*x^4+1)/a^2/x^4)^(1/2)*x^2*((I*a)^(1/2)*x^7*a^3+x^3*a*(I*a)^(1/2)+2*I*(1-I*a*x^2)^(1/2)*(1+I*a*x^2)^(1/2)*EllipticF(x*(I*a)^(1/2),I)-2*I*(1-I*a*x^2)^(1/2)*(1+I*a*x^2)^(1/2)*EllipticE(x*(I*a)^(1/2),I))/a/(a^2*x^4+1)/(I*a)^(1/2)+1/3*x^3/a","C"
39,1,94,42,0.168000," ","int((1/a/x^2+(1+1/a^2/x^4)^(1/2))*x^3,x)","\frac{\sqrt{\frac{a^{2} x^{4}+1}{a^{2} x^{4}}}\, x^{2} \left(x^{2} \sqrt{\frac{a^{2} x^{4}+1}{a^{2}}}\, a^{2}+\ln \left(x^{2}+\sqrt{\frac{a^{2} x^{4}+1}{a^{2}}}\right)\right)}{4 \sqrt{\frac{a^{2} x^{4}+1}{a^{2}}}\, a^{2}}+\frac{x^{2}}{2 a}"," ",0,"1/4*((a^2*x^4+1)/a^2/x^4)^(1/2)*x^2*(x^2*((a^2*x^4+1)/a^2)^(1/2)*a^2+ln(x^2+((a^2*x^4+1)/a^2)^(1/2)))/((a^2*x^4+1)/a^2)^(1/2)/a^2+1/2*x^2/a","B"
40,1,104,99,0.048000," ","int((1/a/x^2+(1+1/a^2/x^4)^(1/2))*x^2,x)","\frac{\sqrt{\frac{a^{2} x^{4}+1}{a^{2} x^{4}}}\, x^{2} \left(\sqrt{i a}\, x^{5} a^{2}+2 \sqrt{-i a \,x^{2}+1}\, \sqrt{i a \,x^{2}+1}\, \EllipticF \left(x \sqrt{i a}, i\right)+x \sqrt{i a}\right)}{3 \left(a^{2} x^{4}+1\right) \sqrt{i a}}+\frac{x}{a}"," ",0,"1/3*((a^2*x^4+1)/a^2/x^4)^(1/2)*x^2*((I*a)^(1/2)*x^5*a^2+2*(1-I*a*x^2)^(1/2)*(1+I*a*x^2)^(1/2)*EllipticF(x*(I*a)^(1/2),I)+x*(I*a)^(1/2))/(a^2*x^4+1)/(I*a)^(1/2)+x/a","C"
41,1,116,34,0.153000," ","int((1/a/x^2+(1+1/a^2/x^4)^(1/2))*x,x)","\frac{\sqrt{\frac{a^{2} x^{4}+1}{a^{2} x^{4}}}\, x^{2} \left(\sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{4}+1}{a^{2}}}\, a^{2}-\ln \left(\frac{2 \sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{4}+1}{a^{2}}}\, a^{2}+2}{a^{2} x^{2}}\right)\right)}{2 \sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{4}+1}{a^{2}}}\, a^{2}}+\frac{\ln \left(x \right)}{a}"," ",0,"1/2*((a^2*x^4+1)/a^2/x^4)^(1/2)*x^2*((1/a^2)^(1/2)*((a^2*x^4+1)/a^2)^(1/2)*a^2-ln(2*((1/a^2)^(1/2)*((a^2*x^4+1)/a^2)^(1/2)*a^2+1)/a^2/x^2))/(1/a^2)^(1/2)/((a^2*x^4+1)/a^2)^(1/2)/a^2+ln(x)/a","B"
42,1,146,199,0.056000," ","int(1/a/x^2+(1+1/a^2/x^4)^(1/2),x)","\frac{\sqrt{\frac{a^{2} x^{4}+1}{a^{2} x^{4}}}\, x \left(-\sqrt{i a}\, x^{4} a^{2}+2 i \sqrt{-i a \,x^{2}+1}\, \sqrt{i a \,x^{2}+1}\, x \EllipticF \left(x \sqrt{i a}, i\right) a -2 i \sqrt{-i a \,x^{2}+1}\, \sqrt{i a \,x^{2}+1}\, x \EllipticE \left(x \sqrt{i a}, i\right) a -\sqrt{i a}\right)}{\left(a^{2} x^{4}+1\right) \sqrt{i a}}-\frac{1}{a x}"," ",0,"((a^2*x^4+1)/a^2/x^4)^(1/2)*x*(-(I*a)^(1/2)*x^4*a^2+2*I*(1-I*a*x^2)^(1/2)*(1+I*a*x^2)^(1/2)*x*EllipticF(x*(I*a)^(1/2),I)*a-2*I*(1-I*a*x^2)^(1/2)*(1+I*a*x^2)^(1/2)*x*EllipticE(x*(I*a)^(1/2),I)*a-(I*a)^(1/2))/(a^2*x^4+1)/(I*a)^(1/2)-1/a/x","C"
43,1,86,36,0.160000," ","int((1/a/x^2+(1+1/a^2/x^4)^(1/2))/x,x)","-\frac{\sqrt{\frac{a^{2} x^{4}+1}{a^{2} x^{4}}}\, \left(-\ln \left(x^{2}+\sqrt{\frac{a^{2} x^{4}+1}{a^{2}}}\right) x^{2}+\sqrt{\frac{a^{2} x^{4}+1}{a^{2}}}\right)}{2 \sqrt{\frac{a^{2} x^{4}+1}{a^{2}}}}-\frac{1}{2 a \,x^{2}}"," ",0,"-1/2*((a^2*x^4+1)/a^2/x^4)^(1/2)*(-ln(x^2+((a^2*x^4+1)/a^2)^(1/2))*x^2+((a^2*x^4+1)/a^2)^(1/2))/((a^2*x^4+1)/a^2)^(1/2)-1/2/a/x^2","B"
44,1,111,102,0.053000," ","int((1/a/x^2+(1+1/a^2/x^4)^(1/2))/x^2,x)","-\frac{\sqrt{\frac{a^{2} x^{4}+1}{a^{2} x^{4}}}\, \left(-2 \sqrt{-i a \,x^{2}+1}\, \sqrt{i a \,x^{2}+1}\, \EllipticF \left(x \sqrt{i a}, i\right) x^{3} a^{2}+\sqrt{i a}\, x^{4} a^{2}+\sqrt{i a}\right)}{3 x \left(a^{2} x^{4}+1\right) \sqrt{i a}}-\frac{1}{3 x^{3} a}"," ",0,"-1/3*((a^2*x^4+1)/a^2/x^4)^(1/2)*(-2*(1-I*a*x^2)^(1/2)*(1+I*a*x^2)^(1/2)*EllipticF(x*(I*a)^(1/2),I)*x^3*a^2+(I*a)^(1/2)*x^4*a^2+(I*a)^(1/2))/x/(a^2*x^4+1)/(I*a)^(1/2)-1/3/x^3/a","C"
45,1,114,34,0.148000," ","int((1/a/x^2+(1+1/a^2/x^4)^(1/2))/x^3,x)","-\frac{\sqrt{\frac{a^{2} x^{4}+1}{a^{2} x^{4}}}\, \left(\ln \left(\frac{2 \sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{4}+1}{a^{2}}}\, a^{2}+2}{a^{2} x^{2}}\right) x^{4}+\sqrt{\frac{a^{2} x^{4}+1}{a^{2}}}\, \sqrt{\frac{1}{a^{2}}}\right)}{4 x^{2} \sqrt{\frac{a^{2} x^{4}+1}{a^{2}}}\, \sqrt{\frac{1}{a^{2}}}}-\frac{1}{4 x^{4} a}"," ",0,"-1/4*((a^2*x^4+1)/a^2/x^4)^(1/2)/x^2*(ln(2*((1/a^2)^(1/2)*((a^2*x^4+1)/a^2)^(1/2)*a^2+1)/a^2/x^2)*x^4+((a^2*x^4+1)/a^2)^(1/2)*(1/a^2)^(1/2))/((a^2*x^4+1)/a^2)^(1/2)/(1/a^2)^(1/2)-1/4/x^4/a","B"
46,1,171,205,0.056000," ","int((1/a/x^2+(1+1/a^2/x^4)^(1/2))/x^4,x)","\frac{\sqrt{\frac{a^{2} x^{4}+1}{a^{2} x^{4}}}\, \left(-2 \sqrt{i a}\, x^{8} a^{4}+2 i a^{3} \sqrt{-i a \,x^{2}+1}\, \sqrt{i a \,x^{2}+1}\, x^{5} \EllipticF \left(x \sqrt{i a}, i\right)-2 i a^{3} \sqrt{-i a \,x^{2}+1}\, \sqrt{i a \,x^{2}+1}\, x^{5} \EllipticE \left(x \sqrt{i a}, i\right)-3 \sqrt{i a}\, x^{4} a^{2}-\sqrt{i a}\right)}{5 x^{3} \left(a^{2} x^{4}+1\right) \sqrt{i a}}-\frac{1}{5 a \,x^{5}}"," ",0,"1/5*((a^2*x^4+1)/a^2/x^4)^(1/2)*(-2*(I*a)^(1/2)*x^8*a^4+2*I*a^3*(1-I*a*x^2)^(1/2)*(1+I*a*x^2)^(1/2)*x^5*EllipticF(x*(I*a)^(1/2),I)-2*I*a^3*(1-I*a*x^2)^(1/2)*(1+I*a*x^2)^(1/2)*x^5*EllipticE(x*(I*a)^(1/2),I)-3*(I*a)^(1/2)*x^4*a^2-(I*a)^(1/2))/x^3/(a^2*x^4+1)/(I*a)^(1/2)-1/5/a/x^5","C"
47,1,42,25,0.135000," ","int((1/a/x^2+(1+1/a^2/x^4)^(1/2))/x^5,x)","-\frac{\sqrt{\frac{a^{2} x^{4}+1}{a^{2} x^{4}}}\, \left(a^{2} x^{4}+1\right)}{6 x^{4}}-\frac{1}{6 x^{6} a}"," ",0,"-1/6*((a^2*x^4+1)/a^2/x^4)^(1/2)/x^4*(a^2*x^4+1)-1/6/x^6/a","A"
48,0,0,60,0.046000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))^2*x^m,x)","\int \left(\frac{1}{a x}+\sqrt{1+\frac{1}{x^{2} a^{2}}}\right)^{2} x^{m}\, dx"," ",0,"int((1/a/x+(1+1/x^2/a^2)^(1/2))^2*x^m,x)","F"
49,1,114,69,0.041000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))^2*x^4,x)","\frac{x^{5}}{5}+\frac{2 x^{3}}{3 a^{2}}-\frac{\sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, x \left(-2 x \left(\frac{a^{2} x^{2}+1}{a^{2}}\right)^{\frac{3}{2}} a^{4}+x \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, a^{2}+\ln \left(x +\sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\right)\right)}{4 a^{5} \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}}"," ",0,"1/5*x^5+2/3*x^3/a^2-1/4/a^5*((a^2*x^2+1)/a^2/x^2)^(1/2)*x*(-2*x*((a^2*x^2+1)/a^2)^(3/2)*a^4+x*((a^2*x^2+1)/a^2)^(1/2)*a^2+ln(x+((a^2*x^2+1)/a^2)^(1/2)))/((a^2*x^2+1)/a^2)^(1/2)","A"
50,1,61,32,0.051000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))^2*x^3,x)","\frac{\frac{1}{4} a^{2} x^{4}+\frac{1}{2} x^{2}}{a^{2}}+\frac{2 \sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, x \left(a^{2} x^{2}+1\right)}{3 a^{3}}+\frac{x^{2}}{2 a^{2}}"," ",0,"1/a^2*(1/4*a^2*x^4+1/2*x^2)+2/3/a^3*((a^2*x^2+1)/a^2/x^2)^(1/2)*x*(a^2*x^2+1)+1/2*x^2/a^2","A"
51,1,90,46,0.051000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))^2*x^2,x)","\frac{x^{3}}{3}+\frac{2 x}{a^{2}}+\frac{\sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, x \left(x \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, a^{2}+\ln \left(x +\sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\right)\right)}{a^{3} \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}}"," ",0,"1/3*x^3+2*x/a^2+1/a^3*((a^2*x^2+1)/a^2/x^2)^(1/2)*x*(x*((a^2*x^2+1)/a^2)^(1/2)*a^2+ln(x+((a^2*x^2+1)/a^2)^(1/2)))/((a^2*x^2+1)/a^2)^(1/2)","A"
52,1,120,39,0.055000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))^2*x,x)","\frac{x^{2}}{2}+\frac{2 \ln \left(x \right)}{a^{2}}+\frac{2 \sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, x \left(\sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, a^{2}-\ln \left(\frac{2 \sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, a^{2}+2}{a^{2} x}\right)\right)}{a^{3} \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, \sqrt{\frac{1}{a^{2}}}}"," ",0,"1/2*x^2+2*ln(x)/a^2+2/a^3*((a^2*x^2+1)/a^2/x^2)^(1/2)*x*((1/a^2)^(1/2)*((a^2*x^2+1)/a^2)^(1/2)*a^2-ln(2*((1/a^2)^(1/2)*((a^2*x^2+1)/a^2)^(1/2)*a^2+1)/a^2/x))/((a^2*x^2+1)/a^2)^(1/2)/(1/a^2)^(1/2)","B"
53,1,112,43,0.053000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))^2,x)","x -\frac{2}{a^{2} x}+\frac{2 \sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, \left(-a^{2} \left(\frac{a^{2} x^{2}+1}{a^{2}}\right)^{\frac{3}{2}}+\sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, x^{2} a^{2}+\ln \left(x +\sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\right) x \right)}{a \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}}"," ",0,"x-2/a^2/x+2/a*((a^2*x^2+1)/a^2/x^2)^(1/2)*(-a^2*((a^2*x^2+1)/a^2)^(3/2)+((a^2*x^2+1)/a^2)^(1/2)*x^2*a^2+ln(x+((a^2*x^2+1)/a^2)^(1/2))*x)/((a^2*x^2+1)/a^2)^(1/2)","B"
54,1,150,36,0.050000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))^2/x,x)","\ln \left(x \right)-\frac{1}{x^{2} a^{2}}-\frac{\sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, \left(a^{2} \left(\frac{a^{2} x^{2}+1}{a^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{a^{2}}}-\sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, x^{2} a^{2}+\ln \left(\frac{2 \sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, a^{2}+2}{a^{2} x}\right) x^{2}\right)}{a x \sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}}"," ",0,"ln(x)-1/x^2/a^2-1/a*((a^2*x^2+1)/a^2/x^2)^(1/2)/x*(a^2*((a^2*x^2+1)/a^2)^(3/2)*(1/a^2)^(1/2)-(1/a^2)^(1/2)*((a^2*x^2+1)/a^2)^(1/2)*x^2*a^2+ln(2*((1/a^2)^(1/2)*((a^2*x^2+1)/a^2)^(1/2)*a^2+1)/a^2/x)*x^2)/(1/a^2)^(1/2)/((a^2*x^2+1)/a^2)^(1/2)","B"
55,1,63,28,0.050000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))^2/x^2,x)","\frac{-\frac{a^{2}}{x}-\frac{1}{3 x^{3}}}{a^{2}}-\frac{2 \sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, \left(a^{2} x^{2}+1\right)}{3 a \,x^{2}}-\frac{1}{3 x^{3} a^{2}}"," ",0,"1/a^2*(-a^2/x-1/3/x^3)-2/3/a*((a^2*x^2+1)/a^2/x^2)^(1/2)/x^2*(a^2*x^2+1)-1/3/x^3/a^2","B"
56,1,176,59,0.053000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))^2/x^3,x)","-\frac{1}{2 x^{2}}-\frac{1}{2 a^{2} x^{4}}+\frac{a \sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, \left(\sqrt{\frac{1}{a^{2}}}\, \left(\frac{a^{2} x^{2}+1}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}-\sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, x^{4} a^{2}+\ln \left(\frac{2 \sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, a^{2}+2}{a^{2} x}\right) x^{4}-2 \left(\frac{a^{2} x^{2}+1}{a^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{a^{2}}}\right)}{4 x^{3} \sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}}"," ",0,"-1/2/x^2-1/2/a^2/x^4+1/4*a*((a^2*x^2+1)/a^2/x^2)^(1/2)/x^3*((1/a^2)^(1/2)*((a^2*x^2+1)/a^2)^(3/2)*x^2*a^2-(1/a^2)^(1/2)*((a^2*x^2+1)/a^2)^(1/2)*x^4*a^2+ln(2*((1/a^2)^(1/2)*((a^2*x^2+1)/a^2)^(1/2)*a^2+1)/a^2/x)*x^4-2*((a^2*x^2+1)/a^2)^(3/2)*(1/a^2)^(1/2))/(1/a^2)^(1/2)/((a^2*x^2+1)/a^2)^(1/2)","B"
57,1,73,46,0.050000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))^2/x^4,x)","\frac{-\frac{a^{2}}{3 x^{3}}-\frac{1}{5 x^{5}}}{a^{2}}+\frac{2 \sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, \left(a^{2} x^{2}+1\right) \left(2 a^{2} x^{2}-3\right)}{15 a \,x^{4}}-\frac{1}{5 x^{5} a^{2}}"," ",0,"1/a^2*(-1/3*a^2/x^3-1/5/x^5)+2/15/a*((a^2*x^2+1)/a^2/x^2)^(1/2)/x^4*(a^2*x^2+1)*(2*a^2*x^2-3)-1/5/x^5/a^2","A"
58,1,209,78,0.053000," ","int((1/a/x+(1+1/x^2/a^2)^(1/2))^2/x^5,x)","-\frac{1}{3 a^{2} x^{6}}-\frac{1}{4 x^{4}}-\frac{a \sqrt{\frac{a^{2} x^{2}+1}{a^{2} x^{2}}}\, \left(3 \left(\frac{a^{2} x^{2}+1}{a^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{a^{2}}}\, x^{4} a^{4}-3 \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, \sqrt{\frac{1}{a^{2}}}\, x^{6} a^{4}+3 \ln \left(\frac{2 \sqrt{\frac{1}{a^{2}}}\, \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, a^{2}+2}{a^{2} x}\right) x^{6} a^{2}-6 \sqrt{\frac{1}{a^{2}}}\, \left(\frac{a^{2} x^{2}+1}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}+8 \left(\frac{a^{2} x^{2}+1}{a^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{a^{2}}}\right)}{24 x^{5} \sqrt{\frac{a^{2} x^{2}+1}{a^{2}}}\, \sqrt{\frac{1}{a^{2}}}}"," ",0,"-1/3/a^2/x^6-1/4/x^4-1/24*a*((a^2*x^2+1)/a^2/x^2)^(1/2)/x^5*(3*((a^2*x^2+1)/a^2)^(3/2)*(1/a^2)^(1/2)*x^4*a^4-3*((a^2*x^2+1)/a^2)^(1/2)*(1/a^2)^(1/2)*x^6*a^4+3*ln(2*((1/a^2)^(1/2)*((a^2*x^2+1)/a^2)^(1/2)*a^2+1)/a^2/x)*x^6*a^2-6*(1/a^2)^(1/2)*((a^2*x^2+1)/a^2)^(3/2)*x^2*a^2+8*((a^2*x^2+1)/a^2)^(3/2)*(1/a^2)^(1/2))/((a^2*x^2+1)/a^2)^(1/2)/(1/a^2)^(1/2)","B"
59,0,0,75,0.464000," ","int((1/c/x+(1+1/c^2/x^2)^(1/2))*(d*x)^m/(c^2*x^2+1),x)","\int \frac{\left(\frac{1}{c x}+\sqrt{1+\frac{1}{c^{2} x^{2}}}\right) \left(d x \right)^{m}}{c^{2} x^{2}+1}\, dx"," ",0,"int((1/c/x+(1+1/c^2/x^2)^(1/2))*(d*x)^m/(c^2*x^2+1),x)","F"
60,1,165,78,0.119000," ","int((1/c/x+(1+1/c^2/x^2)^(1/2))*x^5/(c^2*x^2+1),x)","\frac{\sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \left(2 x \left(\frac{c^{2} x^{2}+1}{c^{2}}\right)^{\frac{3}{2}} c^{4}-5 x \sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\, c^{2}-5 \ln \left(x +\sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\right)+8 \ln \left(x +\sqrt{-\frac{\left(-c^{2} x +\sqrt{-c^{2}}\right) \left(c^{2} x +\sqrt{-c^{2}}\right)}{c^{4}}}\right)\right)}{8 \sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\, c^{6}}+\frac{x^{3}}{3 c^{3}}-\frac{x}{c^{5}}+\frac{\arctan \left(c x \right)}{c^{6}}"," ",0,"1/8*((c^2*x^2+1)/c^2/x^2)^(1/2)*x*(2*x*((c^2*x^2+1)/c^2)^(3/2)*c^4-5*x*((c^2*x^2+1)/c^2)^(1/2)*c^2-5*ln(x+((c^2*x^2+1)/c^2)^(1/2))+8*ln(x+(-(-c^2*x+(-c^2)^(1/2))*(c^2*x+(-c^2)^(1/2))/c^4)^(1/2)))/((c^2*x^2+1)/c^2)^(1/2)/c^6+1/3*x^3/c^3-x/c^5+arctan(c*x)/c^6","B"
61,1,120,60,0.059000," ","int((1/c/x+(1+1/c^2/x^2)^(1/2))*x^4/(c^2*x^2+1),x)","\frac{\sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \left(\left(\frac{c^{2} x^{2}+1}{c^{2}}\right)^{\frac{3}{2}} c^{2}-3 \sqrt{-\frac{\left(-c^{2} x +\sqrt{-c^{2}}\right) \left(c^{2} x +\sqrt{-c^{2}}\right)}{c^{4}}}\right)}{3 c^{4} \sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}}+\frac{x^{2}}{2 c^{3}}-\frac{\ln \left(c^{2} x^{2}+1\right)}{2 c^{5}}"," ",0,"1/3*((c^2*x^2+1)/c^2/x^2)^(1/2)*x/c^4*(((c^2*x^2+1)/c^2)^(3/2)*c^2-3*(-(-c^2*x+(-c^2)^(1/2))*(c^2*x+(-c^2)^(1/2))/c^4)^(1/2))/((c^2*x^2+1)/c^2)^(1/2)+1/2*x^2/c^3-1/2*ln(c^2*x^2+1)/c^5","A"
62,1,133,51,0.059000," ","int((1/c/x+(1+1/c^2/x^2)^(1/2))*x^3/(c^2*x^2+1),x)","\frac{\sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \left(x \sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\, c^{2}+\ln \left(x +\sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\right)-2 \ln \left(x +\sqrt{-\frac{\left(-c^{2} x +\sqrt{-c^{2}}\right) \left(c^{2} x +\sqrt{-c^{2}}\right)}{c^{4}}}\right)\right)}{2 \sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\, c^{4}}+\frac{x}{c^{3}}-\frac{\arctan \left(c x \right)}{c^{4}}"," ",0,"1/2*((c^2*x^2+1)/c^2/x^2)^(1/2)*x*(x*((c^2*x^2+1)/c^2)^(1/2)*c^2+ln(x+((c^2*x^2+1)/c^2)^(1/2))-2*ln(x+(-(-c^2*x+(-c^2)^(1/2))*(c^2*x+(-c^2)^(1/2))/c^4)^(1/2)))/((c^2*x^2+1)/c^2)^(1/2)/c^4+x/c^3-arctan(c*x)/c^4","B"
63,1,89,32,0.055000," ","int((1/c/x+(1+1/c^2/x^2)^(1/2))*x^2/(c^2*x^2+1),x)","\frac{\sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \sqrt{-\frac{\left(-c^{2} x +\sqrt{-c^{2}}\right) \left(c^{2} x +\sqrt{-c^{2}}\right)}{c^{4}}}}{\sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\, c^{2}}+\frac{\ln \left(c^{2} x^{2}+1\right)}{2 c^{3}}"," ",0,"((c^2*x^2+1)/c^2/x^2)^(1/2)*x*(-(-c^2*x+(-c^2)^(1/2))*(c^2*x+(-c^2)^(1/2))/c^4)^(1/2)/((c^2*x^2+1)/c^2)^(1/2)/c^2+1/2*ln(c^2*x^2+1)/c^3","B"
64,1,85,25,0.056000," ","int((1/c/x+(1+1/c^2/x^2)^(1/2))*x/(c^2*x^2+1),x)","\frac{\sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \ln \left(x +\sqrt{-\frac{\left(-c^{2} x +\sqrt{-c^{2}}\right) \left(c^{2} x +\sqrt{-c^{2}}\right)}{c^{4}}}\right)}{\sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\, c^{2}}+\frac{\arctan \left(c x \right)}{c^{2}}"," ",0,"((c^2*x^2+1)/c^2/x^2)^(1/2)*x*ln(x+(-(-c^2*x+(-c^2)^(1/2))*(c^2*x+(-c^2)^(1/2))/c^4)^(1/2))/((c^2*x^2+1)/c^2)^(1/2)/c^2+arctan(c*x)/c^2","B"
65,1,172,31,0.063000," ","int((1/c/x+(1+1/c^2/x^2)^(1/2))/(c^2*x^2+1),x)","\frac{\sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, x \left(\sqrt{\frac{1}{c^{2}}}\, \sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\, c^{2}-\sqrt{-\frac{\left(-c^{2} x +\sqrt{-c^{2}}\right) \left(c^{2} x +\sqrt{-c^{2}}\right)}{c^{4}}}\, c^{2} \sqrt{\frac{1}{c^{2}}}-\ln \left(\frac{2 \sqrt{\frac{1}{c^{2}}}\, \sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\, c^{2}+2}{c^{2} x}\right)\right)}{\sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\, c^{2} \sqrt{\frac{1}{c^{2}}}}+\frac{\ln \left(x \right)}{c}-\frac{\ln \left(c^{2} x^{2}+1\right)}{2 c}"," ",0,"((c^2*x^2+1)/c^2/x^2)^(1/2)*x*((1/c^2)^(1/2)*((c^2*x^2+1)/c^2)^(1/2)*c^2-(-(-c^2*x+(-c^2)^(1/2))*(c^2*x+(-c^2)^(1/2))/c^4)^(1/2)*c^2*(1/c^2)^(1/2)-ln(2*((1/c^2)^(1/2)*((c^2*x^2+1)/c^2)^(1/2)*c^2+1)/x/c^2))/((c^2*x^2+1)/c^2)^(1/2)/c^2/(1/c^2)^(1/2)+ln(x)/c-1/2*ln(c^2*x^2+1)/c","B"
66,1,154,28,0.066000," ","int((1/c/x+(1+1/c^2/x^2)^(1/2))/x/(c^2*x^2+1),x)","-\frac{\sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, \left(\left(\frac{c^{2} x^{2}+1}{c^{2}}\right)^{\frac{3}{2}} c^{2}-\sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\, x^{2} c^{2}+\ln \left(x +\sqrt{-\frac{\left(-c^{2} x +\sqrt{-c^{2}}\right) \left(c^{2} x +\sqrt{-c^{2}}\right)}{c^{4}}}\right) x -\ln \left(x +\sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\right) x \right)}{\sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}}-\frac{1}{c x}-\arctan \left(c x \right)"," ",0,"-((c^2*x^2+1)/c^2/x^2)^(1/2)*(((c^2*x^2+1)/c^2)^(3/2)*c^2-((c^2*x^2+1)/c^2)^(1/2)*x^2*c^2+ln(x+(-(-c^2*x+(-c^2)^(1/2))*(c^2*x+(-c^2)^(1/2))/c^4)^(1/2))*x-ln(x+((c^2*x^2+1)/c^2)^(1/2))*x)/((c^2*x^2+1)/c^2)^(1/2)-1/c/x-arctan(c*x)","B"
67,1,210,50,0.067000," ","int((1/c/x+(1+1/c^2/x^2)^(1/2))/x^2/(c^2*x^2+1),x)","-\frac{\sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, \left(c^{2} \left(\frac{c^{2} x^{2}+1}{c^{2}}\right)^{\frac{3}{2}} \sqrt{\frac{1}{c^{2}}}+\sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\, \sqrt{\frac{1}{c^{2}}}\, x^{2} c^{2}-2 \sqrt{\frac{1}{c^{2}}}\, \sqrt{-\frac{\left(-c^{2} x +\sqrt{-c^{2}}\right) \left(c^{2} x +\sqrt{-c^{2}}\right)}{c^{4}}}\, x^{2} c^{2}-\ln \left(\frac{2 \sqrt{\frac{1}{c^{2}}}\, \sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\, c^{2}+2}{c^{2} x}\right) x^{2}\right)}{2 x \sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\, \sqrt{\frac{1}{c^{2}}}}-\frac{1}{2 c \,x^{2}}-c \ln \left(x \right)+\frac{c \ln \left(c^{2} x^{2}+1\right)}{2}"," ",0,"-1/2*((c^2*x^2+1)/c^2/x^2)^(1/2)/x*(c^2*((c^2*x^2+1)/c^2)^(3/2)*(1/c^2)^(1/2)+((c^2*x^2+1)/c^2)^(1/2)*(1/c^2)^(1/2)*x^2*c^2-2*(1/c^2)^(1/2)*(-(-c^2*x+(-c^2)^(1/2))*(c^2*x+(-c^2)^(1/2))/c^4)^(1/2)*x^2*c^2-ln(2*((1/c^2)^(1/2)*((c^2*x^2+1)/c^2)^(1/2)*c^2+1)/x/c^2)*x^2)/((c^2*x^2+1)/c^2)^(1/2)/(1/c^2)^(1/2)-1/2/c/x^2-c*ln(x)+1/2*c*ln(c^2*x^2+1)","B"
68,1,193,53,0.071000," ","int((1/c/x+(1+1/c^2/x^2)^(1/2))/x^3/(c^2*x^2+1),x)","\frac{\sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, c^{2} \left(3 \left(\frac{c^{2} x^{2}+1}{c^{2}}\right)^{\frac{3}{2}} x^{2} c^{2}-3 \sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\, x^{4} c^{2}-3 \ln \left(x +\sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}\right) x^{3}+3 \ln \left(x +\sqrt{-\frac{\left(-c^{2} x +\sqrt{-c^{2}}\right) \left(c^{2} x +\sqrt{-c^{2}}\right)}{c^{4}}}\right) x^{3}-\left(\frac{c^{2} x^{2}+1}{c^{2}}\right)^{\frac{3}{2}}\right)}{3 x^{2} \sqrt{\frac{c^{2} x^{2}+1}{c^{2}}}}-\frac{1}{3 c \,x^{3}}+\frac{c}{x}+c^{2} \arctan \left(c x \right)"," ",0,"1/3*((c^2*x^2+1)/c^2/x^2)^(1/2)/x^2*c^2*(3*((c^2*x^2+1)/c^2)^(3/2)*x^2*c^2-3*((c^2*x^2+1)/c^2)^(1/2)*x^4*c^2-3*ln(x+((c^2*x^2+1)/c^2)^(1/2))*x^3+3*ln(x+(-(-c^2*x+(-c^2)^(1/2))*(c^2*x+(-c^2)^(1/2))/c^4)^(1/2))*x^3-((c^2*x^2+1)/c^2)^(3/2))/((c^2*x^2+1)/c^2)^(1/2)-1/3/c/x^3+c/x+c^2*arctan(c*x)","B"
69,0,0,79,0.546000," ","int(arccsch(b*x+a)/(a*d/b+d*x),x)","\int \frac{\mathrm{arccsch}\left(b x +a \right)}{\frac{a d}{b}+d x}\, dx"," ",0,"int(arccsch(b*x+a)/(a*d/b+d*x),x)","F"
70,1,63,40,0.085000," ","int(x^3*arccsch(b*x^4+a),x)","\frac{\mathrm{arccsch}\left(b \,x^{4}+a \right) x^{4}}{4}+\frac{\mathrm{arccsch}\left(b \,x^{4}+a \right) a}{4 b}+\frac{\ln \left(b \,x^{4}+a +\left(b \,x^{4}+a \right) \sqrt{1+\frac{1}{\left(b \,x^{4}+a \right)^{2}}}\right)}{4 b}"," ",0,"1/4*arccsch(b*x^4+a)*x^4+1/4/b*arccsch(b*x^4+a)*a+1/4/b*ln(b*x^4+a+(b*x^4+a)*(1+1/(b*x^4+a)^2)^(1/2))","A"
71,0,0,44,0.171000," ","int(x^(-1+n)*arccsch(a+b*x^n),x)","\int x^{-1+n} \mathrm{arccsch}\left(a +b \,x^{n}\right)\, dx"," ",0,"int(x^(-1+n)*arccsch(a+b*x^n),x)","F"