1,0,-1,203,0.000000,"\text{Not used}","int(x^3*acosh(1/(a + b*x)),x)","\int x^3\,\mathrm{acosh}\left(\frac{1}{a+b\,x}\right) \,d x","Not used",1,"int(x^3*acosh(1/(a + b*x)), x)","F"
2,0,-1,153,0.000000,"\text{Not used}","int(x^2*acosh(1/(a + b*x)),x)","\int x^2\,\mathrm{acosh}\left(\frac{1}{a+b\,x}\right) \,d x","Not used",1,"int(x^2*acosh(1/(a + b*x)), x)","F"
3,0,-1,107,0.000000,"\text{Not used}","int(x*acosh(1/(a + b*x)),x)","\int x\,\mathrm{acosh}\left(\frac{1}{a+b\,x}\right) \,d x","Not used",1,"int(x*acosh(1/(a + b*x)), x)","F"
4,1,43,44,2.161453,"\text{Not used}","int(acosh(1/(a + b*x)),x)","\frac{\mathrm{atan}\left(\frac{1}{\sqrt{\frac{1}{a+b\,x}-1}\,\sqrt{\frac{1}{a+b\,x}+1}}\right)+\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)\,\left(a+b\,x\right)}{b}","Not used",1,"(atan(1/((1/(a + b*x) - 1)^(1/2)*(1/(a + b*x) + 1)^(1/2))) + acosh(1/(a + b*x))*(a + b*x))/b","B"
5,0,-1,170,0.000000,"\text{Not used}","int(acosh(1/(a + b*x))/x,x)","\int \frac{\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)}{x} \,d x","Not used",1,"int(acosh(1/(a + b*x))/x, x)","F"
6,0,-1,70,0.000000,"\text{Not used}","int(acosh(1/(a + b*x))/x^2,x)","\int \frac{\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)}{x^2} \,d x","Not used",1,"int(acosh(1/(a + b*x))/x^2, x)","F"
7,0,-1,133,0.000000,"\text{Not used}","int(acosh(1/(a + b*x))/x^3,x)","\int \frac{\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)}{x^3} \,d x","Not used",1,"int(acosh(1/(a + b*x))/x^3, x)","F"
8,0,-1,197,0.000000,"\text{Not used}","int(acosh(1/(a + b*x))/x^4,x)","\int \frac{\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)}{x^4} \,d x","Not used",1,"int(acosh(1/(a + b*x))/x^4, x)","F"
9,0,-1,279,0.000000,"\text{Not used}","int(x^2*acosh(1/(a + b*x))^2,x)","\int x^2\,{\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)}^2 \,d x","Not used",1,"int(x^2*acosh(1/(a + b*x))^2, x)","F"
10,0,-1,149,0.000000,"\text{Not used}","int(x*acosh(1/(a + b*x))^2,x)","\int x\,{\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)}^2 \,d x","Not used",1,"int(x*acosh(1/(a + b*x))^2, x)","F"
11,0,-1,80,0.000000,"\text{Not used}","int(acosh(1/(a + b*x))^2,x)","\int {\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)}^2 \,d x","Not used",1,"int(acosh(1/(a + b*x))^2, x)","F"
12,0,-1,274,0.000000,"\text{Not used}","int(acosh(1/(a + b*x))^2/x,x)","\int \frac{{\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)}^2}{x} \,d x","Not used",1,"int(acosh(1/(a + b*x))^2/x, x)","F"
13,0,-1,224,0.000000,"\text{Not used}","int(acosh(1/(a + b*x))^2/x^2,x)","\int \frac{{\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)}^2}{x^2} \,d x","Not used",1,"int(acosh(1/(a + b*x))^2/x^2, x)","F"
14,0,-1,537,0.000000,"\text{Not used}","int(acosh(1/(a + b*x))^2/x^3,x)","\int \frac{{\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)}^2}{x^3} \,d x","Not used",1,"int(acosh(1/(a + b*x))^2/x^3, x)","F"
15,0,-1,260,0.000000,"\text{Not used}","int(x*acosh(1/(a + b*x))^3,x)","\int x\,{\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)}^3 \,d x","Not used",1,"int(x*acosh(1/(a + b*x))^3, x)","F"
16,0,-1,136,0.000000,"\text{Not used}","int(acosh(1/(a + b*x))^3,x)","\int {\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)}^3 \,d x","Not used",1,"int(acosh(1/(a + b*x))^3, x)","F"
17,0,-1,378,0.000000,"\text{Not used}","int(acosh(1/(a + b*x))^3/x,x)","\int \frac{{\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)}^3}{x} \,d x","Not used",1,"int(acosh(1/(a + b*x))^3/x, x)","F"
18,0,-1,330,0.000000,"\text{Not used}","int(acosh(1/(a + b*x))^3/x^2,x)","\int \frac{{\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)}^3}{x^2} \,d x","Not used",1,"int(acosh(1/(a + b*x))^3/x^2, x)","F"
19,0,-1,965,0.000000,"\text{Not used}","int(acosh(1/(a + b*x))^3/x^3,x)","\int \frac{{\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)}^3}{x^3} \,d x","Not used",1,"int(acosh(1/(a + b*x))^3/x^3, x)","F"
20,0,-1,164,0.000000,"\text{Not used}","int(x^3*acosh(1/x^(1/2)),x)","\int x^3\,\mathrm{acosh}\left(\frac{1}{\sqrt{x}}\right) \,d x","Not used",1,"int(x^3*acosh(1/x^(1/2)), x)","F"
21,0,-1,126,0.000000,"\text{Not used}","int(x^2*acosh(1/x^(1/2)),x)","\int x^2\,\mathrm{acosh}\left(\frac{1}{\sqrt{x}}\right) \,d x","Not used",1,"int(x^2*acosh(1/x^(1/2)), x)","F"
22,0,-1,88,0.000000,"\text{Not used}","int(x*acosh(1/x^(1/2)),x)","\int x\,\mathrm{acosh}\left(\frac{1}{\sqrt{x}}\right) \,d x","Not used",1,"int(x*acosh(1/x^(1/2)), x)","F"
23,0,-1,43,0.000000,"\text{Not used}","int(acosh(1/x^(1/2)),x)","\int \mathrm{acosh}\left(\frac{1}{\sqrt{x}}\right) \,d x","Not used",1,"int(acosh(1/x^(1/2)), x)","F"
24,0,-1,46,0.000000,"\text{Not used}","int(acosh(1/x^(1/2))/x,x)","\int \frac{\mathrm{acosh}\left(\frac{1}{\sqrt{x}}\right)}{x} \,d x","Not used",1,"int(acosh(1/x^(1/2))/x, x)","F"
25,1,40,98,2.150451,"\text{Not used}","int(acosh(1/x^(1/2))/x^2,x)","\frac{\sqrt{\frac{1}{\sqrt{x}}-1}\,\sqrt{\frac{1}{\sqrt{x}}+1}}{2\,\sqrt{x}}-\frac{2\,\mathrm{acosh}\left(\frac{1}{\sqrt{x}}\right)\,\left(\frac{1}{2\,\sqrt{x}}-\frac{\sqrt{x}}{4}\right)}{\sqrt{x}}","Not used",1,"((1/x^(1/2) - 1)^(1/2)*(1/x^(1/2) + 1)^(1/2))/(2*x^(1/2)) - (2*acosh(1/x^(1/2))*(1/(2*x^(1/2)) - x^(1/2)/4))/x^(1/2)","B"
26,0,-1,136,0.000000,"\text{Not used}","int(acosh(1/x^(1/2))/x^3,x)","\int \frac{\mathrm{acosh}\left(\frac{1}{\sqrt{x}}\right)}{x^3} \,d x","Not used",1,"int(acosh(1/x^(1/2))/x^3, x)","F"
27,0,-1,172,0.000000,"\text{Not used}","int(acosh(1/x^(1/2))/x^4,x)","\int \frac{\mathrm{acosh}\left(\frac{1}{\sqrt{x}}\right)}{x^4} \,d x","Not used",1,"int(acosh(1/x^(1/2))/x^4, x)","F"
28,1,17,21,1.348808,"\text{Not used}","int(acosh(x),x)","x\,\mathrm{acosh}\left(x\right)-\sqrt{x-1}\,\sqrt{x+1}","Not used",1,"x*acosh(x) - (x - 1)^(1/2)*(x + 1)^(1/2)","B"
29,0,-1,61,0.000000,"\text{Not used}","int(acosh(1/(a*x^n))/x,x)","\int \frac{\mathrm{acosh}\left(\frac{1}{a\,x^n}\right)}{x} \,d x","Not used",1,"int(acosh(1/(a*x^n))/x, x)","F"
30,0,-1,54,0.000000,"\text{Not used}","int(acosh(1/(a*x^5))/x,x)","\int \frac{\mathrm{acosh}\left(\frac{1}{a\,x^5}\right)}{x} \,d x","Not used",1,"int(acosh(1/(a*x^5))/x, x)","F"
31,0,-1,77,0.000000,"\text{Not used}","int(acosh(exp(- a - b*x)/c),x)","\int \mathrm{acosh}\left(\frac{{\mathrm{e}}^{-a-b\,x}}{c}\right) \,d x","Not used",1,"int(acosh(exp(- a - b*x)/c), x)","F"
32,1,75,64,1.469286,"\text{Not used}","int(x^4*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x)),x)","\frac{x^4}{4\,a}-\sqrt{\frac{1}{a\,x}-1}\,\left(\frac{2\,x\,\sqrt{\frac{1}{a\,x}+1}}{15\,a^4}-\frac{x^5\,\sqrt{\frac{1}{a\,x}+1}}{5}+\frac{x^3\,\sqrt{\frac{1}{a\,x}+1}}{15\,a^2}\right)","Not used",1,"x^4/(4*a) - (1/(a*x) - 1)^(1/2)*((2*x*(1/(a*x) + 1)^(1/2))/(15*a^4) - (x^5*(1/(a*x) + 1)^(1/2))/5 + (x^3*(1/(a*x) + 1)^(1/2))/(15*a^2))","B"
33,1,521,84,11.925358,"\text{Not used}","int(x^3*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x)),x)","\frac{\ln\left(\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}+1\right)\,1{}\mathrm{i}}{8\,a^4}-\frac{\frac{1{}\mathrm{i}}{1024\,a^4}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{128\,a^4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4\,11{}\mathrm{i}}{512\,a^4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6\,7{}\mathrm{i}}{256\,a^4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}-\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8\,239{}\mathrm{i}}{1024\,a^4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}\,1{}\mathrm{i}}{256\,a^4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}}{\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}+\frac{4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{6\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}+\frac{4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}}-\frac{\ln\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)\,1{}\mathrm{i}}{8\,a^4}+\frac{x^3}{3\,a}-\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{256\,a^4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}-\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4\,1{}\mathrm{i}}{1024\,a^4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}","Not used",1,"(log(((1/(a*x) - 1)^(1/2) - 1i)^2/((1/(a*x) + 1)^(1/2) - 1)^2 + 1)*1i)/(8*a^4) - (1i/(1024*a^4) + (((1/(a*x) - 1)^(1/2) - 1i)^2*1i)/(128*a^4*((1/(a*x) + 1)^(1/2) - 1)^2) + (((1/(a*x) - 1)^(1/2) - 1i)^4*11i)/(512*a^4*((1/(a*x) + 1)^(1/2) - 1)^4) + (((1/(a*x) - 1)^(1/2) - 1i)^6*7i)/(256*a^4*((1/(a*x) + 1)^(1/2) - 1)^6) - (((1/(a*x) - 1)^(1/2) - 1i)^8*239i)/(1024*a^4*((1/(a*x) + 1)^(1/2) - 1)^8) + (((1/(a*x) - 1)^(1/2) - 1i)^10*1i)/(256*a^4*((1/(a*x) + 1)^(1/2) - 1)^10))/(((1/(a*x) - 1)^(1/2) - 1i)^4/((1/(a*x) + 1)^(1/2) - 1)^4 + (4*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (6*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 + (4*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + ((1/(a*x) - 1)^(1/2) - 1i)^12/((1/(a*x) + 1)^(1/2) - 1)^12) - (log(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1))*1i)/(8*a^4) + x^3/(3*a) - (((1/(a*x) - 1)^(1/2) - 1i)^2*1i)/(256*a^4*((1/(a*x) + 1)^(1/2) - 1)^2) - (((1/(a*x) - 1)^(1/2) - 1i)^4*1i)/(1024*a^4*((1/(a*x) + 1)^(1/2) - 1)^4)","B"
34,1,55,38,1.433064,"\text{Not used}","int(x^2*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x)),x)","\sqrt{\frac{1}{a\,x}-1}\,\left(\frac{x^3\,\sqrt{\frac{1}{a\,x}+1}}{3}-\frac{x\,\sqrt{\frac{1}{a\,x}+1}}{3\,a^2}\right)+\frac{x^2}{2\,a}","Not used",1,"(1/(a*x) - 1)^(1/2)*((x^3*(1/(a*x) + 1)^(1/2))/3 - (x*(1/(a*x) + 1)^(1/2))/(3*a^2)) + x^2/(2*a)","B"
35,1,303,53,6.959459,"\text{Not used}","int(x*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x)),x)","\frac{\ln\left(\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}+1\right)\,1{}\mathrm{i}}{2\,a^2}-\frac{\ln\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)\,1{}\mathrm{i}}{2\,a^2}+\frac{\frac{1{}\mathrm{i}}{32\,a^2}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{16\,a^2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}-\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4\,15{}\mathrm{i}}{32\,a^2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}}{\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}+\frac{2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}}+\frac{x}{a}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{32\,a^2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}","Not used",1,"(log(((1/(a*x) - 1)^(1/2) - 1i)^2/((1/(a*x) + 1)^(1/2) - 1)^2 + 1)*1i)/(2*a^2) - (log(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1))*1i)/(2*a^2) + (1i/(32*a^2) + (((1/(a*x) - 1)^(1/2) - 1i)^2*1i)/(16*a^2*((1/(a*x) + 1)^(1/2) - 1)^2) - (((1/(a*x) - 1)^(1/2) - 1i)^4*15i)/(32*a^2*((1/(a*x) + 1)^(1/2) - 1)^4))/(((1/(a*x) - 1)^(1/2) - 1i)^2/((1/(a*x) + 1)^(1/2) - 1)^2 + (2*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 + ((1/(a*x) - 1)^(1/2) - 1i)^6/((1/(a*x) + 1)^(1/2) - 1)^6) + x/a + (((1/(a*x) - 1)^(1/2) - 1i)^2*1i)/(32*a^2*((1/(a*x) + 1)^(1/2) - 1)^2)","B"
36,1,182,24,2.983490,"\text{Not used}","int((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x),x)","\frac{\ln\left(x\right)}{a}-\frac{4\,\mathrm{atanh}\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)}{a}+\frac{\frac{5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}+1}{\frac{4\,a\,\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}{\sqrt{\frac{1}{a\,x}+1}-1}+\frac{4\,a\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^3}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^3}}+\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{4\,a\,\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}","Not used",1,"log(x)/a - (4*atanh(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1)))/a + ((5*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 + 1)/((4*a*((1/(a*x) - 1)^(1/2) - 1i))/((1/(a*x) + 1)^(1/2) - 1) + (4*a*((1/(a*x) - 1)^(1/2) - 1i)^3)/((1/(a*x) + 1)^(1/2) - 1)^3) + ((1/(a*x) - 1)^(1/2) - 1i)/(4*a*((1/(a*x) + 1)^(1/2) - 1))","B"
37,1,184,48,3.103571,"\text{Not used}","int(((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))/x,x)","-\ln\left(\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}+1\right)\,1{}\mathrm{i}+\ln\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)\,1{}\mathrm{i}-\frac{1}{a\,x}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2\,8{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2\,\left(1+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}\right)}","Not used",1,"log(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1))*1i - log(((1/(a*x) - 1)^(1/2) - 1i)^2/((1/(a*x) + 1)^(1/2) - 1)^2 + 1)*1i - 1/(a*x) + (((1/(a*x) - 1)^(1/2) - 1i)^2*8i)/(((1/(a*x) + 1)^(1/2) - 1)^2*(((1/(a*x) - 1)^(1/2) - 1i)^4/((1/(a*x) + 1)^(1/2) - 1)^4 - (2*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 + 1))","B"
38,1,71,35,1.841926,"\text{Not used}","int(((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))/x^2,x)","\frac{a\,\ln\left(\sqrt{\frac{1}{a\,x}-1}\,\sqrt{\frac{1}{a\,x}+1}+\frac{1}{a\,x}\right)}{2}-\frac{1}{2\,a\,x^2}-\frac{\sqrt{\frac{1}{a\,x}-1}\,\sqrt{\frac{1}{a\,x}+1}}{2\,x}","Not used",1,"(a*log((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x)))/2 - 1/(2*a*x^2) - ((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2))/(2*x)","B"
39,1,58,55,1.472958,"\text{Not used}","int(((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))/x^3,x)","-\frac{1}{3\,a\,x^3}-\frac{\left(\frac{\sqrt{\frac{1}{a\,x}+1}}{3}-\frac{a^2\,x^2\,\sqrt{\frac{1}{a\,x}+1}}{3}\right)\,\sqrt{\frac{1}{a\,x}-1}}{x^2}","Not used",1,"- 1/(3*a*x^3) - (((1/(a*x) + 1)^(1/2)/3 - (a^2*x^2*(1/(a*x) + 1)^(1/2))/3)*(1/(a*x) - 1)^(1/2))/x^2","B"
40,1,602,132,13.421277,"\text{Not used}","int(((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))/x^4,x)","\frac{a^3\,\mathrm{atanh}\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)}{2}-\frac{\frac{35\,a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^3}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^3}+\frac{273\,a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^5}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^5}+\frac{715\,a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^7}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^7}+\frac{715\,a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^9}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^9}+\frac{273\,a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{11}}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{11}}+\frac{35\,a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{13}}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{13}}+\frac{a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{15}}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{15}}+\frac{a^3\,\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}{2\,\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}}{1+\frac{28\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{56\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{70\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{56\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{28\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}-\frac{8\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{16}}-\frac{8\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}}-\frac{1}{4\,a\,x^4}","Not used",1,"(a^3*atanh(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1)))/2 - ((35*a^3*((1/(a*x) - 1)^(1/2) - 1i)^3)/(2*((1/(a*x) + 1)^(1/2) - 1)^3) + (273*a^3*((1/(a*x) - 1)^(1/2) - 1i)^5)/(2*((1/(a*x) + 1)^(1/2) - 1)^5) + (715*a^3*((1/(a*x) - 1)^(1/2) - 1i)^7)/(2*((1/(a*x) + 1)^(1/2) - 1)^7) + (715*a^3*((1/(a*x) - 1)^(1/2) - 1i)^9)/(2*((1/(a*x) + 1)^(1/2) - 1)^9) + (273*a^3*((1/(a*x) - 1)^(1/2) - 1i)^11)/(2*((1/(a*x) + 1)^(1/2) - 1)^11) + (35*a^3*((1/(a*x) - 1)^(1/2) - 1i)^13)/(2*((1/(a*x) + 1)^(1/2) - 1)^13) + (a^3*((1/(a*x) - 1)^(1/2) - 1i)^15)/(2*((1/(a*x) + 1)^(1/2) - 1)^15) + (a^3*((1/(a*x) - 1)^(1/2) - 1i))/(2*((1/(a*x) + 1)^(1/2) - 1)))/((28*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (8*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (56*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (70*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 - (56*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + (28*((1/(a*x) - 1)^(1/2) - 1i)^12)/((1/(a*x) + 1)^(1/2) - 1)^12 - (8*((1/(a*x) - 1)^(1/2) - 1i)^14)/((1/(a*x) + 1)^(1/2) - 1)^14 + ((1/(a*x) - 1)^(1/2) - 1i)^16/((1/(a*x) + 1)^(1/2) - 1)^16 + 1) - 1/(4*a*x^4)","B"
41,1,76,115,1.562365,"\text{Not used}","int(((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))/x^5,x)","\frac{\sqrt{\frac{1}{a\,x}-1}\,\left(\frac{a^2\,x^2\,\sqrt{\frac{1}{a\,x}+1}}{15}-\frac{\sqrt{\frac{1}{a\,x}+1}}{5}+\frac{2\,a^4\,x^4\,\sqrt{\frac{1}{a\,x}+1}}{15}\right)}{x^4}-\frac{1}{5\,a\,x^5}","Not used",1,"((1/(a*x) - 1)^(1/2)*((a^2*x^2*(1/(a*x) + 1)^(1/2))/15 - (1/(a*x) + 1)^(1/2)/5 + (2*a^4*x^4*(1/(a*x) + 1)^(1/2))/15))/x^4 - 1/(5*a*x^5)","B"
42,1,878,163,34.076177,"\text{Not used}","int(((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))/x^6,x)","\frac{\frac{35\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^3}{12\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^3}+\frac{757\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^5}{4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^5}+\frac{7339\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^7}{4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^7}+\frac{41929\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^9}{6\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^9}+\frac{25661\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{11}}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{11}}+\frac{25661\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{13}}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{13}}+\frac{41929\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{15}}{6\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{15}}+\frac{7339\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{17}}{4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{17}}+\frac{757\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{19}}{4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{19}}+\frac{35\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{21}}{12\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{21}}-\frac{a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{23}}{4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{23}}-\frac{a^5\,\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}{4\,\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}}{1+\frac{66\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{220\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{495\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{792\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{924\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}-\frac{792\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}+\frac{495\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{16}}-\frac{220\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{18}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{18}}+\frac{66\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{20}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{20}}-\frac{12\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{22}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{22}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{24}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{24}}-\frac{12\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}}+\frac{a^5\,\mathrm{atanh}\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)}{4}-\frac{1}{6\,a\,x^6}","Not used",1,"((35*a^5*((1/(a*x) - 1)^(1/2) - 1i)^3)/(12*((1/(a*x) + 1)^(1/2) - 1)^3) + (757*a^5*((1/(a*x) - 1)^(1/2) - 1i)^5)/(4*((1/(a*x) + 1)^(1/2) - 1)^5) + (7339*a^5*((1/(a*x) - 1)^(1/2) - 1i)^7)/(4*((1/(a*x) + 1)^(1/2) - 1)^7) + (41929*a^5*((1/(a*x) - 1)^(1/2) - 1i)^9)/(6*((1/(a*x) + 1)^(1/2) - 1)^9) + (25661*a^5*((1/(a*x) - 1)^(1/2) - 1i)^11)/(2*((1/(a*x) + 1)^(1/2) - 1)^11) + (25661*a^5*((1/(a*x) - 1)^(1/2) - 1i)^13)/(2*((1/(a*x) + 1)^(1/2) - 1)^13) + (41929*a^5*((1/(a*x) - 1)^(1/2) - 1i)^15)/(6*((1/(a*x) + 1)^(1/2) - 1)^15) + (7339*a^5*((1/(a*x) - 1)^(1/2) - 1i)^17)/(4*((1/(a*x) + 1)^(1/2) - 1)^17) + (757*a^5*((1/(a*x) - 1)^(1/2) - 1i)^19)/(4*((1/(a*x) + 1)^(1/2) - 1)^19) + (35*a^5*((1/(a*x) - 1)^(1/2) - 1i)^21)/(12*((1/(a*x) + 1)^(1/2) - 1)^21) - (a^5*((1/(a*x) - 1)^(1/2) - 1i)^23)/(4*((1/(a*x) + 1)^(1/2) - 1)^23) - (a^5*((1/(a*x) - 1)^(1/2) - 1i))/(4*((1/(a*x) + 1)^(1/2) - 1)))/((66*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (12*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (220*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (495*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 - (792*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + (924*((1/(a*x) - 1)^(1/2) - 1i)^12)/((1/(a*x) + 1)^(1/2) - 1)^12 - (792*((1/(a*x) - 1)^(1/2) - 1i)^14)/((1/(a*x) + 1)^(1/2) - 1)^14 + (495*((1/(a*x) - 1)^(1/2) - 1i)^16)/((1/(a*x) + 1)^(1/2) - 1)^16 - (220*((1/(a*x) - 1)^(1/2) - 1i)^18)/((1/(a*x) + 1)^(1/2) - 1)^18 + (66*((1/(a*x) - 1)^(1/2) - 1i)^20)/((1/(a*x) + 1)^(1/2) - 1)^20 - (12*((1/(a*x) - 1)^(1/2) - 1i)^22)/((1/(a*x) + 1)^(1/2) - 1)^22 + ((1/(a*x) - 1)^(1/2) - 1i)^24/((1/(a*x) + 1)^(1/2) - 1)^24 + 1) + (a^5*atanh(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1)))/4 - 1/(6*a*x^6)","B"
43,1,95,146,1.675340,"\text{Not used}","int(((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))/x^7,x)","\frac{\sqrt{\frac{1}{a\,x}-1}\,\left(\frac{a^2\,x^2\,\sqrt{\frac{1}{a\,x}+1}}{35}-\frac{\sqrt{\frac{1}{a\,x}+1}}{7}+\frac{4\,a^4\,x^4\,\sqrt{\frac{1}{a\,x}+1}}{105}+\frac{8\,a^6\,x^6\,\sqrt{\frac{1}{a\,x}+1}}{105}\right)}{x^6}-\frac{1}{7\,a\,x^7}","Not used",1,"((1/(a*x) - 1)^(1/2)*((a^2*x^2*(1/(a*x) + 1)^(1/2))/35 - (1/(a*x) + 1)^(1/2)/7 + (4*a^4*x^4*(1/(a*x) + 1)^(1/2))/105 + (8*a^6*x^6*(1/(a*x) + 1)^(1/2))/105))/x^6 - 1/(7*a*x^7)","B"
44,1,1155,194,38.559907,"\text{Not used}","int(((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))/x^8,x)","-\frac{-\frac{235\,a^7\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^3}{96\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^3}+\frac{1723\,a^7\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^5}{96\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^5}+\frac{72283\,a^7\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^7}{32\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^7}+\frac{848801\,a^7\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^9}{32\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^9}+\frac{4181067\,a^7\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{11}}{32\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{11}}+\frac{10994181\,a^7\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{13}}{32\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{13}}+\frac{17457599\,a^7\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{15}}{32\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{15}}+\frac{17457599\,a^7\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{17}}{32\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{17}}+\frac{10994181\,a^7\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{19}}{32\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{19}}+\frac{4181067\,a^7\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{21}}{32\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{21}}+\frac{848801\,a^7\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{23}}{32\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{23}}+\frac{72283\,a^7\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{25}}{32\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{25}}+\frac{1723\,a^7\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{27}}{96\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{27}}-\frac{235\,a^7\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{29}}{96\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{29}}+\frac{5\,a^7\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{31}}{32\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{31}}+\frac{5\,a^7\,\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}{32\,\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}}{1+\frac{120\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{560\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{1820\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{4368\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{8008\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}-\frac{11440\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}+\frac{12870\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{16}}-\frac{11440\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{18}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{18}}+\frac{8008\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{20}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{20}}-\frac{4368\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{22}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{22}}+\frac{1820\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{24}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{24}}-\frac{560\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{26}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{26}}+\frac{120\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{28}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{28}}-\frac{16\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{30}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{30}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{32}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{32}}-\frac{16\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}}+\frac{5\,a^7\,\mathrm{atanh}\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)}{32}-\frac{1}{8\,a\,x^8}","Not used",1,"(5*a^7*atanh(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1)))/32 - ((1723*a^7*((1/(a*x) - 1)^(1/2) - 1i)^5)/(96*((1/(a*x) + 1)^(1/2) - 1)^5) - (235*a^7*((1/(a*x) - 1)^(1/2) - 1i)^3)/(96*((1/(a*x) + 1)^(1/2) - 1)^3) + (72283*a^7*((1/(a*x) - 1)^(1/2) - 1i)^7)/(32*((1/(a*x) + 1)^(1/2) - 1)^7) + (848801*a^7*((1/(a*x) - 1)^(1/2) - 1i)^9)/(32*((1/(a*x) + 1)^(1/2) - 1)^9) + (4181067*a^7*((1/(a*x) - 1)^(1/2) - 1i)^11)/(32*((1/(a*x) + 1)^(1/2) - 1)^11) + (10994181*a^7*((1/(a*x) - 1)^(1/2) - 1i)^13)/(32*((1/(a*x) + 1)^(1/2) - 1)^13) + (17457599*a^7*((1/(a*x) - 1)^(1/2) - 1i)^15)/(32*((1/(a*x) + 1)^(1/2) - 1)^15) + (17457599*a^7*((1/(a*x) - 1)^(1/2) - 1i)^17)/(32*((1/(a*x) + 1)^(1/2) - 1)^17) + (10994181*a^7*((1/(a*x) - 1)^(1/2) - 1i)^19)/(32*((1/(a*x) + 1)^(1/2) - 1)^19) + (4181067*a^7*((1/(a*x) - 1)^(1/2) - 1i)^21)/(32*((1/(a*x) + 1)^(1/2) - 1)^21) + (848801*a^7*((1/(a*x) - 1)^(1/2) - 1i)^23)/(32*((1/(a*x) + 1)^(1/2) - 1)^23) + (72283*a^7*((1/(a*x) - 1)^(1/2) - 1i)^25)/(32*((1/(a*x) + 1)^(1/2) - 1)^25) + (1723*a^7*((1/(a*x) - 1)^(1/2) - 1i)^27)/(96*((1/(a*x) + 1)^(1/2) - 1)^27) - (235*a^7*((1/(a*x) - 1)^(1/2) - 1i)^29)/(96*((1/(a*x) + 1)^(1/2) - 1)^29) + (5*a^7*((1/(a*x) - 1)^(1/2) - 1i)^31)/(32*((1/(a*x) + 1)^(1/2) - 1)^31) + (5*a^7*((1/(a*x) - 1)^(1/2) - 1i))/(32*((1/(a*x) + 1)^(1/2) - 1)))/((120*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (16*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (560*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (1820*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 - (4368*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + (8008*((1/(a*x) - 1)^(1/2) - 1i)^12)/((1/(a*x) + 1)^(1/2) - 1)^12 - (11440*((1/(a*x) - 1)^(1/2) - 1i)^14)/((1/(a*x) + 1)^(1/2) - 1)^14 + (12870*((1/(a*x) - 1)^(1/2) - 1i)^16)/((1/(a*x) + 1)^(1/2) - 1)^16 - (11440*((1/(a*x) - 1)^(1/2) - 1i)^18)/((1/(a*x) + 1)^(1/2) - 1)^18 + (8008*((1/(a*x) - 1)^(1/2) - 1i)^20)/((1/(a*x) + 1)^(1/2) - 1)^20 - (4368*((1/(a*x) - 1)^(1/2) - 1i)^22)/((1/(a*x) + 1)^(1/2) - 1)^22 + (1820*((1/(a*x) - 1)^(1/2) - 1i)^24)/((1/(a*x) + 1)^(1/2) - 1)^24 - (560*((1/(a*x) - 1)^(1/2) - 1i)^26)/((1/(a*x) + 1)^(1/2) - 1)^26 + (120*((1/(a*x) - 1)^(1/2) - 1i)^28)/((1/(a*x) + 1)^(1/2) - 1)^28 - (16*((1/(a*x) - 1)^(1/2) - 1i)^30)/((1/(a*x) + 1)^(1/2) - 1)^30 + ((1/(a*x) - 1)^(1/2) - 1i)^32/((1/(a*x) + 1)^(1/2) - 1)^32 + 1) - 1/(8*a*x^8)","B"
45,1,521,111,14.445307,"\text{Not used}","int(x^7*((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2)),x)","\frac{\ln\left(\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^2}+1\right)\,1{}\mathrm{i}}{16\,a^4}-\frac{\frac{1{}\mathrm{i}}{2048\,a^4}+\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{256\,a^4\,{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^2}+\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^4\,11{}\mathrm{i}}{1024\,a^4\,{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^4}+\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^6\,7{}\mathrm{i}}{512\,a^4\,{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^6}-\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^8\,239{}\mathrm{i}}{2048\,a^4\,{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^8}+\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^{10}\,1{}\mathrm{i}}{512\,a^4\,{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^{10}}}{\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^4}+\frac{4\,{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^6}+\frac{6\,{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^8}+\frac{4\,{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^{10}}+\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^{12}}}-\frac{\ln\left(\frac{\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x^2}+1}-1}\right)\,1{}\mathrm{i}}{16\,a^4}+\frac{x^6}{6\,a}-\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{512\,a^4\,{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^2}-\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^4\,1{}\mathrm{i}}{2048\,a^4\,{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^4}","Not used",1,"(log(((1/(a*x^2) - 1)^(1/2) - 1i)^2/((1/(a*x^2) + 1)^(1/2) - 1)^2 + 1)*1i)/(16*a^4) - (1i/(2048*a^4) + (((1/(a*x^2) - 1)^(1/2) - 1i)^2*1i)/(256*a^4*((1/(a*x^2) + 1)^(1/2) - 1)^2) + (((1/(a*x^2) - 1)^(1/2) - 1i)^4*11i)/(1024*a^4*((1/(a*x^2) + 1)^(1/2) - 1)^4) + (((1/(a*x^2) - 1)^(1/2) - 1i)^6*7i)/(512*a^4*((1/(a*x^2) + 1)^(1/2) - 1)^6) - (((1/(a*x^2) - 1)^(1/2) - 1i)^8*239i)/(2048*a^4*((1/(a*x^2) + 1)^(1/2) - 1)^8) + (((1/(a*x^2) - 1)^(1/2) - 1i)^10*1i)/(512*a^4*((1/(a*x^2) + 1)^(1/2) - 1)^10))/(((1/(a*x^2) - 1)^(1/2) - 1i)^4/((1/(a*x^2) + 1)^(1/2) - 1)^4 + (4*((1/(a*x^2) - 1)^(1/2) - 1i)^6)/((1/(a*x^2) + 1)^(1/2) - 1)^6 + (6*((1/(a*x^2) - 1)^(1/2) - 1i)^8)/((1/(a*x^2) + 1)^(1/2) - 1)^8 + (4*((1/(a*x^2) - 1)^(1/2) - 1i)^10)/((1/(a*x^2) + 1)^(1/2) - 1)^10 + ((1/(a*x^2) - 1)^(1/2) - 1i)^12/((1/(a*x^2) + 1)^(1/2) - 1)^12) - (log(((1/(a*x^2) - 1)^(1/2) - 1i)/((1/(a*x^2) + 1)^(1/2) - 1))*1i)/(16*a^4) + x^6/(6*a) - (((1/(a*x^2) - 1)^(1/2) - 1i)^2*1i)/(512*a^4*((1/(a*x^2) + 1)^(1/2) - 1)^2) - (((1/(a*x^2) - 1)^(1/2) - 1i)^4*1i)/(2048*a^4*((1/(a*x^2) + 1)^(1/2) - 1)^4)","B"
46,0,-1,115,0.000000,"\text{Not used}","int(x^6*((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2)),x)","\int x^6\,\left(\sqrt{\frac{1}{a\,x^2}-1}\,\sqrt{\frac{1}{a\,x^2}+1}+\frac{1}{a\,x^2}\right) \,d x","Not used",1,"int(x^6*((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2)), x)","F"
47,1,57,58,1.638118,"\text{Not used}","int(x^5*((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2)),x)","\sqrt{\frac{1}{a\,x^2}-1}\,\left(\frac{x^6\,\sqrt{\frac{1}{a\,x^2}+1}}{6}-\frac{x^2\,\sqrt{\frac{1}{a\,x^2}+1}}{6\,a^2}\right)+\frac{x^4}{4\,a}","Not used",1,"(1/(a*x^2) - 1)^(1/2)*((x^6*(1/(a*x^2) + 1)^(1/2))/6 - (x^2*(1/(a*x^2) + 1)^(1/2))/(6*a^2)) + x^4/(4*a)","B"
48,0,-1,112,0.000000,"\text{Not used}","int(x^4*((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2)),x)","\int x^4\,\left(\sqrt{\frac{1}{a\,x^2}-1}\,\sqrt{\frac{1}{a\,x^2}+1}+\frac{1}{a\,x^2}\right) \,d x","Not used",1,"int(x^4*((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2)), x)","F"
49,1,306,63,7.139435,"\text{Not used}","int(x^3*((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2)),x)","\frac{\ln\left(\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^2}+1\right)\,1{}\mathrm{i}}{4\,a^2}-\frac{\ln\left(\frac{\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x^2}+1}-1}\right)\,1{}\mathrm{i}}{4\,a^2}+\frac{\frac{1{}\mathrm{i}}{64\,a^2}+\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{32\,a^2\,{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^2}-\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^4\,15{}\mathrm{i}}{64\,a^2\,{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^4}}{\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^2}+\frac{2\,{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^4}+\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^6}}+\frac{x^2}{2\,a}+\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{64\,a^2\,{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^2}","Not used",1,"(log(((1/(a*x^2) - 1)^(1/2) - 1i)^2/((1/(a*x^2) + 1)^(1/2) - 1)^2 + 1)*1i)/(4*a^2) - (log(((1/(a*x^2) - 1)^(1/2) - 1i)/((1/(a*x^2) + 1)^(1/2) - 1))*1i)/(4*a^2) + (1i/(64*a^2) + (((1/(a*x^2) - 1)^(1/2) - 1i)^2*1i)/(32*a^2*((1/(a*x^2) + 1)^(1/2) - 1)^2) - (((1/(a*x^2) - 1)^(1/2) - 1i)^4*15i)/(64*a^2*((1/(a*x^2) + 1)^(1/2) - 1)^4))/(((1/(a*x^2) - 1)^(1/2) - 1i)^2/((1/(a*x^2) + 1)^(1/2) - 1)^2 + (2*((1/(a*x^2) - 1)^(1/2) - 1i)^4)/((1/(a*x^2) + 1)^(1/2) - 1)^4 + ((1/(a*x^2) - 1)^(1/2) - 1i)^6/((1/(a*x^2) + 1)^(1/2) - 1)^6) + x^2/(2*a) + (((1/(a*x^2) - 1)^(1/2) - 1i)^2*1i)/(64*a^2*((1/(a*x^2) + 1)^(1/2) - 1)^2)","B"
50,0,-1,67,0.000000,"\text{Not used}","int(x^2*((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2)),x)","\int x^2\,\left(\sqrt{\frac{1}{a\,x^2}-1}\,\sqrt{\frac{1}{a\,x^2}+1}+\frac{1}{a\,x^2}\right) \,d x","Not used",1,"int(x^2*((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2)), x)","F"
51,1,182,68,3.202005,"\text{Not used}","int(x*((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2)),x)","\frac{\ln\left(x\right)}{a}-\frac{2\,\mathrm{atanh}\left(\frac{\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x^2}+1}-1}\right)}{a}+\frac{\frac{5\,{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^2}+1}{\frac{8\,a\,\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}{\sqrt{\frac{1}{a\,x^2}+1}-1}+\frac{8\,a\,{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^3}{{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^3}}+\frac{\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}}{8\,a\,\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}","Not used",1,"log(x)/a - (2*atanh(((1/(a*x^2) - 1)^(1/2) - 1i)/((1/(a*x^2) + 1)^(1/2) - 1)))/a + ((5*((1/(a*x^2) - 1)^(1/2) - 1i)^2)/((1/(a*x^2) + 1)^(1/2) - 1)^2 + 1)/((8*a*((1/(a*x^2) - 1)^(1/2) - 1i))/((1/(a*x^2) + 1)^(1/2) - 1) + (8*a*((1/(a*x^2) - 1)^(1/2) - 1i)^3)/((1/(a*x^2) + 1)^(1/2) - 1)^3) + ((1/(a*x^2) - 1)^(1/2) - 1i)/(8*a*((1/(a*x^2) + 1)^(1/2) - 1))","B"
52,0,-1,147,0.000000,"\text{Not used}","int((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2),x)","\int \sqrt{\frac{1}{a\,x^2}-1}\,\sqrt{\frac{1}{a\,x^2}+1}+\frac{1}{a\,x^2} \,d x","Not used",1,"int((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2), x)","F"
53,1,185,80,3.995982,"\text{Not used}","int(((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2))/x,x)","-\frac{\ln\left(\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^2}+1\right)\,1{}\mathrm{i}}{2}+\frac{\ln\left(\frac{\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x^2}+1}-1}\right)\,1{}\mathrm{i}}{2}-\frac{1}{2\,a\,x^2}+\frac{{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^2\,8{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^2\,\left(2+\frac{2\,{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^4}-\frac{4\,{\left(\sqrt{\frac{1}{a\,x^2}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x^2}+1}-1\right)}^2}\right)}","Not used",1,"(log(((1/(a*x^2) - 1)^(1/2) - 1i)/((1/(a*x^2) + 1)^(1/2) - 1))*1i)/2 - (log(((1/(a*x^2) - 1)^(1/2) - 1i)^2/((1/(a*x^2) + 1)^(1/2) - 1)^2 + 1)*1i)/2 - 1/(2*a*x^2) + (((1/(a*x^2) - 1)^(1/2) - 1i)^2*8i)/(((1/(a*x^2) + 1)^(1/2) - 1)^2*((2*((1/(a*x^2) - 1)^(1/2) - 1i)^4)/((1/(a*x^2) + 1)^(1/2) - 1)^4 - (4*((1/(a*x^2) - 1)^(1/2) - 1i)^2)/((1/(a*x^2) + 1)^(1/2) - 1)^2 + 2))","B"
54,0,-1,115,0.000000,"\text{Not used}","int(((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2))/x^2,x)","\int \frac{\sqrt{\frac{1}{a\,x^2}-1}\,\sqrt{\frac{1}{a\,x^2}+1}+\frac{1}{a\,x^2}}{x^2} \,d x","Not used",1,"int(((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2))/x^2, x)","F"
55,1,71,118,2.016673,"\text{Not used}","int(((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2))/x^3,x)","\frac{a\,\ln\left(\sqrt{\frac{1}{a\,x^2}-1}\,\sqrt{\frac{1}{a\,x^2}+1}+\frac{1}{a\,x^2}\right)}{4}-\frac{1}{4\,a\,x^4}-\frac{\sqrt{\frac{1}{a\,x^2}-1}\,\sqrt{\frac{1}{a\,x^2}+1}}{4\,x^2}","Not used",1,"(a*log((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2)))/4 - 1/(4*a*x^4) - ((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2))/(4*x^2)","B"
56,0,-1,109,0.000000,"\text{Not used}","int(x^m*((1/(a*x^3) - 1)^(1/2)*(1/(a*x^3) + 1)^(1/2) + 1/(a*x^3)),x)","\int x^m\,\left(\sqrt{\frac{1}{a\,x^3}-1}\,\sqrt{\frac{1}{a\,x^3}+1}+\frac{1}{a\,x^3}\right) \,d x","Not used",1,"int(x^m*((1/(a*x^3) - 1)^(1/2)*(1/(a*x^3) + 1)^(1/2) + 1/(a*x^3)), x)","F"
57,0,-1,107,0.000000,"\text{Not used}","int(x^m*((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2)),x)","\int x^m\,\left(\sqrt{\frac{1}{a\,x^2}-1}\,\sqrt{\frac{1}{a\,x^2}+1}+\frac{1}{a\,x^2}\right) \,d x","Not used",1,"int(x^m*((1/(a*x^2) - 1)^(1/2)*(1/(a*x^2) + 1)^(1/2) + 1/(a*x^2)), x)","F"
58,0,-1,91,0.000000,"\text{Not used}","int(x^m*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x)),x)","\int x^m\,\left(\sqrt{\frac{1}{a\,x}-1}\,\sqrt{\frac{1}{a\,x}+1}+\frac{1}{a\,x}\right) \,d x","Not used",1,"int(x^m*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x)), x)","F"
59,0,-1,109,0.000000,"\text{Not used}","int(x^m*((x/a - 1)^(1/2)*(x/a + 1)^(1/2) + x/a),x)","\int x^m\,\left(\sqrt{\frac{x}{a}-1}\,\sqrt{\frac{x}{a}+1}+\frac{x}{a}\right) \,d x","Not used",1,"int(x^m*((x/a - 1)^(1/2)*(x/a + 1)^(1/2) + x/a), x)","F"
60,0,-1,133,0.000000,"\text{Not used}","int(x^m*((1/(a*x^p) - 1)^(1/2)*(1/(a*x^p) + 1)^(1/2) + 1/(a*x^p)),x)","\int x^m\,\left(\sqrt{\frac{1}{a\,x^p}-1}\,\sqrt{\frac{1}{a\,x^p}+1}+\frac{1}{a\,x^p}\right) \,d x","Not used",1,"int(x^m*((1/(a*x^p) - 1)^(1/2)*(1/(a*x^p) + 1)^(1/2) + 1/(a*x^p)), x)","F"
61,0,-1,119,0.000000,"\text{Not used}","int(x*((1/(a*x^p) - 1)^(1/2)*(1/(a*x^p) + 1)^(1/2) + 1/(a*x^p)),x)","\int x\,\left(\sqrt{\frac{1}{a\,x^p}-1}\,\sqrt{\frac{1}{a\,x^p}+1}+\frac{1}{a\,x^p}\right) \,d x","Not used",1,"int(x*((1/(a*x^p) - 1)^(1/2)*(1/(a*x^p) + 1)^(1/2) + 1/(a*x^p)), x)","F"
62,0,-1,105,0.000000,"\text{Not used}","int((1/(a*x^p) - 1)^(1/2)*(1/(a*x^p) + 1)^(1/2) + 1/(a*x^p),x)","\int \sqrt{\frac{1}{a\,x^p}-1}\,\sqrt{\frac{1}{a\,x^p}+1}+\frac{1}{a\,x^p} \,d x","Not used",1,"int((1/(a*x^p) - 1)^(1/2)*(1/(a*x^p) + 1)^(1/2) + 1/(a*x^p), x)","F"
63,0,-1,87,0.000000,"\text{Not used}","int(((1/(a*x^p) - 1)^(1/2)*(1/(a*x^p) + 1)^(1/2) + 1/(a*x^p))/x,x)","\int \frac{\sqrt{\frac{1}{a\,x^p}-1}\,\sqrt{\frac{1}{a\,x^p}+1}+\frac{1}{a\,x^p}}{x} \,d x","Not used",1,"int(((1/(a*x^p) - 1)^(1/2)*(1/(a*x^p) + 1)^(1/2) + 1/(a*x^p))/x, x)","F"
64,0,-1,107,0.000000,"\text{Not used}","int(((1/(a*x^p) - 1)^(1/2)*(1/(a*x^p) + 1)^(1/2) + 1/(a*x^p))/x^2,x)","\int \frac{\sqrt{\frac{1}{a\,x^p}-1}\,\sqrt{\frac{1}{a\,x^p}+1}+\frac{1}{a\,x^p}}{x^2} \,d x","Not used",1,"int(((1/(a*x^p) - 1)^(1/2)*(1/(a*x^p) + 1)^(1/2) + 1/(a*x^p))/x^2, x)","F"
65,1,808,203,19.727214,"\text{Not used}","int(x^4*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))^2,x)","-\frac{\frac{1{}\mathrm{i}}{512\,a^5}-\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2\,3{}\mathrm{i}}{64\,a^5\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}-\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4\,53{}\mathrm{i}}{256\,a^5\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6\,87{}\mathrm{i}}{128\,a^5\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8\,657{}\mathrm{i}}{512\,a^5\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}\,121{}\mathrm{i}}{128\,a^5\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}}{\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}+\frac{4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{6\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}+\frac{4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}}-\frac{\frac{1{}\mathrm{i}}{16\,a^5}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{8\,a^5\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}-\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4\,15{}\mathrm{i}}{16\,a^5\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}}{\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}+\frac{2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}}-\frac{x^5\,\left(\frac{a^2}{5}-\frac{2}{3\,x^2}\right)}{a^2}-\frac{\ln\left(\frac{a\,\sqrt{\frac{1}{a\,x}+1}-\frac{1}{x}+a\,\sqrt{\frac{1}{a\,x}-1}\,1{}\mathrm{i}}{2\,a-2\,a\,\sqrt{\frac{1}{a\,x}+1}+\frac{1}{x}}\right)\,3{}\mathrm{i}}{4\,a^5}-\frac{\ln\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)\,1{}\mathrm{i}}{4\,a^5}+\frac{\ln\left(\frac{2\,a\,\sqrt{\frac{a+\frac{1}{x}}{a}}-\frac{2}{x}+a\,\sqrt{-\frac{a-\frac{1}{x}}{a}}\,2{}\mathrm{i}}{2\,a+\frac{1}{x}-2\,a\,\sqrt{\frac{a+\frac{1}{x}}{a}}}\right)\,1{}\mathrm{i}}{a^5}-\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{128\,a^5\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}-\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4\,1{}\mathrm{i}}{512\,a^5\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}","Not used",1,"(log((a*(-(a - 1/x)/a)^(1/2)*2i - 2/x + 2*a*((a + 1/x)/a)^(1/2))/(2*a + 1/x - 2*a*((a + 1/x)/a)^(1/2)))*1i)/a^5 - (1i/(512*a^5) - (((1/(a*x) - 1)^(1/2) - 1i)^2*3i)/(64*a^5*((1/(a*x) + 1)^(1/2) - 1)^2) - (((1/(a*x) - 1)^(1/2) - 1i)^4*53i)/(256*a^5*((1/(a*x) + 1)^(1/2) - 1)^4) + (((1/(a*x) - 1)^(1/2) - 1i)^6*87i)/(128*a^5*((1/(a*x) + 1)^(1/2) - 1)^6) + (((1/(a*x) - 1)^(1/2) - 1i)^8*657i)/(512*a^5*((1/(a*x) + 1)^(1/2) - 1)^8) + (((1/(a*x) - 1)^(1/2) - 1i)^10*121i)/(128*a^5*((1/(a*x) + 1)^(1/2) - 1)^10))/(((1/(a*x) - 1)^(1/2) - 1i)^4/((1/(a*x) + 1)^(1/2) - 1)^4 + (4*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (6*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 + (4*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + ((1/(a*x) - 1)^(1/2) - 1i)^12/((1/(a*x) + 1)^(1/2) - 1)^12) - (log(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1))*1i)/(4*a^5) - (1i/(16*a^5) + (((1/(a*x) - 1)^(1/2) - 1i)^2*1i)/(8*a^5*((1/(a*x) + 1)^(1/2) - 1)^2) - (((1/(a*x) - 1)^(1/2) - 1i)^4*15i)/(16*a^5*((1/(a*x) + 1)^(1/2) - 1)^4))/(((1/(a*x) - 1)^(1/2) - 1i)^2/((1/(a*x) + 1)^(1/2) - 1)^2 + (2*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 + ((1/(a*x) - 1)^(1/2) - 1i)^6/((1/(a*x) + 1)^(1/2) - 1)^6) - (log((a*(1/(a*x) - 1)^(1/2)*1i + a*(1/(a*x) + 1)^(1/2) - 1/x)/(2*a - 2*a*(1/(a*x) + 1)^(1/2) + 1/x))*3i)/(4*a^5) - (((1/(a*x) - 1)^(1/2) - 1i)^2*1i)/(128*a^5*((1/(a*x) + 1)^(1/2) - 1)^2) - (((1/(a*x) - 1)^(1/2) - 1i)^4*1i)/(512*a^5*((1/(a*x) + 1)^(1/2) - 1)^4) - (x^5*(a^2/5 - 2/(3*x^2)))/a^2","B"
66,1,63,117,1.750653,"\text{Not used}","int(x^3*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))^2,x)","\frac{x^2}{a^2}-\frac{x^4}{4}-\sqrt{\frac{1}{a\,x}-1}\,\left(\frac{2\,x\,\sqrt{\frac{1}{a\,x}+1}}{3\,a^3}-\frac{2\,x^3\,\sqrt{\frac{1}{a\,x}+1}}{3\,a}\right)","Not used",1,"x^2/a^2 - x^4/4 - (1/(a*x) - 1)^(1/2)*((2*x*(1/(a*x) + 1)^(1/2))/(3*a^3) - (2*x^3*(1/(a*x) + 1)^(1/2))/(3*a))","B"
67,1,420,169,8.956283,"\text{Not used}","int(x^2*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))^2,x)","\frac{\frac{1{}\mathrm{i}}{16\,a^3}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{8\,a^3\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}-\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4\,15{}\mathrm{i}}{16\,a^3\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}}{\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}+\frac{2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}}-\frac{x^3\,\left(\frac{a^2}{3}-\frac{2}{x^2}\right)}{a^2}+\frac{\left(\ln\left(\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}+1\right)-\ln\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)\right)\,2{}\mathrm{i}}{a^3}+\frac{\ln\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)\,1{}\mathrm{i}}{a^3}-\frac{\ln\left(\frac{2\,a\,\sqrt{\frac{a+\frac{1}{x}}{a}}-\frac{2}{x}+a\,\sqrt{-\frac{a-\frac{1}{x}}{a}}\,2{}\mathrm{i}}{2\,a+\frac{1}{x}-2\,a\,\sqrt{\frac{a+\frac{1}{x}}{a}}}\right)\,1{}\mathrm{i}}{a^3}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{16\,a^3\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}","Not used",1,"((log(((1/(a*x) - 1)^(1/2) - 1i)^2/((1/(a*x) + 1)^(1/2) - 1)^2 + 1) - log(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1)))*2i)/a^3 + (log(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1))*1i)/a^3 + (1i/(16*a^3) + (((1/(a*x) - 1)^(1/2) - 1i)^2*1i)/(8*a^3*((1/(a*x) + 1)^(1/2) - 1)^2) - (((1/(a*x) - 1)^(1/2) - 1i)^4*15i)/(16*a^3*((1/(a*x) + 1)^(1/2) - 1)^4))/(((1/(a*x) - 1)^(1/2) - 1i)^2/((1/(a*x) + 1)^(1/2) - 1)^2 + (2*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 + ((1/(a*x) - 1)^(1/2) - 1i)^6/((1/(a*x) + 1)^(1/2) - 1)^6) - (log((a*(-(a - 1/x)/a)^(1/2)*2i - 2/x + 2*a*((a + 1/x)/a)^(1/2))/(2*a + 1/x - 2*a*((a + 1/x)/a)^(1/2)))*1i)/a^3 + (((1/(a*x) - 1)^(1/2) - 1i)^2*1i)/(16*a^3*((1/(a*x) + 1)^(1/2) - 1)^2) - (x^3*(a^2/3 - 2/x^2))/a^2","B"
68,1,56,85,3.691701,"\text{Not used}","int(x*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))^2,x)","\frac{2\,x\,\sqrt{\frac{1}{a\,x}-1}\,\sqrt{\frac{1}{a\,x}+1}}{a}-\frac{2\,\mathrm{acosh}\left(\frac{1}{a\,x}\right)}{a^2}-\frac{x^2}{2}-\frac{2\,\ln\left(\frac{1}{x}\right)}{a^2}","Not used",1,"(2*x*(1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2))/a - (2*acosh(1/(a*x)))/a^2 - x^2/2 - (2*log(1/x))/a^2","B"
69,1,162,57,4.636217,"\text{Not used}","int(((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))^2,x)","-x-\frac{\left(\ln\left(\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}+1\right)-\ln\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)\right)\,2{}\mathrm{i}}{a}-\frac{2}{a^2\,x}+\frac{{\left(1+\sqrt{-\frac{a-\frac{1}{x}}{a}}\,1{}\mathrm{i}\right)}^2\,{\left(\sqrt{\frac{a+\frac{1}{x}}{a}}-1\right)}^2\,4{}\mathrm{i}}{a\,{\left(\sqrt{\frac{a+\frac{1}{x}}{a}}\,1{}\mathrm{i}+\sqrt{-\frac{a-\frac{1}{x}}{a}}-2{}\mathrm{i}\right)}^2}","Not used",1,"(((-(a - 1/x)/a)^(1/2)*1i + 1)^2*(((a + 1/x)/a)^(1/2) - 1)^2*4i)/(a*(((a + 1/x)/a)^(1/2)*1i + (-(a - 1/x)/a)^(1/2) - 2i)^2) - ((log(((1/(a*x) - 1)^(1/2) - 1i)^2/((1/(a*x) + 1)^(1/2) - 1)^2 + 1) - log(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1)))*2i)/a - 2/(a^2*x) - x","B"
70,1,323,86,11.205117,"\text{Not used}","int(((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))^2/x,x)","\ln\left(\frac{1}{x}\right)-4\,\mathrm{atanh}\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)+2\,\mathrm{acosh}\left(\frac{1}{a\,x}\right)+\frac{\frac{28\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^3}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^3}+\frac{28\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^5}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^5}+\frac{4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^7}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^7}+\frac{4\,\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}{\sqrt{\frac{1}{a\,x}+1}-1}}{1+\frac{6\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}}-\frac{1}{a^2\,x^2}","Not used",1,"log(1/x) - 4*atanh(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1)) + 2*acosh(1/(a*x)) + ((28*((1/(a*x) - 1)^(1/2) - 1i)^3)/((1/(a*x) + 1)^(1/2) - 1)^3 + (28*((1/(a*x) - 1)^(1/2) - 1i)^5)/((1/(a*x) + 1)^(1/2) - 1)^5 + (4*((1/(a*x) - 1)^(1/2) - 1i)^7)/((1/(a*x) + 1)^(1/2) - 1)^7 + (4*((1/(a*x) - 1)^(1/2) - 1i))/((1/(a*x) + 1)^(1/2) - 1))/((6*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (4*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (4*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + ((1/(a*x) - 1)^(1/2) - 1i)^8/((1/(a*x) + 1)^(1/2) - 1)^8 + 1) - 1/(a^2*x^2)","B"
71,1,67,57,1.795900,"\text{Not used}","int(((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))^2/x^2,x)","\frac{a^2\,x^2-\frac{2}{3}}{a^2\,x^3}-\frac{\sqrt{\frac{1}{a\,x}-1}\,\left(\frac{2\,\sqrt{\frac{1}{a\,x}+1}}{3\,a}-\frac{2\,a\,x^2\,\sqrt{\frac{1}{a\,x}+1}}{3}\right)}{x^2}","Not used",1,"(a^2*x^2 - 2/3)/(a^2*x^3) - ((1/(a*x) - 1)^(1/2)*((2*(1/(a*x) + 1)^(1/2))/(3*a) - (2*a*x^2*(1/(a*x) + 1)^(1/2))/3))/x^2","B"
72,1,885,147,46.991404,"\text{Not used}","int(((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))^2/x^3,x)","a^2\,\mathrm{atanh}\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)-\frac{\frac{28\,a^2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^3}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^3}+\frac{28\,a^2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^5}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^5}+\frac{4\,a^2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^7}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^7}+\frac{4\,a^2\,\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}{\sqrt{\frac{1}{a\,x}+1}-1}}{1+\frac{6\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}}-\frac{\frac{23\,a^2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^3}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^3}+\frac{333\,a^2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^5}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^5}+\frac{671\,a^2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^7}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^7}+\frac{671\,a^2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^9}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^9}+\frac{333\,a^2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{11}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{11}}+\frac{23\,a^2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{13}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{13}}-\frac{3\,a^2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{15}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{15}}-\frac{3\,a^2\,\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}{\sqrt{\frac{1}{a\,x}+1}-1}}{1+\frac{28\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{56\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{70\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{56\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{28\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}-\frac{8\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{16}}-\frac{8\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}}+\frac{1}{2\,x^2}-\frac{1}{2\,a^2\,x^4}","Not used",1,"a^2*atanh(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1)) - ((28*a^2*((1/(a*x) - 1)^(1/2) - 1i)^3)/((1/(a*x) + 1)^(1/2) - 1)^3 + (28*a^2*((1/(a*x) - 1)^(1/2) - 1i)^5)/((1/(a*x) + 1)^(1/2) - 1)^5 + (4*a^2*((1/(a*x) - 1)^(1/2) - 1i)^7)/((1/(a*x) + 1)^(1/2) - 1)^7 + (4*a^2*((1/(a*x) - 1)^(1/2) - 1i))/((1/(a*x) + 1)^(1/2) - 1))/((6*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (4*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (4*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + ((1/(a*x) - 1)^(1/2) - 1i)^8/((1/(a*x) + 1)^(1/2) - 1)^8 + 1) - ((23*a^2*((1/(a*x) - 1)^(1/2) - 1i)^3)/((1/(a*x) + 1)^(1/2) - 1)^3 + (333*a^2*((1/(a*x) - 1)^(1/2) - 1i)^5)/((1/(a*x) + 1)^(1/2) - 1)^5 + (671*a^2*((1/(a*x) - 1)^(1/2) - 1i)^7)/((1/(a*x) + 1)^(1/2) - 1)^7 + (671*a^2*((1/(a*x) - 1)^(1/2) - 1i)^9)/((1/(a*x) + 1)^(1/2) - 1)^9 + (333*a^2*((1/(a*x) - 1)^(1/2) - 1i)^11)/((1/(a*x) + 1)^(1/2) - 1)^11 + (23*a^2*((1/(a*x) - 1)^(1/2) - 1i)^13)/((1/(a*x) + 1)^(1/2) - 1)^13 - (3*a^2*((1/(a*x) - 1)^(1/2) - 1i)^15)/((1/(a*x) + 1)^(1/2) - 1)^15 - (3*a^2*((1/(a*x) - 1)^(1/2) - 1i))/((1/(a*x) + 1)^(1/2) - 1))/((28*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (8*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (56*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (70*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 - (56*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + (28*((1/(a*x) - 1)^(1/2) - 1i)^12)/((1/(a*x) + 1)^(1/2) - 1)^12 - (8*((1/(a*x) - 1)^(1/2) - 1i)^14)/((1/(a*x) + 1)^(1/2) - 1)^14 + ((1/(a*x) - 1)^(1/2) - 1i)^16/((1/(a*x) + 1)^(1/2) - 1)^16 + 1) + 1/(2*x^2) - 1/(2*a^2*x^4)","B"
73,1,86,183,1.938409,"\text{Not used}","int(((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))^2/x^4,x)","\frac{\sqrt{\frac{1}{a\,x}-1}\,\left(\frac{2\,a\,x^2\,\sqrt{\frac{1}{a\,x}+1}}{15}-\frac{2\,\sqrt{\frac{1}{a\,x}+1}}{5\,a}+\frac{4\,a^3\,x^4\,\sqrt{\frac{1}{a\,x}+1}}{15}\right)}{x^4}+\frac{\frac{a^2\,x^2}{3}-\frac{2}{5}}{a^2\,x^5}","Not used",1,"((1/(a*x) - 1)^(1/2)*((2*a*x^2*(1/(a*x) + 1)^(1/2))/15 - (2*(1/(a*x) + 1)^(1/2))/(5*a) + (4*a^3*x^4*(1/(a*x) + 1)^(1/2))/15))/x^4 + ((a^2*x^2)/3 - 2/5)/(a^2*x^5)","B"
74,1,2480,267,65.189392,"\text{Not used}","int(((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))^2/x^5,x)","\frac{-\frac{175\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^3}{6\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^3}+\frac{311\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^5}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^5}+\frac{8361\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^7}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^7}+\frac{42259\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^9}{3\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^9}+\frac{25295\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{11}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{11}}+\frac{25295\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{13}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{13}}+\frac{42259\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{15}}{3\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{15}}+\frac{8361\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{17}}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{17}}+\frac{311\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{19}}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{19}}-\frac{175\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{21}}{6\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{21}}+\frac{5\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{23}}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{23}}+\frac{5\,a^4\,\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}{2\,\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}}{1+\frac{66\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{220\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{495\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{792\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{924\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}-\frac{792\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}+\frac{495\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{16}}-\frac{220\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{18}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{18}}+\frac{66\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{20}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{20}}-\frac{12\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{22}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{22}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{24}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{24}}-\frac{12\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}}+\frac{a^4\,\mathrm{atanh}\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)}{2}-\frac{\frac{a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6\,4096{}\mathrm{i}}{3\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8\,8192{}\mathrm{i}}{3\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}+\frac{a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}\,24576{}\mathrm{i}}{5\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}\,8192{}\mathrm{i}}{3\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}+\frac{a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}\,4096{}\mathrm{i}}{3\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}}{1+\frac{45\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{120\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{210\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{252\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{210\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}-\frac{120\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}+\frac{45\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{16}}-\frac{10\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{18}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{18}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{20}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{20}}-\frac{10\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}}+\frac{\frac{a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6\,20480{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8\,40960{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}+\frac{a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}\,73728{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}\,40960{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}+\frac{a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}\,20480{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}}{15\,\left(1+\frac{45\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{120\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{210\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{252\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{210\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}-\frac{120\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}+\frac{45\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{16}}-\frac{10\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{18}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{18}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{20}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{20}}-\frac{10\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}\right)}+\frac{\frac{23\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^3}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^3}+\frac{333\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^5}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^5}+\frac{671\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^7}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^7}+\frac{671\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^9}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^9}+\frac{333\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{11}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{11}}+\frac{23\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{13}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{13}}-\frac{3\,a^4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{15}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{15}}-\frac{3\,a^4\,\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}{\sqrt{\frac{1}{a\,x}+1}-1}}{1+\frac{28\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{56\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{70\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{56\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{28\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}-\frac{8\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{16}}-\frac{8\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}}+\frac{1}{4\,x^4}-\frac{1}{3\,a^2\,x^6}","Not used",1,"((311*a^4*((1/(a*x) - 1)^(1/2) - 1i)^5)/(2*((1/(a*x) + 1)^(1/2) - 1)^5) - (175*a^4*((1/(a*x) - 1)^(1/2) - 1i)^3)/(6*((1/(a*x) + 1)^(1/2) - 1)^3) + (8361*a^4*((1/(a*x) - 1)^(1/2) - 1i)^7)/(2*((1/(a*x) + 1)^(1/2) - 1)^7) + (42259*a^4*((1/(a*x) - 1)^(1/2) - 1i)^9)/(3*((1/(a*x) + 1)^(1/2) - 1)^9) + (25295*a^4*((1/(a*x) - 1)^(1/2) - 1i)^11)/((1/(a*x) + 1)^(1/2) - 1)^11 + (25295*a^4*((1/(a*x) - 1)^(1/2) - 1i)^13)/((1/(a*x) + 1)^(1/2) - 1)^13 + (42259*a^4*((1/(a*x) - 1)^(1/2) - 1i)^15)/(3*((1/(a*x) + 1)^(1/2) - 1)^15) + (8361*a^4*((1/(a*x) - 1)^(1/2) - 1i)^17)/(2*((1/(a*x) + 1)^(1/2) - 1)^17) + (311*a^4*((1/(a*x) - 1)^(1/2) - 1i)^19)/(2*((1/(a*x) + 1)^(1/2) - 1)^19) - (175*a^4*((1/(a*x) - 1)^(1/2) - 1i)^21)/(6*((1/(a*x) + 1)^(1/2) - 1)^21) + (5*a^4*((1/(a*x) - 1)^(1/2) - 1i)^23)/(2*((1/(a*x) + 1)^(1/2) - 1)^23) + (5*a^4*((1/(a*x) - 1)^(1/2) - 1i))/(2*((1/(a*x) + 1)^(1/2) - 1)))/((66*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (12*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (220*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (495*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 - (792*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + (924*((1/(a*x) - 1)^(1/2) - 1i)^12)/((1/(a*x) + 1)^(1/2) - 1)^12 - (792*((1/(a*x) - 1)^(1/2) - 1i)^14)/((1/(a*x) + 1)^(1/2) - 1)^14 + (495*((1/(a*x) - 1)^(1/2) - 1i)^16)/((1/(a*x) + 1)^(1/2) - 1)^16 - (220*((1/(a*x) - 1)^(1/2) - 1i)^18)/((1/(a*x) + 1)^(1/2) - 1)^18 + (66*((1/(a*x) - 1)^(1/2) - 1i)^20)/((1/(a*x) + 1)^(1/2) - 1)^20 - (12*((1/(a*x) - 1)^(1/2) - 1i)^22)/((1/(a*x) + 1)^(1/2) - 1)^22 + ((1/(a*x) - 1)^(1/2) - 1i)^24/((1/(a*x) + 1)^(1/2) - 1)^24 + 1) + (a^4*atanh(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1)))/2 - ((a^4*((1/(a*x) - 1)^(1/2) - 1i)^6*4096i)/(3*((1/(a*x) + 1)^(1/2) - 1)^6) + (a^4*((1/(a*x) - 1)^(1/2) - 1i)^8*8192i)/(3*((1/(a*x) + 1)^(1/2) - 1)^8) + (a^4*((1/(a*x) - 1)^(1/2) - 1i)^10*24576i)/(5*((1/(a*x) + 1)^(1/2) - 1)^10) + (a^4*((1/(a*x) - 1)^(1/2) - 1i)^12*8192i)/(3*((1/(a*x) + 1)^(1/2) - 1)^12) + (a^4*((1/(a*x) - 1)^(1/2) - 1i)^14*4096i)/(3*((1/(a*x) + 1)^(1/2) - 1)^14))/((45*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (10*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (120*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (210*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 - (252*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + (210*((1/(a*x) - 1)^(1/2) - 1i)^12)/((1/(a*x) + 1)^(1/2) - 1)^12 - (120*((1/(a*x) - 1)^(1/2) - 1i)^14)/((1/(a*x) + 1)^(1/2) - 1)^14 + (45*((1/(a*x) - 1)^(1/2) - 1i)^16)/((1/(a*x) + 1)^(1/2) - 1)^16 - (10*((1/(a*x) - 1)^(1/2) - 1i)^18)/((1/(a*x) + 1)^(1/2) - 1)^18 + ((1/(a*x) - 1)^(1/2) - 1i)^20/((1/(a*x) + 1)^(1/2) - 1)^20 + 1) + ((a^4*((1/(a*x) - 1)^(1/2) - 1i)^6*20480i)/((1/(a*x) + 1)^(1/2) - 1)^6 + (a^4*((1/(a*x) - 1)^(1/2) - 1i)^8*40960i)/((1/(a*x) + 1)^(1/2) - 1)^8 + (a^4*((1/(a*x) - 1)^(1/2) - 1i)^10*73728i)/((1/(a*x) + 1)^(1/2) - 1)^10 + (a^4*((1/(a*x) - 1)^(1/2) - 1i)^12*40960i)/((1/(a*x) + 1)^(1/2) - 1)^12 + (a^4*((1/(a*x) - 1)^(1/2) - 1i)^14*20480i)/((1/(a*x) + 1)^(1/2) - 1)^14)/(15*((45*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (10*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (120*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (210*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 - (252*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + (210*((1/(a*x) - 1)^(1/2) - 1i)^12)/((1/(a*x) + 1)^(1/2) - 1)^12 - (120*((1/(a*x) - 1)^(1/2) - 1i)^14)/((1/(a*x) + 1)^(1/2) - 1)^14 + (45*((1/(a*x) - 1)^(1/2) - 1i)^16)/((1/(a*x) + 1)^(1/2) - 1)^16 - (10*((1/(a*x) - 1)^(1/2) - 1i)^18)/((1/(a*x) + 1)^(1/2) - 1)^18 + ((1/(a*x) - 1)^(1/2) - 1i)^20/((1/(a*x) + 1)^(1/2) - 1)^20 + 1)) + ((23*a^4*((1/(a*x) - 1)^(1/2) - 1i)^3)/((1/(a*x) + 1)^(1/2) - 1)^3 + (333*a^4*((1/(a*x) - 1)^(1/2) - 1i)^5)/((1/(a*x) + 1)^(1/2) - 1)^5 + (671*a^4*((1/(a*x) - 1)^(1/2) - 1i)^7)/((1/(a*x) + 1)^(1/2) - 1)^7 + (671*a^4*((1/(a*x) - 1)^(1/2) - 1i)^9)/((1/(a*x) + 1)^(1/2) - 1)^9 + (333*a^4*((1/(a*x) - 1)^(1/2) - 1i)^11)/((1/(a*x) + 1)^(1/2) - 1)^11 + (23*a^4*((1/(a*x) - 1)^(1/2) - 1i)^13)/((1/(a*x) + 1)^(1/2) - 1)^13 - (3*a^4*((1/(a*x) - 1)^(1/2) - 1i)^15)/((1/(a*x) + 1)^(1/2) - 1)^15 - (3*a^4*((1/(a*x) - 1)^(1/2) - 1i))/((1/(a*x) + 1)^(1/2) - 1))/((28*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (8*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (56*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (70*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 - (56*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + (28*((1/(a*x) - 1)^(1/2) - 1i)^12)/((1/(a*x) + 1)^(1/2) - 1)^12 - (8*((1/(a*x) - 1)^(1/2) - 1i)^14)/((1/(a*x) + 1)^(1/2) - 1)^14 + ((1/(a*x) - 1)^(1/2) - 1i)^16/((1/(a*x) + 1)^(1/2) - 1)^16 + 1) + 1/(4*x^4) - 1/(3*a^2*x^6)","B"
75,1,105,301,2.124706,"\text{Not used}","int(((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))^2/x^6,x)","\frac{\frac{a^2\,x^2}{5}-\frac{2}{7}}{a^2\,x^7}+\frac{\sqrt{\frac{1}{a\,x}-1}\,\left(\frac{2\,a\,x^2\,\sqrt{\frac{1}{a\,x}+1}}{35}-\frac{2\,\sqrt{\frac{1}{a\,x}+1}}{7\,a}+\frac{8\,a^3\,x^4\,\sqrt{\frac{1}{a\,x}+1}}{105}+\frac{16\,a^5\,x^6\,\sqrt{\frac{1}{a\,x}+1}}{105}\right)}{x^6}","Not used",1,"((a^2*x^2)/5 - 2/7)/(a^2*x^7) + ((1/(a*x) - 1)^(1/2)*((2*a*x^2*(1/(a*x) + 1)^(1/2))/35 - (2*(1/(a*x) + 1)^(1/2))/(7*a) + (8*a^3*x^4*(1/(a*x) + 1)^(1/2))/105 + (16*a^5*x^6*(1/(a*x) + 1)^(1/2))/105))/x^6","B"
76,1,73,147,2.138359,"\text{Not used}","int(x^4/((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x)),x)","\frac{x^4}{4\,a}+\frac{\sqrt{\frac{1}{a\,x}-1}\,\left(\frac{2\,x}{15\,a^4}+\frac{2}{15\,a^5}-\frac{x^5}{5}-\frac{x^4}{5\,a}+\frac{x^3}{15\,a^2}+\frac{x^2}{15\,a^3}\right)}{\sqrt{\frac{1}{a\,x}+1}}","Not used",1,"x^4/(4*a) + ((1/(a*x) - 1)^(1/2)*((2*x)/(15*a^4) + 2/(15*a^5) - x^5/5 - x^4/(5*a) + x^3/(15*a^2) + x^2/(15*a^3)))/(1/(a*x) + 1)^(1/2)","B"
77,1,795,163,19.825185,"\text{Not used}","int(x^3/((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x)),x)","\frac{\ln\left(\frac{a\,\sqrt{\frac{1}{a\,x}+1}-\frac{1}{x}+a\,\sqrt{\frac{1}{a\,x}-1}\,1{}\mathrm{i}}{2\,a-2\,a\,\sqrt{\frac{1}{a\,x}+1}+\frac{1}{x}}\right)\,3{}\mathrm{i}}{8\,a^4}+\frac{\frac{1{}\mathrm{i}}{1024\,a^4}-\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2\,3{}\mathrm{i}}{128\,a^4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}-\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4\,53{}\mathrm{i}}{512\,a^4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6\,87{}\mathrm{i}}{256\,a^4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8\,657{}\mathrm{i}}{1024\,a^4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}\,121{}\mathrm{i}}{256\,a^4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}}{\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}+\frac{4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{6\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}+\frac{4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}}+\frac{\ln\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)\,1{}\mathrm{i}}{8\,a^4}+\frac{\frac{1{}\mathrm{i}}{32\,a^4}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{16\,a^4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}-\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4\,15{}\mathrm{i}}{32\,a^4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}}{\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}+\frac{2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}}-\frac{\ln\left(\frac{2\,a\,\sqrt{\frac{a+\frac{1}{x}}{a}}-\frac{2}{x}+a\,\sqrt{-\frac{a-\frac{1}{x}}{a}}\,2{}\mathrm{i}}{2\,a+\frac{1}{x}-2\,a\,\sqrt{\frac{a+\frac{1}{x}}{a}}}\right)\,1{}\mathrm{i}}{2\,a^4}+\frac{x^3}{3\,a}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{256\,a^4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4\,1{}\mathrm{i}}{1024\,a^4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}","Not used",1,"(log((a*(1/(a*x) - 1)^(1/2)*1i + a*(1/(a*x) + 1)^(1/2) - 1/x)/(2*a - 2*a*(1/(a*x) + 1)^(1/2) + 1/x))*3i)/(8*a^4) + (1i/(1024*a^4) - (((1/(a*x) - 1)^(1/2) - 1i)^2*3i)/(128*a^4*((1/(a*x) + 1)^(1/2) - 1)^2) - (((1/(a*x) - 1)^(1/2) - 1i)^4*53i)/(512*a^4*((1/(a*x) + 1)^(1/2) - 1)^4) + (((1/(a*x) - 1)^(1/2) - 1i)^6*87i)/(256*a^4*((1/(a*x) + 1)^(1/2) - 1)^6) + (((1/(a*x) - 1)^(1/2) - 1i)^8*657i)/(1024*a^4*((1/(a*x) + 1)^(1/2) - 1)^8) + (((1/(a*x) - 1)^(1/2) - 1i)^10*121i)/(256*a^4*((1/(a*x) + 1)^(1/2) - 1)^10))/(((1/(a*x) - 1)^(1/2) - 1i)^4/((1/(a*x) + 1)^(1/2) - 1)^4 + (4*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (6*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 + (4*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + ((1/(a*x) - 1)^(1/2) - 1i)^12/((1/(a*x) + 1)^(1/2) - 1)^12) + (log(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1))*1i)/(8*a^4) + (1i/(32*a^4) + (((1/(a*x) - 1)^(1/2) - 1i)^2*1i)/(16*a^4*((1/(a*x) + 1)^(1/2) - 1)^2) - (((1/(a*x) - 1)^(1/2) - 1i)^4*15i)/(32*a^4*((1/(a*x) + 1)^(1/2) - 1)^4))/(((1/(a*x) - 1)^(1/2) - 1i)^2/((1/(a*x) + 1)^(1/2) - 1)^2 + (2*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 + ((1/(a*x) - 1)^(1/2) - 1i)^6/((1/(a*x) + 1)^(1/2) - 1)^6) - (log((a*(-(a - 1/x)/a)^(1/2)*2i - 2/x + 2*a*((a + 1/x)/a)^(1/2))/(2*a + 1/x - 2*a*((a + 1/x)/a)^(1/2)))*1i)/(2*a^4) + x^3/(3*a) + (((1/(a*x) - 1)^(1/2) - 1i)^2*1i)/(256*a^4*((1/(a*x) + 1)^(1/2) - 1)^2) + (((1/(a*x) - 1)^(1/2) - 1i)^4*1i)/(1024*a^4*((1/(a*x) + 1)^(1/2) - 1)^4)","B"
78,1,57,75,2.063270,"\text{Not used}","int(x^2/((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x)),x)","\frac{x^2}{2\,a}+\frac{\sqrt{\frac{1}{a\,x}-1}\,\left(\frac{x}{3\,a^2}+\frac{1}{3\,a^3}-\frac{x^3}{3}-\frac{x^2}{3\,a}\right)}{\sqrt{\frac{1}{a\,x}+1}}","Not used",1,"x^2/(2*a) + ((1/(a*x) - 1)^(1/2)*(x/(3*a^2) + 1/(3*a^3) - x^3/3 - x^2/(3*a)))/(1/(a*x) + 1)^(1/2)","B"
79,1,407,94,9.222959,"\text{Not used}","int(x/((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x)),x)","\frac{x}{a}-\frac{\ln\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)\,1{}\mathrm{i}}{2\,a^2}-\frac{\frac{1{}\mathrm{i}}{32\,a^2}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{16\,a^2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}-\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4\,15{}\mathrm{i}}{32\,a^2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}}{\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}+\frac{2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}}-\frac{\left(\ln\left(\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}+1\right)-\ln\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)\right)\,1{}\mathrm{i}}{a^2}+\frac{\ln\left(\frac{2\,a\,\sqrt{\frac{a+\frac{1}{x}}{a}}-\frac{2}{x}+a\,\sqrt{-\frac{a-\frac{1}{x}}{a}}\,2{}\mathrm{i}}{2\,a+\frac{1}{x}-2\,a\,\sqrt{\frac{a+\frac{1}{x}}{a}}}\right)\,1{}\mathrm{i}}{2\,a^2}-\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{32\,a^2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}","Not used",1,"x/a - (log(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1))*1i)/(2*a^2) - (1i/(32*a^2) + (((1/(a*x) - 1)^(1/2) - 1i)^2*1i)/(16*a^2*((1/(a*x) + 1)^(1/2) - 1)^2) - (((1/(a*x) - 1)^(1/2) - 1i)^4*15i)/(32*a^2*((1/(a*x) + 1)^(1/2) - 1)^4))/(((1/(a*x) - 1)^(1/2) - 1i)^2/((1/(a*x) + 1)^(1/2) - 1)^2 + (2*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 + ((1/(a*x) - 1)^(1/2) - 1i)^6/((1/(a*x) + 1)^(1/2) - 1)^6) - ((log(((1/(a*x) - 1)^(1/2) - 1i)^2/((1/(a*x) + 1)^(1/2) - 1)^2 + 1) - log(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1)))*1i)/a^2 + (log((a*(-(a - 1/x)/a)^(1/2)*2i - 2/x + 2*a*((a + 1/x)/a)^(1/2))/(2*a + 1/x - 2*a*((a + 1/x)/a)^(1/2)))*1i)/(2*a^2) - (((1/(a*x) - 1)^(1/2) - 1i)^2*1i)/(32*a^2*((1/(a*x) + 1)^(1/2) - 1)^2)","B"
80,1,47,65,4.168807,"\text{Not used}","int(1/((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x)),x)","\frac{\mathrm{acosh}\left(\frac{1}{a\,x}\right)}{a}-\frac{\ln\left(\frac{1}{x}\right)}{a}-x\,\sqrt{\frac{1}{a\,x}-1}\,\sqrt{\frac{1}{a\,x}+1}","Not used",1,"acosh(1/(a*x))/a - log(1/x)/a - x*(1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2)","B"
81,1,184,46,3.845228,"\text{Not used}","int(1/(x*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))),x)","\ln\left(\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}+1\right)\,1{}\mathrm{i}-\ln\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)\,1{}\mathrm{i}-\frac{1}{a\,x}-\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2\,8{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2\,\left(1+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}\right)}","Not used",1,"log(((1/(a*x) - 1)^(1/2) - 1i)^2/((1/(a*x) + 1)^(1/2) - 1)^2 + 1)*1i - log(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1))*1i - 1/(a*x) - (((1/(a*x) - 1)^(1/2) - 1i)^2*8i)/(((1/(a*x) + 1)^(1/2) - 1)^2*(((1/(a*x) - 1)^(1/2) - 1i)^4/((1/(a*x) + 1)^(1/2) - 1)^4 - (2*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 + 1))","B"
82,1,323,72,12.052626,"\text{Not used}","int(1/(x^2*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))),x)","2\,a\,\mathrm{atanh}\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)-a\,\mathrm{acosh}\left(\frac{1}{a\,x}\right)-\frac{1}{2\,a\,x^2}-\frac{a\,\left(\frac{14\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^3}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^3}+\frac{14\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^5}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^5}+\frac{2\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^7}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^7}+\frac{2\,\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}{\sqrt{\frac{1}{a\,x}+1}-1}\right)}{1+\frac{6\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}}","Not used",1,"2*a*atanh(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1)) - a*acosh(1/(a*x)) - 1/(2*a*x^2) - (a*((14*((1/(a*x) - 1)^(1/2) - 1i)^3)/((1/(a*x) + 1)^(1/2) - 1)^3 + (14*((1/(a*x) - 1)^(1/2) - 1i)^5)/((1/(a*x) + 1)^(1/2) - 1)^5 + (2*((1/(a*x) - 1)^(1/2) - 1i)^7)/((1/(a*x) + 1)^(1/2) - 1)^7 + (2*((1/(a*x) - 1)^(1/2) - 1i))/((1/(a*x) + 1)^(1/2) - 1)))/((6*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (4*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (4*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + ((1/(a*x) - 1)^(1/2) - 1i)^8/((1/(a*x) + 1)^(1/2) - 1)^8 + 1)","B"
83,1,58,116,2.137322,"\text{Not used}","int(1/(x^3*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))),x)","\frac{\sqrt{\frac{1}{a\,x}-1}\,\left(\frac{x}{3}-\frac{a\,x^2}{3}+\frac{1}{3\,a}-\frac{a^2\,x^3}{3}\right)}{x^3\,\sqrt{\frac{1}{a\,x}+1}}-\frac{1}{3\,a\,x^3}","Not used",1,"((1/(a*x) - 1)^(1/2)*(x/3 - (a*x^2)/3 + 1/(3*a) - (a^2*x^3)/3))/(x^3*(1/(a*x) + 1)^(1/2)) - 1/(3*a*x^3)","B"
84,1,1511,200,43.714153,"\text{Not used}","int(1/(x^4*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))),x)","-\frac{\frac{a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4\,64{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}+\frac{a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6\,128{}\mathrm{i}}{3\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8\,64{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}}{1+\frac{15\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{20\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{15\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{6\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}-\frac{6\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}}+\frac{\frac{a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4\,192{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}+\frac{a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6\,128{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8\,192{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}}{3\,\left(1+\frac{15\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{20\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{15\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{6\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}-\frac{6\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}\right)}-\frac{a^3\,\mathrm{atanh}\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)}{2}+\frac{\frac{14\,a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^3}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^3}+\frac{14\,a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^5}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^5}+\frac{2\,a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^7}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^7}+\frac{2\,a^3\,\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}{\sqrt{\frac{1}{a\,x}+1}-1}}{1+\frac{6\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{4\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}}+\frac{\frac{23\,a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^3}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^3}+\frac{333\,a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^5}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^5}+\frac{671\,a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^7}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^7}+\frac{671\,a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^9}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^9}+\frac{333\,a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{11}}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{11}}+\frac{23\,a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{13}}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{13}}-\frac{3\,a^3\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{15}}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{15}}-\frac{3\,a^3\,\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}{2\,\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}}{1+\frac{28\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{56\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{70\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{56\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{28\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}-\frac{8\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{16}}-\frac{8\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}}-\frac{1}{4\,a\,x^4}","Not used",1,"((a^3*((1/(a*x) - 1)^(1/2) - 1i)^4*192i)/((1/(a*x) + 1)^(1/2) - 1)^4 + (a^3*((1/(a*x) - 1)^(1/2) - 1i)^6*128i)/((1/(a*x) + 1)^(1/2) - 1)^6 + (a^3*((1/(a*x) - 1)^(1/2) - 1i)^8*192i)/((1/(a*x) + 1)^(1/2) - 1)^8)/(3*((15*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (6*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (20*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (15*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 - (6*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + ((1/(a*x) - 1)^(1/2) - 1i)^12/((1/(a*x) + 1)^(1/2) - 1)^12 + 1)) - ((a^3*((1/(a*x) - 1)^(1/2) - 1i)^4*64i)/((1/(a*x) + 1)^(1/2) - 1)^4 + (a^3*((1/(a*x) - 1)^(1/2) - 1i)^6*128i)/(3*((1/(a*x) + 1)^(1/2) - 1)^6) + (a^3*((1/(a*x) - 1)^(1/2) - 1i)^8*64i)/((1/(a*x) + 1)^(1/2) - 1)^8)/((15*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (6*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (20*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (15*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 - (6*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + ((1/(a*x) - 1)^(1/2) - 1i)^12/((1/(a*x) + 1)^(1/2) - 1)^12 + 1) - (a^3*atanh(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1)))/2 + ((14*a^3*((1/(a*x) - 1)^(1/2) - 1i)^3)/((1/(a*x) + 1)^(1/2) - 1)^3 + (14*a^3*((1/(a*x) - 1)^(1/2) - 1i)^5)/((1/(a*x) + 1)^(1/2) - 1)^5 + (2*a^3*((1/(a*x) - 1)^(1/2) - 1i)^7)/((1/(a*x) + 1)^(1/2) - 1)^7 + (2*a^3*((1/(a*x) - 1)^(1/2) - 1i))/((1/(a*x) + 1)^(1/2) - 1))/((6*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (4*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (4*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + ((1/(a*x) - 1)^(1/2) - 1i)^8/((1/(a*x) + 1)^(1/2) - 1)^8 + 1) + ((23*a^3*((1/(a*x) - 1)^(1/2) - 1i)^3)/(2*((1/(a*x) + 1)^(1/2) - 1)^3) + (333*a^3*((1/(a*x) - 1)^(1/2) - 1i)^5)/(2*((1/(a*x) + 1)^(1/2) - 1)^5) + (671*a^3*((1/(a*x) - 1)^(1/2) - 1i)^7)/(2*((1/(a*x) + 1)^(1/2) - 1)^7) + (671*a^3*((1/(a*x) - 1)^(1/2) - 1i)^9)/(2*((1/(a*x) + 1)^(1/2) - 1)^9) + (333*a^3*((1/(a*x) - 1)^(1/2) - 1i)^11)/(2*((1/(a*x) + 1)^(1/2) - 1)^11) + (23*a^3*((1/(a*x) - 1)^(1/2) - 1i)^13)/(2*((1/(a*x) + 1)^(1/2) - 1)^13) - (3*a^3*((1/(a*x) - 1)^(1/2) - 1i)^15)/(2*((1/(a*x) + 1)^(1/2) - 1)^15) - (3*a^3*((1/(a*x) - 1)^(1/2) - 1i))/(2*((1/(a*x) + 1)^(1/2) - 1)))/((28*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (8*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (56*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (70*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 - (56*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + (28*((1/(a*x) - 1)^(1/2) - 1i)^12)/((1/(a*x) + 1)^(1/2) - 1)^12 - (8*((1/(a*x) - 1)^(1/2) - 1i)^14)/((1/(a*x) + 1)^(1/2) - 1)^14 + ((1/(a*x) - 1)^(1/2) - 1i)^16/((1/(a*x) + 1)^(1/2) - 1)^16 + 1) - 1/(4*a*x^4)","B"
85,1,75,233,2.365940,"\text{Not used}","int(1/(x^5*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))),x)","-\frac{1}{5\,a\,x^5}-\frac{\sqrt{\frac{1}{a\,x}-1}\,\left(\frac{a\,x^2}{15}-\frac{x}{5}-\frac{1}{5\,a}+\frac{a^2\,x^3}{15}+\frac{2\,a^3\,x^4}{15}+\frac{2\,a^4\,x^5}{15}\right)}{x^5\,\sqrt{\frac{1}{a\,x}+1}}","Not used",1,"- 1/(5*a*x^5) - ((1/(a*x) - 1)^(1/2)*((a*x^2)/15 - x/5 - 1/(5*a) + (a^2*x^3)/15 + (2*a^3*x^4)/15 + (2*a^4*x^5)/15))/(x^5*(1/(a*x) + 1)^(1/2))","B"
86,1,2479,320,65.403762,"\text{Not used}","int(1/(x^6*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))),x)","-\frac{-\frac{175\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^3}{12\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^3}+\frac{311\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^5}{4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^5}+\frac{8361\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^7}{4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^7}+\frac{42259\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^9}{6\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^9}+\frac{25295\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{11}}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{11}}+\frac{25295\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{13}}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{13}}+\frac{42259\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{15}}{6\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{15}}+\frac{8361\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{17}}{4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{17}}+\frac{311\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{19}}{4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{19}}-\frac{175\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{21}}{12\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{21}}+\frac{5\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{23}}{4\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{23}}+\frac{5\,a^5\,\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}{4\,\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}}{1+\frac{66\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{220\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{495\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{792\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{924\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}-\frac{792\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}+\frac{495\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{16}}-\frac{220\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{18}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{18}}+\frac{66\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{20}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{20}}-\frac{12\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{22}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{22}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{24}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{24}}-\frac{12\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}}-\frac{a^5\,\mathrm{atanh}\left(\frac{\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{a\,x}+1}-1}\right)}{4}-\frac{\frac{a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6\,2048{}\mathrm{i}}{3\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8\,4096{}\mathrm{i}}{3\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}+\frac{a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}\,12288{}\mathrm{i}}{5\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}\,4096{}\mathrm{i}}{3\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}+\frac{a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}\,2048{}\mathrm{i}}{3\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}}{1+\frac{45\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{120\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{210\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{252\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{210\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}-\frac{120\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}+\frac{45\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{16}}-\frac{10\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{18}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{18}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{20}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{20}}-\frac{10\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}}+\frac{\frac{a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6\,10240{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8\,20480{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}+\frac{a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}\,36864{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}\,20480{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}+\frac{a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}\,10240{}\mathrm{i}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}}{15\,\left(1+\frac{45\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{120\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{210\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{252\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{210\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}-\frac{120\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}+\frac{45\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{16}}-\frac{10\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{18}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{18}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{20}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{20}}-\frac{10\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}\right)}-\frac{\frac{23\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^3}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^3}+\frac{333\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^5}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^5}+\frac{671\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^7}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^7}+\frac{671\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^9}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^9}+\frac{333\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{11}}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{11}}+\frac{23\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{13}}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{13}}-\frac{3\,a^5\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{15}}{2\,{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{15}}-\frac{3\,a^5\,\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}{2\,\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}}{1+\frac{28\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^4}-\frac{56\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^6}+\frac{70\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^8}-\frac{56\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{10}}+\frac{28\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{12}}-\frac{8\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{14}}+\frac{{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^{16}}-\frac{8\,{\left(\sqrt{\frac{1}{a\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{a\,x}+1}-1\right)}^2}}-\frac{1}{6\,a\,x^6}","Not used",1,"((a^5*((1/(a*x) - 1)^(1/2) - 1i)^6*10240i)/((1/(a*x) + 1)^(1/2) - 1)^6 + (a^5*((1/(a*x) - 1)^(1/2) - 1i)^8*20480i)/((1/(a*x) + 1)^(1/2) - 1)^8 + (a^5*((1/(a*x) - 1)^(1/2) - 1i)^10*36864i)/((1/(a*x) + 1)^(1/2) - 1)^10 + (a^5*((1/(a*x) - 1)^(1/2) - 1i)^12*20480i)/((1/(a*x) + 1)^(1/2) - 1)^12 + (a^5*((1/(a*x) - 1)^(1/2) - 1i)^14*10240i)/((1/(a*x) + 1)^(1/2) - 1)^14)/(15*((45*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (10*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (120*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (210*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 - (252*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + (210*((1/(a*x) - 1)^(1/2) - 1i)^12)/((1/(a*x) + 1)^(1/2) - 1)^12 - (120*((1/(a*x) - 1)^(1/2) - 1i)^14)/((1/(a*x) + 1)^(1/2) - 1)^14 + (45*((1/(a*x) - 1)^(1/2) - 1i)^16)/((1/(a*x) + 1)^(1/2) - 1)^16 - (10*((1/(a*x) - 1)^(1/2) - 1i)^18)/((1/(a*x) + 1)^(1/2) - 1)^18 + ((1/(a*x) - 1)^(1/2) - 1i)^20/((1/(a*x) + 1)^(1/2) - 1)^20 + 1)) - (a^5*atanh(((1/(a*x) - 1)^(1/2) - 1i)/((1/(a*x) + 1)^(1/2) - 1)))/4 - ((a^5*((1/(a*x) - 1)^(1/2) - 1i)^6*2048i)/(3*((1/(a*x) + 1)^(1/2) - 1)^6) + (a^5*((1/(a*x) - 1)^(1/2) - 1i)^8*4096i)/(3*((1/(a*x) + 1)^(1/2) - 1)^8) + (a^5*((1/(a*x) - 1)^(1/2) - 1i)^10*12288i)/(5*((1/(a*x) + 1)^(1/2) - 1)^10) + (a^5*((1/(a*x) - 1)^(1/2) - 1i)^12*4096i)/(3*((1/(a*x) + 1)^(1/2) - 1)^12) + (a^5*((1/(a*x) - 1)^(1/2) - 1i)^14*2048i)/(3*((1/(a*x) + 1)^(1/2) - 1)^14))/((45*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (10*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (120*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (210*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 - (252*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + (210*((1/(a*x) - 1)^(1/2) - 1i)^12)/((1/(a*x) + 1)^(1/2) - 1)^12 - (120*((1/(a*x) - 1)^(1/2) - 1i)^14)/((1/(a*x) + 1)^(1/2) - 1)^14 + (45*((1/(a*x) - 1)^(1/2) - 1i)^16)/((1/(a*x) + 1)^(1/2) - 1)^16 - (10*((1/(a*x) - 1)^(1/2) - 1i)^18)/((1/(a*x) + 1)^(1/2) - 1)^18 + ((1/(a*x) - 1)^(1/2) - 1i)^20/((1/(a*x) + 1)^(1/2) - 1)^20 + 1) - ((311*a^5*((1/(a*x) - 1)^(1/2) - 1i)^5)/(4*((1/(a*x) + 1)^(1/2) - 1)^5) - (175*a^5*((1/(a*x) - 1)^(1/2) - 1i)^3)/(12*((1/(a*x) + 1)^(1/2) - 1)^3) + (8361*a^5*((1/(a*x) - 1)^(1/2) - 1i)^7)/(4*((1/(a*x) + 1)^(1/2) - 1)^7) + (42259*a^5*((1/(a*x) - 1)^(1/2) - 1i)^9)/(6*((1/(a*x) + 1)^(1/2) - 1)^9) + (25295*a^5*((1/(a*x) - 1)^(1/2) - 1i)^11)/(2*((1/(a*x) + 1)^(1/2) - 1)^11) + (25295*a^5*((1/(a*x) - 1)^(1/2) - 1i)^13)/(2*((1/(a*x) + 1)^(1/2) - 1)^13) + (42259*a^5*((1/(a*x) - 1)^(1/2) - 1i)^15)/(6*((1/(a*x) + 1)^(1/2) - 1)^15) + (8361*a^5*((1/(a*x) - 1)^(1/2) - 1i)^17)/(4*((1/(a*x) + 1)^(1/2) - 1)^17) + (311*a^5*((1/(a*x) - 1)^(1/2) - 1i)^19)/(4*((1/(a*x) + 1)^(1/2) - 1)^19) - (175*a^5*((1/(a*x) - 1)^(1/2) - 1i)^21)/(12*((1/(a*x) + 1)^(1/2) - 1)^21) + (5*a^5*((1/(a*x) - 1)^(1/2) - 1i)^23)/(4*((1/(a*x) + 1)^(1/2) - 1)^23) + (5*a^5*((1/(a*x) - 1)^(1/2) - 1i))/(4*((1/(a*x) + 1)^(1/2) - 1)))/((66*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (12*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (220*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (495*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 - (792*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + (924*((1/(a*x) - 1)^(1/2) - 1i)^12)/((1/(a*x) + 1)^(1/2) - 1)^12 - (792*((1/(a*x) - 1)^(1/2) - 1i)^14)/((1/(a*x) + 1)^(1/2) - 1)^14 + (495*((1/(a*x) - 1)^(1/2) - 1i)^16)/((1/(a*x) + 1)^(1/2) - 1)^16 - (220*((1/(a*x) - 1)^(1/2) - 1i)^18)/((1/(a*x) + 1)^(1/2) - 1)^18 + (66*((1/(a*x) - 1)^(1/2) - 1i)^20)/((1/(a*x) + 1)^(1/2) - 1)^20 - (12*((1/(a*x) - 1)^(1/2) - 1i)^22)/((1/(a*x) + 1)^(1/2) - 1)^22 + ((1/(a*x) - 1)^(1/2) - 1i)^24/((1/(a*x) + 1)^(1/2) - 1)^24 + 1) - ((23*a^5*((1/(a*x) - 1)^(1/2) - 1i)^3)/(2*((1/(a*x) + 1)^(1/2) - 1)^3) + (333*a^5*((1/(a*x) - 1)^(1/2) - 1i)^5)/(2*((1/(a*x) + 1)^(1/2) - 1)^5) + (671*a^5*((1/(a*x) - 1)^(1/2) - 1i)^7)/(2*((1/(a*x) + 1)^(1/2) - 1)^7) + (671*a^5*((1/(a*x) - 1)^(1/2) - 1i)^9)/(2*((1/(a*x) + 1)^(1/2) - 1)^9) + (333*a^5*((1/(a*x) - 1)^(1/2) - 1i)^11)/(2*((1/(a*x) + 1)^(1/2) - 1)^11) + (23*a^5*((1/(a*x) - 1)^(1/2) - 1i)^13)/(2*((1/(a*x) + 1)^(1/2) - 1)^13) - (3*a^5*((1/(a*x) - 1)^(1/2) - 1i)^15)/(2*((1/(a*x) + 1)^(1/2) - 1)^15) - (3*a^5*((1/(a*x) - 1)^(1/2) - 1i))/(2*((1/(a*x) + 1)^(1/2) - 1)))/((28*((1/(a*x) - 1)^(1/2) - 1i)^4)/((1/(a*x) + 1)^(1/2) - 1)^4 - (8*((1/(a*x) - 1)^(1/2) - 1i)^2)/((1/(a*x) + 1)^(1/2) - 1)^2 - (56*((1/(a*x) - 1)^(1/2) - 1i)^6)/((1/(a*x) + 1)^(1/2) - 1)^6 + (70*((1/(a*x) - 1)^(1/2) - 1i)^8)/((1/(a*x) + 1)^(1/2) - 1)^8 - (56*((1/(a*x) - 1)^(1/2) - 1i)^10)/((1/(a*x) + 1)^(1/2) - 1)^10 + (28*((1/(a*x) - 1)^(1/2) - 1i)^12)/((1/(a*x) + 1)^(1/2) - 1)^12 - (8*((1/(a*x) - 1)^(1/2) - 1i)^14)/((1/(a*x) + 1)^(1/2) - 1)^14 + ((1/(a*x) - 1)^(1/2) - 1i)^16/((1/(a*x) + 1)^(1/2) - 1)^16 + 1) - 1/(6*a*x^6)","B"
87,1,91,353,2.593406,"\text{Not used}","int(1/(x^7*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x))),x)","-\frac{1}{7\,a\,x^7}-\frac{\sqrt{\frac{1}{a\,x}-1}\,\left(\frac{a\,x^2}{35}-\frac{x}{7}-\frac{1}{7\,a}+\frac{a^2\,x^3}{35}+\frac{4\,a^3\,x^4}{105}+\frac{4\,a^4\,x^5}{105}+\frac{8\,a^5\,x^6}{105}+\frac{8\,a^6\,x^7}{105}\right)}{x^7\,\sqrt{\frac{1}{a\,x}+1}}","Not used",1,"- 1/(7*a*x^7) - ((1/(a*x) - 1)^(1/2)*((a*x^2)/35 - x/7 - 1/(7*a) + (a^2*x^3)/35 + (4*a^3*x^4)/105 + (4*a^4*x^5)/105 + (8*a^5*x^6)/105 + (8*a^6*x^7)/105))/(x^7*(1/(a*x) + 1)^(1/2))","B"
88,0,-1,89,0.000000,"\text{Not used}","int(-(((1/(c*x) - 1)^(1/2)*(1/(c*x) + 1)^(1/2) + 1/(c*x))*(d*x)^m)/(c^2*x^2 - 1),x)","-\int \frac{\left(\sqrt{\frac{1}{c\,x}-1}\,\sqrt{\frac{1}{c\,x}+1}+\frac{1}{c\,x}\right)\,{\left(d\,x\right)}^m}{c^2\,x^2-1} \,d x","Not used",1,"-int((((1/(c*x) - 1)^(1/2)*(1/(c*x) + 1)^(1/2) + 1/(c*x))*(d*x)^m)/(c^2*x^2 - 1), x)","F"
89,1,76,88,2.602565,"\text{Not used}","int(-(x^4*((1/(c*x) - 1)^(1/2)*(1/(c*x) + 1)^(1/2) + 1/(c*x)))/(c^2*x^2 - 1),x)","-\frac{\ln\left(c^2\,x^2-1\right)+c^2\,x^2}{2\,c^5}-x^3\,\sqrt{\frac{1}{c\,x}-1}\,\left(\frac{\sqrt{\frac{1}{c\,x}+1}}{3\,c^2}+\frac{2\,\sqrt{\frac{1}{c\,x}+1}}{3\,c^4\,x^2}\right)","Not used",1,"- (log(c^2*x^2 - 1) + c^2*x^2)/(2*c^5) - x^3*(1/(c*x) - 1)^(1/2)*((1/(c*x) + 1)^(1/2)/(3*c^2) + (2*(1/(c*x) + 1)^(1/2))/(3*c^4*x^2))","B"
90,1,340,75,8.084818,"\text{Not used}","int(-(x^3*((1/(c*x) - 1)^(1/2)*(1/(c*x) + 1)^(1/2) + 1/(c*x)))/(c^2*x^2 - 1),x)","\frac{\mathrm{atanh}\left(c\,x\right)-c\,x}{c^4}-\frac{\ln\left(\frac{\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{c\,x}+1}-1}\right)\,1{}\mathrm{i}}{2\,c^4}-\frac{\frac{1{}\mathrm{i}}{32\,c^4}+\frac{{\left(\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{16\,c^4\,{\left(\sqrt{\frac{1}{c\,x}+1}-1\right)}^2}-\frac{{\left(\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}\right)}^4\,15{}\mathrm{i}}{32\,c^4\,{\left(\sqrt{\frac{1}{c\,x}+1}-1\right)}^4}}{\frac{{\left(\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{c\,x}+1}-1\right)}^2}+\frac{2\,{\left(\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{c\,x}+1}-1\right)}^4}+\frac{{\left(\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{c\,x}+1}-1\right)}^6}}+\frac{\ln\left(\frac{2\,c\,\sqrt{\frac{c+\frac{1}{x}}{c}}-\frac{2}{x}+c\,\sqrt{-\frac{c-\frac{1}{x}}{c}}\,2{}\mathrm{i}}{2\,c+\frac{1}{x}-2\,c\,\sqrt{\frac{c+\frac{1}{x}}{c}}}\right)\,1{}\mathrm{i}}{2\,c^4}-\frac{{\left(\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{32\,c^4\,{\left(\sqrt{\frac{1}{c\,x}+1}-1\right)}^2}","Not used",1,"(atanh(c*x) - c*x)/c^4 - (log(((1/(c*x) - 1)^(1/2) - 1i)/((1/(c*x) + 1)^(1/2) - 1))*1i)/(2*c^4) - (1i/(32*c^4) + (((1/(c*x) - 1)^(1/2) - 1i)^2*1i)/(16*c^4*((1/(c*x) + 1)^(1/2) - 1)^2) - (((1/(c*x) - 1)^(1/2) - 1i)^4*15i)/(32*c^4*((1/(c*x) + 1)^(1/2) - 1)^4))/(((1/(c*x) - 1)^(1/2) - 1i)^2/((1/(c*x) + 1)^(1/2) - 1)^2 + (2*((1/(c*x) - 1)^(1/2) - 1i)^4)/((1/(c*x) + 1)^(1/2) - 1)^4 + ((1/(c*x) - 1)^(1/2) - 1i)^6/((1/(c*x) + 1)^(1/2) - 1)^6) + (log((c*(-(c - 1/x)/c)^(1/2)*2i - 2/x + 2*c*((c + 1/x)/c)^(1/2))/(2*c + 1/x - 2*c*((c + 1/x)/c)^(1/2)))*1i)/(2*c^4) - (((1/(c*x) - 1)^(1/2) - 1i)^2*1i)/(32*c^4*((1/(c*x) + 1)^(1/2) - 1)^2)","B"
91,1,44,45,2.700087,"\text{Not used}","int(-(x^2*((1/(c*x) - 1)^(1/2)*(1/(c*x) + 1)^(1/2) + 1/(c*x)))/(c^2*x^2 - 1),x)","-\frac{\ln\left(c^2\,x^2-1\right)}{2\,c^3}-\frac{x\,\sqrt{\frac{1}{c\,x}-1}\,\sqrt{\frac{1}{c\,x}+1}}{c^2}","Not used",1,"- log(c^2*x^2 - 1)/(2*c^3) - (x*(1/(c*x) - 1)^(1/2)*(1/(c*x) + 1)^(1/2))/c^2","B"
92,1,84,37,3.567023,"\text{Not used}","int(-(x*((1/(c*x) - 1)^(1/2)*(1/(c*x) + 1)^(1/2) + 1/(c*x)))/(c^2*x^2 - 1),x)","\frac{\mathrm{atanh}\left(c\,x\right)}{c^2}+\frac{\left(\ln\left(\frac{{\left(\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{c\,x}+1}-1\right)}^2}+1\right)-\ln\left(\frac{\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{c\,x}+1}-1}\right)\right)\,1{}\mathrm{i}}{c^2}","Not used",1,"((log(((1/(c*x) - 1)^(1/2) - 1i)^2/((1/(c*x) + 1)^(1/2) - 1)^2 + 1) - log(((1/(c*x) - 1)^(1/2) - 1i)/((1/(c*x) + 1)^(1/2) - 1)))*1i)/c^2 + atanh(c*x)/c^2","B"
93,1,59,71,2.917960,"\text{Not used}","int(-((1/(c*x) - 1)^(1/2)*(1/(c*x) + 1)^(1/2) + 1/(c*x))/(c^2*x^2 - 1),x)","\frac{\ln\left(x\right)}{c}-\frac{4\,\mathrm{atanh}\left(\frac{\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{c\,x}+1}-1}\right)}{c}-\frac{\ln\left(3\,c^2\,x^2-3\right)}{2\,c}","Not used",1,"log(x)/c - (4*atanh(((1/(c*x) - 1)^(1/2) - 1i)/((1/(c*x) + 1)^(1/2) - 1)))/c - log(3*c^2*x^2 - 3)/(2*c)","B"
94,1,37,42,2.527606,"\text{Not used}","int(-((1/(c*x) - 1)^(1/2)*(1/(c*x) + 1)^(1/2) + 1/(c*x))/(x*(c^2*x^2 - 1)),x)","\mathrm{atanh}\left(c\,x\right)-\sqrt{\frac{1}{c\,x}-1}\,\sqrt{\frac{1}{c\,x}+1}-\frac{1}{c\,x}","Not used",1,"atanh(c*x) - (1/(c*x) - 1)^(1/2)*(1/(c*x) + 1)^(1/2) - 1/(c*x)","B"
95,1,331,108,14.525314,"\text{Not used}","int(-((1/(c*x) - 1)^(1/2)*(1/(c*x) + 1)^(1/2) + 1/(c*x))/(x^2*(c^2*x^2 - 1)),x)","c\,\ln\left(x\right)+\frac{\frac{2\,c\,\left(\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}\right)}{\sqrt{\frac{1}{c\,x}+1}-1}+\frac{14\,c\,{\left(\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}\right)}^3}{{\left(\sqrt{\frac{1}{c\,x}+1}-1\right)}^3}+\frac{14\,c\,{\left(\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}\right)}^5}{{\left(\sqrt{\frac{1}{c\,x}+1}-1\right)}^5}+\frac{2\,c\,{\left(\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}\right)}^7}{{\left(\sqrt{\frac{1}{c\,x}+1}-1\right)}^7}}{1+\frac{6\,{\left(\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\frac{1}{c\,x}+1}-1\right)}^4}-\frac{4\,{\left(\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\frac{1}{c\,x}+1}-1\right)}^6}+\frac{{\left(\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\frac{1}{c\,x}+1}-1\right)}^8}-\frac{4\,{\left(\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\frac{1}{c\,x}+1}-1\right)}^2}}-\frac{c\,\ln\left(c^2\,x^2-1\right)}{2}-2\,c\,\mathrm{atanh}\left(\frac{\sqrt{\frac{1}{c\,x}-1}-\mathrm{i}}{\sqrt{\frac{1}{c\,x}+1}-1}\right)-\frac{1}{2\,c\,x^2}","Not used",1,"((2*c*((1/(c*x) - 1)^(1/2) - 1i))/((1/(c*x) + 1)^(1/2) - 1) + (14*c*((1/(c*x) - 1)^(1/2) - 1i)^3)/((1/(c*x) + 1)^(1/2) - 1)^3 + (14*c*((1/(c*x) - 1)^(1/2) - 1i)^5)/((1/(c*x) + 1)^(1/2) - 1)^5 + (2*c*((1/(c*x) - 1)^(1/2) - 1i)^7)/((1/(c*x) + 1)^(1/2) - 1)^7)/((6*((1/(c*x) - 1)^(1/2) - 1i)^4)/((1/(c*x) + 1)^(1/2) - 1)^4 - (4*((1/(c*x) - 1)^(1/2) - 1i)^2)/((1/(c*x) + 1)^(1/2) - 1)^2 - (4*((1/(c*x) - 1)^(1/2) - 1i)^6)/((1/(c*x) + 1)^(1/2) - 1)^6 + ((1/(c*x) - 1)^(1/2) - 1i)^8/((1/(c*x) + 1)^(1/2) - 1)^8 + 1) - 2*c*atanh(((1/(c*x) - 1)^(1/2) - 1i)/((1/(c*x) + 1)^(1/2) - 1)) - (c*log(c^2*x^2 - 1))/2 + c*log(x) - 1/(2*c*x^2)","B"
96,1,75,85,2.505016,"\text{Not used}","int(-((1/(c*x) - 1)^(1/2)*(1/(c*x) + 1)^(1/2) + 1/(c*x))/(x^3*(c^2*x^2 - 1)),x)","c^2\,\mathrm{atanh}\left(c\,x\right)-\frac{\left(\frac{\sqrt{\frac{1}{c\,x}+1}}{3}+\frac{2\,c^2\,x^2\,\sqrt{\frac{1}{c\,x}+1}}{3}\right)\,\sqrt{\frac{1}{c\,x}-1}}{x^2}-\frac{c^2\,x^2+\frac{1}{3}}{c\,x^3}","Not used",1,"c^2*atanh(c*x) - (((1/(c*x) + 1)^(1/2)/3 + (2*c^2*x^2*(1/(c*x) + 1)^(1/2))/3)*(1/(c*x) - 1)^(1/2))/x^2 - (c^2*x^2 + 1/3)/(c*x^3)","B"
97,1,76,12,2.961753,"\text{Not used}","int(-(x*(a*x*((1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2) + 1/(a*x)) - 1))/(a^2*x^2 - 1),x)","\frac{\ln\left(\frac{1}{x}\right)}{a^2}-\frac{\ln\left(a+\frac{1}{x}\right)}{2\,a^2}-\frac{\ln\left(\frac{1}{x}-a\right)}{2\,a^2}+\frac{\ln\left(a^2\,x^2-1\right)}{2\,a^2}-\frac{x\,\sqrt{\frac{1}{a\,x}-1}\,\sqrt{\frac{1}{a\,x}+1}}{a}","Not used",1,"log(1/x)/a^2 - log(a + 1/x)/(2*a^2) - log(1/x - a)/(2*a^2) + log(a^2*x^2 - 1)/(2*a^2) - (x*(1/(a*x) - 1)^(1/2)*(1/(a*x) + 1)^(1/2))/a","B"
98,0,-1,61,0.000000,"\text{Not used}","int(acosh(1/(a + b*x))/(d*x + (a*d)/b),x)","\int \frac{\mathrm{acosh}\left(\frac{1}{a+b\,x}\right)}{d\,x+\frac{a\,d}{b}} \,d x","Not used",1,"int(acosh(1/(a + b*x))/(d*x + (a*d)/b), x)","F"
99,1,56,57,2.991684,"\text{Not used}","int(x^3*acosh(1/(a + b*x^4)),x)","\frac{\mathrm{atan}\left(\frac{1}{\sqrt{\frac{1}{b\,x^4+a}-1}\,\sqrt{\frac{1}{b\,x^4+a}+1}}\right)}{4\,b}+\frac{\mathrm{acosh}\left(\frac{1}{b\,x^4+a}\right)\,\left(b\,x^4+a\right)}{4\,b}","Not used",1,"atan(1/((1/(a + b*x^4) - 1)^(1/2)*(1/(a + b*x^4) + 1)^(1/2)))/(4*b) + (acosh(1/(a + b*x^4))*(a + b*x^4))/(4*b)","B"
100,1,54,58,2.349242,"\text{Not used}","int(x^(n - 1)*acosh(1/(a + b*x^n)),x)","\frac{\mathrm{atan}\left(\frac{1}{\sqrt{\frac{1}{a+b\,x^n}-1}\,\sqrt{\frac{1}{a+b\,x^n}+1}}\right)+\mathrm{acosh}\left(\frac{1}{a+b\,x^n}\right)\,\left(a+b\,x^n\right)}{b\,n}","Not used",1,"(atan(1/((1/(a + b*x^n) - 1)^(1/2)*(1/(a + b*x^n) + 1)^(1/2))) + acosh(1/(a + b*x^n))*(a + b*x^n))/(b*n)","B"