1,0,-1,147,0.000000,"\text{Not used}","int(x^3*asinh(1/(a + b*x)),x)","\int x^3\,\mathrm{asinh}\left(\frac{1}{a+b\,x}\right) \,d x","Not used",1,"int(x^3*asinh(1/(a + b*x)), x)","F"
2,0,-1,110,0.000000,"\text{Not used}","int(x^2*asinh(1/(a + b*x)),x)","\int x^2\,\mathrm{asinh}\left(\frac{1}{a+b\,x}\right) \,d x","Not used",1,"int(x^2*asinh(1/(a + b*x)), x)","F"
3,0,-1,75,0.000000,"\text{Not used}","int(x*asinh(1/(a + b*x)),x)","\int x\,\mathrm{asinh}\left(\frac{1}{a+b\,x}\right) \,d x","Not used",1,"int(x*asinh(1/(a + b*x)), x)","F"
4,0,-1,162,0.000000,"\text{Not used}","int(asinh(1/(a + b*x))/x,x)","\int \frac{\mathrm{asinh}\left(\frac{1}{a+b\,x}\right)}{x} \,d x","Not used",1,"int(asinh(1/(a + b*x))/x, x)","F"
5,0,-1,63,0.000000,"\text{Not used}","int(asinh(1/(a + b*x))/x^2,x)","\int \frac{\mathrm{asinh}\left(\frac{1}{a+b\,x}\right)}{x^2} \,d x","Not used",1,"int(asinh(1/(a + b*x))/x^2, x)","F"
6,0,-1,114,0.000000,"\text{Not used}","int(asinh(1/(a + b*x))/x^3,x)","\int \frac{\mathrm{asinh}\left(\frac{1}{a+b\,x}\right)}{x^3} \,d x","Not used",1,"int(asinh(1/(a + b*x))/x^3, x)","F"
7,0,-1,501,0.000000,"\text{Not used}","int((e + f*x)^3*(a + b*asinh(1/(c + d*x)))^2,x)","\int {\left(e+f\,x\right)}^3\,{\left(a+b\,\mathrm{asinh}\left(\frac{1}{c+d\,x}\right)\right)}^2 \,d x","Not used",1,"int((e + f*x)^3*(a + b*asinh(1/(c + d*x)))^2, x)","F"
8,0,-1,351,0.000000,"\text{Not used}","int((e + f*x)^2*(a + b*asinh(1/(c + d*x)))^2,x)","\int {\left(e+f\,x\right)}^2\,{\left(a+b\,\mathrm{asinh}\left(\frac{1}{c+d\,x}\right)\right)}^2 \,d x","Not used",1,"int((e + f*x)^2*(a + b*asinh(1/(c + d*x)))^2, x)","F"
9,0,-1,194,0.000000,"\text{Not used}","int((e + f*x)*(a + b*asinh(1/(c + d*x)))^2,x)","\int \left(e+f\,x\right)\,{\left(a+b\,\mathrm{asinh}\left(\frac{1}{c+d\,x}\right)\right)}^2 \,d x","Not used",1,"int((e + f*x)*(a + b*asinh(1/(c + d*x)))^2, x)","F"
10,0,-1,85,0.000000,"\text{Not used}","int((a + b*asinh(1/(c + d*x)))^2,x)","\int {\left(a+b\,\mathrm{asinh}\left(\frac{1}{c+d\,x}\right)\right)}^2 \,d x","Not used",1,"int((a + b*asinh(1/(c + d*x)))^2, x)","F"
11,0,-1,475,0.000000,"\text{Not used}","int((a + b*asinh(1/(c + d*x)))^2/(e + f*x),x)","\int \frac{{\left(a+b\,\mathrm{asinh}\left(\frac{1}{c+d\,x}\right)\right)}^2}{e+f\,x} \,d x","Not used",1,"int((a + b*asinh(1/(c + d*x)))^2/(e + f*x), x)","F"
12,0,-1,448,0.000000,"\text{Not used}","int((a + b*asinh(1/(c + d*x)))^2/(e + f*x)^2,x)","\int \frac{{\left(a+b\,\mathrm{asinh}\left(\frac{1}{c+d\,x}\right)\right)}^2}{{\left(e+f\,x\right)}^2} \,d x","Not used",1,"int((a + b*asinh(1/(c + d*x)))^2/(e + f*x)^2, x)","F"
13,0,-1,1024,0.000000,"\text{Not used}","int((a + b*asinh(1/(c + d*x)))^2/(e + f*x)^3,x)","\int \frac{{\left(a+b\,\mathrm{asinh}\left(\frac{1}{c+d\,x}\right)\right)}^2}{{\left(e+f\,x\right)}^3} \,d x","Not used",1,"int((a + b*asinh(1/(c + d*x)))^2/(e + f*x)^3, x)","F"
14,0,-1,114,0.000000,"\text{Not used}","int(x^3*asinh(1/x^(1/2)),x)","\int x^3\,\mathrm{asinh}\left(\frac{1}{\sqrt{x}}\right) \,d x","Not used",1,"int(x^3*asinh(1/x^(1/2)), x)","F"
15,0,-1,89,0.000000,"\text{Not used}","int(x^2*asinh(1/x^(1/2)),x)","\int x^2\,\mathrm{asinh}\left(\frac{1}{\sqrt{x}}\right) \,d x","Not used",1,"int(x^2*asinh(1/x^(1/2)), x)","F"
16,0,-1,64,0.000000,"\text{Not used}","int(x*asinh(1/x^(1/2)),x)","\int x\,\mathrm{asinh}\left(\frac{1}{\sqrt{x}}\right) \,d x","Not used",1,"int(x*asinh(1/x^(1/2)), x)","F"
17,1,18,31,2.570693,"\text{Not used}","int(asinh(1/x^(1/2)),x)","x\,\mathrm{asinh}\left(\frac{1}{\sqrt{x}}\right)+\sqrt{x}\,\sqrt{\frac{1}{x}+1}","Not used",1,"x*asinh(1/x^(1/2)) + x^(1/2)*(1/x + 1)^(1/2)","B"
18,0,-1,46,0.000000,"\text{Not used}","int(asinh(1/x^(1/2))/x,x)","\int \frac{\mathrm{asinh}\left(\frac{1}{\sqrt{x}}\right)}{x} \,d x","Not used",1,"int(asinh(1/x^(1/2))/x, x)","F"
19,1,33,63,2.221449,"\text{Not used}","int(asinh(1/x^(1/2))/x^2,x)","\frac{\sqrt{\frac{1}{x}+1}}{2\,\sqrt{x}}-\frac{2\,\mathrm{asinh}\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)^(1/2)/(2*x^(1/2)) - (2*asinh(1/x^(1/2))*(1/(2*x^(1/2)) + x^(1/2)/4))/x^(1/2)","B"
20,0,-1,90,0.000000,"\text{Not used}","int(asinh(1/x^(1/2))/x^3,x)","\int \frac{\mathrm{asinh}\left(\frac{1}{\sqrt{x}}\right)}{x^3} \,d x","Not used",1,"int(asinh(1/x^(1/2))/x^3, x)","F"
21,0,-1,115,0.000000,"\text{Not used}","int(asinh(1/x^(1/2))/x^4,x)","\int \frac{\mathrm{asinh}\left(\frac{1}{\sqrt{x}}\right)}{x^4} \,d x","Not used",1,"int(asinh(1/x^(1/2))/x^4, x)","F"
22,1,14,16,0.073937,"\text{Not used}","int(asinh(x),x)","x\,\mathrm{asinh}\left(x\right)-\sqrt{x^2+1}","Not used",1,"x*asinh(x) - (x^2 + 1)^(1/2)","B"
23,0,-1,61,0.000000,"\text{Not used}","int(asinh(1/(a*x^n))/x,x)","\int \frac{\mathrm{asinh}\left(\frac{1}{a\,x^n}\right)}{x} \,d x","Not used",1,"int(asinh(1/(a*x^n))/x, x)","F"
24,0,-1,54,0.000000,"\text{Not used}","int(asinh(1/(a*x^5))/x,x)","\int \frac{\mathrm{asinh}\left(\frac{1}{a\,x^5}\right)}{x} \,d x","Not used",1,"int(asinh(1/(a*x^5))/x, x)","F"
25,0,-1,77,0.000000,"\text{Not used}","int(asinh(exp(- a - b*x)/c),x)","\int \mathrm{asinh}\left(\frac{{\mathrm{e}}^{-a-b\,x}}{c}\right) \,d x","Not used",1,"int(asinh(exp(- a - b*x)/c), x)","F"
26,0,-1,52,0.000000,"\text{Not used}","int(x^m*((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x)),x)","\int x^m\,\left(\sqrt{\frac{1}{a^2\,x^2}+1}+\frac{1}{a\,x}\right) \,d x","Not used",1,"int(x^m*((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x)), x)","F"
27,1,41,54,2.177292,"\text{Not used}","int(x^4*((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x)),x)","\sqrt{\frac{1}{a^2\,x^2}+1}\,\left(\frac{x^5}{5}-\frac{2\,x}{15\,a^4}+\frac{x^3}{15\,a^2}\right)+\frac{x^4}{4\,a}","Not used",1,"(1/(a^2*x^2) + 1)^(1/2)*(x^5/5 - (2*x)/(15*a^4) + x^3/(15*a^2)) + x^4/(4*a)","B"
28,1,61,75,2.407398,"\text{Not used}","int(x^3*((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x)),x)","\frac{x^4\,\sqrt{\frac{1}{a^2\,x^2}+1}}{4}-\frac{\mathrm{atanh}\left(\sqrt{\frac{1}{a^2\,x^2}+1}\right)}{8\,a^4}+\frac{x^3}{3\,a}+\frac{x^2\,\sqrt{\frac{1}{a^2\,x^2}+1}}{8\,a^2}","Not used",1,"(x^4*(1/(a^2*x^2) + 1)^(1/2))/4 - atanh((1/(a^2*x^2) + 1)^(1/2))/(8*a^4) + x^3/(3*a) + (x^2*(1/(a^2*x^2) + 1)^(1/2))/(8*a^2)","B"
29,1,33,31,2.165823,"\text{Not used}","int(x^2*((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x)),x)","\left(\frac{x}{3\,a^2}+\frac{x^3}{3}\right)\,\sqrt{\frac{1}{a^2\,x^2}+1}+\frac{x^2}{2\,a}","Not used",1,"(x/(3*a^2) + x^3/3)*(1/(a^2*x^2) + 1)^(1/2) + x^2/(2*a)","B"
30,1,39,47,2.213983,"\text{Not used}","int(x*((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x)),x)","\frac{\mathrm{atanh}\left(\sqrt{\frac{1}{a^2\,x^2}+1}\right)}{2\,a^2}+\frac{x}{a}+\frac{x^2\,\sqrt{\frac{1}{a^2\,x^2}+1}}{2}","Not used",1,"atanh((1/(a^2*x^2) + 1)^(1/2))/(2*a^2) + x/a + (x^2*(1/(a^2*x^2) + 1)^(1/2))/2","B"
31,1,36,24,2.252868,"\text{Not used}","int((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x),x)","\frac{\ln\left(x\right)}{a}+x\,\sqrt{\frac{1}{a^2\,x^2}+1}+\frac{\mathrm{asin}\left(\frac{1{}\mathrm{i}}{a\,x}\right)\,1{}\mathrm{i}}{a}","Not used",1,"log(x)/a + (asin(1i/(a*x))*1i)/a + x*(1/(a^2*x^2) + 1)^(1/2)","B"
32,1,34,38,2.455562,"\text{Not used}","int(((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))/x,x)","\mathrm{atanh}\left(\sqrt{\frac{1}{a^2\,x^2}+1}\right)-\sqrt{\frac{1}{a^2\,x^2}+1}-\frac{1}{a\,x}","Not used",1,"atanh((1/(a^2*x^2) + 1)^(1/2)) - (1/(a^2*x^2) + 1)^(1/2) - 1/(a*x)","B"
33,1,42,40,2.556467,"\text{Not used}","int(((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))/x^2,x)","-\frac{\mathrm{asinh}\left(\frac{\sqrt{\frac{1}{a^2}}}{x}\right)}{2\,\sqrt{\frac{1}{a^2}}}-\frac{\sqrt{\frac{1}{a^2\,x^2}+1}}{2\,x}-\frac{1}{2\,a\,x^2}","Not used",1,"- asinh((1/a^2)^(1/2)/x)/(2*(1/a^2)^(1/2)) - (1/(a^2*x^2) + 1)^(1/2)/(2*x) - 1/(2*a*x^2)","B"
34,1,42,31,2.155356,"\text{Not used}","int(((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))/x^3,x)","-\frac{\frac{x\,\sqrt{\frac{1}{a^2\,x^2}+1}}{3}+\frac{1}{3\,a}}{x^3}-\frac{a^2\,\sqrt{\frac{1}{a^2\,x^2}+1}}{3}","Not used",1,"- ((x*(1/(a^2*x^2) + 1)^(1/2))/3 + 1/(3*a))/x^3 - (a^2*(1/(a^2*x^2) + 1)^(1/2))/3","B"
35,1,61,65,2.543349,"\text{Not used}","int(((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))/x^4,x)","\frac{\mathrm{asinh}\left(\frac{\sqrt{\frac{1}{a^2}}}{x}\right)}{8\,{\left(\frac{1}{a^2}\right)}^{3/2}}-\frac{\sqrt{\frac{1}{a^2\,x^2}+1}}{4\,x^3}-\frac{1}{4\,a\,x^4}-\frac{a^2\,\sqrt{\frac{1}{a^2\,x^2}+1}}{8\,x}","Not used",1,"asinh((1/a^2)^(1/2)/x)/(8*(1/a^2)^(3/2)) - (1/(a^2*x^2) + 1)^(1/2)/(4*x^3) - 1/(4*a*x^4) - (a^2*(1/(a^2*x^2) + 1)^(1/2))/(8*x)","B"
36,1,61,51,2.201124,"\text{Not used}","int(((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))/x^5,x)","\frac{2\,a^4\,\sqrt{\frac{1}{a^2\,x^2}+1}}{15}-\frac{\frac{x\,\sqrt{\frac{1}{a^2\,x^2}+1}}{5}+\frac{1}{5\,a}}{x^5}-\frac{a^2\,\sqrt{\frac{1}{a^2\,x^2}+1}}{15\,x^2}","Not used",1,"(2*a^4*(1/(a^2*x^2) + 1)^(1/2))/15 - ((x*(1/(a^2*x^2) + 1)^(1/2))/5 + 1/(5*a))/x^5 - (a^2*(1/(a^2*x^2) + 1)^(1/2))/(15*x^2)","B"
37,0,-1,59,0.000000,"\text{Not used}","int(x^m*((1/(a^2*x^4) + 1)^(1/2) + 1/(a*x^2)),x)","\int x^m\,\left(\sqrt{\frac{1}{a^2\,x^4}+1}+\frac{1}{a\,x^2}\right) \,d x","Not used",1,"int(x^m*((1/(a^2*x^4) + 1)^(1/2) + 1/(a*x^2)), x)","F"
38,0,-1,202,0.000000,"\text{Not used}","int(x^4*((1/(a^2*x^4) + 1)^(1/2) + 1/(a*x^2)),x)","\int x^4\,\left(\sqrt{\frac{1}{a^2\,x^4}+1}+\frac{1}{a\,x^2}\right) \,d x","Not used",1,"int(x^4*((1/(a^2*x^4) + 1)^(1/2) + 1/(a*x^2)), x)","F"
39,1,42,52,2.610147,"\text{Not used}","int(x^3*((1/(a^2*x^4) + 1)^(1/2) + 1/(a*x^2)),x)","\frac{\mathrm{atanh}\left(\sqrt{\frac{1}{a^2\,x^4}+1}\right)}{4\,a^2}+\frac{x^4\,\sqrt{\frac{1}{a^2\,x^4}+1}}{4}+\frac{x^2}{2\,a}","Not used",1,"atanh((1/(a^2*x^4) + 1)^(1/2))/(4*a^2) + (x^4*(1/(a^2*x^4) + 1)^(1/2))/4 + x^2/(2*a)","B"
40,0,-1,86,0.000000,"\text{Not used}","int(x^2*((1/(a^2*x^4) + 1)^(1/2) + 1/(a*x^2)),x)","\int x^2\,\left(\sqrt{\frac{1}{a^2\,x^4}+1}+\frac{1}{a\,x^2}\right) \,d x","Not used",1,"int(x^2*((1/(a^2*x^4) + 1)^(1/2) + 1/(a*x^2)), x)","F"
41,1,43,40,2.971455,"\text{Not used}","int(x*((1/(a^2*x^4) + 1)^(1/2) + 1/(a*x^2)),x)","\frac{x^2\,\sqrt{\frac{1}{a^2\,x^4}+1}}{2}-\frac{\ln\left(\frac{1}{x^2}\right)}{2\,a}-\frac{\mathrm{asinh}\left(\frac{\sqrt{\frac{1}{a^2}}}{x^2}\right)\,\sqrt{\frac{1}{a^2}}}{2}","Not used",1,"(x^2*(1/(a^2*x^4) + 1)^(1/2))/2 - log(1/x^2)/(2*a) - (asinh((1/a^2)^(1/2)/x^2)*(1/a^2)^(1/2))/2","B"
42,1,24,165,2.326374,"\text{Not used}","int((1/(a^2*x^4) + 1)^(1/2) + 1/(a*x^2),x)","x\,{{}}_2{\mathrm{F}}_1\left(-\frac{1}{2},-\frac{1}{4};\ \frac{3}{4};\ -\frac{1}{a^2\,x^4}\right)-\frac{1}{a\,x}","Not used",1,"x*hypergeom([-1/2, -1/4], 3/4, -1/(a^2*x^4)) - 1/(a*x)","B"
43,1,36,46,2.379509,"\text{Not used}","int(((1/(a^2*x^4) + 1)^(1/2) + 1/(a*x^2))/x,x)","\frac{\mathrm{atanh}\left(\sqrt{\frac{1}{a^2\,x^4}+1}\right)}{2}-\frac{\sqrt{\frac{1}{a^2\,x^4}+1}}{2}-\frac{1}{2\,a\,x^2}","Not used",1,"atanh((1/(a^2*x^4) + 1)^(1/2))/2 - (1/(a^2*x^4) + 1)^(1/2)/2 - 1/(2*a*x^2)","B"
44,1,27,91,2.368726,"\text{Not used}","int(((1/(a^2*x^4) + 1)^(1/2) + 1/(a*x^2))/x^2,x)","-\frac{{{}}_2{\mathrm{F}}_1\left(-\frac{1}{2},\frac{1}{4};\ \frac{5}{4};\ -\frac{1}{a^2\,x^4}\right)}{x}-\frac{1}{3\,a\,x^3}","Not used",1,"- hypergeom([-1/2, 1/4], 5/4, -1/(a^2*x^4))/x - 1/(3*a*x^3)","B"
45,1,42,42,2.829141,"\text{Not used}","int(((1/(a^2*x^4) + 1)^(1/2) + 1/(a*x^2))/x^3,x)","-\frac{\mathrm{asinh}\left(\frac{\sqrt{\frac{1}{a^2}}}{x^2}\right)}{4\,\sqrt{\frac{1}{a^2}}}-\frac{\sqrt{\frac{1}{a^2\,x^4}+1}}{4\,x^2}-\frac{1}{4\,a\,x^4}","Not used",1,"- asinh((1/a^2)^(1/2)/x^2)/(4*(1/a^2)^(1/2)) - (1/(a^2*x^4) + 1)^(1/2)/(4*x^2) - 1/(4*a*x^4)","B"
46,0,-1,181,0.000000,"\text{Not used}","int(((1/(a^2*x^4) + 1)^(1/2) + 1/(a*x^2))/x^4,x)","\int \frac{\sqrt{\frac{1}{a^2\,x^4}+1}+\frac{1}{a\,x^2}}{x^4} \,d x","Not used",1,"int(((1/(a^2*x^4) + 1)^(1/2) + 1/(a*x^2))/x^4, x)","F"
47,1,44,31,2.162666,"\text{Not used}","int(((1/(a^2*x^4) + 1)^(1/2) + 1/(a*x^2))/x^5,x)","-\frac{\frac{1}{6\,a}+\frac{x^2\,\sqrt{\frac{1}{a^2\,x^4}+1}}{6}}{x^6}-\frac{a^2\,\sqrt{\frac{1}{a^2\,x^4}+1}}{6}","Not used",1,"- (1/(6*a) + (x^2*(1/(a^2*x^4) + 1)^(1/2))/6)/x^6 - (a^2*(1/(a^2*x^4) + 1)^(1/2))/6","B"
48,0,-1,64,0.000000,"\text{Not used}","int(x^m*((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))^2,x)","\int x^m\,{\left(\sqrt{\frac{1}{a^2\,x^2}+1}+\frac{1}{a\,x}\right)}^2 \,d x","Not used",1,"int(x^m*((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))^2, x)","F"
49,1,73,85,2.170780,"\text{Not used}","int(x^4*((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))^2,x)","\frac{x^5}{5}+\frac{2\,x^3}{3\,a^2}+\frac{x^4\,\sqrt{\frac{1}{a^2\,x^2}+1}}{2\,a}+\frac{x^2\,\sqrt{\frac{1}{a^2\,x^2}+1}}{4\,a^3}+\frac{\mathrm{atan}\left(\sqrt{\frac{1}{a^2\,x^2}+1}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{4\,a^5}","Not used",1,"(atan((1/(a^2*x^2) + 1)^(1/2)*1i)*1i)/(4*a^5) + x^5/5 + (2*x^3)/(3*a^2) + (x^4*(1/(a^2*x^2) + 1)^(1/2))/(2*a) + (x^2*(1/(a^2*x^2) + 1)^(1/2))/(4*a^3)","B"
50,1,40,38,2.142317,"\text{Not used}","int(x^3*((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))^2,x)","\sqrt{\frac{1}{a^2\,x^2}+1}\,\left(\frac{2\,x}{3\,a^3}+\frac{2\,x^3}{3\,a}\right)+\frac{x^4}{4}+\frac{x^2}{a^2}","Not used",1,"(1/(a^2*x^2) + 1)^(1/2)*((2*x)/(3*a^3) + (2*x^3)/(3*a)) + x^4/4 + x^2/a^2","B"
51,1,51,52,2.128482,"\text{Not used}","int(x^2*((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))^2,x)","\frac{2\,x}{a^2}+\frac{x^3}{3}+\frac{x^2\,\sqrt{\frac{1}{a^2\,x^2}+1}}{a}-\frac{\mathrm{atan}\left(\sqrt{\frac{1}{a^2\,x^2}+1}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{a^3}","Not used",1,"(2*x)/a^2 - (atan((1/(a^2*x^2) + 1)^(1/2)*1i)*1i)/a^3 + x^3/3 + (x^2*(1/(a^2*x^2) + 1)^(1/2))/a","B"
52,1,52,43,2.198260,"\text{Not used}","int(x*((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))^2,x)","\frac{x^2}{2}-\frac{2\,\ln\left(\frac{1}{x}\right)}{a^2}+\frac{2\,x\,\sqrt{\frac{1}{a^2\,x^2}+1}}{a}-\frac{2\,\mathrm{asinh}\left(\frac{\sqrt{\frac{1}{a^2}}}{x}\right)}{a^3\,\sqrt{\frac{1}{a^2}}}","Not used",1,"x^2/2 - (2*log(1/x))/a^2 + (2*x*(1/(a^2*x^2) + 1)^(1/2))/a - (2*asinh((1/a^2)^(1/2)/x))/(a^3*(1/a^2)^(1/2))","B"
53,1,47,47,2.260129,"\text{Not used}","int(((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))^2,x)","x-\frac{2\,\sqrt{\frac{1}{a^2\,x^2}+1}}{a}-\frac{2}{a^2\,x}-\frac{\mathrm{atan}\left(\sqrt{\frac{1}{a^2\,x^2}+1}\,1{}\mathrm{i}\right)\,2{}\mathrm{i}}{a}","Not used",1,"x - (atan((1/(a^2*x^2) + 1)^(1/2)*1i)*2i)/a - (2*(1/(a^2*x^2) + 1)^(1/2))/a - 2/(a^2*x)","B"
54,1,44,38,2.249553,"\text{Not used}","int(((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))^2/x,x)","-\ln\left(\frac{1}{x}\right)-\mathrm{asinh}\left(\frac{1}{a\,x}\right)-\frac{1}{a^2\,x^2}-\frac{\sqrt{\frac{1}{a^2\,x^2}+1}}{a\,x}","Not used",1,"- log(1/x) - asinh(1/(a*x)) - 1/(a^2*x^2) - (1/(a^2*x^2) + 1)^(1/2)/(a*x)","B"
55,1,51,34,2.208191,"\text{Not used}","int(((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))^2/x^2,x)","-\frac{\frac{2}{3\,a^2}+\frac{2\,x\,\sqrt{\frac{1}{a^2\,x^2}+1}}{3\,a}}{x^3}-\frac{\frac{2\,a\,x\,\sqrt{\frac{1}{a^2\,x^2}+1}}{3}+1}{x}","Not used",1,"- (2/(3*a^2) + (2*x*(1/(a^2*x^2) + 1)^(1/2))/(3*a))/x^3 - ((2*a*x*(1/(a^2*x^2) + 1)^(1/2))/3 + 1)/x","B"
56,1,68,73,2.305997,"\text{Not used}","int(((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))^2/x^3,x)","\frac{a\,\mathrm{asinh}\left(\frac{\sqrt{\frac{1}{a^2}}}{x}\right)}{4\,\sqrt{\frac{1}{a^2}}}-\frac{1}{2\,a^2\,x^4}-\frac{a\,\sqrt{\frac{1}{a^2\,x^2}+1}}{4\,x}-\frac{1}{2\,x^2}-\frac{\sqrt{\frac{1}{a^2\,x^2}+1}}{2\,a\,x^3}","Not used",1,"(a*asinh((1/a^2)^(1/2)/x))/(4*(1/a^2)^(1/2)) - 1/(2*a^2*x^4) - (a*(1/(a^2*x^2) + 1)^(1/2))/(4*x) - 1/(2*x^2) - (1/(a^2*x^2) + 1)^(1/2)/(2*a*x^3)","B"
57,1,67,58,2.263011,"\text{Not used}","int(((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))^2/x^4,x)","\frac{4\,a^3\,\sqrt{\frac{1}{a^2\,x^2}+1}}{15}-\frac{\frac{2\,a\,x\,\sqrt{\frac{1}{a^2\,x^2}+1}}{15}+\frac{1}{3}}{x^3}-\frac{\frac{2}{5\,a^2}+\frac{2\,x\,\sqrt{\frac{1}{a^2\,x^2}+1}}{5\,a}}{x^5}","Not used",1,"(4*a^3*(1/(a^2*x^2) + 1)^(1/2))/15 - ((2*a*x*(1/(a^2*x^2) + 1)^(1/2))/15 + 1/3)/x^3 - (2/(5*a^2) + (2*x*(1/(a^2*x^2) + 1)^(1/2))/(5*a))/x^5","B"
58,1,89,96,2.370567,"\text{Not used}","int(((1/(a^2*x^2) + 1)^(1/2) + 1/(a*x))^2/x^5,x)","\frac{a^3\,\sqrt{\frac{1}{a^2\,x^2}+1}}{8\,x}-\frac{1}{3\,a^2\,x^6}-\frac{a\,\sqrt{\frac{1}{a^2\,x^2}+1}}{12\,x^3}-\frac{1}{4\,x^4}-\frac{\sqrt{\frac{1}{a^2\,x^2}+1}}{3\,a\,x^5}-\frac{a^3\,\mathrm{asinh}\left(\frac{\sqrt{\frac{1}{a^2}}}{x}\right)}{8\,\sqrt{\frac{1}{a^2}}}","Not used",1,"(a^3*(1/(a^2*x^2) + 1)^(1/2))/(8*x) - 1/(3*a^2*x^6) - (a*(1/(a^2*x^2) + 1)^(1/2))/(12*x^3) - 1/(4*x^4) - (1/(a^2*x^2) + 1)^(1/2)/(3*a*x^5) - (a^3*asinh((1/a^2)^(1/2)/x))/(8*(1/a^2)^(1/2))","B"
59,0,-1,85,0.000000,"\text{Not used}","int((((1/(c^2*x^2) + 1)^(1/2) + 1/(c*x))*(d*x)^m)/(c^2*x^2 + 1),x)","\int \frac{\left(\sqrt{\frac{1}{c^2\,x^2}+1}+\frac{1}{c\,x}\right)\,{\left(d\,x\right)}^m}{c^2\,x^2+1} \,d x","Not used",1,"int((((1/(c^2*x^2) + 1)^(1/2) + 1/(c*x))*(d*x)^m)/(c^2*x^2 + 1), x)","F"
60,1,79,92,2.433909,"\text{Not used}","int((x^5*((1/(c^2*x^2) + 1)^(1/2) + 1/(c*x)))/(c^2*x^2 + 1),x)","\frac{3\,\mathrm{atanh}\left(\sqrt{\frac{1}{c^2\,x^2}+1}\right)}{8\,c^6}+\frac{3\,\mathrm{atan}\left(c\,x\right)-3\,c\,x+c^3\,x^3}{3\,c^6}+\frac{x^4\,\sqrt{\frac{1}{c^2\,x^2}+1}}{4\,c^2}-\frac{3\,x^2\,\sqrt{\frac{1}{c^2\,x^2}+1}}{8\,c^4}","Not used",1,"(3*atanh((1/(c^2*x^2) + 1)^(1/2)))/(8*c^6) + (3*atan(c*x) - 3*c*x + c^3*x^3)/(3*c^6) + (x^4*(1/(c^2*x^2) + 1)^(1/2))/(4*c^2) - (3*x^2*(1/(c^2*x^2) + 1)^(1/2))/(8*c^4)","B"
61,1,61,72,2.346625,"\text{Not used}","int((x^4*((1/(c^2*x^2) + 1)^(1/2) + 1/(c*x)))/(c^2*x^2 + 1),x)","\frac{x^3\,\sqrt{\frac{1}{c^2\,x^2}+1}}{3\,c^2}-\frac{2\,x\,\sqrt{\frac{1}{c^2\,x^2}+1}}{3\,c^4}-\frac{\ln\left(c^2\,x^2+1\right)-c^2\,x^2}{2\,c^5}","Not used",1,"(x^3*(1/(c^2*x^2) + 1)^(1/2))/(3*c^2) - (2*x*(1/(c^2*x^2) + 1)^(1/2))/(3*c^4) - (log(c^2*x^2 + 1) - c^2*x^2)/(2*c^5)","B"
62,1,51,59,2.338958,"\text{Not used}","int((x^3*((1/(c^2*x^2) + 1)^(1/2) + 1/(c*x)))/(c^2*x^2 + 1),x)","\frac{x^2\,\sqrt{\frac{1}{c^2\,x^2}+1}}{2\,c^2}-\frac{\mathrm{atan}\left(c\,x\right)-c\,x}{c^4}-\frac{\mathrm{atanh}\left(\sqrt{\frac{1}{c^2\,x^2}+1}\right)}{2\,c^4}","Not used",1,"(x^2*(1/(c^2*x^2) + 1)^(1/2))/(2*c^2) - (atan(c*x) - c*x)/c^4 - atanh((1/(c^2*x^2) + 1)^(1/2))/(2*c^4)","B"
63,1,31,36,2.336313,"\text{Not used}","int((x^2*((1/(c^2*x^2) + 1)^(1/2) + 1/(c*x)))/(c^2*x^2 + 1),x)","\frac{\ln\left(c^2\,x^2+1\right)+2\,c\,x\,\sqrt{\frac{1}{c^2\,x^2}+1}}{2\,c^3}","Not used",1,"(log(c^2*x^2 + 1) + 2*c*x*(1/(c^2*x^2) + 1)^(1/2))/(2*c^3)","B"
64,1,21,27,2.358818,"\text{Not used}","int((x*((1/(c^2*x^2) + 1)^(1/2) + 1/(c*x)))/(c^2*x^2 + 1),x)","\frac{\mathrm{atanh}\left(\sqrt{\frac{1}{c^2\,x^2}+1}\right)+\mathrm{atan}\left(c\,x\right)}{c^2}","Not used",1,"(atanh((1/(c^2*x^2) + 1)^(1/2)) + atan(c*x))/c^2","B"
65,1,38,33,2.356196,"\text{Not used}","int(((1/(c^2*x^2) + 1)^(1/2) + 1/(c*x))/(c^2*x^2 + 1),x)","-\mathrm{asinh}\left(\frac{\sqrt{\frac{1}{c^2}}}{x}\right)\,\sqrt{\frac{1}{c^2}}-\frac{\ln\left(c^2\,x^2+1\right)-2\,\ln\left(x\right)}{2\,c}","Not used",1,"- asinh((1/c^2)^(1/2)/x)*(1/c^2)^(1/2) - (log(c^2*x^2 + 1) - 2*log(x))/(2*c)","B"
66,1,29,30,2.145939,"\text{Not used}","int(((1/(c^2*x^2) + 1)^(1/2) + 1/(c*x))/(x*(c^2*x^2 + 1)),x)","-\mathrm{atan}\left(c\,x\right)-\frac{x\,\sqrt{\frac{1}{c^2\,x^2}+1}+\frac{1}{c}}{x}","Not used",1,"- atan(c*x) - (x*(1/(c^2*x^2) + 1)^(1/2) + 1/c)/x","B"
67,1,61,60,2.417631,"\text{Not used}","int(((1/(c^2*x^2) + 1)^(1/2) + 1/(c*x))/(x^2*(c^2*x^2 + 1)),x)","\frac{\mathrm{asinh}\left(\frac{\sqrt{\frac{1}{c^2}}}{x}\right)}{2\,\sqrt{\frac{1}{c^2}}}+\frac{c\,\ln\left(-c^2\,x^2-1\right)}{2}-c\,\ln\left(x\right)-\frac{\sqrt{\frac{1}{c^2\,x^2}+1}}{2\,x}-\frac{1}{2\,c\,x^2}","Not used",1,"asinh((1/c^2)^(1/2)/x)/(2*(1/c^2)^(1/2)) + (c*log(- c^2*x^2 - 1))/2 - c*log(x) - (1/(c^2*x^2) + 1)^(1/2)/(2*x) - 1/(2*c*x^2)","B"
68,1,57,61,2.218280,"\text{Not used}","int(((1/(c^2*x^2) + 1)^(1/2) + 1/(c*x))/(x^3*(c^2*x^2 + 1)),x)","\frac{c+\frac{2\,c^2\,x\,\sqrt{\frac{1}{c^2\,x^2}+1}}{3}}{x}-\frac{\frac{x\,\sqrt{\frac{1}{c^2\,x^2}+1}}{3}+\frac{1}{3\,c}}{x^3}+c^2\,\mathrm{atan}\left(c\,x\right)","Not used",1,"(c + (2*c^2*x*(1/(c^2*x^2) + 1)^(1/2))/3)/x - ((x*(1/(c^2*x^2) + 1)^(1/2))/3 + 1/(3*c))/x^3 + c^2*atan(c*x)","B"
69,0,-1,61,0.000000,"\text{Not used}","int(asinh(1/(a + b*x))/(d*x + (a*d)/b),x)","\int \frac{\mathrm{asinh}\left(\frac{1}{a+b\,x}\right)}{d\,x+\frac{a\,d}{b}} \,d x","Not used",1,"int(asinh(1/(a + b*x))/(d*x + (a*d)/b), x)","F"
70,1,42,46,2.713864,"\text{Not used}","int(x^3*asinh(1/(a + b*x^4)),x)","\frac{\mathrm{atanh}\left(\sqrt{\frac{1}{{\left(b\,x^4+a\right)}^2}+1}\right)}{4\,b}+\frac{\mathrm{asinh}\left(\frac{1}{b\,x^4+a}\right)\,\left(b\,x^4+a\right)}{4\,b}","Not used",1,"atanh((1/(a + b*x^4)^2 + 1)^(1/2))/(4*b) + (asinh(1/(a + b*x^4))*(a + b*x^4))/(4*b)","B"
71,1,40,46,2.213849,"\text{Not used}","int(x^(n - 1)*asinh(1/(a + b*x^n)),x)","\frac{\mathrm{atanh}\left(\sqrt{\frac{1}{{\left(a+b\,x^n\right)}^2}+1}\right)+\mathrm{asinh}\left(\frac{1}{a+b\,x^n}\right)\,\left(a+b\,x^n\right)}{b\,n}","Not used",1,"(atanh((1/(a + b*x^n)^2 + 1)^(1/2)) + asinh(1/(a + b*x^n))*(a + b*x^n))/(b*n)","B"