1,1,325,0,0.628250," ","integrate(x^3*arccsch(b*x+a),x, algorithm=""fricas"")","\frac{3 \, b^{4} x^{4} \log\left(\frac{{\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{b x + a}\right) - 3 \, a^{4} \log\left(-b x + {\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - a + 1\right) + 3 \, a^{4} \log\left(-b x + {\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - a - 1\right) + 6 \, {\left(2 \, a^{3} - a\right)} \log\left(-b x + {\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - a\right) + {\left(b^{3} x^{3} - 3 \, a b^{2} x^{2} + 13 \, a^{3} + {\left(9 \, a^{2} - 2\right)} b x - 2 \, a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{12 \, b^{4}}"," ",0,"1/12*(3*b^4*x^4*log(((b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/(b*x + a)) - 3*a^4*log(-b*x + (b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) - a + 1) + 3*a^4*log(-b*x + (b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) - a - 1) + 6*(2*a^3 - a)*log(-b*x + (b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) - a) + (b^3*x^3 - 3*a*b^2*x^2 + 13*a^3 + (9*a^2 - 2)*b*x - 2*a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)))/b^4","B",0
2,1,306,0,0.622309," ","integrate(x^2*arccsch(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} \log\left(\frac{{\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{b x + a}\right) + 2 \, a^{3} \log\left(-b x + {\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - a + 1\right) - 2 \, a^{3} \log\left(-b x + {\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - a - 1\right) - {\left(6 \, a^{2} - 1\right)} \log\left(-b x + {\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - a\right) + {\left(b^{2} x^{2} - 4 \, a b x - 5 \, a^{2}\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{6 \, b^{3}}"," ",0,"1/6*(2*b^3*x^3*log(((b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/(b*x + a)) + 2*a^3*log(-b*x + (b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) - a + 1) - 2*a^3*log(-b*x + (b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) - a - 1) - (6*a^2 - 1)*log(-b*x + (b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) - a) + (b^2*x^2 - 4*a*b*x - 5*a^2)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)))/b^3","B",0
3,1,285,0,0.565729," ","integrate(x*arccsch(b*x+a),x, algorithm=""fricas"")","\frac{b^{2} x^{2} \log\left(\frac{{\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{b x + a}\right) - a^{2} \log\left(-b x + {\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - a + 1\right) + a^{2} \log\left(-b x + {\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - a - 1\right) + 2 \, a \log\left(-b x + {\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - a\right) + {\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{2 \, b^{2}}"," ",0,"1/2*(b^2*x^2*log(((b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/(b*x + a)) - a^2*log(-b*x + (b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) - a + 1) + a^2*log(-b*x + (b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) - a - 1) + 2*a*log(-b*x + (b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) - a) + (b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)))/b^2","B",0
4,0,0,0,0.636233," ","integrate(arccsch(b*x+a)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcsch}\left(b x + a\right)}{x}, x\right)"," ",0,"integral(arccsch(b*x + a)/x, x)","F",0
5,1,343,0,0.487166," ","integrate(arccsch(b*x+a)/x^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} + 1\right)} b x \log\left(-b x + {\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - a + 1\right) - {\left(a^{2} + 1\right)} b x \log\left(-b x + {\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - a - 1\right) - \sqrt{a^{2} + 1} b x \log\left(-\frac{a^{2} b x + a^{3} + {\left(a b x + a^{2} + {\left(a b x + a^{2}\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1\right)} \sqrt{a^{2} + 1} + {\left(a^{3} + {\left(a^{2} + 1\right)} b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + a}{x}\right) + {\left(a^{3} + a\right)} \log\left(\frac{{\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{b x + a}\right)}{{\left(a^{3} + a\right)} x}"," ",0,"-((a^2 + 1)*b*x*log(-b*x + (b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) - a + 1) - (a^2 + 1)*b*x*log(-b*x + (b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) - a - 1) - sqrt(a^2 + 1)*b*x*log(-(a^2*b*x + a^3 + (a*b*x + a^2 + (a*b*x + a^2)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)*sqrt(a^2 + 1) + (a^3 + (a^2 + 1)*b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) + a)/x) + (a^3 + a)*log(((b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/(b*x + a)))/((a^3 + a)*x)","B",0
6,1,461,0,0.511603," ","integrate(arccsch(b*x+a)/x^3,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} + 1\right)} \sqrt{a^{2} + 1} b^{2} x^{2} \log\left(-\frac{a^{2} b x + a^{3} - {\left(a b x + a^{2} + {\left(a b x + a^{2}\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1\right)} \sqrt{a^{2} + 1} + {\left(a^{3} + {\left(a^{2} + 1\right)} b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + a}{x}\right) + {\left(a^{4} + 2 \, a^{2} + 1\right)} b^{2} x^{2} \log\left(-b x + {\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - a + 1\right) - {\left(a^{4} + 2 \, a^{2} + 1\right)} b^{2} x^{2} \log\left(-b x + {\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - a - 1\right) + {\left(a^{3} + a\right)} b^{2} x^{2} - {\left(a^{6} + 2 \, a^{4} + a^{2}\right)} \log\left(\frac{{\left(b x + a\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{b x + a}\right) + {\left({\left(a^{3} + a\right)} b^{2} x^{2} + {\left(a^{4} + a^{2}\right)} b x\right)} \sqrt{\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{2 \, {\left(a^{6} + 2 \, a^{4} + a^{2}\right)} x^{2}}"," ",0,"1/2*((2*a^2 + 1)*sqrt(a^2 + 1)*b^2*x^2*log(-(a^2*b*x + a^3 - (a*b*x + a^2 + (a*b*x + a^2)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)*sqrt(a^2 + 1) + (a^3 + (a^2 + 1)*b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) + a)/x) + (a^4 + 2*a^2 + 1)*b^2*x^2*log(-b*x + (b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) - a + 1) - (a^4 + 2*a^2 + 1)*b^2*x^2*log(-b*x + (b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) - a - 1) + (a^3 + a)*b^2*x^2 - (a^6 + 2*a^4 + a^2)*log(((b*x + a)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/(b*x + a)) + ((a^3 + a)*b^2*x^2 + (a^4 + a^2)*b*x)*sqrt((b^2*x^2 + 2*a*b*x + a^2 + 1)/(b^2*x^2 + 2*a*b*x + a^2)))/((a^6 + 2*a^4 + a^2)*x^2)","B",0
7,0,0,0,0.547435," ","integrate((f*x+e)^3*(a+b*arccsch(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} f^{3} x^{3} + 3 \, a^{2} e f^{2} x^{2} + 3 \, a^{2} e^{2} f x + a^{2} e^{3} + {\left(b^{2} f^{3} x^{3} + 3 \, b^{2} e f^{2} x^{2} + 3 \, b^{2} e^{2} f x + b^{2} e^{3}\right)} \operatorname{arcsch}\left(d x + c\right)^{2} + 2 \, {\left(a b f^{3} x^{3} + 3 \, a b e f^{2} x^{2} + 3 \, a b e^{2} f x + a b e^{3}\right)} \operatorname{arcsch}\left(d x + c\right), x\right)"," ",0,"integral(a^2*f^3*x^3 + 3*a^2*e*f^2*x^2 + 3*a^2*e^2*f*x + a^2*e^3 + (b^2*f^3*x^3 + 3*b^2*e*f^2*x^2 + 3*b^2*e^2*f*x + b^2*e^3)*arccsch(d*x + c)^2 + 2*(a*b*f^3*x^3 + 3*a*b*e*f^2*x^2 + 3*a*b*e^2*f*x + a*b*e^3)*arccsch(d*x + c), x)","F",0
8,0,0,0,0.581060," ","integrate((f*x+e)^2*(a+b*arccsch(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} f^{2} x^{2} + 2 \, a^{2} e f x + a^{2} e^{2} + {\left(b^{2} f^{2} x^{2} + 2 \, b^{2} e f x + b^{2} e^{2}\right)} \operatorname{arcsch}\left(d x + c\right)^{2} + 2 \, {\left(a b f^{2} x^{2} + 2 \, a b e f x + a b e^{2}\right)} \operatorname{arcsch}\left(d x + c\right), x\right)"," ",0,"integral(a^2*f^2*x^2 + 2*a^2*e*f*x + a^2*e^2 + (b^2*f^2*x^2 + 2*b^2*e*f*x + b^2*e^2)*arccsch(d*x + c)^2 + 2*(a*b*f^2*x^2 + 2*a*b*e*f*x + a*b*e^2)*arccsch(d*x + c), x)","F",0
9,0,0,0,0.687665," ","integrate((f*x+e)*(a+b*arccsch(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} f x + a^{2} e + {\left(b^{2} f x + b^{2} e\right)} \operatorname{arcsch}\left(d x + c\right)^{2} + 2 \, {\left(a b f x + a b e\right)} \operatorname{arcsch}\left(d x + c\right), x\right)"," ",0,"integral(a^2*f*x + a^2*e + (b^2*f*x + b^2*e)*arccsch(d*x + c)^2 + 2*(a*b*f*x + a*b*e)*arccsch(d*x + c), x)","F",0
10,0,0,0,0.485248," ","integrate((a+b*arccsch(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \operatorname{arcsch}\left(d x + c\right)^{2} + 2 \, a b \operatorname{arcsch}\left(d x + c\right) + a^{2}, x\right)"," ",0,"integral(b^2*arccsch(d*x + c)^2 + 2*a*b*arccsch(d*x + c) + a^2, x)","F",0
11,0,0,0,0.492254," ","integrate((a+b*arccsch(d*x+c))^2/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{arcsch}\left(d x + c\right)^{2} + 2 \, a b \operatorname{arcsch}\left(d x + c\right) + a^{2}}{f x + e}, x\right)"," ",0,"integral((b^2*arccsch(d*x + c)^2 + 2*a*b*arccsch(d*x + c) + a^2)/(f*x + e), x)","F",0
12,0,0,0,0.520644," ","integrate((a+b*arccsch(d*x+c))^2/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{arcsch}\left(d x + c\right)^{2} + 2 \, a b \operatorname{arcsch}\left(d x + c\right) + a^{2}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b^2*arccsch(d*x + c)^2 + 2*a*b*arccsch(d*x + c) + a^2)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
13,0,0,0,0.561345," ","integrate((a+b*arccsch(d*x+c))^2/(f*x+e)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{arcsch}\left(d x + c\right)^{2} + 2 \, a b \operatorname{arcsch}\left(d x + c\right) + a^{2}}{f^{3} x^{3} + 3 \, e f^{2} x^{2} + 3 \, e^{2} f x + e^{3}}, x\right)"," ",0,"integral((b^2*arccsch(d*x + c)^2 + 2*a*b*arccsch(d*x + c) + a^2)/(f^3*x^3 + 3*e*f^2*x^2 + 3*e^2*f*x + e^3), x)","F",0
14,1,55,0,0.584011," ","integrate(x^3*arccsch(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{4} \, x^{4} \log\left(\frac{x \sqrt{\frac{x + 1}{x}} + \sqrt{x}}{x}\right) + \frac{1}{140} \, {\left(5 \, x^{3} - 6 \, x^{2} + 8 \, x - 16\right)} \sqrt{x} \sqrt{\frac{x + 1}{x}}"," ",0,"1/4*x^4*log((x*sqrt((x + 1)/x) + sqrt(x))/x) + 1/140*(5*x^3 - 6*x^2 + 8*x - 16)*sqrt(x)*sqrt((x + 1)/x)","A",0
15,1,50,0,0.588213," ","integrate(x^2*arccsch(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{3} \, x^{3} \log\left(\frac{x \sqrt{\frac{x + 1}{x}} + \sqrt{x}}{x}\right) + \frac{1}{45} \, {\left(3 \, x^{2} - 4 \, x + 8\right)} \sqrt{x} \sqrt{\frac{x + 1}{x}}"," ",0,"1/3*x^3*log((x*sqrt((x + 1)/x) + sqrt(x))/x) + 1/45*(3*x^2 - 4*x + 8)*sqrt(x)*sqrt((x + 1)/x)","A",0
16,1,43,0,0.758391," ","integrate(x*arccsch(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} \log\left(\frac{x \sqrt{\frac{x + 1}{x}} + \sqrt{x}}{x}\right) + \frac{1}{6} \, {\left(x - 2\right)} \sqrt{x} \sqrt{\frac{x + 1}{x}}"," ",0,"1/2*x^2*log((x*sqrt((x + 1)/x) + sqrt(x))/x) + 1/6*(x - 2)*sqrt(x)*sqrt((x + 1)/x)","A",0
17,1,36,0,0.524532," ","integrate(arccsch(x^(1/2)),x, algorithm=""fricas"")","x \log\left(\frac{x \sqrt{\frac{x + 1}{x}} + \sqrt{x}}{x}\right) + \sqrt{x} \sqrt{\frac{x + 1}{x}}"," ",0,"x*log((x*sqrt((x + 1)/x) + sqrt(x))/x) + sqrt(x)*sqrt((x + 1)/x)","A",0
18,0,0,0,0.665552," ","integrate(arccsch(x^(1/2))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcsch}\left(\sqrt{x}\right)}{x}, x\right)"," ",0,"integral(arccsch(sqrt(x))/x, x)","F",0
19,1,44,0,0.628467," ","integrate(arccsch(x^(1/2))/x^2,x, algorithm=""fricas"")","-\frac{{\left(x + 2\right)} \log\left(\frac{x \sqrt{\frac{x + 1}{x}} + \sqrt{x}}{x}\right) - \sqrt{x} \sqrt{\frac{x + 1}{x}}}{2 \, x}"," ",0,"-1/2*((x + 2)*log((x*sqrt((x + 1)/x) + sqrt(x))/x) - sqrt(x)*sqrt((x + 1)/x))/x","A",0
20,1,53,0,0.703041," ","integrate(arccsch(x^(1/2))/x^3,x, algorithm=""fricas"")","-\frac{{\left(3 \, x - 2\right)} \sqrt{x} \sqrt{\frac{x + 1}{x}} - {\left(3 \, x^{2} - 8\right)} \log\left(\frac{x \sqrt{\frac{x + 1}{x}} + \sqrt{x}}{x}\right)}{16 \, x^{2}}"," ",0,"-1/16*((3*x - 2)*sqrt(x)*sqrt((x + 1)/x) - (3*x^2 - 8)*log((x*sqrt((x + 1)/x) + sqrt(x))/x))/x^2","A",0
21,1,58,0,0.645354," ","integrate(arccsch(x^(1/2))/x^4,x, algorithm=""fricas"")","\frac{{\left(15 \, x^{2} - 10 \, x + 8\right)} \sqrt{x} \sqrt{\frac{x + 1}{x}} - 3 \, {\left(5 \, x^{3} + 16\right)} \log\left(\frac{x \sqrt{\frac{x + 1}{x}} + \sqrt{x}}{x}\right)}{144 \, x^{3}}"," ",0,"1/144*((15*x^2 - 10*x + 8)*sqrt(x)*sqrt((x + 1)/x) - 3*(5*x^3 + 16)*log((x*sqrt((x + 1)/x) + sqrt(x))/x))/x^3","A",0
22,1,22,0,0.728685," ","integrate(arccsch(1/x),x, algorithm=""fricas"")","x \log\left(x + \sqrt{x^{2} + 1}\right) - \sqrt{x^{2} + 1}"," ",0,"x*log(x + sqrt(x^2 + 1)) - sqrt(x^2 + 1)","A",0
23,-2,0,0,0.000000," ","integrate(arccsch(a*x^n)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
24,0,0,0,0.629559," ","integrate(arccsch(a*x^5)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcsch}\left(a x^{5}\right)}{x}, x\right)"," ",0,"integral(arccsch(a*x^5)/x, x)","F",0
25,-2,0,0,0.000000," ","integrate(arccsch(c*exp(b*x+a)),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
26,0,0,0,0.737832," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x x^{m} \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} + x^{m}}{a x}, x\right)"," ",0,"integral((a*x*x^m*sqrt((a^2*x^2 + 1)/(a^2*x^2)) + x^m)/(a*x), x)","F",0
27,1,53,0,0.395423," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))*x^4,x, algorithm=""fricas"")","\frac{15 \, a^{3} x^{4} + 4 \, {\left(3 \, a^{4} x^{5} + a^{2} x^{3} - 2 \, x\right)} \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}}}{60 \, a^{4}}"," ",0,"1/60*(15*a^3*x^4 + 4*(3*a^4*x^5 + a^2*x^3 - 2*x)*sqrt((a^2*x^2 + 1)/(a^2*x^2)))/a^4","A",0
28,1,79,0,0.396831," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))*x^3,x, algorithm=""fricas"")","\frac{8 \, a^{3} x^{3} + 3 \, {\left(2 \, a^{4} x^{4} + a^{2} x^{2}\right)} \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} + 3 \, \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x\right)}{24 \, a^{4}}"," ",0,"1/24*(8*a^3*x^3 + 3*(2*a^4*x^4 + a^2*x^2)*sqrt((a^2*x^2 + 1)/(a^2*x^2)) + 3*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x))/a^4","A",0
29,1,41,0,0.559517," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))*x^2,x, algorithm=""fricas"")","\frac{3 \, a x^{2} + 2 \, {\left(a^{2} x^{3} + x\right)} \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}}}{6 \, a^{2}}"," ",0,"1/6*(3*a*x^2 + 2*(a^2*x^3 + x)*sqrt((a^2*x^2 + 1)/(a^2*x^2)))/a^2","A",0
30,1,64,0,0.774723," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))*x,x, algorithm=""fricas"")","\frac{a^{2} x^{2} \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} + 2 \, a x - \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x\right)}{2 \, a^{2}}"," ",0,"1/2*(a^2*x^2*sqrt((a^2*x^2 + 1)/(a^2*x^2)) + 2*a*x - log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x))/a^2","A",0
31,1,86,0,0.447664," ","integrate(1/a/x+(1+1/a^2/x^2)^(1/2),x, algorithm=""fricas"")","\frac{a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x + 1\right) + \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x - 1\right) + \log\left(x\right)}{a}"," ",0,"(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x + 1) + log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x - 1) + log(x))/a","B",0
32,1,64,0,0.594893," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))/x,x, algorithm=""fricas"")","-\frac{a x \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x\right) + a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} + a x + 1}{a x}"," ",0,"-(a*x*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x) + a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) + a*x + 1)/(a*x)","A",0
33,1,102,0,0.462176," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))/x^2,x, algorithm=""fricas"")","-\frac{a^{2} x^{2} \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x + 1\right) - a^{2} x^{2} \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x - 1\right) + a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} + 1}{2 \, a x^{2}}"," ",0,"-1/2*(a^2*x^2*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x + 1) - a^2*x^2*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x - 1) + a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) + 1)/(a*x^2)","B",0
34,1,47,0,0.704165," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))/x^3,x, algorithm=""fricas"")","-\frac{a^{3} x^{3} + {\left(a^{3} x^{3} + a x\right)} \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} + 1}{3 \, a x^{3}}"," ",0,"-1/3*(a^3*x^3 + (a^3*x^3 + a*x)*sqrt((a^2*x^2 + 1)/(a^2*x^2)) + 1)/(a*x^3)","A",0
35,1,113,0,0.678059," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))/x^4,x, algorithm=""fricas"")","\frac{a^{4} x^{4} \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x + 1\right) - a^{4} x^{4} \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x - 1\right) - {\left(a^{3} x^{3} + 2 \, a x\right)} \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - 2}{8 \, a x^{4}}"," ",0,"1/8*(a^4*x^4*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x + 1) - a^4*x^4*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x - 1) - (a^3*x^3 + 2*a*x)*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - 2)/(a*x^4)","B",0
36,1,58,0,1.017197," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))/x^5,x, algorithm=""fricas"")","\frac{2 \, a^{5} x^{5} + {\left(2 \, a^{5} x^{5} - a^{3} x^{3} - 3 \, a x\right)} \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - 3}{15 \, a x^{5}}"," ",0,"1/15*(2*a^5*x^5 + (2*a^5*x^5 - a^3*x^3 - 3*a*x)*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - 3)/(a*x^5)","A",0
37,0,0,0,0.665559," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x^{2} x^{m} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} + x^{m}}{a x^{2}}, x\right)"," ",0,"integral((a*x^2*x^m*sqrt((a^2*x^4 + 1)/(a^2*x^4)) + x^m)/(a*x^2), x)","F",0
38,0,0,0,0.573946," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))*x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x^{4} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} + x^{2}}{a}, x\right)"," ",0,"integral((a*x^4*sqrt((a^2*x^4 + 1)/(a^2*x^4)) + x^2)/a, x)","F",0
39,1,70,0,0.649446," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))*x^3,x, algorithm=""fricas"")","\frac{a^{2} x^{4} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} + 2 \, a x^{2} - \log\left(a x^{2} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} - a x^{2}\right)}{4 \, a^{2}}"," ",0,"1/4*(a^2*x^4*sqrt((a^2*x^4 + 1)/(a^2*x^4)) + 2*a*x^2 - log(a*x^2*sqrt((a^2*x^4 + 1)/(a^2*x^4)) - a*x^2))/a^2","A",0
40,0,0,0,2.604578," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))*x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x^{2} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} + 1}{a}, x\right)"," ",0,"integral((a*x^2*sqrt((a^2*x^4 + 1)/(a^2*x^4)) + 1)/a, x)","F",0
41,1,88,0,0.614456," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))*x,x, algorithm=""fricas"")","\frac{2 \, a x^{2} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} - \log\left(a x^{2} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} + 1\right) + \log\left(a x^{2} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} - 1\right) + 4 \, \log\left(x\right)}{4 \, a}"," ",0,"1/4*(2*a*x^2*sqrt((a^2*x^4 + 1)/(a^2*x^4)) - log(a*x^2*sqrt((a^2*x^4 + 1)/(a^2*x^4)) + 1) + log(a*x^2*sqrt((a^2*x^4 + 1)/(a^2*x^4)) - 1) + 4*log(x))/a","B",0
42,0,0,0,0.647727," ","integrate(1/a/x^2+(1+1/a^2/x^4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x^{2} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} + 1}{a x^{2}}, x\right)"," ",0,"integral((a*x^2*sqrt((a^2*x^4 + 1)/(a^2*x^4)) + 1)/(a*x^2), x)","F",0
43,1,74,0,0.871100," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))/x,x, algorithm=""fricas"")","-\frac{a x^{2} \log\left(a x^{2} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} - a x^{2}\right) + a x^{2} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} + a x^{2} + 1}{2 \, a x^{2}}"," ",0,"-1/2*(a*x^2*log(a*x^2*sqrt((a^2*x^4 + 1)/(a^2*x^4)) - a*x^2) + a*x^2*sqrt((a^2*x^4 + 1)/(a^2*x^4)) + a*x^2 + 1)/(a*x^2)","B",0
44,0,0,0,0.647840," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x^{2} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} + 1}{a x^{4}}, x\right)"," ",0,"integral((a*x^2*sqrt((a^2*x^4 + 1)/(a^2*x^4)) + 1)/(a*x^4), x)","F",0
45,1,101,0,0.720745," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))/x^3,x, algorithm=""fricas"")","-\frac{a^{2} x^{4} \log\left(a x^{2} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} + 1\right) - a^{2} x^{4} \log\left(a x^{2} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} - 1\right) + 2 \, a x^{2} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} + 2}{8 \, a x^{4}}"," ",0,"-1/8*(a^2*x^4*log(a*x^2*sqrt((a^2*x^4 + 1)/(a^2*x^4)) + 1) - a^2*x^4*log(a*x^2*sqrt((a^2*x^4 + 1)/(a^2*x^4)) - 1) + 2*a*x^2*sqrt((a^2*x^4 + 1)/(a^2*x^4)) + 2)/(a*x^4)","B",0
46,0,0,0,0.521447," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x^{2} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} + 1}{a x^{6}}, x\right)"," ",0,"integral((a*x^2*sqrt((a^2*x^4 + 1)/(a^2*x^4)) + 1)/(a*x^6), x)","F",0
47,1,49,0,0.563195," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))/x^5,x, algorithm=""fricas"")","-\frac{a^{3} x^{6} + {\left(a^{3} x^{6} + a x^{2}\right)} \sqrt{\frac{a^{2} x^{4} + 1}{a^{2} x^{4}}} + 1}{6 \, a x^{6}}"," ",0,"-1/6*(a^3*x^6 + (a^3*x^6 + a*x^2)*sqrt((a^2*x^4 + 1)/(a^2*x^4)) + 1)/(a*x^6)","A",0
48,0,0,0,0.651035," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, a x x^{m} \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} + {\left(a^{2} x^{2} + 2\right)} x^{m}}{a^{2} x^{2}}, x\right)"," ",0,"integral((2*a*x*x^m*sqrt((a^2*x^2 + 1)/(a^2*x^2)) + (a^2*x^2 + 2)*x^m)/(a^2*x^2), x)","F",0
49,1,87,0,0.665215," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2*x^4,x, algorithm=""fricas"")","\frac{12 \, a^{5} x^{5} + 40 \, a^{3} x^{3} + 15 \, {\left(2 \, a^{4} x^{4} + a^{2} x^{2}\right)} \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} + 15 \, \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x\right)}{60 \, a^{5}}"," ",0,"1/60*(12*a^5*x^5 + 40*a^3*x^3 + 15*(2*a^4*x^4 + a^2*x^2)*sqrt((a^2*x^2 + 1)/(a^2*x^2)) + 15*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x))/a^5","A",0
50,1,49,0,0.528310," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2*x^3,x, algorithm=""fricas"")","\frac{3 \, a^{3} x^{4} + 12 \, a x^{2} + 8 \, {\left(a^{2} x^{3} + x\right)} \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}}}{12 \, a^{3}}"," ",0,"1/12*(3*a^3*x^4 + 12*a*x^2 + 8*(a^2*x^3 + x)*sqrt((a^2*x^2 + 1)/(a^2*x^2)))/a^3","A",0
51,1,72,0,0.767505," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2*x^2,x, algorithm=""fricas"")","\frac{a^{3} x^{3} + 3 \, a^{2} x^{2} \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} + 6 \, a x - 3 \, \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x\right)}{3 \, a^{3}}"," ",0,"1/3*(a^3*x^3 + 3*a^2*x^2*sqrt((a^2*x^2 + 1)/(a^2*x^2)) + 6*a*x - 3*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x))/a^3","A",0
52,1,99,0,0.613441," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2*x,x, algorithm=""fricas"")","\frac{a^{2} x^{2} + 4 \, a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - 4 \, \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x + 1\right) + 4 \, \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x - 1\right) + 4 \, \log\left(x\right)}{2 \, a^{2}}"," ",0,"1/2*(a^2*x^2 + 4*a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - 4*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x + 1) + 4*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x - 1) + 4*log(x))/a^2","B",0
53,1,73,0,0.936723," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2,x, algorithm=""fricas"")","\frac{a^{2} x^{2} - 2 \, a x \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x\right) - 2 \, a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - 2 \, a x - 2}{a^{2} x}"," ",0,"(a^2*x^2 - 2*a*x*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x) - 2*a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - 2*a*x - 2)/(a^2*x)","A",0
54,1,112,0,0.596792," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2/x,x, algorithm=""fricas"")","-\frac{a^{2} x^{2} \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x + 1\right) - a^{2} x^{2} \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x - 1\right) - a^{2} x^{2} \log\left(x\right) + a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} + 1}{a^{2} x^{2}}"," ",0,"-(a^2*x^2*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x + 1) - a^2*x^2*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x - 1) - a^2*x^2*log(x) + a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) + 1)/(a^2*x^2)","B",0
55,1,57,0,0.587187," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2/x^2,x, algorithm=""fricas"")","-\frac{2 \, a^{3} x^{3} + 3 \, a^{2} x^{2} + 2 \, {\left(a^{3} x^{3} + a x\right)} \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} + 2}{3 \, a^{2} x^{3}}"," ",0,"-1/3*(2*a^3*x^3 + 3*a^2*x^2 + 2*(a^3*x^3 + a*x)*sqrt((a^2*x^2 + 1)/(a^2*x^2)) + 2)/(a^2*x^3)","B",0
56,1,121,0,0.508865," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2/x^3,x, algorithm=""fricas"")","\frac{a^{4} x^{4} \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x + 1\right) - a^{4} x^{4} \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x - 1\right) - 2 \, a^{2} x^{2} - {\left(a^{3} x^{3} + 2 \, a x\right)} \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - 2}{4 \, a^{2} x^{4}}"," ",0,"1/4*(a^4*x^4*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x + 1) - a^4*x^4*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x - 1) - 2*a^2*x^2 - (a^3*x^3 + 2*a*x)*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - 2)/(a^2*x^4)","B",0
57,1,67,0,0.733929," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2/x^4,x, algorithm=""fricas"")","\frac{4 \, a^{5} x^{5} - 5 \, a^{2} x^{2} + 2 \, {\left(2 \, a^{5} x^{5} - a^{3} x^{3} - 3 \, a x\right)} \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - 6}{15 \, a^{2} x^{5}}"," ",0,"1/15*(4*a^5*x^5 - 5*a^2*x^2 + 2*(2*a^5*x^5 - a^3*x^3 - 3*a*x)*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - 6)/(a^2*x^5)","A",0
58,1,131,0,2.314604," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2/x^5,x, algorithm=""fricas"")","-\frac{3 \, a^{6} x^{6} \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x + 1\right) - 3 \, a^{6} x^{6} \log\left(a x \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} - a x - 1\right) + 6 \, a^{2} x^{2} - {\left(3 \, a^{5} x^{5} - 2 \, a^{3} x^{3} - 8 \, a x\right)} \sqrt{\frac{a^{2} x^{2} + 1}{a^{2} x^{2}}} + 8}{24 \, a^{2} x^{6}}"," ",0,"-1/24*(3*a^6*x^6*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x + 1) - 3*a^6*x^6*log(a*x*sqrt((a^2*x^2 + 1)/(a^2*x^2)) - a*x - 1) + 6*a^2*x^2 - (3*a^5*x^5 - 2*a^3*x^3 - 8*a*x)*sqrt((a^2*x^2 + 1)/(a^2*x^2)) + 8)/(a^2*x^6)","A",0
59,0,0,0,2.163812," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))*(d*x)^m/(c^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m} c x \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} + \left(d x\right)^{m}}{c^{3} x^{3} + c x}, x\right)"," ",0,"integral(((d*x)^m*c*x*sqrt((c^2*x^2 + 1)/(c^2*x^2)) + (d*x)^m)/(c^3*x^3 + c*x), x)","F",0
60,1,90,0,1.641808," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))*x^5/(c^2*x^2+1),x, algorithm=""fricas"")","\frac{8 \, c^{3} x^{3} - 24 \, c x + 3 \, {\left(2 \, c^{4} x^{4} - 3 \, c^{2} x^{2}\right)} \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} + 24 \, \arctan\left(c x\right) - 9 \, \log\left(c x \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} - c x\right)}{24 \, c^{6}}"," ",0,"1/24*(8*c^3*x^3 - 24*c*x + 3*(2*c^4*x^4 - 3*c^2*x^2)*sqrt((c^2*x^2 + 1)/(c^2*x^2)) + 24*arctan(c*x) - 9*log(c*x*sqrt((c^2*x^2 + 1)/(c^2*x^2)) - c*x))/c^6","A",0
61,1,58,0,0.556915," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))*x^4/(c^2*x^2+1),x, algorithm=""fricas"")","\frac{3 \, c^{2} x^{2} + 2 \, {\left(c^{3} x^{3} - 2 \, c x\right)} \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} - 3 \, \log\left(c^{2} x^{2} + 1\right)}{6 \, c^{5}}"," ",0,"1/6*(3*c^2*x^2 + 2*(c^3*x^3 - 2*c*x)*sqrt((c^2*x^2 + 1)/(c^2*x^2)) - 3*log(c^2*x^2 + 1))/c^5","A",0
62,1,68,0,0.888086," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))*x^3/(c^2*x^2+1),x, algorithm=""fricas"")","\frac{c^{2} x^{2} \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} + 2 \, c x - 2 \, \arctan\left(c x\right) + \log\left(c x \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} - c x\right)}{2 \, c^{4}}"," ",0,"1/2*(c^2*x^2*sqrt((c^2*x^2 + 1)/(c^2*x^2)) + 2*c*x - 2*arctan(c*x) + log(c*x*sqrt((c^2*x^2 + 1)/(c^2*x^2)) - c*x))/c^4","A",0
63,1,38,0,0.641678," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))*x^2/(c^2*x^2+1),x, algorithm=""fricas"")","\frac{2 \, c x \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} + \log\left(c^{2} x^{2} + 1\right)}{2 \, c^{3}}"," ",0,"1/2*(2*c*x*sqrt((c^2*x^2 + 1)/(c^2*x^2)) + log(c^2*x^2 + 1))/c^3","A",0
64,1,38,0,0.658093," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))*x/(c^2*x^2+1),x, algorithm=""fricas"")","\frac{\arctan\left(c x\right) - \log\left(c x \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} - c x\right)}{c^{2}}"," ",0,"(arctan(c*x) - log(c*x*sqrt((c^2*x^2 + 1)/(c^2*x^2)) - c*x))/c^2","A",0
65,1,80,0,0.667958," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))/(c^2*x^2+1),x, algorithm=""fricas"")","-\frac{\log\left(c^{2} x^{2} + 1\right) + 2 \, \log\left(c x \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} - c x + 1\right) - 2 \, \log\left(c x \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} - c x - 1\right) - 2 \, \log\left(x\right)}{2 \, c}"," ",0,"-1/2*(log(c^2*x^2 + 1) + 2*log(c*x*sqrt((c^2*x^2 + 1)/(c^2*x^2)) - c*x + 1) - 2*log(c*x*sqrt((c^2*x^2 + 1)/(c^2*x^2)) - c*x - 1) - 2*log(x))/c","B",0
66,1,41,0,0.543193," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))/x/(c^2*x^2+1),x, algorithm=""fricas"")","-\frac{c x \arctan\left(c x\right) + c x \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} + c x + 1}{c x}"," ",0,"-(c*x*arctan(c*x) + c*x*sqrt((c^2*x^2 + 1)/(c^2*x^2)) + c*x + 1)/(c*x)","A",0
67,1,130,0,1.337320," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))/x^2/(c^2*x^2+1),x, algorithm=""fricas"")","\frac{c^{2} x^{2} \log\left(c^{2} x^{2} + 1\right) + c^{2} x^{2} \log\left(c x \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} - c x + 1\right) - c^{2} x^{2} \log\left(c x \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} - c x - 1\right) - 2 \, c^{2} x^{2} \log\left(x\right) - c x \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} - 1}{2 \, c x^{2}}"," ",0,"1/2*(c^2*x^2*log(c^2*x^2 + 1) + c^2*x^2*log(c*x*sqrt((c^2*x^2 + 1)/(c^2*x^2)) - c*x + 1) - c^2*x^2*log(c*x*sqrt((c^2*x^2 + 1)/(c^2*x^2)) - c*x - 1) - 2*c^2*x^2*log(x) - c*x*sqrt((c^2*x^2 + 1)/(c^2*x^2)) - 1)/(c*x^2)","B",0
68,1,70,0,0.551074," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))/x^3/(c^2*x^2+1),x, algorithm=""fricas"")","\frac{3 \, c^{3} x^{3} \arctan\left(c x\right) + 2 \, c^{3} x^{3} + 3 \, c^{2} x^{2} + {\left(2 \, c^{3} x^{3} - c x\right)} \sqrt{\frac{c^{2} x^{2} + 1}{c^{2} x^{2}}} - 1}{3 \, c x^{3}}"," ",0,"1/3*(3*c^3*x^3*arctan(c*x) + 2*c^3*x^3 + 3*c^2*x^2 + (2*c^3*x^3 - c*x)*sqrt((c^2*x^2 + 1)/(c^2*x^2)) - 1)/(c*x^3)","A",0
69,0,0,0,0.522770," ","integrate(arccsch(b*x+a)/(a*d/b+d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arcsch}\left(b x + a\right)}{b d x + a d}, x\right)"," ",0,"integral(b*arccsch(b*x + a)/(b*d*x + a*d), x)","F",0
70,1,266,0,0.608522," ","integrate(x^3*arccsch(b*x^4+a),x, algorithm=""fricas"")","\frac{b x^{4} \log\left(\frac{{\left(b x^{4} + a\right)} \sqrt{\frac{b^{2} x^{8} + 2 \, a b x^{4} + a^{2} + 1}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}} + 1}{b x^{4} + a}\right) + a \log\left(-b x^{4} + {\left(b x^{4} + a\right)} \sqrt{\frac{b^{2} x^{8} + 2 \, a b x^{4} + a^{2} + 1}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}} - a + 1\right) - a \log\left(-b x^{4} + {\left(b x^{4} + a\right)} \sqrt{\frac{b^{2} x^{8} + 2 \, a b x^{4} + a^{2} + 1}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}} - a - 1\right) - \log\left(-b x^{4} + {\left(b x^{4} + a\right)} \sqrt{\frac{b^{2} x^{8} + 2 \, a b x^{4} + a^{2} + 1}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}} - a\right)}{4 \, b}"," ",0,"1/4*(b*x^4*log(((b*x^4 + a)*sqrt((b^2*x^8 + 2*a*b*x^4 + a^2 + 1)/(b^2*x^8 + 2*a*b*x^4 + a^2)) + 1)/(b*x^4 + a)) + a*log(-b*x^4 + (b*x^4 + a)*sqrt((b^2*x^8 + 2*a*b*x^4 + a^2 + 1)/(b^2*x^8 + 2*a*b*x^4 + a^2)) - a + 1) - a*log(-b*x^4 + (b*x^4 + a)*sqrt((b^2*x^8 + 2*a*b*x^4 + a^2 + 1)/(b^2*x^8 + 2*a*b*x^4 + a^2)) - a - 1) - log(-b*x^4 + (b*x^4 + a)*sqrt((b^2*x^8 + 2*a*b*x^4 + a^2 + 1)/(b^2*x^8 + 2*a*b*x^4 + a^2)) - a))/b","B",0
71,1,334,0,0.654713," ","integrate(x^(-1+n)*arccsch(a+b*x^n),x, algorithm=""fricas"")","\frac{a \log\left(-b \cosh\left(n \log\left(x\right)\right) - b \sinh\left(n \log\left(x\right)\right) - a + \sqrt{\frac{2 \, a b + {\left(a^{2} + b^{2} + 1\right)} \cosh\left(n \log\left(x\right)\right) - {\left(a^{2} - b^{2} + 1\right)} \sinh\left(n \log\left(x\right)\right)}{\cosh\left(n \log\left(x\right)\right) - \sinh\left(n \log\left(x\right)\right)}} + 1\right) - a \log\left(-b \cosh\left(n \log\left(x\right)\right) - b \sinh\left(n \log\left(x\right)\right) - a + \sqrt{\frac{2 \, a b + {\left(a^{2} + b^{2} + 1\right)} \cosh\left(n \log\left(x\right)\right) - {\left(a^{2} - b^{2} + 1\right)} \sinh\left(n \log\left(x\right)\right)}{\cosh\left(n \log\left(x\right)\right) - \sinh\left(n \log\left(x\right)\right)}} - 1\right) + {\left(b \cosh\left(n \log\left(x\right)\right) + b \sinh\left(n \log\left(x\right)\right)\right)} \log\left(\frac{\sqrt{\frac{2 \, a b + {\left(a^{2} + b^{2} + 1\right)} \cosh\left(n \log\left(x\right)\right) - {\left(a^{2} - b^{2} + 1\right)} \sinh\left(n \log\left(x\right)\right)}{\cosh\left(n \log\left(x\right)\right) - \sinh\left(n \log\left(x\right)\right)}} + 1}{b \cosh\left(n \log\left(x\right)\right) + b \sinh\left(n \log\left(x\right)\right) + a}\right) - \log\left(-b \cosh\left(n \log\left(x\right)\right) - b \sinh\left(n \log\left(x\right)\right) - a + \sqrt{\frac{2 \, a b + {\left(a^{2} + b^{2} + 1\right)} \cosh\left(n \log\left(x\right)\right) - {\left(a^{2} - b^{2} + 1\right)} \sinh\left(n \log\left(x\right)\right)}{\cosh\left(n \log\left(x\right)\right) - \sinh\left(n \log\left(x\right)\right)}}\right)}{b n}"," ",0,"(a*log(-b*cosh(n*log(x)) - b*sinh(n*log(x)) - a + sqrt((2*a*b + (a^2 + b^2 + 1)*cosh(n*log(x)) - (a^2 - b^2 + 1)*sinh(n*log(x)))/(cosh(n*log(x)) - sinh(n*log(x)))) + 1) - a*log(-b*cosh(n*log(x)) - b*sinh(n*log(x)) - a + sqrt((2*a*b + (a^2 + b^2 + 1)*cosh(n*log(x)) - (a^2 - b^2 + 1)*sinh(n*log(x)))/(cosh(n*log(x)) - sinh(n*log(x)))) - 1) + (b*cosh(n*log(x)) + b*sinh(n*log(x)))*log((sqrt((2*a*b + (a^2 + b^2 + 1)*cosh(n*log(x)) - (a^2 - b^2 + 1)*sinh(n*log(x)))/(cosh(n*log(x)) - sinh(n*log(x)))) + 1)/(b*cosh(n*log(x)) + b*sinh(n*log(x)) + a)) - log(-b*cosh(n*log(x)) - b*sinh(n*log(x)) - a + sqrt((2*a*b + (a^2 + b^2 + 1)*cosh(n*log(x)) - (a^2 - b^2 + 1)*sinh(n*log(x)))/(cosh(n*log(x)) - sinh(n*log(x))))))/(b*n)","B",0
