1,0,0,0,0.000000," ","integrate(arccsc(a*x^5)/x,x, algorithm=""maxima"")","5 \, a^{2} \int \frac{\sqrt{a x^{5} + 1} \sqrt{a x^{5} - 1} \log\left(x\right)}{a^{4} x^{11} - a^{2} x}\,{d x} - 5 i \, a^{2} \int \frac{\log\left(x\right)}{a^{4} x^{11} - a^{2} x}\,{d x} + {\left(\arctan\left(1, \sqrt{a x^{5} + 1} \sqrt{a x^{5} - 1}\right) + i \, \log\left(a\right)\right)} \log\left(x\right) - \frac{1}{2} i \, \log\left(a^{2} x^{10}\right) \log\left(x\right) + \frac{1}{2} i \, \log\left(a x^{5} + 1\right) \log\left(x\right) + \frac{1}{2} i \, \log\left(-a x^{5} + 1\right) \log\left(x\right) + \frac{5}{2} i \, \log\left(x\right)^{2} + \frac{1}{10} i \, {\rm Li}_2\left(a x^{5}\right) + \frac{1}{10} i \, {\rm Li}_2\left(-a x^{5}\right)"," ",0,"5*a^2*integrate(sqrt(a*x^5 + 1)*sqrt(a*x^5 - 1)*log(x)/(a^4*x^11 - a^2*x), x) - 5*I*a^2*integrate(log(x)/(a^4*x^11 - a^2*x), x) + (arctan2(1, sqrt(a*x^5 + 1)*sqrt(a*x^5 - 1)) + I*log(a))*log(x) - 1/2*I*log(a^2*x^10)*log(x) + 1/2*I*log(a*x^5 + 1)*log(x) + 1/2*I*log(-a*x^5 + 1)*log(x) + 5/2*I*log(x)^2 + 1/10*I*dilog(a*x^5) + 1/10*I*dilog(-a*x^5)","F",0
2,1,66,0,0.346559," ","integrate(x^3*arccsc(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{28} \, x^{\frac{7}{2}} {\left(-\frac{1}{x} + 1\right)}^{\frac{7}{2}} + \frac{3}{20} \, x^{\frac{5}{2}} {\left(-\frac{1}{x} + 1\right)}^{\frac{5}{2}} + \frac{1}{4} \, x^{4} \operatorname{arccsc}\left(\sqrt{x}\right) + \frac{1}{4} \, x^{\frac{3}{2}} {\left(-\frac{1}{x} + 1\right)}^{\frac{3}{2}} + \frac{1}{4} \, \sqrt{x} \sqrt{-\frac{1}{x} + 1}"," ",0,"1/28*x^(7/2)*(-1/x + 1)^(7/2) + 3/20*x^(5/2)*(-1/x + 1)^(5/2) + 1/4*x^4*arccsc(sqrt(x)) + 1/4*x^(3/2)*(-1/x + 1)^(3/2) + 1/4*sqrt(x)*sqrt(-1/x + 1)","A",0
3,1,52,0,0.334295," ","integrate(x^2*arccsc(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{15} \, x^{\frac{5}{2}} {\left(-\frac{1}{x} + 1\right)}^{\frac{5}{2}} + \frac{1}{3} \, x^{3} \operatorname{arccsc}\left(\sqrt{x}\right) + \frac{2}{9} \, x^{\frac{3}{2}} {\left(-\frac{1}{x} + 1\right)}^{\frac{3}{2}} + \frac{1}{3} \, \sqrt{x} \sqrt{-\frac{1}{x} + 1}"," ",0,"1/15*x^(5/2)*(-1/x + 1)^(5/2) + 1/3*x^3*arccsc(sqrt(x)) + 2/9*x^(3/2)*(-1/x + 1)^(3/2) + 1/3*sqrt(x)*sqrt(-1/x + 1)","A",0
4,1,38,0,0.338430," ","integrate(x*arccsc(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{6} \, x^{\frac{3}{2}} {\left(-\frac{1}{x} + 1\right)}^{\frac{3}{2}} + \frac{1}{2} \, x^{2} \operatorname{arccsc}\left(\sqrt{x}\right) + \frac{1}{2} \, \sqrt{x} \sqrt{-\frac{1}{x} + 1}"," ",0,"1/6*x^(3/2)*(-1/x + 1)^(3/2) + 1/2*x^2*arccsc(sqrt(x)) + 1/2*sqrt(x)*sqrt(-1/x + 1)","A",0
5,1,20,0,0.335281," ","integrate(arccsc(x^(1/2)),x, algorithm=""maxima"")","x \operatorname{arccsc}\left(\sqrt{x}\right) + \sqrt{x} \sqrt{-\frac{1}{x} + 1}"," ",0,"x*arccsc(sqrt(x)) + sqrt(x)*sqrt(-1/x + 1)","A",0
6,0,0,0,0.000000," ","integrate(arccsc(x^(1/2))/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arccsc}\left(\sqrt{x}\right)}{x}\,{d x}"," ",0,"integrate(arccsc(sqrt(x))/x, x)","F",0
7,1,51,0,0.474983," ","integrate(arccsc(x^(1/2))/x^2,x, algorithm=""maxima"")","\frac{\sqrt{x} \sqrt{-\frac{1}{x} + 1}}{2 \, {\left(x {\left(\frac{1}{x} - 1\right)} - 1\right)}} - \frac{\operatorname{arccsc}\left(\sqrt{x}\right)}{x} - \frac{1}{2} \, \arctan\left(\sqrt{x} \sqrt{-\frac{1}{x} + 1}\right)"," ",0,"1/2*sqrt(x)*sqrt(-1/x + 1)/(x*(1/x - 1) - 1) - arccsc(sqrt(x))/x - 1/2*arctan(sqrt(x)*sqrt(-1/x + 1))","A",0
8,1,80,0,0.458717," ","integrate(arccsc(x^(1/2))/x^3,x, algorithm=""maxima"")","-\frac{3 \, x^{\frac{3}{2}} {\left(-\frac{1}{x} + 1\right)}^{\frac{3}{2}} + 5 \, \sqrt{x} \sqrt{-\frac{1}{x} + 1}}{16 \, {\left(x^{2} {\left(\frac{1}{x} - 1\right)}^{2} - 2 \, x {\left(\frac{1}{x} - 1\right)} + 1\right)}} - \frac{\operatorname{arccsc}\left(\sqrt{x}\right)}{2 \, x^{2}} - \frac{3}{16} \, \arctan\left(\sqrt{x} \sqrt{-\frac{1}{x} + 1}\right)"," ",0,"-1/16*(3*x^(3/2)*(-1/x + 1)^(3/2) + 5*sqrt(x)*sqrt(-1/x + 1))/(x^2*(1/x - 1)^2 - 2*x*(1/x - 1) + 1) - 1/2*arccsc(sqrt(x))/x^2 - 3/16*arctan(sqrt(x)*sqrt(-1/x + 1))","B",0
9,1,54,0,0.484745," ","integrate(x^2*arccsc(a/x),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arccsc}\left(\frac{a}{x}\right) + \frac{2 \, a^{4} \sqrt{-\frac{x^{2}}{a^{2}} + 1} + a^{2} x^{2} \sqrt{-\frac{x^{2}}{a^{2}} + 1}}{9 \, a}"," ",0,"1/3*x^3*arccsc(a/x) + 1/9*(2*a^4*sqrt(-x^2/a^2 + 1) + a^2*x^2*sqrt(-x^2/a^2 + 1))/a","A",0
10,1,46,0,0.446146," ","integrate(x*arccsc(a/x),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arccsc}\left(\frac{a}{x}\right) - \frac{a^{3} \arcsin\left(\frac{x}{a}\right) - a^{2} x \sqrt{-\frac{x^{2}}{a^{2}} + 1}}{4 \, a}"," ",0,"1/2*x^2*arccsc(a/x) - 1/4*(a^3*arcsin(x/a) - a^2*x*sqrt(-x^2/a^2 + 1))/a","A",0
11,1,23,0,0.456747," ","integrate(arccsc(a/x),x, algorithm=""maxima"")","x \operatorname{arccsc}\left(\frac{a}{x}\right) + a \sqrt{-\frac{x^{2}}{a^{2}} + 1}"," ",0,"x*arccsc(a/x) + a*sqrt(-x^2/a^2 + 1)","A",0
12,0,0,0,0.000000," ","integrate(arccsc(a/x)/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arccsc}\left(\frac{a}{x}\right)}{x}\,{d x}"," ",0,"integrate(arccsc(a/x)/x, x)","F",0
13,1,52,0,0.334754," ","integrate(arccsc(a/x)/x^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, a \operatorname{arccsc}\left(\frac{a}{x}\right)}{x} + \log\left(\sqrt{-\frac{x^{2}}{a^{2}} + 1} + 1\right) - \log\left(-\sqrt{-\frac{x^{2}}{a^{2}} + 1} + 1\right)}{2 \, a}"," ",0,"-1/2*(2*a*arccsc(a/x)/x + log(sqrt(-x^2/a^2 + 1) + 1) - log(-sqrt(-x^2/a^2 + 1) + 1))/a","A",0
14,1,32,0,0.466919," ","integrate(arccsc(a/x)/x^3,x, algorithm=""maxima"")","-\frac{\operatorname{arccsc}\left(\frac{a}{x}\right)}{2 \, x^{2}} - \frac{\sqrt{-\frac{x^{2}}{a^{2}} + 1}}{2 \, a x}"," ",0,"-1/2*arccsc(a/x)/x^2 - 1/2*sqrt(-x^2/a^2 + 1)/(a*x)","A",0
15,1,64,0,0.460675," ","integrate(arccsc(a/x)/x^4,x, algorithm=""maxima"")","-\frac{\frac{\log\left(\frac{2 \, \sqrt{-\frac{x^{2}}{a^{2}} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right)}{a^{2}} + \frac{\sqrt{-\frac{x^{2}}{a^{2}} + 1}}{x^{2}}}{6 \, a} - \frac{\operatorname{arccsc}\left(\frac{a}{x}\right)}{3 \, x^{3}}"," ",0,"-1/6*(log(2*sqrt(-x^2/a^2 + 1)/abs(x) + 2/abs(x))/a^2 + sqrt(-x^2/a^2 + 1)/x^2)/a - 1/3*arccsc(a/x)/x^3","A",0
16,0,0,0,0.000000," ","integrate(arccsc(a*x^n)/x,x, algorithm=""maxima"")","a^{2} n \int \frac{\sqrt{a x^{n} + 1} \sqrt{a x^{n} - 1} \log\left(x\right)}{a^{4} x x^{2 \, n} - a^{2} x}\,{d x} + \arctan\left(1, \sqrt{a x^{n} + 1} \sqrt{a x^{n} - 1}\right) \log\left(x\right)"," ",0,"a^2*n*integrate(sqrt(a*x^n + 1)*sqrt(a*x^n - 1)*log(x)/(a^4*x*x^(2*n) - a^2*x), x) + arctan2(1, sqrt(a*x^n + 1)*sqrt(a*x^n - 1))*log(x)","F",0
17,0,0,0,0.000000," ","integrate(x^4*arccsc(b*x+a),x, algorithm=""maxima"")","\frac{1}{5} \, x^{5} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + \int \frac{{\left(b^{2} x^{6} + a b x^{5}\right)} e^{\left(\frac{1}{2} \, \log\left(b x + a + 1\right) + \frac{1}{2} \, \log\left(b x + a - 1\right)\right)}}{5 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)} e^{\left(\log\left(b x + a + 1\right) + \log\left(b x + a - 1\right)\right)} - 1\right)}}\,{d x}"," ",0,"1/5*x^5*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + integrate(1/5*(b^2*x^6 + a*b*x^5)*e^(1/2*log(b*x + a + 1) + 1/2*log(b*x + a - 1))/(b^2*x^2 + 2*a*b*x + a^2 + (b^2*x^2 + 2*a*b*x + a^2 - 1)*e^(log(b*x + a + 1) + log(b*x + a - 1)) - 1), x)","F",0
18,0,0,0,0.000000," ","integrate(x^3*arccsc(b*x+a),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + \int \frac{{\left(b^{2} x^{5} + a b x^{4}\right)} e^{\left(\frac{1}{2} \, \log\left(b x + a + 1\right) + \frac{1}{2} \, \log\left(b x + a - 1\right)\right)}}{4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)} e^{\left(\log\left(b x + a + 1\right) + \log\left(b x + a - 1\right)\right)} - 1\right)}}\,{d x}"," ",0,"1/4*x^4*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + integrate(1/4*(b^2*x^5 + a*b*x^4)*e^(1/2*log(b*x + a + 1) + 1/2*log(b*x + a - 1))/(b^2*x^2 + 2*a*b*x + a^2 + (b^2*x^2 + 2*a*b*x + a^2 - 1)*e^(log(b*x + a + 1) + log(b*x + a - 1)) - 1), x)","F",0
19,0,0,0,0.000000," ","integrate(x^2*arccsc(b*x+a),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + \int \frac{{\left(b^{2} x^{4} + a b x^{3}\right)} e^{\left(\frac{1}{2} \, \log\left(b x + a + 1\right) + \frac{1}{2} \, \log\left(b x + a - 1\right)\right)}}{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)} e^{\left(\log\left(b x + a + 1\right) + \log\left(b x + a - 1\right)\right)} - 1\right)}}\,{d x}"," ",0,"1/3*x^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + integrate(1/3*(b^2*x^4 + a*b*x^3)*e^(1/2*log(b*x + a + 1) + 1/2*log(b*x + a - 1))/(b^2*x^2 + 2*a*b*x + a^2 + (b^2*x^2 + 2*a*b*x + a^2 - 1)*e^(log(b*x + a + 1) + log(b*x + a - 1)) - 1), x)","F",0
20,0,0,0,0.000000," ","integrate(x*arccsc(b*x+a),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + \int \frac{{\left(b^{2} x^{3} + a b x^{2}\right)} e^{\left(\frac{1}{2} \, \log\left(b x + a + 1\right) + \frac{1}{2} \, \log\left(b x + a - 1\right)\right)}}{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)} e^{\left(\log\left(b x + a + 1\right) + \log\left(b x + a - 1\right)\right)} - 1\right)}}\,{d x}"," ",0,"1/2*x^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + integrate(1/2*(b^2*x^3 + a*b*x^2)*e^(1/2*log(b*x + a + 1) + 1/2*log(b*x + a - 1))/(b^2*x^2 + 2*a*b*x + a^2 + (b^2*x^2 + 2*a*b*x + a^2 - 1)*e^(log(b*x + a + 1) + log(b*x + a - 1)) - 1), x)","F",0
21,1,55,0,0.331503," ","integrate(arccsc(b*x+a),x, algorithm=""maxima"")","\frac{2 \, {\left(b x + a\right)} \operatorname{arccsc}\left(b x + a\right) + \log\left(\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} + 1\right) - \log\left(-\sqrt{-\frac{1}{{\left(b x + a\right)}^{2}} + 1} + 1\right)}{2 \, b}"," ",0,"1/2*(2*(b*x + a)*arccsc(b*x + a) + log(sqrt(-1/(b*x + a)^2 + 1) + 1) - log(-sqrt(-1/(b*x + a)^2 + 1) + 1))/b","A",0
22,0,0,0,0.000000," ","integrate(arccsc(b*x+a)/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arccsc}\left(b x + a\right)}{x}\,{d x}"," ",0,"integrate(arccsc(b*x + a)/x, x)","F",0
23,0,0,0,0.000000," ","integrate(arccsc(b*x+a)/x^2,x, algorithm=""maxima"")","-\frac{b x \int \frac{1}{\sqrt{b x + a + 1} \sqrt{b x + a - 1} b x^{2} + \sqrt{b x + a + 1} \sqrt{b x + a - 1} a x}\,{d x} + \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)}{x}"," ",0,"-(x*integrate((b^2*x + a*b)*e^(1/2*log(b*x + a + 1) + 1/2*log(b*x + a - 1))/(b^2*x^3 + 2*a*b*x^2 + (a^2 - 1)*x + (b^2*x^3 + 2*a*b*x^2 + (a^2 - 1)*x)*e^(log(b*x + a + 1) + log(b*x + a - 1))), x) + arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))/x","F",0
24,0,0,0,0.000000," ","integrate(arccsc(b*x+a)/x^3,x, algorithm=""maxima"")","-\frac{x^{2} \int \frac{{\left(b^{2} x + a b\right)} e^{\left(\frac{1}{2} \, \log\left(b x + a + 1\right) + \frac{1}{2} \, \log\left(b x + a - 1\right)\right)}}{b^{2} x^{4} + 2 \, a b x^{3} + {\left(b^{2} x^{4} + 2 \, a b x^{3} + {\left(a^{2} - 1\right)} x^{2}\right)} {\left(b x + a + 1\right)} {\left(b x + a - 1\right)} + {\left(a^{2} - 1\right)} x^{2}}\,{d x} + \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)}{2 \, x^{2}}"," ",0,"-1/2*(2*x^2*integrate(1/2*(b^2*x + a*b)*e^(1/2*log(b*x + a + 1) + 1/2*log(b*x + a - 1))/(b^2*x^4 + 2*a*b*x^3 + (a^2 - 1)*x^2 + (b^2*x^4 + 2*a*b*x^3 + (a^2 - 1)*x^2)*e^(log(b*x + a + 1) + log(b*x + a - 1))), x) + arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))/x^2","F",0
25,0,0,0,0.000000," ","integrate(arccsc(b*x+a)/x^4,x, algorithm=""maxima"")","-\frac{x^{3} \int \frac{{\left(b^{2} x + a b\right)} e^{\left(\frac{1}{2} \, \log\left(b x + a + 1\right) + \frac{1}{2} \, \log\left(b x + a - 1\right)\right)}}{b^{2} x^{5} + 2 \, a b x^{4} + {\left(a^{2} - 1\right)} x^{3} + {\left(b^{2} x^{5} + 2 \, a b x^{4} + {\left(a^{2} - 1\right)} x^{3}\right)} {\left(b x + a + 1\right)} {\left(b x + a - 1\right)}}\,{d x} + \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)}{3 \, x^{3}}"," ",0,"-1/3*(3*x^3*integrate(1/3*(b^2*x + a*b)*e^(1/2*log(b*x + a + 1) + 1/2*log(b*x + a - 1))/(b^2*x^5 + 2*a*b*x^4 + (a^2 - 1)*x^3 + (b^2*x^5 + 2*a*b*x^4 + (a^2 - 1)*x^3)*e^(log(b*x + a + 1) + log(b*x + a - 1))), x) + arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))/x^3","F",0
26,0,0,0,0.000000," ","integrate(arccsc(b*x+a)/x^5,x, algorithm=""maxima"")","-\frac{x^{4} \int \frac{{\left(b^{2} x + a b\right)} e^{\left(\frac{1}{2} \, \log\left(b x + a + 1\right) + \frac{1}{2} \, \log\left(b x + a - 1\right)\right)}}{b^{2} x^{6} + 2 \, a b x^{5} + {\left(a^{2} - 1\right)} x^{4} + {\left(b^{2} x^{6} + 2 \, a b x^{5} + {\left(a^{2} - 1\right)} x^{4}\right)} {\left(b x + a + 1\right)} {\left(b x + a - 1\right)}}\,{d x} + \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)}{4 \, x^{4}}"," ",0,"-1/4*(4*x^4*integrate(1/4*(b^2*x + a*b)*e^(1/2*log(b*x + a + 1) + 1/2*log(b*x + a - 1))/(b^2*x^6 + 2*a*b*x^5 + (a^2 - 1)*x^4 + (b^2*x^6 + 2*a*b*x^5 + (a^2 - 1)*x^4)*e^(log(b*x + a + 1) + log(b*x + a - 1))), x) + arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))/x^4","F",0
27,0,0,0,0.000000," ","integrate(x^3*arccsc(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)^{2} - \frac{1}{16} \, x^{4} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)^{2} + \int \frac{2 \, \sqrt{b x + a + 1} \sqrt{b x + a - 1} b x^{4} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - 4 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{5} + {\left(3 \, a^{2} - 1\right)} b x^{4} + {\left(a^{3} - a\right)} x^{3}\right)} \log\left(b x + a\right)^{2} + {\left(b^{3} x^{6} + 2 \, a b^{2} x^{5} + {\left(a^{2} - 1\right)} b x^{4} + 4 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{5} + {\left(3 \, a^{2} - 1\right)} b x^{4} + {\left(a^{3} - a\right)} x^{3}\right)} \log\left(b x + a\right)\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}{4 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} - 1\right)} b x - a\right)}}\,{d x}"," ",0,"1/4*x^4*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1))^2 - 1/16*x^4*log(b^2*x^2 + 2*a*b*x + a^2)^2 + integrate(1/4*(2*sqrt(b*x + a + 1)*sqrt(b*x + a - 1)*b*x^4*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - 4*(b^3*x^6 + 3*a*b^2*x^5 + (3*a^2 - 1)*b*x^4 + (a^3 - a)*x^3)*log(b*x + a)^2 + (b^3*x^6 + 2*a*b^2*x^5 + (a^2 - 1)*b*x^4 + 4*(b^3*x^6 + 3*a*b^2*x^5 + (3*a^2 - 1)*b*x^4 + (a^3 - a)*x^3)*log(b*x + a))*log(b^2*x^2 + 2*a*b*x + a^2))/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2 - 1)*b*x - a), x)","F",0
28,0,0,0,0.000000," ","integrate(x^2*arccsc(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)^{2} - \frac{1}{12} \, x^{3} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)^{2} + \int \frac{2 \, \sqrt{b x + a + 1} \sqrt{b x + a - 1} b x^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - 3 \, {\left(b^{3} x^{5} + 3 \, a b^{2} x^{4} + {\left(3 \, a^{2} - 1\right)} b x^{3} + {\left(a^{3} - a\right)} x^{2}\right)} \log\left(b x + a\right)^{2} + {\left(b^{3} x^{5} + 2 \, a b^{2} x^{4} + {\left(a^{2} - 1\right)} b x^{3} + 3 \, {\left(b^{3} x^{5} + 3 \, a b^{2} x^{4} + {\left(3 \, a^{2} - 1\right)} b x^{3} + {\left(a^{3} - a\right)} x^{2}\right)} \log\left(b x + a\right)\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}{3 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} - 1\right)} b x - a\right)}}\,{d x}"," ",0,"1/3*x^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1))^2 - 1/12*x^3*log(b^2*x^2 + 2*a*b*x + a^2)^2 + integrate(1/3*(2*sqrt(b*x + a + 1)*sqrt(b*x + a - 1)*b*x^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - 3*(b^3*x^5 + 3*a*b^2*x^4 + (3*a^2 - 1)*b*x^3 + (a^3 - a)*x^2)*log(b*x + a)^2 + (b^3*x^5 + 2*a*b^2*x^4 + (a^2 - 1)*b*x^3 + 3*(b^3*x^5 + 3*a*b^2*x^4 + (3*a^2 - 1)*b*x^3 + (a^3 - a)*x^2)*log(b*x + a))*log(b^2*x^2 + 2*a*b*x + a^2))/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2 - 1)*b*x - a), x)","F",0
29,0,0,0,0.000000," ","integrate(x*arccsc(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)^{2} - \frac{1}{8} \, x^{2} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)^{2} + \int \frac{2 \, \sqrt{b x + a + 1} \sqrt{b x + a - 1} b x^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - 2 \, {\left(b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} - 1\right)} b x^{2} + {\left(a^{3} - a\right)} x\right)} \log\left(b x + a\right)^{2} + {\left(b^{3} x^{4} + 2 \, a b^{2} x^{3} + {\left(a^{2} - 1\right)} b x^{2} + 2 \, {\left(b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} - 1\right)} b x^{2} + {\left(a^{3} - a\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}{2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} - 1\right)} b x - a\right)}}\,{d x}"," ",0,"1/2*x^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1))^2 - 1/8*x^2*log(b^2*x^2 + 2*a*b*x + a^2)^2 + integrate(1/2*(2*sqrt(b*x + a + 1)*sqrt(b*x + a - 1)*b*x^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - 2*(b^3*x^4 + 3*a*b^2*x^3 + (3*a^2 - 1)*b*x^2 + (a^3 - a)*x)*log(b*x + a)^2 + (b^3*x^4 + 2*a*b^2*x^3 + (a^2 - 1)*b*x^2 + 2*(b^3*x^4 + 3*a*b^2*x^3 + (3*a^2 - 1)*b*x^2 + (a^3 - a)*x)*log(b*x + a))*log(b^2*x^2 + 2*a*b*x + a^2))/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2 - 1)*b*x - a), x)","F",0
30,0,0,0,0.000000," ","integrate(arccsc(b*x+a)^2,x, algorithm=""maxima"")","x \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)^{2} - \frac{1}{4} \, x \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)^{2} + \int \frac{2 \, \sqrt{b x + a + 1} \sqrt{b x + a - 1} b x \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} - 1\right)} b x - a\right)} \log\left(b x + a\right)^{2} + {\left(b^{3} x^{3} + 2 \, a b^{2} x^{2} + {\left(a^{2} - 1\right)} b x + {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} - 1\right)} b x - a\right)} \log\left(b x + a\right)\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} - 1\right)} b x - a}\,{d x}"," ",0,"x*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1))^2 - 1/4*x*log(b^2*x^2 + 2*a*b*x + a^2)^2 + integrate((2*sqrt(b*x + a + 1)*sqrt(b*x + a - 1)*b*x*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - (b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2 - 1)*b*x - a)*log(b*x + a)^2 + (b^3*x^3 + 2*a*b^2*x^2 + (a^2 - 1)*b*x + (b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2 - 1)*b*x - a)*log(b*x + a))*log(b^2*x^2 + 2*a*b*x + a^2))/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2 - 1)*b*x - a), x)","F",0
31,0,0,0,0.000000," ","integrate(arccsc(b*x+a)^2/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arccsc}\left(b x + a\right)^{2}}{x}\,{d x}"," ",0,"integrate(arccsc(b*x + a)^2/x, x)","F",0
32,-1,0,0,0.000000," ","integrate(arccsc(b*x+a)^2/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,0,0,0,0.000000," ","integrate(x^2*arccsc(b*x+a)^3,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)^{3} - \frac{1}{4} \, x^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)^{2} - \int \frac{12 \, {\left(b^{3} x^{5} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + 3 \, a b^{2} x^{4} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + {\left(3 \, a^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} b x^{3} + {\left(a^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - a \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} x^{2}\right)} \log\left(b x + a\right)^{2} - {\left(4 \, b x^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)^{2} - b x^{3} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)^{2}\right)} \sqrt{b x + a + 1} \sqrt{b x + a - 1} - 4 \, {\left(b^{3} x^{5} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + 2 \, a b^{2} x^{4} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + {\left(a^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} b x^{3} + 3 \, {\left(b^{3} x^{5} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + 3 \, a b^{2} x^{4} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + {\left(3 \, a^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} b x^{3} + {\left(a^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - a \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} x^{2}\right)} \log\left(b x + a\right)\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}{4 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} - 1\right)} b x - a\right)}}\,{d x}"," ",0,"1/3*x^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1))^3 - 1/4*x^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1))*log(b^2*x^2 + 2*a*b*x + a^2)^2 - integrate(1/4*(12*(b^3*x^5*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + 3*a*b^2*x^4*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + (3*a^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*b*x^3 + (a^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - a*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*x^2)*log(b*x + a)^2 - (4*b*x^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1))^2 - b*x^3*log(b^2*x^2 + 2*a*b*x + a^2)^2)*sqrt(b*x + a + 1)*sqrt(b*x + a - 1) - 4*(b^3*x^5*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + 2*a*b^2*x^4*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + (a^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*b*x^3 + 3*(b^3*x^5*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + 3*a*b^2*x^4*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + (3*a^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*b*x^3 + (a^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - a*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*x^2)*log(b*x + a))*log(b^2*x^2 + 2*a*b*x + a^2))/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2 - 1)*b*x - a), x)","F",0
34,0,0,0,0.000000," ","integrate(x*arccsc(b*x+a)^3,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)^{3} - \frac{3}{8} \, x^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)^{2} - \int \frac{3 \, {\left(8 \, {\left(b^{3} x^{4} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + 3 \, a b^{2} x^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + {\left(3 \, a^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} b x^{2} + {\left(a^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - a \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} x\right)} \log\left(b x + a\right)^{2} - {\left(4 \, b x^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)^{2} - b x^{2} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)^{2}\right)} \sqrt{b x + a + 1} \sqrt{b x + a - 1} - 4 \, {\left(b^{3} x^{4} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + 2 \, a b^{2} x^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + {\left(a^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} b x^{2} + 2 \, {\left(b^{3} x^{4} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + 3 \, a b^{2} x^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + {\left(3 \, a^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} b x^{2} + {\left(a^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - a \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)\right)}}{8 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} - 1\right)} b x - a\right)}}\,{d x}"," ",0,"1/2*x^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1))^3 - 3/8*x^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1))*log(b^2*x^2 + 2*a*b*x + a^2)^2 - integrate(3/8*(8*(b^3*x^4*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + 3*a*b^2*x^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + (3*a^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*b*x^2 + (a^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - a*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*x)*log(b*x + a)^2 - (4*b*x^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1))^2 - b*x^2*log(b^2*x^2 + 2*a*b*x + a^2)^2)*sqrt(b*x + a + 1)*sqrt(b*x + a - 1) - 4*(b^3*x^4*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + 2*a*b^2*x^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + (a^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*b*x^2 + 2*(b^3*x^4*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + 3*a*b^2*x^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + (3*a^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*b*x^2 + (a^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - a*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*x)*log(b*x + a))*log(b^2*x^2 + 2*a*b*x + a^2))/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2 - 1)*b*x - a), x)","F",0
35,0,0,0,0.000000," ","integrate(arccsc(b*x+a)^3,x, algorithm=""maxima"")","x \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)^{3} - \frac{3}{4} \, x \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)^{2} - \int \frac{3 \, {\left(4 \, {\left(b^{3} x^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + 3 \, a b^{2} x^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + a^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + {\left(3 \, a^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} b x - a \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} \log\left(b x + a\right)^{2} - {\left(4 \, b x \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)^{2} - b x \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)^{2}\right)} \sqrt{b x + a + 1} \sqrt{b x + a - 1} - 4 \, {\left(b^{3} x^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + 2 \, a b^{2} x^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + {\left(a^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} b x + {\left(b^{3} x^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + 3 \, a b^{2} x^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + a^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + {\left(3 \, a^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} b x - a \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} \log\left(b x + a\right)\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)\right)}}{4 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} - 1\right)} b x - a\right)}}\,{d x}"," ",0,"x*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1))^3 - 3/4*x*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1))*log(b^2*x^2 + 2*a*b*x + a^2)^2 - integrate(3/4*(4*(b^3*x^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + 3*a*b^2*x^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + a^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + (3*a^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*b*x - a*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*log(b*x + a)^2 - (4*b*x*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1))^2 - b*x*log(b^2*x^2 + 2*a*b*x + a^2)^2)*sqrt(b*x + a + 1)*sqrt(b*x + a - 1) - 4*(b^3*x^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + 2*a*b^2*x^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + (a^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*b*x + (b^3*x^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + 3*a*b^2*x^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + a^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + (3*a^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*b*x - a*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*log(b*x + a))*log(b^2*x^2 + 2*a*b*x + a^2))/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2 - 1)*b*x - a), x)","F",0
36,0,0,0,0.000000," ","integrate(arccsc(b*x+a)^3/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arccsc}\left(b x + a\right)^{3}}{x}\,{d x}"," ",0,"integrate(arccsc(b*x + a)^3/x, x)","F",0
37,0,0,0,0.000000," ","integrate(arccsc(b*x+a)^3/x^2,x, algorithm=""maxima"")","-\frac{4 \, \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)^{3} - 3 \, \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)^{2} + 3 \, x \int \frac{4 \, {\left(b^{3} x^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + 3 \, a b^{2} x^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + a^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + {\left(3 \, a^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} b x - a \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} \log\left(b x + a\right)^{2} + {\left(4 \, b x \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)^{2} - b x \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)^{2}\right)} \sqrt{b x + a + 1} \sqrt{b x + a - 1} + 4 \, {\left(b^{3} x^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + 2 \, a b^{2} x^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + {\left(a^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} b x - {\left(b^{3} x^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + 3 \, a b^{2} x^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + a^{3} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + {\left(3 \, a^{2} \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) - \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} b x - a \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right)\right)} \log\left(b x + a\right)\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)}{b^{3} x^{5} + 3 \, a b^{2} x^{4} + {\left(3 \, a^{2} - 1\right)} b x^{3} + {\left(a^{3} - a\right)} x^{2}}\,{d x}}{4 \, x}"," ",0,"-1/4*(4*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1))^3 - 3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1))*log(b^2*x^2 + 2*a*b*x + a^2)^2 - 4*x*integrate(-3/4*(4*(b^3*x^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + 3*a*b^2*x^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + a^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + (3*a^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*b*x - a*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*log(b*x + a)^2 + (4*b*x*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1))^2 - b*x*log(b^2*x^2 + 2*a*b*x + a^2)^2)*sqrt(b*x + a + 1)*sqrt(b*x + a - 1) + 4*(b^3*x^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + 2*a*b^2*x^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + (a^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*b*x - (b^3*x^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + 3*a*b^2*x^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + a^3*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + (3*a^2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) - arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*b*x - a*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)))*log(b*x + a))*log(b^2*x^2 + 2*a*b*x + a^2))/(b^3*x^5 + 3*a*b^2*x^4 + (3*a^2 - 1)*b*x^3 + (a^3 - a)*x^2), x))/x","F",0
38,1,63,0,0.359566," ","integrate(x^3*arccsc(b*x^4+a),x, algorithm=""maxima"")","\frac{2 \, {\left(b x^{4} + a\right)} \operatorname{arccsc}\left(b x^{4} + a\right) + \log\left(\sqrt{-\frac{1}{{\left(b x^{4} + a\right)}^{2}} + 1} + 1\right) - \log\left(-\sqrt{-\frac{1}{{\left(b x^{4} + a\right)}^{2}} + 1} + 1\right)}{8 \, b}"," ",0,"1/8*(2*(b*x^4 + a)*arccsc(b*x^4 + a) + log(sqrt(-1/(b*x^4 + a)^2 + 1) + 1) - log(-sqrt(-1/(b*x^4 + a)^2 + 1) + 1))/b","A",0
39,1,66,0,0.389714," ","integrate(x^(-1+n)*arccsc(a+b*x^n),x, algorithm=""maxima"")","\frac{2 \, {\left(b x^{n} + a\right)} \operatorname{arccsc}\left(b x^{n} + a\right) + \log\left(\sqrt{-\frac{1}{{\left(b x^{n} + a\right)}^{2}} + 1} + 1\right) - \log\left(-\sqrt{-\frac{1}{{\left(b x^{n} + a\right)}^{2}} + 1} + 1\right)}{2 \, b n}"," ",0,"1/2*(2*(b*x^n + a)*arccsc(b*x^n + a) + log(sqrt(-1/(b*x^n + a)^2 + 1) + 1) - log(-sqrt(-1/(b*x^n + a)^2 + 1) + 1))/(b*n)","A",0
40,-1,0,0,0.000000," ","integrate(arccsc(c*exp(b*x+a)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
41,0,0,0,0.000000," ","integrate(exp(arccsc(a*x))*x^2,x, algorithm=""maxima"")","\int x^{2} e^{\left(\operatorname{arccsc}\left(a x\right)\right)}\,{d x}"," ",0,"integrate(x^2*e^(arccsc(a*x)), x)","F",0
42,0,0,0,0.000000," ","integrate(exp(arccsc(a*x))*x,x, algorithm=""maxima"")","\int x e^{\left(\operatorname{arccsc}\left(a x\right)\right)}\,{d x}"," ",0,"integrate(x*e^(arccsc(a*x)), x)","F",0
43,0,0,0,0.000000," ","integrate(exp(arccsc(a*x)),x, algorithm=""maxima"")","\int e^{\left(\operatorname{arccsc}\left(a x\right)\right)}\,{d x}"," ",0,"integrate(e^(arccsc(a*x)), x)","F",0
44,0,0,0,0.000000," ","integrate(exp(arccsc(a*x))/x,x, algorithm=""maxima"")","\int \frac{e^{\left(\operatorname{arccsc}\left(a x\right)\right)}}{x}\,{d x}"," ",0,"integrate(e^(arccsc(a*x))/x, x)","F",0
45,0,0,0,0.000000," ","integrate(exp(arccsc(a*x))/x^2,x, algorithm=""maxima"")","\int \frac{e^{\left(\operatorname{arccsc}\left(a x\right)\right)}}{x^{2}}\,{d x}"," ",0,"integrate(e^(arccsc(a*x))/x^2, x)","F",0
46,0,0,0,0.000000," ","integrate(exp(arccsc(a*x))/x^3,x, algorithm=""maxima"")","\int \frac{e^{\left(\operatorname{arccsc}\left(a x\right)\right)}}{x^{3}}\,{d x}"," ",0,"integrate(e^(arccsc(a*x))/x^3, x)","F",0
47,0,0,0,0.000000," ","integrate(exp(arccsc(a*x))/x^4,x, algorithm=""maxima"")","\int \frac{e^{\left(\operatorname{arccsc}\left(a x\right)\right)}}{x^{4}}\,{d x}"," ",0,"integrate(e^(arccsc(a*x))/x^4, x)","F",0
48,0,0,0,0.000000," ","integrate(exp(arccsc(a*x))/x^5,x, algorithm=""maxima"")","\int \frac{e^{\left(\operatorname{arccsc}\left(a x\right)\right)}}{x^{5}}\,{d x}"," ",0,"integrate(e^(arccsc(a*x))/x^5, x)","F",0
49,0,0,0,0.000000," ","integrate(arccsc(b*x+a)/(a*d/b+d*x),x, algorithm=""maxima"")","\frac{i \, {\left(b {\left(\frac{\log\left(b x + a + 1\right) \log\left(b x + a\right) - \log\left(b x + a\right)^{2} + \log\left(b x + a\right) \log\left(b x + a - 1\right)}{b^{2} d} - \frac{\log\left(b x + a + 1\right) \log\left(b x + a\right) + {\rm Li}_2\left(-b x - a\right)}{b^{2} d} - \frac{\log\left(b x + a\right) \log\left(-b x - a + 1\right) + {\rm Li}_2\left(b x + a\right)}{b^{2} d}\right)} - {\left(\frac{\log\left(b x + a + 1\right)}{b d} - \frac{2 \, \log\left(b x + a\right)}{b d} + \frac{\log\left(b x + a - 1\right)}{b d}\right)} \log\left(b x + a\right)\right)} b d + 2 \, b \int \frac{\log\left(b x + a\right)}{\sqrt{b x + a + 1} \sqrt{b x + a - 1} b x + \sqrt{b x + a + 1} \sqrt{b x + a - 1} a}\,{d x} + {\left(2 \, \arctan\left(1, \sqrt{b x + a + 1} \sqrt{b x + a - 1}\right) + i \, \log\left(-b x - a + 1\right)\right)} \log\left(b x + a\right) - i \, \log\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right) \log\left(b x + a\right) + i \, \log\left(b x + a + 1\right) \log\left(b x + a\right) + i \, \log\left(b x + a\right)^{2} + i \, {\rm Li}_2\left(b x + a\right) + i \, {\rm Li}_2\left(-b x - a\right)}{2 \, d}"," ",0,"1/2*(2*b*d*integrate(sqrt(b*x + a + 1)*sqrt(b*x + a - 1)*log(b*x + a)/(b^3*d*x^3 + 3*a*b^2*d*x^2 + (3*a^2 - 1)*b*d*x + (a^3 - a)*d), x) - 2*I*b*d*integrate(log(b*x + a)/(b^3*d*x^3 + 3*a*b^2*d*x^2 + (3*a^2 - 1)*b*d*x + (a^3 - a)*d), x) + (2*arctan2(1, sqrt(b*x + a + 1)*sqrt(b*x + a - 1)) + I*log(-b*x - a + 1))*log(b*x + a) - I*log(b^2*x^2 + 2*a*b*x + a^2)*log(b*x + a) + I*log(b*x + a + 1)*log(b*x + a) + I*log(b*x + a)^2 + I*dilog(b*x + a) + I*dilog(-b*x - a))/d","F",0
