1,0,0,0,0.583809," ","integrate(arccsc(a*x^5)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccsc}\left(a x^{5}\right)}{x}, x\right)"," ",0,"integral(arccsc(a*x^5)/x, x)","F",0
2,1,32,0,0.921199," ","integrate(x^3*arccsc(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{4} \, x^{4} \operatorname{arccsc}\left(\sqrt{x}\right) + \frac{1}{140} \, {\left(5 \, x^{3} + 6 \, x^{2} + 8 \, x + 16\right)} \sqrt{x - 1}"," ",0,"1/4*x^4*arccsc(sqrt(x)) + 1/140*(5*x^3 + 6*x^2 + 8*x + 16)*sqrt(x - 1)","A",0
3,1,27,0,1.914605," ","integrate(x^2*arccsc(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{3} \, x^{3} \operatorname{arccsc}\left(\sqrt{x}\right) + \frac{1}{45} \, {\left(3 \, x^{2} + 4 \, x + 8\right)} \sqrt{x - 1}"," ",0,"1/3*x^3*arccsc(sqrt(x)) + 1/45*(3*x^2 + 4*x + 8)*sqrt(x - 1)","A",0
4,1,20,0,1.988267," ","integrate(x*arccsc(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} \operatorname{arccsc}\left(\sqrt{x}\right) + \frac{1}{6} \, {\left(x + 2\right)} \sqrt{x - 1}"," ",0,"1/2*x^2*arccsc(sqrt(x)) + 1/6*(x + 2)*sqrt(x - 1)","A",0
5,1,12,0,1.861751," ","integrate(arccsc(x^(1/2)),x, algorithm=""fricas"")","x \operatorname{arccsc}\left(\sqrt{x}\right) + \sqrt{x - 1}"," ",0,"x*arccsc(sqrt(x)) + sqrt(x - 1)","A",0
6,0,0,0,0.811642," ","integrate(arccsc(x^(1/2))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccsc}\left(\sqrt{x}\right)}{x}, x\right)"," ",0,"integral(arccsc(sqrt(x))/x, x)","F",0
7,1,21,0,0.857205," ","integrate(arccsc(x^(1/2))/x^2,x, algorithm=""fricas"")","\frac{{\left(x - 2\right)} \operatorname{arccsc}\left(\sqrt{x}\right) - \sqrt{x - 1}}{2 \, x}"," ",0,"1/2*((x - 2)*arccsc(sqrt(x)) - sqrt(x - 1))/x","A",0
8,1,30,0,1.722627," ","integrate(arccsc(x^(1/2))/x^3,x, algorithm=""fricas"")","\frac{{\left(3 \, x^{2} - 8\right)} \operatorname{arccsc}\left(\sqrt{x}\right) - {\left(3 \, x + 2\right)} \sqrt{x - 1}}{16 \, x^{2}}"," ",0,"1/16*((3*x^2 - 8)*arccsc(sqrt(x)) - (3*x + 2)*sqrt(x - 1))/x^2","A",0
9,1,39,0,1.047952," ","integrate(x^2*arccsc(a/x),x, algorithm=""fricas"")","\frac{1}{3} \, x^{3} \operatorname{arccsc}\left(\frac{a}{x}\right) + \frac{1}{9} \, {\left(2 \, a^{2} x + x^{3}\right)} \sqrt{\frac{a^{2} - x^{2}}{x^{2}}}"," ",0,"1/3*x^3*arccsc(a/x) + 1/9*(2*a^2*x + x^3)*sqrt((a^2 - x^2)/x^2)","A",0
10,1,38,0,0.795282," ","integrate(x*arccsc(a/x),x, algorithm=""fricas"")","\frac{1}{4} \, x^{2} \sqrt{\frac{a^{2} - x^{2}}{x^{2}}} - \frac{1}{4} \, {\left(a^{2} - 2 \, x^{2}\right)} \operatorname{arccsc}\left(\frac{a}{x}\right)"," ",0,"1/4*x^2*sqrt((a^2 - x^2)/x^2) - 1/4*(a^2 - 2*x^2)*arccsc(a/x)","A",0
11,1,26,0,0.920128," ","integrate(arccsc(a/x),x, algorithm=""fricas"")","x \operatorname{arccsc}\left(\frac{a}{x}\right) + x \sqrt{\frac{a^{2} - x^{2}}{x^{2}}}"," ",0,"x*arccsc(a/x) + x*sqrt((a^2 - x^2)/x^2)","A",0
12,0,0,0,0.956576," ","integrate(arccsc(a/x)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccsc}\left(\frac{a}{x}\right)}{x}, x\right)"," ",0,"integral(arccsc(a/x)/x, x)","F",0
13,1,65,0,0.966824," ","integrate(arccsc(a/x)/x^2,x, algorithm=""fricas"")","-\frac{2 \, a \operatorname{arccsc}\left(\frac{a}{x}\right) + x \log\left(x \sqrt{\frac{a^{2} - x^{2}}{x^{2}}} + a\right) - x \log\left(x \sqrt{\frac{a^{2} - x^{2}}{x^{2}}} - a\right)}{2 \, a x}"," ",0,"-1/2*(2*a*arccsc(a/x) + x*log(x*sqrt((a^2 - x^2)/x^2) + a) - x*log(x*sqrt((a^2 - x^2)/x^2) - a))/(a*x)","B",0
14,1,38,0,0.463834," ","integrate(arccsc(a/x)/x^3,x, algorithm=""fricas"")","-\frac{a^{2} \operatorname{arccsc}\left(\frac{a}{x}\right) + x^{2} \sqrt{\frac{a^{2} - x^{2}}{x^{2}}}}{2 \, a^{2} x^{2}}"," ",0,"-1/2*(a^2*arccsc(a/x) + x^2*sqrt((a^2 - x^2)/x^2))/(a^2*x^2)","A",0
15,1,92,0,0.640568," ","integrate(arccsc(a/x)/x^4,x, algorithm=""fricas"")","-\frac{4 \, a^{3} \operatorname{arccsc}\left(\frac{a}{x}\right) + x^{3} \log\left(x \sqrt{\frac{a^{2} - x^{2}}{x^{2}}} + a\right) - x^{3} \log\left(x \sqrt{\frac{a^{2} - x^{2}}{x^{2}}} - a\right) + 2 \, a x^{2} \sqrt{\frac{a^{2} - x^{2}}{x^{2}}}}{12 \, a^{3} x^{3}}"," ",0,"-1/12*(4*a^3*arccsc(a/x) + x^3*log(x*sqrt((a^2 - x^2)/x^2) + a) - x^3*log(x*sqrt((a^2 - x^2)/x^2) - a) + 2*a*x^2*sqrt((a^2 - x^2)/x^2))/(a^3*x^3)","A",0
16,-2,0,0,0.000000," ","integrate(arccsc(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
17,1,151,0,0.729876," ","integrate(x^4*arccsc(b*x+a),x, algorithm=""fricas"")","\frac{24 \, b^{5} x^{5} \operatorname{arccsc}\left(b x + a\right) - 48 \, a^{5} \arctan\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) - 3 \, {\left(40 \, a^{4} + 40 \, a^{2} + 3\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) + {\left(6 \, b^{3} x^{3} - 22 \, a b^{2} x^{2} - 154 \, a^{3} + {\left(58 \, a^{2} + 9\right)} b x - 71 \, a\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}}{120 \, b^{5}}"," ",0,"1/120*(24*b^5*x^5*arccsc(b*x + a) - 48*a^5*arctan(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) - 3*(40*a^4 + 40*a^2 + 3)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) + (6*b^3*x^3 - 22*a*b^2*x^2 - 154*a^3 + (58*a^2 + 9)*b*x - 71*a)*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1))/b^5","A",0
18,1,129,0,0.768153," ","integrate(x^3*arccsc(b*x+a),x, algorithm=""fricas"")","\frac{3 \, b^{4} x^{4} \operatorname{arccsc}\left(b x + a\right) + 6 \, a^{4} \arctan\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) + 6 \, {\left(2 \, a^{3} + a\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} {\left(b^{2} x^{2} - 4 \, a b x + 13 \, a^{2} + 2\right)}}{12 \, b^{4}}"," ",0,"1/12*(3*b^4*x^4*arccsc(b*x + a) + 6*a^4*arctan(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) + 6*(2*a^3 + a)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*(b^2*x^2 - 4*a*b*x + 13*a^2 + 2))/b^4","A",0
19,1,117,0,0.699044," ","integrate(x^2*arccsc(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} \operatorname{arccsc}\left(b x + a\right) - 4 \, a^{3} \arctan\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) - {\left(6 \, a^{2} + 1\right)} \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} {\left(b x - 5 \, a\right)}}{6 \, b^{3}}"," ",0,"1/6*(2*b^3*x^3*arccsc(b*x + a) - 4*a^3*arctan(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) - (6*a^2 + 1)*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*(b*x - 5*a))/b^3","A",0
20,1,102,0,0.637897," ","integrate(x*arccsc(b*x+a),x, algorithm=""fricas"")","\frac{b^{2} x^{2} \operatorname{arccsc}\left(b x + a\right) + 2 \, a^{2} \arctan\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) + 2 \, a \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}}{2 \, b^{2}}"," ",0,"1/2*(b^2*x^2*arccsc(b*x + a) + 2*a^2*arctan(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) + 2*a*log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1))/b^2","A",0
21,1,75,0,0.552271," ","integrate(arccsc(b*x+a),x, algorithm=""fricas"")","\frac{b x \operatorname{arccsc}\left(b x + a\right) - 2 \, a \arctan\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) - \log\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right)}{b}"," ",0,"(b*x*arccsc(b*x + a) - 2*a*arctan(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) - log(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)))/b","B",0
22,0,0,0,0.587000," ","integrate(arccsc(b*x+a)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccsc}\left(b x + a\right)}{x}, x\right)"," ",0,"integral(arccsc(b*x + a)/x, x)","F",0
23,1,278,0,0.673584," ","integrate(arccsc(b*x+a)/x^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} - 1\right)} b x \arctan\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) + \sqrt{a^{2} - 1} b x \log\left(\frac{a^{2} b x + a^{3} + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} {\left(a^{2} + \sqrt{a^{2} - 1} a - 1\right)} + {\left(a b x + a^{2} - 1\right)} \sqrt{a^{2} - 1} - a}{x}\right) - {\left(a^{3} - a\right)} \operatorname{arccsc}\left(b x + a\right)}{{\left(a^{3} - a\right)} x}, \frac{2 \, {\left(a^{2} - 1\right)} b x \arctan\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) - 2 \, \sqrt{-a^{2} + 1} b x \arctan\left(-\frac{\sqrt{-a^{2} + 1} b x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} \sqrt{-a^{2} + 1}}{a^{2} - 1}\right) - {\left(a^{3} - a\right)} \operatorname{arccsc}\left(b x + a\right)}{{\left(a^{3} - a\right)} x}\right]"," ",0,"[(2*(a^2 - 1)*b*x*arctan(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) + sqrt(a^2 - 1)*b*x*log((a^2*b*x + a^3 + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*(a^2 + sqrt(a^2 - 1)*a - 1) + (a*b*x + a^2 - 1)*sqrt(a^2 - 1) - a)/x) - (a^3 - a)*arccsc(b*x + a))/((a^3 - a)*x), (2*(a^2 - 1)*b*x*arctan(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) - 2*sqrt(-a^2 + 1)*b*x*arctan(-(sqrt(-a^2 + 1)*b*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*sqrt(-a^2 + 1))/(a^2 - 1)) - (a^3 - a)*arccsc(b*x + a))/((a^3 - a)*x)]","B",0
24,1,428,0,0.638323," ","integrate(arccsc(b*x+a)/x^3,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, a^{2} - 1\right)} \sqrt{a^{2} - 1} b^{2} x^{2} \log\left(\frac{a^{2} b x + a^{3} + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} {\left(a^{2} - \sqrt{a^{2} - 1} a - 1\right)} - {\left(a b x + a^{2} - 1\right)} \sqrt{a^{2} - 1} - a}{x}\right) - 2 \, {\left(a^{4} - 2 \, a^{2} + 1\right)} b^{2} x^{2} \arctan\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) + {\left(a^{3} - a\right)} b^{2} x^{2} + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} {\left(a^{3} - a\right)} b x - {\left(a^{6} - 2 \, a^{4} + a^{2}\right)} \operatorname{arccsc}\left(b x + a\right)}{2 \, {\left(a^{6} - 2 \, a^{4} + a^{2}\right)} x^{2}}, \frac{2 \, {\left(2 \, a^{2} - 1\right)} \sqrt{-a^{2} + 1} b^{2} x^{2} \arctan\left(-\frac{\sqrt{-a^{2} + 1} b x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} \sqrt{-a^{2} + 1}}{a^{2} - 1}\right) - 2 \, {\left(a^{4} - 2 \, a^{2} + 1\right)} b^{2} x^{2} \arctan\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) + {\left(a^{3} - a\right)} b^{2} x^{2} + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} {\left(a^{3} - a\right)} b x - {\left(a^{6} - 2 \, a^{4} + a^{2}\right)} \operatorname{arccsc}\left(b x + a\right)}{2 \, {\left(a^{6} - 2 \, a^{4} + a^{2}\right)} x^{2}}\right]"," ",0,"[1/2*((2*a^2 - 1)*sqrt(a^2 - 1)*b^2*x^2*log((a^2*b*x + a^3 + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*(a^2 - sqrt(a^2 - 1)*a - 1) - (a*b*x + a^2 - 1)*sqrt(a^2 - 1) - a)/x) - 2*(a^4 - 2*a^2 + 1)*b^2*x^2*arctan(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) + (a^3 - a)*b^2*x^2 + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*(a^3 - a)*b*x - (a^6 - 2*a^4 + a^2)*arccsc(b*x + a))/((a^6 - 2*a^4 + a^2)*x^2), 1/2*(2*(2*a^2 - 1)*sqrt(-a^2 + 1)*b^2*x^2*arctan(-(sqrt(-a^2 + 1)*b*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*sqrt(-a^2 + 1))/(a^2 - 1)) - 2*(a^4 - 2*a^2 + 1)*b^2*x^2*arctan(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) + (a^3 - a)*b^2*x^2 + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*(a^3 - a)*b*x - (a^6 - 2*a^4 + a^2)*arccsc(b*x + a))/((a^6 - 2*a^4 + a^2)*x^2)]","A",0
25,1,548,0,0.668833," ","integrate(arccsc(b*x+a)/x^4,x, algorithm=""fricas"")","\left[\frac{{\left(6 \, a^{4} - 5 \, a^{2} + 2\right)} \sqrt{a^{2} - 1} b^{3} x^{3} \log\left(\frac{a^{2} b x + a^{3} + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} {\left(a^{2} + \sqrt{a^{2} - 1} a - 1\right)} + {\left(a b x + a^{2} - 1\right)} \sqrt{a^{2} - 1} - a}{x}\right) + 4 \, {\left(a^{6} - 3 \, a^{4} + 3 \, a^{2} - 1\right)} b^{3} x^{3} \arctan\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) - {\left(5 \, a^{5} - 7 \, a^{3} + 2 \, a\right)} b^{3} x^{3} - 2 \, {\left(a^{9} - 3 \, a^{7} + 3 \, a^{5} - a^{3}\right)} \operatorname{arccsc}\left(b x + a\right) - {\left({\left(5 \, a^{5} - 7 \, a^{3} + 2 \, a\right)} b^{2} x^{2} - {\left(a^{6} - 2 \, a^{4} + a^{2}\right)} b x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}}{6 \, {\left(a^{9} - 3 \, a^{7} + 3 \, a^{5} - a^{3}\right)} x^{3}}, -\frac{2 \, {\left(6 \, a^{4} - 5 \, a^{2} + 2\right)} \sqrt{-a^{2} + 1} b^{3} x^{3} \arctan\left(-\frac{\sqrt{-a^{2} + 1} b x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} \sqrt{-a^{2} + 1}}{a^{2} - 1}\right) - 4 \, {\left(a^{6} - 3 \, a^{4} + 3 \, a^{2} - 1\right)} b^{3} x^{3} \arctan\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) + {\left(5 \, a^{5} - 7 \, a^{3} + 2 \, a\right)} b^{3} x^{3} + 2 \, {\left(a^{9} - 3 \, a^{7} + 3 \, a^{5} - a^{3}\right)} \operatorname{arccsc}\left(b x + a\right) + {\left({\left(5 \, a^{5} - 7 \, a^{3} + 2 \, a\right)} b^{2} x^{2} - {\left(a^{6} - 2 \, a^{4} + a^{2}\right)} b x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}}{6 \, {\left(a^{9} - 3 \, a^{7} + 3 \, a^{5} - a^{3}\right)} x^{3}}\right]"," ",0,"[1/6*((6*a^4 - 5*a^2 + 2)*sqrt(a^2 - 1)*b^3*x^3*log((a^2*b*x + a^3 + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*(a^2 + sqrt(a^2 - 1)*a - 1) + (a*b*x + a^2 - 1)*sqrt(a^2 - 1) - a)/x) + 4*(a^6 - 3*a^4 + 3*a^2 - 1)*b^3*x^3*arctan(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) - (5*a^5 - 7*a^3 + 2*a)*b^3*x^3 - 2*(a^9 - 3*a^7 + 3*a^5 - a^3)*arccsc(b*x + a) - ((5*a^5 - 7*a^3 + 2*a)*b^2*x^2 - (a^6 - 2*a^4 + a^2)*b*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1))/((a^9 - 3*a^7 + 3*a^5 - a^3)*x^3), -1/6*(2*(6*a^4 - 5*a^2 + 2)*sqrt(-a^2 + 1)*b^3*x^3*arctan(-(sqrt(-a^2 + 1)*b*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*sqrt(-a^2 + 1))/(a^2 - 1)) - 4*(a^6 - 3*a^4 + 3*a^2 - 1)*b^3*x^3*arctan(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) + (5*a^5 - 7*a^3 + 2*a)*b^3*x^3 + 2*(a^9 - 3*a^7 + 3*a^5 - a^3)*arccsc(b*x + a) + ((5*a^5 - 7*a^3 + 2*a)*b^2*x^2 - (a^6 - 2*a^4 + a^2)*b*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1))/((a^9 - 3*a^7 + 3*a^5 - a^3)*x^3)]","A",0
26,1,673,0,0.910357," ","integrate(arccsc(b*x+a)/x^5,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, a^{6} - 8 \, a^{4} + 7 \, a^{2} - 2\right)} \sqrt{a^{2} - 1} b^{4} x^{4} \log\left(\frac{a^{2} b x + a^{3} + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} {\left(a^{2} - \sqrt{a^{2} - 1} a - 1\right)} - {\left(a b x + a^{2} - 1\right)} \sqrt{a^{2} - 1} - a}{x}\right) - 12 \, {\left(a^{8} - 4 \, a^{6} + 6 \, a^{4} - 4 \, a^{2} + 1\right)} b^{4} x^{4} \arctan\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) + {\left(26 \, a^{7} - 43 \, a^{5} + 23 \, a^{3} - 6 \, a\right)} b^{4} x^{4} - 6 \, {\left(a^{12} - 4 \, a^{10} + 6 \, a^{8} - 4 \, a^{6} + a^{4}\right)} \operatorname{arccsc}\left(b x + a\right) + {\left({\left(26 \, a^{7} - 43 \, a^{5} + 23 \, a^{3} - 6 \, a\right)} b^{3} x^{3} - {\left(8 \, a^{8} - 19 \, a^{6} + 14 \, a^{4} - 3 \, a^{2}\right)} b^{2} x^{2} + 2 \, {\left(a^{9} - 3 \, a^{7} + 3 \, a^{5} - a^{3}\right)} b x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}}{24 \, {\left(a^{12} - 4 \, a^{10} + 6 \, a^{8} - 4 \, a^{6} + a^{4}\right)} x^{4}}, \frac{6 \, {\left(8 \, a^{6} - 8 \, a^{4} + 7 \, a^{2} - 2\right)} \sqrt{-a^{2} + 1} b^{4} x^{4} \arctan\left(-\frac{\sqrt{-a^{2} + 1} b x - \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1} \sqrt{-a^{2} + 1}}{a^{2} - 1}\right) - 12 \, {\left(a^{8} - 4 \, a^{6} + 6 \, a^{4} - 4 \, a^{2} + 1\right)} b^{4} x^{4} \arctan\left(-b x - a + \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) + {\left(26 \, a^{7} - 43 \, a^{5} + 23 \, a^{3} - 6 \, a\right)} b^{4} x^{4} - 6 \, {\left(a^{12} - 4 \, a^{10} + 6 \, a^{8} - 4 \, a^{6} + a^{4}\right)} \operatorname{arccsc}\left(b x + a\right) + {\left({\left(26 \, a^{7} - 43 \, a^{5} + 23 \, a^{3} - 6 \, a\right)} b^{3} x^{3} - {\left(8 \, a^{8} - 19 \, a^{6} + 14 \, a^{4} - 3 \, a^{2}\right)} b^{2} x^{2} + 2 \, {\left(a^{9} - 3 \, a^{7} + 3 \, a^{5} - a^{3}\right)} b x\right)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}}{24 \, {\left(a^{12} - 4 \, a^{10} + 6 \, a^{8} - 4 \, a^{6} + a^{4}\right)} x^{4}}\right]"," ",0,"[1/24*(3*(8*a^6 - 8*a^4 + 7*a^2 - 2)*sqrt(a^2 - 1)*b^4*x^4*log((a^2*b*x + a^3 + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*(a^2 - sqrt(a^2 - 1)*a - 1) - (a*b*x + a^2 - 1)*sqrt(a^2 - 1) - a)/x) - 12*(a^8 - 4*a^6 + 6*a^4 - 4*a^2 + 1)*b^4*x^4*arctan(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) + (26*a^7 - 43*a^5 + 23*a^3 - 6*a)*b^4*x^4 - 6*(a^12 - 4*a^10 + 6*a^8 - 4*a^6 + a^4)*arccsc(b*x + a) + ((26*a^7 - 43*a^5 + 23*a^3 - 6*a)*b^3*x^3 - (8*a^8 - 19*a^6 + 14*a^4 - 3*a^2)*b^2*x^2 + 2*(a^9 - 3*a^7 + 3*a^5 - a^3)*b*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1))/((a^12 - 4*a^10 + 6*a^8 - 4*a^6 + a^4)*x^4), 1/24*(6*(8*a^6 - 8*a^4 + 7*a^2 - 2)*sqrt(-a^2 + 1)*b^4*x^4*arctan(-(sqrt(-a^2 + 1)*b*x - sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)*sqrt(-a^2 + 1))/(a^2 - 1)) - 12*(a^8 - 4*a^6 + 6*a^4 - 4*a^2 + 1)*b^4*x^4*arctan(-b*x - a + sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1)) + (26*a^7 - 43*a^5 + 23*a^3 - 6*a)*b^4*x^4 - 6*(a^12 - 4*a^10 + 6*a^8 - 4*a^6 + a^4)*arccsc(b*x + a) + ((26*a^7 - 43*a^5 + 23*a^3 - 6*a)*b^3*x^3 - (8*a^8 - 19*a^6 + 14*a^4 - 3*a^2)*b^2*x^2 + 2*(a^9 - 3*a^7 + 3*a^5 - a^3)*b*x)*sqrt(b^2*x^2 + 2*a*b*x + a^2 - 1))/((a^12 - 4*a^10 + 6*a^8 - 4*a^6 + a^4)*x^4)]","A",0
27,0,0,0,0.611480," ","integrate(x^3*arccsc(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{3} \operatorname{arccsc}\left(b x + a\right)^{2}, x\right)"," ",0,"integral(x^3*arccsc(b*x + a)^2, x)","F",0
28,0,0,0,0.745781," ","integrate(x^2*arccsc(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \operatorname{arccsc}\left(b x + a\right)^{2}, x\right)"," ",0,"integral(x^2*arccsc(b*x + a)^2, x)","F",0
29,0,0,0,0.783822," ","integrate(x*arccsc(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(x \operatorname{arccsc}\left(b x + a\right)^{2}, x\right)"," ",0,"integral(x*arccsc(b*x + a)^2, x)","F",0
30,0,0,0,0.541164," ","integrate(arccsc(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{arccsc}\left(b x + a\right)^{2}, x\right)"," ",0,"integral(arccsc(b*x + a)^2, x)","F",0
31,0,0,0,0.633760," ","integrate(arccsc(b*x+a)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccsc}\left(b x + a\right)^{2}}{x}, x\right)"," ",0,"integral(arccsc(b*x + a)^2/x, x)","F",0
32,0,0,0,0.925153," ","integrate(arccsc(b*x+a)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccsc}\left(b x + a\right)^{2}}{x^{2}}, x\right)"," ",0,"integral(arccsc(b*x + a)^2/x^2, x)","F",0
33,0,0,0,0.668974," ","integrate(x^2*arccsc(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \operatorname{arccsc}\left(b x + a\right)^{3}, x\right)"," ",0,"integral(x^2*arccsc(b*x + a)^3, x)","F",0
34,0,0,0,0.725726," ","integrate(x*arccsc(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(x \operatorname{arccsc}\left(b x + a\right)^{3}, x\right)"," ",0,"integral(x*arccsc(b*x + a)^3, x)","F",0
35,0,0,0,0.758443," ","integrate(arccsc(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{arccsc}\left(b x + a\right)^{3}, x\right)"," ",0,"integral(arccsc(b*x + a)^3, x)","F",0
36,0,0,0,0.706002," ","integrate(arccsc(b*x+a)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccsc}\left(b x + a\right)^{3}}{x}, x\right)"," ",0,"integral(arccsc(b*x + a)^3/x, x)","F",0
37,0,0,0,0.724530," ","integrate(arccsc(b*x+a)^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccsc}\left(b x + a\right)^{3}}{x^{2}}, x\right)"," ",0,"integral(arccsc(b*x + a)^3/x^2, x)","F",0
38,1,88,0,0.741663," ","integrate(x^3*arccsc(b*x^4+a),x, algorithm=""fricas"")","\frac{b x^{4} \operatorname{arccsc}\left(b x^{4} + a\right) - 2 \, a \arctan\left(-b x^{4} - a + \sqrt{b^{2} x^{8} + 2 \, a b x^{4} + a^{2} - 1}\right) - \log\left(-b x^{4} - a + \sqrt{b^{2} x^{8} + 2 \, a b x^{4} + a^{2} - 1}\right)}{4 \, b}"," ",0,"1/4*(b*x^4*arccsc(b*x^4 + a) - 2*a*arctan(-b*x^4 - a + sqrt(b^2*x^8 + 2*a*b*x^4 + a^2 - 1)) - log(-b*x^4 - a + sqrt(b^2*x^8 + 2*a*b*x^4 + a^2 - 1)))/b","B",0
39,1,94,0,0.726286," ","integrate(x^(-1+n)*arccsc(a+b*x^n),x, algorithm=""fricas"")","\frac{b x^{n} \operatorname{arccsc}\left(b x^{n} + a\right) - 2 \, a \arctan\left(-b x^{n} - a + \sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2} - 1}\right) - \log\left(-b x^{n} - a + \sqrt{b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2} - 1}\right)}{b n}"," ",0,"(b*x^n*arccsc(b*x^n + a) - 2*a*arctan(-b*x^n - a + sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2 - 1)) - log(-b*x^n - a + sqrt(b^2*x^(2*n) + 2*a*b*x^n + a^2 - 1)))/(b*n)","B",0
40,-2,0,0,0.000000," ","integrate(arccsc(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
41,0,0,0,0.748256," ","integrate(exp(arccsc(a*x))*x^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} e^{\left(\operatorname{arccsc}\left(a x\right)\right)}, x\right)"," ",0,"integral(x^2*e^(arccsc(a*x)), x)","F",0
42,0,0,0,0.735541," ","integrate(exp(arccsc(a*x))*x,x, algorithm=""fricas"")","{\rm integral}\left(x e^{\left(\operatorname{arccsc}\left(a x\right)\right)}, x\right)"," ",0,"integral(x*e^(arccsc(a*x)), x)","F",0
43,0,0,0,0.609883," ","integrate(exp(arccsc(a*x)),x, algorithm=""fricas"")","{\rm integral}\left(e^{\left(\operatorname{arccsc}\left(a x\right)\right)}, x\right)"," ",0,"integral(e^(arccsc(a*x)), x)","F",0
44,0,0,0,0.575196," ","integrate(exp(arccsc(a*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{\left(\operatorname{arccsc}\left(a x\right)\right)}}{x}, x\right)"," ",0,"integral(e^(arccsc(a*x))/x, x)","F",0
45,1,23,0,0.710786," ","integrate(exp(arccsc(a*x))/x^2,x, algorithm=""fricas"")","-\frac{{\left(\sqrt{a^{2} x^{2} - 1} + 1\right)} e^{\left(\operatorname{arccsc}\left(a x\right)\right)}}{2 \, x}"," ",0,"-1/2*(sqrt(a^2*x^2 - 1) + 1)*e^(arccsc(a*x))/x","A",0
46,1,32,0,0.796469," ","integrate(exp(arccsc(a*x))/x^3,x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} - \sqrt{a^{2} x^{2} - 1} - 2\right)} e^{\left(\operatorname{arccsc}\left(a x\right)\right)}}{5 \, x^{2}}"," ",0,"1/5*(a^2*x^2 - sqrt(a^2*x^2 - 1) - 2)*e^(arccsc(a*x))/x^2","A",0
47,1,41,0,0.848366," ","integrate(exp(arccsc(a*x))/x^4,x, algorithm=""fricas"")","\frac{{\left(a^{2} x^{2} - {\left(a^{2} x^{2} + 1\right)} \sqrt{a^{2} x^{2} - 1} - 3\right)} e^{\left(\operatorname{arccsc}\left(a x\right)\right)}}{10 \, x^{3}}"," ",0,"1/10*(a^2*x^2 - (a^2*x^2 + 1)*sqrt(a^2*x^2 - 1) - 3)*e^(arccsc(a*x))/x^3","A",0
48,1,51,0,0.821685," ","integrate(exp(arccsc(a*x))/x^5,x, algorithm=""fricas"")","\frac{{\left(6 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - {\left(6 \, a^{2} x^{2} + 5\right)} \sqrt{a^{2} x^{2} - 1} - 20\right)} e^{\left(\operatorname{arccsc}\left(a x\right)\right)}}{85 \, x^{4}}"," ",0,"1/85*(6*a^4*x^4 + 3*a^2*x^2 - (6*a^2*x^2 + 5)*sqrt(a^2*x^2 - 1) - 20)*e^(arccsc(a*x))/x^4","A",0
49,0,0,0,0.774117," ","integrate(arccsc(b*x+a)/(a*d/b+d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arccsc}\left(b x + a\right)}{b d x + a d}, x\right)"," ",0,"integral(b*arccsc(b*x + a)/(b*d*x + a*d), x)","F",0
