1,1,86,0,0.600029," ","integrate(x^5*arctanh(x*e^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, e^{2} x^{5} - 10 \, d e x^{3} + 15 \, d^{2} x\right)} \sqrt{e x^{2} + d} \sqrt{e} - 3 \, {\left(16 \, e^{3} x^{6} + 5 \, d^{3}\right)} \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right)}{576 \, e^{3}}"," ",0,"-1/576*(2*(8*e^2*x^5 - 10*d*e*x^3 + 15*d^2*x)*sqrt(e*x^2 + d)*sqrt(e) - 3*(16*e^3*x^6 + 5*d^3)*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d))/e^3","A",0
2,1,75,0,0.692707," ","integrate(x^3*arctanh(x*e^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, e x^{3} - 3 \, d x\right)} \sqrt{e x^{2} + d} \sqrt{e} - {\left(8 \, e^{2} x^{4} - 3 \, d^{2}\right)} \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right)}{64 \, e^{2}}"," ",0,"-1/64*(2*(2*e*x^3 - 3*d*x)*sqrt(e*x^2 + d)*sqrt(e) - (8*e^2*x^4 - 3*d^2)*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d))/e^2","A",0
3,1,59,0,0.606259," ","integrate(x*arctanh(x*e^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{e x^{2} + d} \sqrt{e} x - {\left(2 \, e x^{2} + d\right)} \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right)}{8 \, e}"," ",0,"-1/8*(2*sqrt(e*x^2 + d)*sqrt(e)*x - (2*e*x^2 + d)*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d))/e","A",0
4,0,0,0,0.573302," ","integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(\frac{\sqrt{e} x}{\sqrt{e x^{2} + d}}\right)}{x}, x\right)"," ",0,"integral(arctanh(sqrt(e)*x/sqrt(e*x^2 + d))/x, x)","F",0
5,1,54,0,0.602628," ","integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x^3,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right)}{4 \, d x^{2}}"," ",0,"-1/4*(2*sqrt(e*x^2 + d)*sqrt(e)*x + d*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d))/(d*x^2)","A",0
6,1,67,0,0.701307," ","integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x^5,x, algorithm=""fricas"")","-\frac{3 \, d^{2} \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right) - 2 \, {\left(2 \, e x^{3} - d x\right)} \sqrt{e x^{2} + d} \sqrt{e}}{24 \, d^{2} x^{4}}"," ",0,"-1/24*(3*d^2*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d) - 2*(2*e*x^3 - d*x)*sqrt(e*x^2 + d)*sqrt(e))/(d^2*x^4)","A",0
7,1,78,0,0.571206," ","integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x^7,x, algorithm=""fricas"")","-\frac{15 \, d^{3} \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right) + 2 \, {\left(8 \, e^{2} x^{5} - 4 \, d e x^{3} + 3 \, d^{2} x\right)} \sqrt{e x^{2} + d} \sqrt{e}}{180 \, d^{3} x^{6}}"," ",0,"-1/180*(15*d^3*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d) + 2*(8*e^2*x^5 - 4*d*e*x^3 + 3*d^2*x)*sqrt(e*x^2 + d)*sqrt(e))/(d^3*x^6)","A",0
8,1,89,0,1.130416," ","integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x^9,x, algorithm=""fricas"")","-\frac{35 \, d^{4} \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right) - 2 \, {\left(16 \, e^{3} x^{7} - 8 \, d e^{2} x^{5} + 6 \, d^{2} e x^{3} - 5 \, d^{3} x\right)} \sqrt{e x^{2} + d} \sqrt{e}}{560 \, d^{4} x^{8}}"," ",0,"-1/560*(35*d^4*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d) - 2*(16*e^3*x^7 - 8*d*e^2*x^5 + 6*d^2*e*x^3 - 5*d^3*x)*sqrt(e*x^2 + d)*sqrt(e))/(d^4*x^8)","A",0
9,1,88,0,0.565571," ","integrate(x^6*arctanh(x*e^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","\frac{35 \, e^{4} x^{7} \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right) - 2 \, {\left(5 \, e^{3} x^{6} - 6 \, d e^{2} x^{4} + 8 \, d^{2} e x^{2} - 16 \, d^{3}\right)} \sqrt{e x^{2} + d} \sqrt{e}}{490 \, e^{4}}"," ",0,"1/490*(35*e^4*x^7*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d) - 2*(5*e^3*x^6 - 6*d*e^2*x^4 + 8*d^2*e*x^2 - 16*d^3)*sqrt(e*x^2 + d)*sqrt(e))/e^4","A",0
10,1,77,0,0.400515," ","integrate(x^4*arctanh(x*e^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","\frac{15 \, e^{3} x^{5} \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right) - 2 \, {\left(3 \, e^{2} x^{4} - 4 \, d e x^{2} + 8 \, d^{2}\right)} \sqrt{e x^{2} + d} \sqrt{e}}{150 \, e^{3}}"," ",0,"1/150*(15*e^3*x^5*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d) - 2*(3*e^2*x^4 - 4*d*e*x^2 + 8*d^2)*sqrt(e*x^2 + d)*sqrt(e))/e^3","A",0
11,1,65,0,0.490177," ","integrate(x^2*arctanh(x*e^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","\frac{3 \, e^{2} x^{3} \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right) - 2 \, \sqrt{e x^{2} + d} {\left(e x^{2} - 2 \, d\right)} \sqrt{e}}{18 \, e^{2}}"," ",0,"1/18*(3*e^2*x^3*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d) - 2*sqrt(e*x^2 + d)*(e*x^2 - 2*d)*sqrt(e))/e^2","A",0
12,1,51,0,0.765335," ","integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","\frac{e x \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right) - 2 \, \sqrt{e x^{2} + d} \sqrt{e}}{2 \, e}"," ",0,"1/2*(e*x*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d) - 2*sqrt(e*x^2 + d)*sqrt(e))/e","A",0
13,1,273,0,0.677931," ","integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x^2,x, algorithm=""fricas"")","\left[\frac{x \sqrt{\frac{e}{d}} \log\left(-\frac{e^{2} x^{2} - 2 \, \sqrt{e x^{2} + d} d \sqrt{e} \sqrt{\frac{e}{d}} + 2 \, d e}{x^{2}}\right) + {\left(x - 1\right)} \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right) - x \log\left(\frac{e x + \sqrt{e x^{2} + d} \sqrt{e}}{x}\right) + x \log\left(\frac{e x - \sqrt{e x^{2} + d} \sqrt{e}}{x}\right)}{2 \, x}, \frac{2 \, x \sqrt{-\frac{e}{d}} \arctan\left(\frac{\sqrt{e x^{2} + d} d \sqrt{e} \sqrt{-\frac{e}{d}}}{e^{2} x^{2} + d e}\right) + {\left(x - 1\right)} \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right) - x \log\left(\frac{e x + \sqrt{e x^{2} + d} \sqrt{e}}{x}\right) + x \log\left(\frac{e x - \sqrt{e x^{2} + d} \sqrt{e}}{x}\right)}{2 \, x}\right]"," ",0,"[1/2*(x*sqrt(e/d)*log(-(e^2*x^2 - 2*sqrt(e*x^2 + d)*d*sqrt(e)*sqrt(e/d) + 2*d*e)/x^2) + (x - 1)*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d) - x*log((e*x + sqrt(e*x^2 + d)*sqrt(e))/x) + x*log((e*x - sqrt(e*x^2 + d)*sqrt(e))/x))/x, 1/2*(2*x*sqrt(-e/d)*arctan(sqrt(e*x^2 + d)*d*sqrt(e)*sqrt(-e/d)/(e^2*x^2 + d*e)) + (x - 1)*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d) - x*log((e*x + sqrt(e*x^2 + d)*sqrt(e))/x) + x*log((e*x - sqrt(e*x^2 + d)*sqrt(e))/x))/x]","B",0
14,1,340,0,0.642024," ","integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x^4,x, algorithm=""fricas"")","\left[\frac{e x^{3} \sqrt{\frac{e}{d}} \log\left(-\frac{e^{2} x^{2} + 2 \, \sqrt{e x^{2} + d} d \sqrt{e} \sqrt{\frac{e}{d}} + 2 \, d e}{x^{2}}\right) - 2 \, d x^{3} \log\left(\frac{e x + \sqrt{e x^{2} + d} \sqrt{e}}{x}\right) + 2 \, d x^{3} \log\left(\frac{e x - \sqrt{e x^{2} + d} \sqrt{e}}{x}\right) - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + 2 \, {\left(d x^{3} - d\right)} \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right)}{12 \, d x^{3}}, -\frac{e x^{3} \sqrt{-\frac{e}{d}} \arctan\left(\frac{\sqrt{e x^{2} + d} d \sqrt{e} \sqrt{-\frac{e}{d}}}{e^{2} x^{2} + d e}\right) + d x^{3} \log\left(\frac{e x + \sqrt{e x^{2} + d} \sqrt{e}}{x}\right) - d x^{3} \log\left(\frac{e x - \sqrt{e x^{2} + d} \sqrt{e}}{x}\right) + \sqrt{e x^{2} + d} \sqrt{e} x - {\left(d x^{3} - d\right)} \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right)}{6 \, d x^{3}}\right]"," ",0,"[1/12*(e*x^3*sqrt(e/d)*log(-(e^2*x^2 + 2*sqrt(e*x^2 + d)*d*sqrt(e)*sqrt(e/d) + 2*d*e)/x^2) - 2*d*x^3*log((e*x + sqrt(e*x^2 + d)*sqrt(e))/x) + 2*d*x^3*log((e*x - sqrt(e*x^2 + d)*sqrt(e))/x) - 2*sqrt(e*x^2 + d)*sqrt(e)*x + 2*(d*x^3 - d)*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d))/(d*x^3), -1/6*(e*x^3*sqrt(-e/d)*arctan(sqrt(e*x^2 + d)*d*sqrt(e)*sqrt(-e/d)/(e^2*x^2 + d*e)) + d*x^3*log((e*x + sqrt(e*x^2 + d)*sqrt(e))/x) - d*x^3*log((e*x - sqrt(e*x^2 + d)*sqrt(e))/x) + sqrt(e*x^2 + d)*sqrt(e)*x - (d*x^3 - d)*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d))/(d*x^3)]","B",0
15,1,383,0,1.502002," ","integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x^6,x, algorithm=""fricas"")","\left[\frac{3 \, e^{2} x^{5} \sqrt{\frac{e}{d}} \log\left(-\frac{e^{2} x^{2} - 2 \, \sqrt{e x^{2} + d} d \sqrt{e} \sqrt{\frac{e}{d}} + 2 \, d e}{x^{2}}\right) - 8 \, d^{2} x^{5} \log\left(\frac{e x + \sqrt{e x^{2} + d} \sqrt{e}}{x}\right) + 8 \, d^{2} x^{5} \log\left(\frac{e x - \sqrt{e x^{2} + d} \sqrt{e}}{x}\right) + 2 \, {\left(3 \, e x^{3} - 2 \, d x\right)} \sqrt{e x^{2} + d} \sqrt{e} + 8 \, {\left(d^{2} x^{5} - d^{2}\right)} \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right)}{80 \, d^{2} x^{5}}, \frac{3 \, e^{2} x^{5} \sqrt{-\frac{e}{d}} \arctan\left(\frac{\sqrt{e x^{2} + d} d \sqrt{e} \sqrt{-\frac{e}{d}}}{e^{2} x^{2} + d e}\right) - 4 \, d^{2} x^{5} \log\left(\frac{e x + \sqrt{e x^{2} + d} \sqrt{e}}{x}\right) + 4 \, d^{2} x^{5} \log\left(\frac{e x - \sqrt{e x^{2} + d} \sqrt{e}}{x}\right) + {\left(3 \, e x^{3} - 2 \, d x\right)} \sqrt{e x^{2} + d} \sqrt{e} + 4 \, {\left(d^{2} x^{5} - d^{2}\right)} \log\left(\frac{2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x + d}{d}\right)}{40 \, d^{2} x^{5}}\right]"," ",0,"[1/80*(3*e^2*x^5*sqrt(e/d)*log(-(e^2*x^2 - 2*sqrt(e*x^2 + d)*d*sqrt(e)*sqrt(e/d) + 2*d*e)/x^2) - 8*d^2*x^5*log((e*x + sqrt(e*x^2 + d)*sqrt(e))/x) + 8*d^2*x^5*log((e*x - sqrt(e*x^2 + d)*sqrt(e))/x) + 2*(3*e*x^3 - 2*d*x)*sqrt(e*x^2 + d)*sqrt(e) + 8*(d^2*x^5 - d^2)*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d))/(d^2*x^5), 1/40*(3*e^2*x^5*sqrt(-e/d)*arctan(sqrt(e*x^2 + d)*d*sqrt(e)*sqrt(-e/d)/(e^2*x^2 + d*e)) - 4*d^2*x^5*log((e*x + sqrt(e*x^2 + d)*sqrt(e))/x) + 4*d^2*x^5*log((e*x - sqrt(e*x^2 + d)*sqrt(e))/x) + (3*e*x^3 - 2*d*x)*sqrt(e*x^2 + d)*sqrt(e) + 4*(d^2*x^5 - d^2)*log((2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x + d)/d))/(d^2*x^5)]","B",0
16,0,0,0,0.628534," ","integrate(x^(9/2)*arctanh(x*e^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(x^{\frac{9}{2}} \operatorname{artanh}\left(\frac{\sqrt{e} x}{\sqrt{e x^{2} + d}}\right), x\right)"," ",0,"integral(x^(9/2)*arctanh(sqrt(e)*x/sqrt(e*x^2 + d)), x)","F",0
17,0,0,0,0.494965," ","integrate(x^(5/2)*arctanh(x*e^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(x^{\frac{5}{2}} \operatorname{artanh}\left(\frac{\sqrt{e} x}{\sqrt{e x^{2} + d}}\right), x\right)"," ",0,"integral(x^(5/2)*arctanh(sqrt(e)*x/sqrt(e*x^2 + d)), x)","F",0
18,0,0,0,0.809413," ","integrate(x^(1/2)*arctanh(x*e^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{x} \operatorname{artanh}\left(\frac{\sqrt{e} x}{\sqrt{e x^{2} + d}}\right), x\right)"," ",0,"integral(sqrt(x)*arctanh(sqrt(e)*x/sqrt(e*x^2 + d)), x)","F",0
19,0,0,0,0.479080," ","integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(\frac{\sqrt{e} x}{\sqrt{e x^{2} + d}}\right)}{x^{\frac{3}{2}}}, x\right)"," ",0,"integral(arctanh(sqrt(e)*x/sqrt(e*x^2 + d))/x^(3/2), x)","F",0
20,0,0,0,0.588539," ","integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(\frac{\sqrt{e} x}{\sqrt{e x^{2} + d}}\right)}{x^{\frac{7}{2}}}, x\right)"," ",0,"integral(arctanh(sqrt(e)*x/sqrt(e*x^2 + d))/x^(7/2), x)","F",0
21,0,0,0,0.581732," ","integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(\frac{\sqrt{e} x}{\sqrt{e x^{2} + d}}\right)}{x^{\frac{11}{2}}}, x\right)"," ",0,"integral(arctanh(sqrt(e)*x/sqrt(e*x^2 + d))/x^(11/2), x)","F",0
22,0,0,0,0.515224," ","integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x^(15/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(\frac{\sqrt{e} x}{\sqrt{e x^{2} + d}}\right)}{x^{\frac{15}{2}}}, x\right)"," ",0,"integral(arctanh(sqrt(e)*x/sqrt(e*x^2 + d))/x^(15/2), x)","F",0
23,0,0,0,0.578556," ","integrate(x^(7/2)*arctanh(x*e^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(x^{\frac{7}{2}} \operatorname{artanh}\left(\frac{\sqrt{e} x}{\sqrt{e x^{2} + d}}\right), x\right)"," ",0,"integral(x^(7/2)*arctanh(sqrt(e)*x/sqrt(e*x^2 + d)), x)","F",0
24,0,0,0,0.849996," ","integrate(x^(3/2)*arctanh(x*e^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(x^{\frac{3}{2}} \operatorname{artanh}\left(\frac{\sqrt{e} x}{\sqrt{e x^{2} + d}}\right), x\right)"," ",0,"integral(x^(3/2)*arctanh(sqrt(e)*x/sqrt(e*x^2 + d)), x)","F",0
25,0,0,0,0.623294," ","integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(\frac{\sqrt{e} x}{\sqrt{e x^{2} + d}}\right)}{\sqrt{x}}, x\right)"," ",0,"integral(arctanh(sqrt(e)*x/sqrt(e*x^2 + d))/sqrt(x), x)","F",0
26,0,0,0,0.602383," ","integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(\frac{\sqrt{e} x}{\sqrt{e x^{2} + d}}\right)}{x^{\frac{5}{2}}}, x\right)"," ",0,"integral(arctanh(sqrt(e)*x/sqrt(e*x^2 + d))/x^(5/2), x)","F",0
27,0,0,0,0.576840," ","integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(\frac{\sqrt{e} x}{\sqrt{e x^{2} + d}}\right)}{x^{\frac{9}{2}}}, x\right)"," ",0,"integral(arctanh(sqrt(e)*x/sqrt(e*x^2 + d))/x^(9/2), x)","F",0
28,1,59,0,0.505257," ","integrate(x^3*arctanh(b*x^4+a),x, algorithm=""fricas"")","\frac{b x^{4} \log\left(-\frac{b x^{4} + a + 1}{b x^{4} + a - 1}\right) + {\left(a + 1\right)} \log\left(b x^{4} + a + 1\right) - {\left(a - 1\right)} \log\left(b x^{4} + a - 1\right)}{8 \, b}"," ",0,"1/8*(b*x^4*log(-(b*x^4 + a + 1)/(b*x^4 + a - 1)) + (a + 1)*log(b*x^4 + a + 1) - (a - 1)*log(b*x^4 + a - 1))/b","A",0
29,1,109,0,0.566087," ","integrate(x^(-1+n)*arctanh(a+b*x^n),x, algorithm=""fricas"")","\frac{{\left(a + 1\right)} \log\left(b \cosh\left(n \log\left(x\right)\right) + b \sinh\left(n \log\left(x\right)\right) + a + 1\right) - {\left(a - 1\right)} \log\left(b \cosh\left(n \log\left(x\right)\right) + b \sinh\left(n \log\left(x\right)\right) + a - 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{b \cosh\left(n \log\left(x\right)\right) + b \sinh\left(n \log\left(x\right)\right) + a + 1}{b \cosh\left(n \log\left(x\right)\right) + b \sinh\left(n \log\left(x\right)\right) + a - 1}\right)}{2 \, b n}"," ",0,"1/2*((a + 1)*log(b*cosh(n*log(x)) + b*sinh(n*log(x)) + a + 1) - (a - 1)*log(b*cosh(n*log(x)) + b*sinh(n*log(x)) + a - 1) + (b*cosh(n*log(x)) + b*sinh(n*log(x)))*log(-(b*cosh(n*log(x)) + b*sinh(n*log(x)) + a + 1)/(b*cosh(n*log(x)) + b*sinh(n*log(x)) + a - 1)))/(b*n)","B",0
30,0,0,0,0.652940," ","integrate((a+b*arctanh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b \operatorname{artanh}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}^{n}}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(b*arctanh(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)^n/(c^2*x^2 - 1), x)","F",0
31,0,0,0,0.507929," ","integrate((a+b*arctanh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^3/(-c^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{3} \operatorname{artanh}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a^{3}}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(b^3*arctanh(sqrt(-c*x + 1)/sqrt(c*x + 1))^3 + 3*a*b^2*arctanh(sqrt(-c*x + 1)/sqrt(c*x + 1))^2 + 3*a^2*b*arctanh(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a^3)/(c^2*x^2 - 1), x)","F",0
32,0,0,0,0.549748," ","integrate((a+b*arctanh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2/(-c^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} \operatorname{artanh}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)^{2} + 2 \, a b \operatorname{artanh}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a^{2}}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(b^2*arctanh(sqrt(-c*x + 1)/sqrt(c*x + 1))^2 + 2*a*b*arctanh(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a^2)/(c^2*x^2 - 1), x)","F",0
33,0,0,0,0.480494," ","integrate((a+b*arctanh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))/(-c^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \operatorname{artanh}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(b*arctanh(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)/(c^2*x^2 - 1), x)","F",0
34,0,0,0,0.464086," ","integrate(1/(-c^2*x^2+1)/(a+b*arctanh((-c*x+1)^(1/2)/(c*x+1)^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{a c^{2} x^{2} + {\left(b c^{2} x^{2} - b\right)} \operatorname{artanh}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) - a}, x\right)"," ",0,"integral(-1/(a*c^2*x^2 + (b*c^2*x^2 - b)*arctanh(sqrt(-c*x + 1)/sqrt(c*x + 1)) - a), x)","F",0
35,0,0,0,0.592553," ","integrate(1/(-c^2*x^2+1)/(a+b*arctanh((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{a^{2} c^{2} x^{2} + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \operatorname{artanh}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)^{2} - a^{2} + 2 \, {\left(a b c^{2} x^{2} - a b\right)} \operatorname{artanh}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)}, x\right)"," ",0,"integral(-1/(a^2*c^2*x^2 + (b^2*c^2*x^2 - b^2)*arctanh(sqrt(-c*x + 1)/sqrt(c*x + 1))^2 - a^2 + 2*(a*b*c^2*x^2 - a*b)*arctanh(sqrt(-c*x + 1)/sqrt(c*x + 1))), x)","F",0
36,1,62,0,0.481187," ","integrate(x^m*arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{{\left({\left(b m + b\right)} x^{2} + {\left(a m + 2 \, a\right)} x\right)} \cosh\left(m \log\left(x\right)\right) + {\left({\left(b m + b\right)} x^{2} + {\left(a m + 2 \, a\right)} x\right)} \sinh\left(m \log\left(x\right)\right)}{m^{2} + 3 \, m + 2}"," ",0,"(((b*m + b)*x^2 + (a*m + 2*a)*x)*cosh(m*log(x)) + ((b*m + b)*x^2 + (a*m + 2*a)*x)*sinh(m*log(x)))/(m^2 + 3*m + 2)","A",0
37,1,13,0,0.366572," ","integrate(x^2*arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{1}{4} \, b x^{4} + \frac{1}{3} \, a x^{3}"," ",0,"1/4*b*x^4 + 1/3*a*x^3","A",0
38,1,13,0,0.615768," ","integrate(x*arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{1}{3} \, b x^{3} + \frac{1}{2} \, a x^{2}"," ",0,"1/3*b*x^3 + 1/2*a*x^2","A",0
39,1,10,0,0.490604," ","integrate(arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{1}{2} \, b x^{2} + a x"," ",0,"1/2*b*x^2 + a*x","A",0
40,1,8,0,0.658504," ","integrate(arctanh(tanh(b*x+a))/x,x, algorithm=""fricas"")","b x + a \log\left(x\right)"," ",0,"b*x + a*log(x)","A",0
41,1,13,0,0.448891," ","integrate(arctanh(tanh(b*x+a))/x^2,x, algorithm=""fricas"")","\frac{b x \log\left(x\right) - a}{x}"," ",0,"(b*x*log(x) - a)/x","A",0
42,1,11,0,0.465753," ","integrate(arctanh(tanh(b*x+a))/x^3,x, algorithm=""fricas"")","-\frac{2 \, b x + a}{2 \, x^{2}}"," ",0,"-1/2*(2*b*x + a)/x^2","A",0
43,1,13,0,0.515452," ","integrate(arctanh(tanh(b*x+a))/x^4,x, algorithm=""fricas"")","-\frac{3 \, b x + 2 \, a}{6 \, x^{3}}"," ",0,"-1/6*(3*b*x + 2*a)/x^3","A",0
44,1,161,0,0.678390," ","integrate(x^m*arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{{\left({\left(b^{2} m^{2} + 3 \, b^{2} m + 2 \, b^{2}\right)} x^{3} + 2 \, {\left(a b m^{2} + 4 \, a b m + 3 \, a b\right)} x^{2} + {\left(a^{2} m^{2} + 5 \, a^{2} m + 6 \, a^{2}\right)} x\right)} \cosh\left(m \log\left(x\right)\right) + {\left({\left(b^{2} m^{2} + 3 \, b^{2} m + 2 \, b^{2}\right)} x^{3} + 2 \, {\left(a b m^{2} + 4 \, a b m + 3 \, a b\right)} x^{2} + {\left(a^{2} m^{2} + 5 \, a^{2} m + 6 \, a^{2}\right)} x\right)} \sinh\left(m \log\left(x\right)\right)}{m^{3} + 6 \, m^{2} + 11 \, m + 6}"," ",0,"(((b^2*m^2 + 3*b^2*m + 2*b^2)*x^3 + 2*(a*b*m^2 + 4*a*b*m + 3*a*b)*x^2 + (a^2*m^2 + 5*a^2*m + 6*a^2)*x)*cosh(m*log(x)) + ((b^2*m^2 + 3*b^2*m + 2*b^2)*x^3 + 2*(a*b*m^2 + 4*a*b*m + 3*a*b)*x^2 + (a^2*m^2 + 5*a^2*m + 6*a^2)*x)*sinh(m*log(x)))/(m^3 + 6*m^2 + 11*m + 6)","B",0
45,1,24,0,0.505699," ","integrate(x^3*arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{1}{6} \, b^{2} x^{6} + \frac{2}{5} \, a b x^{5} + \frac{1}{4} \, a^{2} x^{4}"," ",0,"1/6*b^2*x^6 + 2/5*a*b*x^5 + 1/4*a^2*x^4","A",0
46,1,24,0,0.489573," ","integrate(x^2*arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{1}{5} \, b^{2} x^{5} + \frac{1}{2} \, a b x^{4} + \frac{1}{3} \, a^{2} x^{3}"," ",0,"1/5*b^2*x^5 + 1/2*a*b*x^4 + 1/3*a^2*x^3","A",0
47,1,24,0,0.496326," ","integrate(x*arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{1}{4} \, b^{2} x^{4} + \frac{2}{3} \, a b x^{3} + \frac{1}{2} \, a^{2} x^{2}"," ",0,"1/4*b^2*x^4 + 2/3*a*b*x^3 + 1/2*a^2*x^2","A",0
48,1,20,0,0.642622," ","integrate(arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{1}{3} \, b^{2} x^{3} + a b x^{2} + a^{2} x"," ",0,"1/3*b^2*x^3 + a*b*x^2 + a^2*x","A",0
49,1,20,0,0.575079," ","integrate(arctanh(tanh(b*x+a))^2/x,x, algorithm=""fricas"")","\frac{1}{2} \, b^{2} x^{2} + 2 \, a b x + a^{2} \log\left(x\right)"," ",0,"1/2*b^2*x^2 + 2*a*b*x + a^2*log(x)","A",0
50,1,24,0,0.506751," ","integrate(arctanh(tanh(b*x+a))^2/x^2,x, algorithm=""fricas"")","\frac{b^{2} x^{2} + 2 \, a b x \log\left(x\right) - a^{2}}{x}"," ",0,"(b^2*x^2 + 2*a*b*x*log(x) - a^2)/x","A",0
51,1,26,0,0.418742," ","integrate(arctanh(tanh(b*x+a))^2/x^3,x, algorithm=""fricas"")","\frac{2 \, b^{2} x^{2} \log\left(x\right) - 4 \, a b x - a^{2}}{2 \, x^{2}}"," ",0,"1/2*(2*b^2*x^2*log(x) - 4*a*b*x - a^2)/x^2","A",0
52,1,22,0,0.457002," ","integrate(arctanh(tanh(b*x+a))^2/x^4,x, algorithm=""fricas"")","-\frac{3 \, b^{2} x^{2} + 3 \, a b x + a^{2}}{3 \, x^{3}}"," ",0,"-1/3*(3*b^2*x^2 + 3*a*b*x + a^2)/x^3","A",0
53,1,24,0,0.480679," ","integrate(arctanh(tanh(b*x+a))^2/x^5,x, algorithm=""fricas"")","-\frac{6 \, b^{2} x^{2} + 8 \, a b x + 3 \, a^{2}}{12 \, x^{4}}"," ",0,"-1/12*(6*b^2*x^2 + 8*a*b*x + 3*a^2)/x^4","A",0
54,1,300,0,0.396942," ","integrate(x^m*arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{{\left({\left(b^{3} m^{3} + 6 \, b^{3} m^{2} + 11 \, b^{3} m + 6 \, b^{3}\right)} x^{4} + 3 \, {\left(a b^{2} m^{3} + 7 \, a b^{2} m^{2} + 14 \, a b^{2} m + 8 \, a b^{2}\right)} x^{3} + 3 \, {\left(a^{2} b m^{3} + 8 \, a^{2} b m^{2} + 19 \, a^{2} b m + 12 \, a^{2} b\right)} x^{2} + {\left(a^{3} m^{3} + 9 \, a^{3} m^{2} + 26 \, a^{3} m + 24 \, a^{3}\right)} x\right)} \cosh\left(m \log\left(x\right)\right) + {\left({\left(b^{3} m^{3} + 6 \, b^{3} m^{2} + 11 \, b^{3} m + 6 \, b^{3}\right)} x^{4} + 3 \, {\left(a b^{2} m^{3} + 7 \, a b^{2} m^{2} + 14 \, a b^{2} m + 8 \, a b^{2}\right)} x^{3} + 3 \, {\left(a^{2} b m^{3} + 8 \, a^{2} b m^{2} + 19 \, a^{2} b m + 12 \, a^{2} b\right)} x^{2} + {\left(a^{3} m^{3} + 9 \, a^{3} m^{2} + 26 \, a^{3} m + 24 \, a^{3}\right)} x\right)} \sinh\left(m \log\left(x\right)\right)}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24}"," ",0,"(((b^3*m^3 + 6*b^3*m^2 + 11*b^3*m + 6*b^3)*x^4 + 3*(a*b^2*m^3 + 7*a*b^2*m^2 + 14*a*b^2*m + 8*a*b^2)*x^3 + 3*(a^2*b*m^3 + 8*a^2*b*m^2 + 19*a^2*b*m + 12*a^2*b)*x^2 + (a^3*m^3 + 9*a^3*m^2 + 26*a^3*m + 24*a^3)*x)*cosh(m*log(x)) + ((b^3*m^3 + 6*b^3*m^2 + 11*b^3*m + 6*b^3)*x^4 + 3*(a*b^2*m^3 + 7*a*b^2*m^2 + 14*a*b^2*m + 8*a*b^2)*x^3 + 3*(a^2*b*m^3 + 8*a^2*b*m^2 + 19*a^2*b*m + 12*a^2*b)*x^2 + (a^3*m^3 + 9*a^3*m^2 + 26*a^3*m + 24*a^3)*x)*sinh(m*log(x)))/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)","B",0
55,1,35,0,1.015626," ","integrate(x^3*arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{1}{7} \, b^{3} x^{7} + \frac{1}{2} \, a b^{2} x^{6} + \frac{3}{5} \, a^{2} b x^{5} + \frac{1}{4} \, a^{3} x^{4}"," ",0,"1/7*b^3*x^7 + 1/2*a*b^2*x^6 + 3/5*a^2*b*x^5 + 1/4*a^3*x^4","A",0
56,1,35,0,0.562357," ","integrate(x^2*arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{1}{6} \, b^{3} x^{6} + \frac{3}{5} \, a b^{2} x^{5} + \frac{3}{4} \, a^{2} b x^{4} + \frac{1}{3} \, a^{3} x^{3}"," ",0,"1/6*b^3*x^6 + 3/5*a*b^2*x^5 + 3/4*a^2*b*x^4 + 1/3*a^3*x^3","A",0
57,1,34,0,0.500630," ","integrate(x*arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{1}{5} \, b^{3} x^{5} + \frac{3}{4} \, a b^{2} x^{4} + a^{2} b x^{3} + \frac{1}{2} \, a^{3} x^{2}"," ",0,"1/5*b^3*x^5 + 3/4*a*b^2*x^4 + a^2*b*x^3 + 1/2*a^3*x^2","A",0
58,1,31,0,0.731193," ","integrate(arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{1}{4} \, b^{3} x^{4} + a b^{2} x^{3} + \frac{3}{2} \, a^{2} b x^{2} + a^{3} x"," ",0,"1/4*b^3*x^4 + a*b^2*x^3 + 3/2*a^2*b*x^2 + a^3*x","B",0
59,1,31,0,0.591606," ","integrate(arctanh(tanh(b*x+a))^3/x,x, algorithm=""fricas"")","\frac{1}{3} \, b^{3} x^{3} + \frac{3}{2} \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3} \log\left(x\right)"," ",0,"1/3*b^3*x^3 + 3/2*a*b^2*x^2 + 3*a^2*b*x + a^3*log(x)","A",0
60,1,36,0,0.740857," ","integrate(arctanh(tanh(b*x+a))^3/x^2,x, algorithm=""fricas"")","\frac{b^{3} x^{3} + 6 \, a b^{2} x^{2} + 6 \, a^{2} b x \log\left(x\right) - 2 \, a^{3}}{2 \, x}"," ",0,"1/2*(b^3*x^3 + 6*a*b^2*x^2 + 6*a^2*b*x*log(x) - 2*a^3)/x","A",0
61,1,37,0,0.456009," ","integrate(arctanh(tanh(b*x+a))^3/x^3,x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} \log\left(x\right) - 6 \, a^{2} b x - a^{3}}{2 \, x^{2}}"," ",0,"1/2*(2*b^3*x^3 + 6*a*b^2*x^2*log(x) - 6*a^2*b*x - a^3)/x^2","A",0
62,1,37,0,0.452170," ","integrate(arctanh(tanh(b*x+a))^3/x^4,x, algorithm=""fricas"")","\frac{6 \, b^{3} x^{3} \log\left(x\right) - 18 \, a b^{2} x^{2} - 9 \, a^{2} b x - 2 \, a^{3}}{6 \, x^{3}}"," ",0,"1/6*(6*b^3*x^3*log(x) - 18*a*b^2*x^2 - 9*a^2*b*x - 2*a^3)/x^3","A",0
63,1,33,0,0.923988," ","integrate(arctanh(tanh(b*x+a))^3/x^5,x, algorithm=""fricas"")","-\frac{4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}}{4 \, x^{4}}"," ",0,"-1/4*(4*b^3*x^3 + 6*a*b^2*x^2 + 4*a^2*b*x + a^3)/x^4","A",0
64,1,35,0,0.372936," ","integrate(arctanh(tanh(b*x+a))^3/x^6,x, algorithm=""fricas"")","-\frac{10 \, b^{3} x^{3} + 20 \, a b^{2} x^{2} + 15 \, a^{2} b x + 4 \, a^{3}}{20 \, x^{5}}"," ",0,"-1/20*(10*b^3*x^3 + 20*a*b^2*x^2 + 15*a^2*b*x + 4*a^3)/x^5","A",0
65,1,483,0,0.637329," ","integrate(x^m*arctanh(tanh(b*x+a))^4,x, algorithm=""fricas"")","\frac{{\left({\left(b^{4} m^{4} + 10 \, b^{4} m^{3} + 35 \, b^{4} m^{2} + 50 \, b^{4} m + 24 \, b^{4}\right)} x^{5} + 4 \, {\left(a b^{3} m^{4} + 11 \, a b^{3} m^{3} + 41 \, a b^{3} m^{2} + 61 \, a b^{3} m + 30 \, a b^{3}\right)} x^{4} + 6 \, {\left(a^{2} b^{2} m^{4} + 12 \, a^{2} b^{2} m^{3} + 49 \, a^{2} b^{2} m^{2} + 78 \, a^{2} b^{2} m + 40 \, a^{2} b^{2}\right)} x^{3} + 4 \, {\left(a^{3} b m^{4} + 13 \, a^{3} b m^{3} + 59 \, a^{3} b m^{2} + 107 \, a^{3} b m + 60 \, a^{3} b\right)} x^{2} + {\left(a^{4} m^{4} + 14 \, a^{4} m^{3} + 71 \, a^{4} m^{2} + 154 \, a^{4} m + 120 \, a^{4}\right)} x\right)} \cosh\left(m \log\left(x\right)\right) + {\left({\left(b^{4} m^{4} + 10 \, b^{4} m^{3} + 35 \, b^{4} m^{2} + 50 \, b^{4} m + 24 \, b^{4}\right)} x^{5} + 4 \, {\left(a b^{3} m^{4} + 11 \, a b^{3} m^{3} + 41 \, a b^{3} m^{2} + 61 \, a b^{3} m + 30 \, a b^{3}\right)} x^{4} + 6 \, {\left(a^{2} b^{2} m^{4} + 12 \, a^{2} b^{2} m^{3} + 49 \, a^{2} b^{2} m^{2} + 78 \, a^{2} b^{2} m + 40 \, a^{2} b^{2}\right)} x^{3} + 4 \, {\left(a^{3} b m^{4} + 13 \, a^{3} b m^{3} + 59 \, a^{3} b m^{2} + 107 \, a^{3} b m + 60 \, a^{3} b\right)} x^{2} + {\left(a^{4} m^{4} + 14 \, a^{4} m^{3} + 71 \, a^{4} m^{2} + 154 \, a^{4} m + 120 \, a^{4}\right)} x\right)} \sinh\left(m \log\left(x\right)\right)}{m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120}"," ",0,"(((b^4*m^4 + 10*b^4*m^3 + 35*b^4*m^2 + 50*b^4*m + 24*b^4)*x^5 + 4*(a*b^3*m^4 + 11*a*b^3*m^3 + 41*a*b^3*m^2 + 61*a*b^3*m + 30*a*b^3)*x^4 + 6*(a^2*b^2*m^4 + 12*a^2*b^2*m^3 + 49*a^2*b^2*m^2 + 78*a^2*b^2*m + 40*a^2*b^2)*x^3 + 4*(a^3*b*m^4 + 13*a^3*b*m^3 + 59*a^3*b*m^2 + 107*a^3*b*m + 60*a^3*b)*x^2 + (a^4*m^4 + 14*a^4*m^3 + 71*a^4*m^2 + 154*a^4*m + 120*a^4)*x)*cosh(m*log(x)) + ((b^4*m^4 + 10*b^4*m^3 + 35*b^4*m^2 + 50*b^4*m + 24*b^4)*x^5 + 4*(a*b^3*m^4 + 11*a*b^3*m^3 + 41*a*b^3*m^2 + 61*a*b^3*m + 30*a*b^3)*x^4 + 6*(a^2*b^2*m^4 + 12*a^2*b^2*m^3 + 49*a^2*b^2*m^2 + 78*a^2*b^2*m + 40*a^2*b^2)*x^3 + 4*(a^3*b*m^4 + 13*a^3*b*m^3 + 59*a^3*b*m^2 + 107*a^3*b*m + 60*a^3*b)*x^2 + (a^4*m^4 + 14*a^4*m^3 + 71*a^4*m^2 + 154*a^4*m + 120*a^4)*x)*sinh(m*log(x)))/(m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)","B",0
66,1,46,0,0.454344," ","integrate(x^6*arctanh(tanh(b*x+a))^4,x, algorithm=""fricas"")","\frac{1}{11} \, b^{4} x^{11} + \frac{2}{5} \, a b^{3} x^{10} + \frac{2}{3} \, a^{2} b^{2} x^{9} + \frac{1}{2} \, a^{3} b x^{8} + \frac{1}{7} \, a^{4} x^{7}"," ",0,"1/11*b^4*x^11 + 2/5*a*b^3*x^10 + 2/3*a^2*b^2*x^9 + 1/2*a^3*b*x^8 + 1/7*a^4*x^7","A",0
67,1,46,0,0.517925," ","integrate(x^5*arctanh(tanh(b*x+a))^4,x, algorithm=""fricas"")","\frac{1}{10} \, b^{4} x^{10} + \frac{4}{9} \, a b^{3} x^{9} + \frac{3}{4} \, a^{2} b^{2} x^{8} + \frac{4}{7} \, a^{3} b x^{7} + \frac{1}{6} \, a^{4} x^{6}"," ",0,"1/10*b^4*x^10 + 4/9*a*b^3*x^9 + 3/4*a^2*b^2*x^8 + 4/7*a^3*b*x^7 + 1/6*a^4*x^6","A",0
68,1,46,0,0.520631," ","integrate(x^4*arctanh(tanh(b*x+a))^4,x, algorithm=""fricas"")","\frac{1}{9} \, b^{4} x^{9} + \frac{1}{2} \, a b^{3} x^{8} + \frac{6}{7} \, a^{2} b^{2} x^{7} + \frac{2}{3} \, a^{3} b x^{6} + \frac{1}{5} \, a^{4} x^{5}"," ",0,"1/9*b^4*x^9 + 1/2*a*b^3*x^8 + 6/7*a^2*b^2*x^7 + 2/3*a^3*b*x^6 + 1/5*a^4*x^5","A",0
69,1,45,0,0.623778," ","integrate(x^3*arctanh(tanh(b*x+a))^4,x, algorithm=""fricas"")","\frac{1}{8} \, b^{4} x^{8} + \frac{4}{7} \, a b^{3} x^{7} + a^{2} b^{2} x^{6} + \frac{4}{5} \, a^{3} b x^{5} + \frac{1}{4} \, a^{4} x^{4}"," ",0,"1/8*b^4*x^8 + 4/7*a*b^3*x^7 + a^2*b^2*x^6 + 4/5*a^3*b*x^5 + 1/4*a^4*x^4","A",0
70,1,45,0,0.464325," ","integrate(x^2*arctanh(tanh(b*x+a))^4,x, algorithm=""fricas"")","\frac{1}{7} \, b^{4} x^{7} + \frac{2}{3} \, a b^{3} x^{6} + \frac{6}{5} \, a^{2} b^{2} x^{5} + a^{3} b x^{4} + \frac{1}{3} \, a^{4} x^{3}"," ",0,"1/7*b^4*x^7 + 2/3*a*b^3*x^6 + 6/5*a^2*b^2*x^5 + a^3*b*x^4 + 1/3*a^4*x^3","A",0
71,1,46,0,0.702929," ","integrate(x*arctanh(tanh(b*x+a))^4,x, algorithm=""fricas"")","\frac{1}{6} \, b^{4} x^{6} + \frac{4}{5} \, a b^{3} x^{5} + \frac{3}{2} \, a^{2} b^{2} x^{4} + \frac{4}{3} \, a^{3} b x^{3} + \frac{1}{2} \, a^{4} x^{2}"," ",0,"1/6*b^4*x^6 + 4/5*a*b^3*x^5 + 3/2*a^2*b^2*x^4 + 4/3*a^3*b*x^3 + 1/2*a^4*x^2","A",0
72,1,42,0,0.443359," ","integrate(arctanh(tanh(b*x+a))^4,x, algorithm=""fricas"")","\frac{1}{5} \, b^{4} x^{5} + a b^{3} x^{4} + 2 \, a^{2} b^{2} x^{3} + 2 \, a^{3} b x^{2} + a^{4} x"," ",0,"1/5*b^4*x^5 + a*b^3*x^4 + 2*a^2*b^2*x^3 + 2*a^3*b*x^2 + a^4*x","B",0
73,1,42,0,0.540975," ","integrate(arctanh(tanh(b*x+a))^4/x,x, algorithm=""fricas"")","\frac{1}{4} \, b^{4} x^{4} + \frac{4}{3} \, a b^{3} x^{3} + 3 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4} \log\left(x\right)"," ",0,"1/4*b^4*x^4 + 4/3*a*b^3*x^3 + 3*a^2*b^2*x^2 + 4*a^3*b*x + a^4*log(x)","A",0
74,1,47,0,0.507473," ","integrate(arctanh(tanh(b*x+a))^4/x^2,x, algorithm=""fricas"")","\frac{b^{4} x^{4} + 6 \, a b^{3} x^{3} + 18 \, a^{2} b^{2} x^{2} + 12 \, a^{3} b x \log\left(x\right) - 3 \, a^{4}}{3 \, x}"," ",0,"1/3*(b^4*x^4 + 6*a*b^3*x^3 + 18*a^2*b^2*x^2 + 12*a^3*b*x*log(x) - 3*a^4)/x","A",0
75,1,47,0,0.745282," ","integrate(arctanh(tanh(b*x+a))^4/x^3,x, algorithm=""fricas"")","\frac{b^{4} x^{4} + 8 \, a b^{3} x^{3} + 12 \, a^{2} b^{2} x^{2} \log\left(x\right) - 8 \, a^{3} b x - a^{4}}{2 \, x^{2}}"," ",0,"1/2*(b^4*x^4 + 8*a*b^3*x^3 + 12*a^2*b^2*x^2*log(x) - 8*a^3*b*x - a^4)/x^2","A",0
76,1,48,0,0.663159," ","integrate(arctanh(tanh(b*x+a))^4/x^4,x, algorithm=""fricas"")","\frac{3 \, b^{4} x^{4} + 12 \, a b^{3} x^{3} \log\left(x\right) - 18 \, a^{2} b^{2} x^{2} - 6 \, a^{3} b x - a^{4}}{3 \, x^{3}}"," ",0,"1/3*(3*b^4*x^4 + 12*a*b^3*x^3*log(x) - 18*a^2*b^2*x^2 - 6*a^3*b*x - a^4)/x^3","A",0
77,1,48,0,0.609669," ","integrate(arctanh(tanh(b*x+a))^4/x^5,x, algorithm=""fricas"")","\frac{12 \, b^{4} x^{4} \log\left(x\right) - 48 \, a b^{3} x^{3} - 36 \, a^{2} b^{2} x^{2} - 16 \, a^{3} b x - 3 \, a^{4}}{12 \, x^{4}}"," ",0,"1/12*(12*b^4*x^4*log(x) - 48*a*b^3*x^3 - 36*a^2*b^2*x^2 - 16*a^3*b*x - 3*a^4)/x^4","A",0
78,1,44,0,0.493820," ","integrate(arctanh(tanh(b*x+a))^4/x^6,x, algorithm=""fricas"")","-\frac{5 \, b^{4} x^{4} + 10 \, a b^{3} x^{3} + 10 \, a^{2} b^{2} x^{2} + 5 \, a^{3} b x + a^{4}}{5 \, x^{5}}"," ",0,"-1/5*(5*b^4*x^4 + 10*a*b^3*x^3 + 10*a^2*b^2*x^2 + 5*a^3*b*x + a^4)/x^5","A",0
79,1,46,0,0.404274," ","integrate(arctanh(tanh(b*x+a))^4/x^7,x, algorithm=""fricas"")","-\frac{15 \, b^{4} x^{4} + 40 \, a b^{3} x^{3} + 45 \, a^{2} b^{2} x^{2} + 24 \, a^{3} b x + 5 \, a^{4}}{30 \, x^{6}}"," ",0,"-1/30*(15*b^4*x^4 + 40*a*b^3*x^3 + 45*a^2*b^2*x^2 + 24*a^3*b*x + 5*a^4)/x^6","A",0
80,1,46,0,0.558038," ","integrate(arctanh(tanh(b*x+a))^4/x^8,x, algorithm=""fricas"")","-\frac{35 \, b^{4} x^{4} + 105 \, a b^{3} x^{3} + 126 \, a^{2} b^{2} x^{2} + 70 \, a^{3} b x + 15 \, a^{4}}{105 \, x^{7}}"," ",0,"-1/105*(35*b^4*x^4 + 105*a*b^3*x^3 + 126*a^2*b^2*x^2 + 70*a^3*b*x + 15*a^4)/x^7","A",0
81,1,46,0,0.465060," ","integrate(arctanh(tanh(b*x+a))^4/x^9,x, algorithm=""fricas"")","-\frac{70 \, b^{4} x^{4} + 224 \, a b^{3} x^{3} + 280 \, a^{2} b^{2} x^{2} + 160 \, a^{3} b x + 35 \, a^{4}}{280 \, x^{8}}"," ",0,"-1/280*(70*b^4*x^4 + 224*a*b^3*x^3 + 280*a^2*b^2*x^2 + 160*a^3*b*x + 35*a^4)/x^8","A",0
82,1,46,0,0.549198," ","integrate(arctanh(tanh(b*x+a))^4/x^10,x, algorithm=""fricas"")","-\frac{126 \, b^{4} x^{4} + 420 \, a b^{3} x^{3} + 540 \, a^{2} b^{2} x^{2} + 315 \, a^{3} b x + 70 \, a^{4}}{630 \, x^{9}}"," ",0,"-1/630*(126*b^4*x^4 + 420*a*b^3*x^3 + 540*a^2*b^2*x^2 + 315*a^3*b*x + 70*a^4)/x^9","A",0
83,1,46,0,0.497971," ","integrate(arctanh(tanh(b*x+a))^4/x^11,x, algorithm=""fricas"")","-\frac{210 \, b^{4} x^{4} + 720 \, a b^{3} x^{3} + 945 \, a^{2} b^{2} x^{2} + 560 \, a^{3} b x + 126 \, a^{4}}{1260 \, x^{10}}"," ",0,"-1/1260*(210*b^4*x^4 + 720*a*b^3*x^3 + 945*a^2*b^2*x^2 + 560*a^3*b*x + 126*a^4)/x^10","A",0
84,1,68,0,0.468838," ","integrate(x*arctanh(tanh(b*x+a))^6,x, algorithm=""fricas"")","\frac{1}{8} \, b^{6} x^{8} + \frac{6}{7} \, a b^{5} x^{7} + \frac{5}{2} \, a^{2} b^{4} x^{6} + 4 \, a^{3} b^{3} x^{5} + \frac{15}{4} \, a^{4} b^{2} x^{4} + 2 \, a^{5} b x^{3} + \frac{1}{2} \, a^{6} x^{2}"," ",0,"1/8*b^6*x^8 + 6/7*a*b^5*x^7 + 5/2*a^2*b^4*x^6 + 4*a^3*b^3*x^5 + 15/4*a^4*b^2*x^4 + 2*a^5*b*x^3 + 1/2*a^6*x^2","B",0
85,0,0,0,0.797267," ","integrate(x^m/arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{\operatorname{artanh}\left(\tanh\left(b x + a\right)\right)}, x\right)"," ",0,"integral(x^m/arctanh(tanh(b*x + a)), x)","F",0
86,1,41,0,0.547114," ","integrate(x^3/arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} - 3 \, a b^{2} x^{2} + 6 \, a^{2} b x - 6 \, a^{3} \log\left(b x + a\right)}{6 \, b^{4}}"," ",0,"1/6*(2*b^3*x^3 - 3*a*b^2*x^2 + 6*a^2*b*x - 6*a^3*log(b*x + a))/b^4","A",0
87,1,29,0,0.383072," ","integrate(x^2/arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} - 2 \, a b x + 2 \, a^{2} \log\left(b x + a\right)}{2 \, b^{3}}"," ",0,"1/2*(b^2*x^2 - 2*a*b*x + 2*a^2*log(b*x + a))/b^3","A",0
88,1,17,0,0.433889," ","integrate(x/arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b x - a \log\left(b x + a\right)}{b^{2}}"," ",0,"(b*x - a*log(b*x + a))/b^2","A",0
89,1,10,0,0.488015," ","integrate(1/arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{\log\left(b x + a\right)}{b}"," ",0,"log(b*x + a)/b","A",0
90,1,16,0,0.456608," ","integrate(1/x/arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","-\frac{\log\left(b x + a\right) - \log\left(x\right)}{a}"," ",0,"-(log(b*x + a) - log(x))/a","A",0
91,1,26,0,0.379464," ","integrate(1/x^2/arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b x \log\left(b x + a\right) - b x \log\left(x\right) - a}{a^{2} x}"," ",0,"(b*x*log(b*x + a) - b*x*log(x) - a)/(a^2*x)","A",0
92,1,41,0,0.502428," ","integrate(1/x^3/arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","-\frac{2 \, b^{2} x^{2} \log\left(b x + a\right) - 2 \, b^{2} x^{2} \log\left(x\right) - 2 \, a b x + a^{2}}{2 \, a^{3} x^{2}}"," ",0,"-1/2*(2*b^2*x^2*log(b*x + a) - 2*b^2*x^2*log(x) - 2*a*b*x + a^2)/(a^3*x^2)","A",0
93,0,0,0,0.581624," ","integrate(x^m/arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{\operatorname{artanh}\left(\tanh\left(b x + a\right)\right)^{2}}, x\right)"," ",0,"integral(x^m/arctanh(tanh(b*x + a))^2, x)","F",0
94,1,73,0,0.446259," ","integrate(x^4/arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{b^{4} x^{4} - 2 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 9 \, a^{3} b x - 3 \, a^{4} - 12 \, {\left(a^{3} b x + a^{4}\right)} \log\left(b x + a\right)}{3 \, {\left(b^{6} x + a b^{5}\right)}}"," ",0,"1/3*(b^4*x^4 - 2*a*b^3*x^3 + 6*a^2*b^2*x^2 + 9*a^3*b*x - 3*a^4 - 12*(a^3*b*x + a^4)*log(b*x + a))/(b^6*x + a*b^5)","A",0
95,1,62,0,0.452900," ","integrate(x^3/arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{b^{3} x^{3} - 3 \, a b^{2} x^{2} - 4 \, a^{2} b x + 2 \, a^{3} + 6 \, {\left(a^{2} b x + a^{3}\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x + a b^{4}\right)}}"," ",0,"1/2*(b^3*x^3 - 3*a*b^2*x^2 - 4*a^2*b*x + 2*a^3 + 6*(a^2*b*x + a^3)*log(b*x + a))/(b^5*x + a*b^4)","A",0
96,1,47,0,0.568631," ","integrate(x^2/arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{b^{2} x^{2} + a b x - a^{2} - 2 \, {\left(a b x + a^{2}\right)} \log\left(b x + a\right)}{b^{4} x + a b^{3}}"," ",0,"(b^2*x^2 + a*b*x - a^2 - 2*(a*b*x + a^2)*log(b*x + a))/(b^4*x + a*b^3)","A",0
97,1,28,0,0.431447," ","integrate(x/arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{{\left(b x + a\right)} \log\left(b x + a\right) + a}{b^{3} x + a b^{2}}"," ",0,"((b*x + a)*log(b*x + a) + a)/(b^3*x + a*b^2)","A",0
98,1,13,0,0.444912," ","integrate(1/arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","-\frac{1}{b^{2} x + a b}"," ",0,"-1/(b^2*x + a*b)","A",0
99,1,39,0,0.625865," ","integrate(1/x/arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","-\frac{{\left(b x + a\right)} \log\left(b x + a\right) - {\left(b x + a\right)} \log\left(x\right) - a}{a^{2} b x + a^{3}}"," ",0,"-((b*x + a)*log(b*x + a) - (b*x + a)*log(x) - a)/(a^2*b*x + a^3)","A",0
100,1,63,0,0.542439," ","integrate(1/x^2/arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","-\frac{2 \, a b x + a^{2} - 2 \, {\left(b^{2} x^{2} + a b x\right)} \log\left(b x + a\right) + 2 \, {\left(b^{2} x^{2} + a b x\right)} \log\left(x\right)}{a^{3} b x^{2} + a^{4} x}"," ",0,"-(2*a*b*x + a^2 - 2*(b^2*x^2 + a*b*x)*log(b*x + a) + 2*(b^2*x^2 + a*b*x)*log(x))/(a^3*b*x^2 + a^4*x)","A",0
101,1,86,0,0.454685," ","integrate(1/x^3/arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{6 \, a b^{2} x^{2} + 3 \, a^{2} b x - a^{3} - 6 \, {\left(b^{3} x^{3} + a b^{2} x^{2}\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} x^{3} + a b^{2} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{4} b x^{3} + a^{5} x^{2}\right)}}"," ",0,"1/2*(6*a*b^2*x^2 + 3*a^2*b*x - a^3 - 6*(b^3*x^3 + a*b^2*x^2)*log(b*x + a) + 6*(b^3*x^3 + a*b^2*x^2)*log(x))/(a^4*b*x^3 + a^5*x^2)","A",0
102,0,0,0,0.490880," ","integrate(x^m/arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{\operatorname{artanh}\left(\tanh\left(b x + a\right)\right)^{3}}, x\right)"," ",0,"integral(x^m/arctanh(tanh(b*x + a))^3, x)","F",0
103,1,95,0,0.923017," ","integrate(x^4/arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{b^{4} x^{4} - 4 \, a b^{3} x^{3} - 11 \, a^{2} b^{2} x^{2} + 2 \, a^{3} b x + 7 \, a^{4} + 12 \, {\left(a^{2} b^{2} x^{2} + 2 \, a^{3} b x + a^{4}\right)} \log\left(b x + a\right)}{2 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}"," ",0,"1/2*(b^4*x^4 - 4*a*b^3*x^3 - 11*a^2*b^2*x^2 + 2*a^3*b*x + 7*a^4 + 12*(a^2*b^2*x^2 + 2*a^3*b*x + a^4)*log(b*x + a))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)","A",0
104,1,83,0,1.563116," ","integrate(x^3/arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} + 4 \, a b^{2} x^{2} - 4 \, a^{2} b x - 5 \, a^{3} - 6 \, {\left(a b^{2} x^{2} + 2 \, a^{2} b x + a^{3}\right)} \log\left(b x + a\right)}{2 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}"," ",0,"1/2*(2*b^3*x^3 + 4*a*b^2*x^2 - 4*a^2*b*x - 5*a^3 - 6*(a*b^2*x^2 + 2*a^2*b*x + a^3)*log(b*x + a))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)","A",0
105,1,61,0,1.071094," ","integrate(x^2/arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{4 \, a b x + 3 \, a^{2} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \log\left(b x + a\right)}{2 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}"," ",0,"1/2*(4*a*b*x + 3*a^2 + 2*(b^2*x^2 + 2*a*b*x + a^2)*log(b*x + a))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)","A",0
106,1,32,0,0.511003," ","integrate(x/arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","-\frac{2 \, b x + a}{2 \, {\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)}}"," ",0,"-1/2*(2*b*x + a)/(b^4*x^2 + 2*a*b^3*x + a^2*b^2)","A",0
107,1,24,0,0.400469," ","integrate(1/arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)}}"," ",0,"-1/2/(b^3*x^2 + 2*a*b^2*x + a^2*b)","A",0
108,1,80,0,0.500290," ","integrate(1/x/arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{2 \, a b x + 3 \, a^{2} - 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{3} b^{2} x^{2} + 2 \, a^{4} b x + a^{5}\right)}}"," ",0,"1/2*(2*a*b*x + 3*a^2 - 2*(b^2*x^2 + 2*a*b*x + a^2)*log(b*x + a) + 2*(b^2*x^2 + 2*a*b*x + a^2)*log(x))/(a^3*b^2*x^2 + 2*a^4*b*x + a^5)","A",0
109,1,109,0,0.518686," ","integrate(1/x^2/arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","-\frac{6 \, a b^{2} x^{2} + 9 \, a^{2} b x + 2 \, a^{3} - 6 \, {\left(b^{3} x^{3} + 2 \, a b^{2} x^{2} + a^{2} b x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} x^{3} + 2 \, a b^{2} x^{2} + a^{2} b x\right)} \log\left(x\right)}{2 \, {\left(a^{4} b^{2} x^{3} + 2 \, a^{5} b x^{2} + a^{6} x\right)}}"," ",0,"-1/2*(6*a*b^2*x^2 + 9*a^2*b*x + 2*a^3 - 6*(b^3*x^3 + 2*a*b^2*x^2 + a^2*b*x)*log(b*x + a) + 6*(b^3*x^3 + 2*a*b^2*x^2 + a^2*b*x)*log(x))/(a^4*b^2*x^3 + 2*a^5*b*x^2 + a^6*x)","A",0
110,1,130,0,0.458536," ","integrate(1/x^3/arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{12 \, a b^{3} x^{3} + 18 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x - a^{4} - 12 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{3} + a^{2} b^{2} x^{2}\right)} \log\left(b x + a\right) + 12 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{3} + a^{2} b^{2} x^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{5} b^{2} x^{4} + 2 \, a^{6} b x^{3} + a^{7} x^{2}\right)}}"," ",0,"1/2*(12*a*b^3*x^3 + 18*a^2*b^2*x^2 + 4*a^3*b*x - a^4 - 12*(b^4*x^4 + 2*a*b^3*x^3 + a^2*b^2*x^2)*log(b*x + a) + 12*(b^4*x^4 + 2*a*b^3*x^3 + a^2*b^2*x^2)*log(x))/(a^5*b^2*x^4 + 2*a^6*b*x^3 + a^7*x^2)","A",0
111,1,64,0,0.520963," ","integrate(x^4*arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, b^{5} x^{5} + 35 \, a b^{4} x^{4} - 40 \, a^{2} b^{3} x^{3} + 48 \, a^{3} b^{2} x^{2} - 64 \, a^{4} b x + 128 \, a^{5}\right)} \sqrt{b x + a}}{3465 \, b^{5}}"," ",0,"2/3465*(315*b^5*x^5 + 35*a*b^4*x^4 - 40*a^2*b^3*x^3 + 48*a^3*b^2*x^2 - 64*a^4*b*x + 128*a^5)*sqrt(b*x + a)/b^5","A",0
112,1,53,0,0.458004," ","integrate(x^3*arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, b^{4} x^{4} + 5 \, a b^{3} x^{3} - 6 \, a^{2} b^{2} x^{2} + 8 \, a^{3} b x - 16 \, a^{4}\right)} \sqrt{b x + a}}{315 \, b^{4}}"," ",0,"2/315*(35*b^4*x^4 + 5*a*b^3*x^3 - 6*a^2*b^2*x^2 + 8*a^3*b*x - 16*a^4)*sqrt(b*x + a)/b^4","A",0
113,1,42,0,0.620975," ","integrate(x^2*arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, b^{3} x^{3} + 3 \, a b^{2} x^{2} - 4 \, a^{2} b x + 8 \, a^{3}\right)} \sqrt{b x + a}}{105 \, b^{3}}"," ",0,"2/105*(15*b^3*x^3 + 3*a*b^2*x^2 - 4*a^2*b*x + 8*a^3)*sqrt(b*x + a)/b^3","A",0
114,1,30,0,0.510153," ","integrate(x*arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} x^{2} + a b x - 2 \, a^{2}\right)} \sqrt{b x + a}}{15 \, b^{2}}"," ",0,"2/15*(3*b^2*x^2 + a*b*x - 2*a^2)*sqrt(b*x + a)/b^2","A",0
115,1,12,0,0.529672," ","integrate(arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b x + a\right)}^{\frac{3}{2}}}{3 \, b}"," ",0,"2/3*(b*x + a)^(3/2)/b","A",0
116,1,73,0,0.494817," ","integrate(arctanh(tanh(b*x+a))^(1/2)/x,x, algorithm=""fricas"")","\left[\sqrt{a} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, \sqrt{b x + a}, 2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + 2 \, \sqrt{b x + a}\right]"," ",0,"[sqrt(a)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*sqrt(b*x + a), 2*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) + 2*sqrt(b*x + a)]","A",0
117,1,93,0,0.546169," ","integrate(arctanh(tanh(b*x+a))^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b x \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, \sqrt{b x + a} a}{2 \, a x}, \frac{\sqrt{-a} b x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - \sqrt{b x + a} a}{a x}\right]"," ",0,"[1/2*(sqrt(a)*b*x*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*sqrt(b*x + a)*a)/(a*x), (sqrt(-a)*b*x*arctan(sqrt(b*x + a)*sqrt(-a)/a) - sqrt(b*x + a)*a)/(a*x)]","A",0
118,1,119,0,0.623485," ","integrate(arctanh(tanh(b*x+a))^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b^{2} x^{2} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, {\left(a b x + 2 \, a^{2}\right)} \sqrt{b x + a}}{8 \, a^{2} x^{2}}, -\frac{\sqrt{-a} b^{2} x^{2} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(a b x + 2 \, a^{2}\right)} \sqrt{b x + a}}{4 \, a^{2} x^{2}}\right]"," ",0,"[1/8*(sqrt(a)*b^2*x^2*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*(a*b*x + 2*a^2)*sqrt(b*x + a))/(a^2*x^2), -1/4*(sqrt(-a)*b^2*x^2*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (a*b*x + 2*a^2)*sqrt(b*x + a))/(a^2*x^2)]","A",0
119,1,145,0,0.510133," ","integrate(arctanh(tanh(b*x+a))^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{3} x^{3} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(3 \, a b^{2} x^{2} - 2 \, a^{2} b x - 8 \, a^{3}\right)} \sqrt{b x + a}}{48 \, a^{3} x^{3}}, \frac{3 \, \sqrt{-a} b^{3} x^{3} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(3 \, a b^{2} x^{2} - 2 \, a^{2} b x - 8 \, a^{3}\right)} \sqrt{b x + a}}{24 \, a^{3} x^{3}}\right]"," ",0,"[1/48*(3*sqrt(a)*b^3*x^3*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(3*a*b^2*x^2 - 2*a^2*b*x - 8*a^3)*sqrt(b*x + a))/(a^3*x^3), 1/24*(3*sqrt(-a)*b^3*x^3*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (3*a*b^2*x^2 - 2*a^2*b*x - 8*a^3)*sqrt(b*x + a))/(a^3*x^3)]","A",0
120,1,75,0,0.476953," ","integrate(x^4*arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, b^{6} x^{6} + 1470 \, a b^{5} x^{5} + 35 \, a^{2} b^{4} x^{4} - 40 \, a^{3} b^{3} x^{3} + 48 \, a^{4} b^{2} x^{2} - 64 \, a^{5} b x + 128 \, a^{6}\right)} \sqrt{b x + a}}{15015 \, b^{5}}"," ",0,"2/15015*(1155*b^6*x^6 + 1470*a*b^5*x^5 + 35*a^2*b^4*x^4 - 40*a^3*b^3*x^3 + 48*a^4*b^2*x^2 - 64*a^5*b*x + 128*a^6)*sqrt(b*x + a)/b^5","A",0
121,1,64,0,0.483577," ","integrate(x^3*arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, b^{5} x^{5} + 140 \, a b^{4} x^{4} + 5 \, a^{2} b^{3} x^{3} - 6 \, a^{3} b^{2} x^{2} + 8 \, a^{4} b x - 16 \, a^{5}\right)} \sqrt{b x + a}}{1155 \, b^{4}}"," ",0,"2/1155*(105*b^5*x^5 + 140*a*b^4*x^4 + 5*a^2*b^3*x^3 - 6*a^3*b^2*x^2 + 8*a^4*b*x - 16*a^5)*sqrt(b*x + a)/b^4","A",0
122,1,53,0,0.419647," ","integrate(x^2*arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, b^{4} x^{4} + 50 \, a b^{3} x^{3} + 3 \, a^{2} b^{2} x^{2} - 4 \, a^{3} b x + 8 \, a^{4}\right)} \sqrt{b x + a}}{315 \, b^{3}}"," ",0,"2/315*(35*b^4*x^4 + 50*a*b^3*x^3 + 3*a^2*b^2*x^2 - 4*a^3*b*x + 8*a^4)*sqrt(b*x + a)/b^3","A",0
123,1,41,0,0.527159," ","integrate(x*arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{3} x^{3} + 8 \, a b^{2} x^{2} + a^{2} b x - 2 \, a^{3}\right)} \sqrt{b x + a}}{35 \, b^{2}}"," ",0,"2/35*(5*b^3*x^3 + 8*a*b^2*x^2 + a^2*b*x - 2*a^3)*sqrt(b*x + a)/b^2","A",0
124,1,28,0,0.524403," ","integrate(arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{b x + a}}{5 \, b}"," ",0,"2/5*(b^2*x^2 + 2*a*b*x + a^2)*sqrt(b*x + a)/b","A",0
125,1,88,0,0.641819," ","integrate(arctanh(tanh(b*x+a))^(3/2)/x,x, algorithm=""fricas"")","\left[a^{\frac{3}{2}} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + \frac{2}{3} \, {\left(b x + 4 \, a\right)} \sqrt{b x + a}, 2 \, \sqrt{-a} a \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + \frac{2}{3} \, {\left(b x + 4 \, a\right)} \sqrt{b x + a}\right]"," ",0,"[a^(3/2)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2/3*(b*x + 4*a)*sqrt(b*x + a), 2*sqrt(-a)*a*arctan(sqrt(b*x + a)*sqrt(-a)/a) + 2/3*(b*x + 4*a)*sqrt(b*x + a)]","A",0
126,1,102,0,0.675163," ","integrate(arctanh(tanh(b*x+a))^(3/2)/x^2,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b x \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(2 \, b x - a\right)} \sqrt{b x + a}}{2 \, x}, \frac{3 \, \sqrt{-a} b x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(2 \, b x - a\right)} \sqrt{b x + a}}{x}\right]"," ",0,"[1/2*(3*sqrt(a)*b*x*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(2*b*x - a)*sqrt(b*x + a))/x, (3*sqrt(-a)*b*x*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (2*b*x - a)*sqrt(b*x + a))/x]","A",0
127,1,124,0,0.566817," ","integrate(arctanh(tanh(b*x+a))^(3/2)/x^3,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{2} x^{2} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, {\left(5 \, a b x + 2 \, a^{2}\right)} \sqrt{b x + a}}{8 \, a x^{2}}, \frac{3 \, \sqrt{-a} b^{2} x^{2} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left(5 \, a b x + 2 \, a^{2}\right)} \sqrt{b x + a}}{4 \, a x^{2}}\right]"," ",0,"[1/8*(3*sqrt(a)*b^2*x^2*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*(5*a*b*x + 2*a^2)*sqrt(b*x + a))/(a*x^2), 1/4*(3*sqrt(-a)*b^2*x^2*arctan(sqrt(b*x + a)*sqrt(-a)/a) - (5*a*b*x + 2*a^2)*sqrt(b*x + a))/(a*x^2)]","A",0
128,1,145,0,0.455956," ","integrate(arctanh(tanh(b*x+a))^(3/2)/x^4,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{3} x^{3} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, {\left(3 \, a b^{2} x^{2} + 14 \, a^{2} b x + 8 \, a^{3}\right)} \sqrt{b x + a}}{48 \, a^{2} x^{3}}, -\frac{3 \, \sqrt{-a} b^{3} x^{3} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(3 \, a b^{2} x^{2} + 14 \, a^{2} b x + 8 \, a^{3}\right)} \sqrt{b x + a}}{24 \, a^{2} x^{3}}\right]"," ",0,"[1/48*(3*sqrt(a)*b^3*x^3*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*(3*a*b^2*x^2 + 14*a^2*b*x + 8*a^3)*sqrt(b*x + a))/(a^2*x^3), -1/24*(3*sqrt(-a)*b^3*x^3*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (3*a*b^2*x^2 + 14*a^2*b*x + 8*a^3)*sqrt(b*x + a))/(a^2*x^3)]","A",0
129,1,86,0,0.521703," ","integrate(x^4*arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3003 \, b^{7} x^{7} + 7161 \, a b^{6} x^{6} + 4473 \, a^{2} b^{5} x^{5} + 35 \, a^{3} b^{4} x^{4} - 40 \, a^{4} b^{3} x^{3} + 48 \, a^{5} b^{2} x^{2} - 64 \, a^{6} b x + 128 \, a^{7}\right)} \sqrt{b x + a}}{45045 \, b^{5}}"," ",0,"2/45045*(3003*b^7*x^7 + 7161*a*b^6*x^6 + 4473*a^2*b^5*x^5 + 35*a^3*b^4*x^4 - 40*a^4*b^3*x^3 + 48*a^5*b^2*x^2 - 64*a^6*b*x + 128*a^7)*sqrt(b*x + a)/b^5","A",0
130,1,75,0,0.454570," ","integrate(x^3*arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(231 \, b^{6} x^{6} + 567 \, a b^{5} x^{5} + 371 \, a^{2} b^{4} x^{4} + 5 \, a^{3} b^{3} x^{3} - 6 \, a^{4} b^{2} x^{2} + 8 \, a^{5} b x - 16 \, a^{6}\right)} \sqrt{b x + a}}{3003 \, b^{4}}"," ",0,"2/3003*(231*b^6*x^6 + 567*a*b^5*x^5 + 371*a^2*b^4*x^4 + 5*a^3*b^3*x^3 - 6*a^4*b^2*x^2 + 8*a^5*b*x - 16*a^6)*sqrt(b*x + a)/b^4","A",0
131,1,64,0,0.533317," ","integrate(x^2*arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, b^{5} x^{5} + 161 \, a b^{4} x^{4} + 113 \, a^{2} b^{3} x^{3} + 3 \, a^{3} b^{2} x^{2} - 4 \, a^{4} b x + 8 \, a^{5}\right)} \sqrt{b x + a}}{693 \, b^{3}}"," ",0,"2/693*(63*b^5*x^5 + 161*a*b^4*x^4 + 113*a^2*b^3*x^3 + 3*a^3*b^2*x^2 - 4*a^4*b*x + 8*a^5)*sqrt(b*x + a)/b^3","A",0
132,1,52,0,0.600061," ","integrate(x*arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, b^{4} x^{4} + 19 \, a b^{3} x^{3} + 15 \, a^{2} b^{2} x^{2} + a^{3} b x - 2 \, a^{4}\right)} \sqrt{b x + a}}{63 \, b^{2}}"," ",0,"2/63*(7*b^4*x^4 + 19*a*b^3*x^3 + 15*a^2*b^2*x^2 + a^3*b*x - 2*a^4)*sqrt(b*x + a)/b^2","A",0
133,1,39,0,0.797975," ","integrate(arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right)} \sqrt{b x + a}}{7 \, b}"," ",0,"2/7*(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*sqrt(b*x + a)/b","B",0
134,1,114,0,0.720488," ","integrate(arctanh(tanh(b*x+a))^(5/2)/x,x, algorithm=""fricas"")","\left[a^{\frac{5}{2}} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + \frac{2}{15} \, {\left(3 \, b^{2} x^{2} + 11 \, a b x + 23 \, a^{2}\right)} \sqrt{b x + a}, 2 \, \sqrt{-a} a^{2} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + \frac{2}{15} \, {\left(3 \, b^{2} x^{2} + 11 \, a b x + 23 \, a^{2}\right)} \sqrt{b x + a}\right]"," ",0,"[a^(5/2)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2/15*(3*b^2*x^2 + 11*a*b*x + 23*a^2)*sqrt(b*x + a), 2*sqrt(-a)*a^2*arctan(sqrt(b*x + a)*sqrt(-a)/a) + 2/15*(3*b^2*x^2 + 11*a*b*x + 23*a^2)*sqrt(b*x + a)]","A",0
135,1,126,0,0.619894," ","integrate(arctanh(tanh(b*x+a))^(5/2)/x^2,x, algorithm=""fricas"")","\left[\frac{15 \, a^{\frac{3}{2}} b x \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(2 \, b^{2} x^{2} + 14 \, a b x - 3 \, a^{2}\right)} \sqrt{b x + a}}{6 \, x}, \frac{15 \, \sqrt{-a} a b x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(2 \, b^{2} x^{2} + 14 \, a b x - 3 \, a^{2}\right)} \sqrt{b x + a}}{3 \, x}\right]"," ",0,"[1/6*(15*a^(3/2)*b*x*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(2*b^2*x^2 + 14*a*b*x - 3*a^2)*sqrt(b*x + a))/x, 1/3*(15*sqrt(-a)*a*b*x*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (2*b^2*x^2 + 14*a*b*x - 3*a^2)*sqrt(b*x + a))/x]","A",0
136,1,133,0,0.962639," ","integrate(arctanh(tanh(b*x+a))^(5/2)/x^3,x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a} b^{2} x^{2} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(8 \, b^{2} x^{2} - 9 \, a b x - 2 \, a^{2}\right)} \sqrt{b x + a}}{8 \, x^{2}}, \frac{15 \, \sqrt{-a} b^{2} x^{2} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(8 \, b^{2} x^{2} - 9 \, a b x - 2 \, a^{2}\right)} \sqrt{b x + a}}{4 \, x^{2}}\right]"," ",0,"[1/8*(15*sqrt(a)*b^2*x^2*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(8*b^2*x^2 - 9*a*b*x - 2*a^2)*sqrt(b*x + a))/x^2, 1/4*(15*sqrt(-a)*b^2*x^2*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (8*b^2*x^2 - 9*a*b*x - 2*a^2)*sqrt(b*x + a))/x^2]","A",0
137,1,146,0,0.656074," ","integrate(arctanh(tanh(b*x+a))^(5/2)/x^4,x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a} b^{3} x^{3} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, {\left(33 \, a b^{2} x^{2} + 26 \, a^{2} b x + 8 \, a^{3}\right)} \sqrt{b x + a}}{48 \, a x^{3}}, \frac{15 \, \sqrt{-a} b^{3} x^{3} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left(33 \, a b^{2} x^{2} + 26 \, a^{2} b x + 8 \, a^{3}\right)} \sqrt{b x + a}}{24 \, a x^{3}}\right]"," ",0,"[1/48*(15*sqrt(a)*b^3*x^3*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*(33*a*b^2*x^2 + 26*a^2*b*x + 8*a^3)*sqrt(b*x + a))/(a*x^3), 1/24*(15*sqrt(-a)*b^3*x^3*arctan(sqrt(b*x + a)*sqrt(-a)/a) - (33*a*b^2*x^2 + 26*a^2*b*x + 8*a^3)*sqrt(b*x + a))/(a*x^3)]","A",0
138,1,167,0,0.619136," ","integrate(arctanh(tanh(b*x+a))^(5/2)/x^5,x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a} b^{4} x^{4} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, {\left(15 \, a b^{3} x^{3} + 118 \, a^{2} b^{2} x^{2} + 136 \, a^{3} b x + 48 \, a^{4}\right)} \sqrt{b x + a}}{384 \, a^{2} x^{4}}, -\frac{15 \, \sqrt{-a} b^{4} x^{4} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(15 \, a b^{3} x^{3} + 118 \, a^{2} b^{2} x^{2} + 136 \, a^{3} b x + 48 \, a^{4}\right)} \sqrt{b x + a}}{192 \, a^{2} x^{4}}\right]"," ",0,"[1/384*(15*sqrt(a)*b^4*x^4*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*(15*a*b^3*x^3 + 118*a^2*b^2*x^2 + 136*a^3*b*x + 48*a^4)*sqrt(b*x + a))/(a^2*x^4), -1/192*(15*sqrt(-a)*b^4*x^4*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (15*a*b^3*x^3 + 118*a^2*b^2*x^2 + 136*a^3*b*x + 48*a^4)*sqrt(b*x + a))/(a^2*x^4)]","A",0
139,1,189,0,0.843278," ","integrate(arctanh(tanh(b*x+a))^(5/2)/x^6,x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a} b^{5} x^{5} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(15 \, a b^{4} x^{4} - 10 \, a^{2} b^{3} x^{3} - 248 \, a^{3} b^{2} x^{2} - 336 \, a^{4} b x - 128 \, a^{5}\right)} \sqrt{b x + a}}{1280 \, a^{3} x^{5}}, \frac{15 \, \sqrt{-a} b^{5} x^{5} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(15 \, a b^{4} x^{4} - 10 \, a^{2} b^{3} x^{3} - 248 \, a^{3} b^{2} x^{2} - 336 \, a^{4} b x - 128 \, a^{5}\right)} \sqrt{b x + a}}{640 \, a^{3} x^{5}}\right]"," ",0,"[1/1280*(15*sqrt(a)*b^5*x^5*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(15*a*b^4*x^4 - 10*a^2*b^3*x^3 - 248*a^3*b^2*x^2 - 336*a^4*b*x - 128*a^5)*sqrt(b*x + a))/(a^3*x^5), 1/640*(15*sqrt(-a)*b^5*x^5*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (15*a*b^4*x^4 - 10*a^2*b^3*x^3 - 248*a^3*b^2*x^2 - 336*a^4*b*x - 128*a^5)*sqrt(b*x + a))/(a^3*x^5)]","A",0
140,1,53,0,0.654573," ","integrate(x^4/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, b^{4} x^{4} - 40 \, a b^{3} x^{3} + 48 \, a^{2} b^{2} x^{2} - 64 \, a^{3} b x + 128 \, a^{4}\right)} \sqrt{b x + a}}{315 \, b^{5}}"," ",0,"2/315*(35*b^4*x^4 - 40*a*b^3*x^3 + 48*a^2*b^2*x^2 - 64*a^3*b*x + 128*a^4)*sqrt(b*x + a)/b^5","A",0
141,1,42,0,0.469280," ","integrate(x^3/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{3} x^{3} - 6 \, a b^{2} x^{2} + 8 \, a^{2} b x - 16 \, a^{3}\right)} \sqrt{b x + a}}{35 \, b^{4}}"," ",0,"2/35*(5*b^3*x^3 - 6*a*b^2*x^2 + 8*a^2*b*x - 16*a^3)*sqrt(b*x + a)/b^4","A",0
142,1,31,0,0.472710," ","integrate(x^2/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} x^{2} - 4 \, a b x + 8 \, a^{2}\right)} \sqrt{b x + a}}{15 \, b^{3}}"," ",0,"2/15*(3*b^2*x^2 - 4*a*b*x + 8*a^2)*sqrt(b*x + a)/b^3","A",0
143,1,19,0,0.495078," ","integrate(x/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{b x + a} {\left(b x - 2 \, a\right)}}{3 \, b^{2}}"," ",0,"2/3*sqrt(b*x + a)*(b*x - 2*a)/b^2","A",0
144,1,12,0,0.444733," ","integrate(1/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{b x + a}}{b}"," ",0,"2*sqrt(b*x + a)/b","A",0
145,1,56,0,0.533455," ","integrate(1/x/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right)}{\sqrt{a}}, \frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right)}{a}\right]"," ",0,"[log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x)/sqrt(a), 2*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a)/a]","A",0
146,1,93,0,0.581244," ","integrate(1/x^2/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} b x \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, \sqrt{b x + a} a}{2 \, a^{2} x}, -\frac{\sqrt{-a} b x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + \sqrt{b x + a} a}{a^{2} x}\right]"," ",0,"[1/2*(sqrt(a)*b*x*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*sqrt(b*x + a)*a)/(a^2*x), -(sqrt(-a)*b*x*arctan(sqrt(b*x + a)*sqrt(-a)/a) + sqrt(b*x + a)*a)/(a^2*x)]","A",0
147,1,123,0,0.578852," ","integrate(1/x^3/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b^{2} x^{2} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(3 \, a b x - 2 \, a^{2}\right)} \sqrt{b x + a}}{8 \, a^{3} x^{2}}, \frac{3 \, \sqrt{-a} b^{2} x^{2} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(3 \, a b x - 2 \, a^{2}\right)} \sqrt{b x + a}}{4 \, a^{3} x^{2}}\right]"," ",0,"[1/8*(3*sqrt(a)*b^2*x^2*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(3*a*b*x - 2*a^2)*sqrt(b*x + a))/(a^3*x^2), 1/4*(3*sqrt(-a)*b^2*x^2*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (3*a*b*x - 2*a^2)*sqrt(b*x + a))/(a^3*x^2)]","A",0
148,1,145,0,0.563638," ","integrate(1/x^4/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a} b^{3} x^{3} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, {\left(15 \, a b^{2} x^{2} - 10 \, a^{2} b x + 8 \, a^{3}\right)} \sqrt{b x + a}}{48 \, a^{4} x^{3}}, -\frac{15 \, \sqrt{-a} b^{3} x^{3} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(15 \, a b^{2} x^{2} - 10 \, a^{2} b x + 8 \, a^{3}\right)} \sqrt{b x + a}}{24 \, a^{4} x^{3}}\right]"," ",0,"[1/48*(15*sqrt(a)*b^3*x^3*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*(15*a*b^2*x^2 - 10*a^2*b*x + 8*a^3)*sqrt(b*x + a))/(a^4*x^3), -1/24*(15*sqrt(-a)*b^3*x^3*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (15*a*b^2*x^2 - 10*a^2*b*x + 8*a^3)*sqrt(b*x + a))/(a^4*x^3)]","A",0
149,1,63,0,0.516151," ","integrate(x^4/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{4} x^{4} - 8 \, a b^{3} x^{3} + 16 \, a^{2} b^{2} x^{2} - 64 \, a^{3} b x - 128 \, a^{4}\right)} \sqrt{b x + a}}{35 \, {\left(b^{6} x + a b^{5}\right)}}"," ",0,"2/35*(5*b^4*x^4 - 8*a*b^3*x^3 + 16*a^2*b^2*x^2 - 64*a^3*b*x - 128*a^4)*sqrt(b*x + a)/(b^6*x + a*b^5)","A",0
150,1,51,0,0.517773," ","integrate(x^3/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} x^{3} - 2 \, a b^{2} x^{2} + 8 \, a^{2} b x + 16 \, a^{3}\right)} \sqrt{b x + a}}{5 \, {\left(b^{5} x + a b^{4}\right)}}"," ",0,"2/5*(b^3*x^3 - 2*a*b^2*x^2 + 8*a^2*b*x + 16*a^3)*sqrt(b*x + a)/(b^5*x + a*b^4)","A",0
151,1,40,0,0.737221," ","integrate(x^2/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} x^{2} - 4 \, a b x - 8 \, a^{2}\right)} \sqrt{b x + a}}{3 \, {\left(b^{4} x + a b^{3}\right)}}"," ",0,"2/3*(b^2*x^2 - 4*a*b*x - 8*a^2)*sqrt(b*x + a)/(b^4*x + a*b^3)","A",0
152,1,29,0,0.460235," ","integrate(x/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b x + 2 \, a\right)} \sqrt{b x + a}}{b^{3} x + a b^{2}}"," ",0,"2*(b*x + 2*a)*sqrt(b*x + a)/(b^3*x + a*b^2)","A",0
153,1,20,0,0.416940," ","integrate(1/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{b x + a}}{b^{2} x + a b}"," ",0,"-2*sqrt(b*x + a)/(b^2*x + a*b)","A",0
154,1,110,0,0.628982," ","integrate(1/x/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(b x + a\right)} \sqrt{a} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, \sqrt{b x + a} a}{a^{2} b x + a^{3}}, \frac{2 \, {\left({\left(b x + a\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + \sqrt{b x + a} a\right)}}{a^{2} b x + a^{3}}\right]"," ",0,"[((b*x + a)*sqrt(a)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*sqrt(b*x + a)*a)/(a^2*b*x + a^3), 2*((b*x + a)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) + sqrt(b*x + a)*a)/(a^2*b*x + a^3)]","A",0
155,1,151,0,0.543826," ","integrate(1/x^2/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} x^{2} + a b x\right)} \sqrt{a} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, {\left(3 \, a b x + a^{2}\right)} \sqrt{b x + a}}{2 \, {\left(a^{3} b x^{2} + a^{4} x\right)}}, -\frac{3 \, {\left(b^{2} x^{2} + a b x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(3 \, a b x + a^{2}\right)} \sqrt{b x + a}}{a^{3} b x^{2} + a^{4} x}\right]"," ",0,"[1/2*(3*(b^2*x^2 + a*b*x)*sqrt(a)*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*(3*a*b*x + a^2)*sqrt(b*x + a))/(a^3*b*x^2 + a^4*x), -(3*(b^2*x^2 + a*b*x)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (3*a*b*x + a^2)*sqrt(b*x + a))/(a^3*b*x^2 + a^4*x)]","A",0
156,1,189,0,0.626271," ","integrate(1/x^3/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{3} x^{3} + a b^{2} x^{2}\right)} \sqrt{a} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(15 \, a b^{2} x^{2} + 5 \, a^{2} b x - 2 \, a^{3}\right)} \sqrt{b x + a}}{8 \, {\left(a^{4} b x^{3} + a^{5} x^{2}\right)}}, \frac{15 \, {\left(b^{3} x^{3} + a b^{2} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(15 \, a b^{2} x^{2} + 5 \, a^{2} b x - 2 \, a^{3}\right)} \sqrt{b x + a}}{4 \, {\left(a^{4} b x^{3} + a^{5} x^{2}\right)}}\right]"," ",0,"[1/8*(15*(b^3*x^3 + a*b^2*x^2)*sqrt(a)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(15*a*b^2*x^2 + 5*a^2*b*x - 2*a^3)*sqrt(b*x + a))/(a^4*b*x^3 + a^5*x^2), 1/4*(15*(b^3*x^3 + a*b^2*x^2)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (15*a*b^2*x^2 + 5*a^2*b*x - 2*a^3)*sqrt(b*x + a))/(a^4*b*x^3 + a^5*x^2)]","A",0
157,1,211,0,0.576503," ","integrate(1/x^4/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{4} x^{4} + a b^{3} x^{3}\right)} \sqrt{a} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, {\left(105 \, a b^{3} x^{3} + 35 \, a^{2} b^{2} x^{2} - 14 \, a^{3} b x + 8 \, a^{4}\right)} \sqrt{b x + a}}{48 \, {\left(a^{5} b x^{4} + a^{6} x^{3}\right)}}, -\frac{105 \, {\left(b^{4} x^{4} + a b^{3} x^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(105 \, a b^{3} x^{3} + 35 \, a^{2} b^{2} x^{2} - 14 \, a^{3} b x + 8 \, a^{4}\right)} \sqrt{b x + a}}{24 \, {\left(a^{5} b x^{4} + a^{6} x^{3}\right)}}\right]"," ",0,"[1/48*(105*(b^4*x^4 + a*b^3*x^3)*sqrt(a)*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*(105*a*b^3*x^3 + 35*a^2*b^2*x^2 - 14*a^3*b*x + 8*a^4)*sqrt(b*x + a))/(a^5*b*x^4 + a^6*x^3), -1/24*(105*(b^4*x^4 + a*b^3*x^3)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (105*a*b^3*x^3 + 35*a^2*b^2*x^2 - 14*a^3*b*x + 8*a^4)*sqrt(b*x + a))/(a^5*b*x^4 + a^6*x^3)]","A",0
158,1,74,0,0.487429," ","integrate(x^4/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{4} x^{4} - 8 \, a b^{3} x^{3} + 48 \, a^{2} b^{2} x^{2} + 192 \, a^{3} b x + 128 \, a^{4}\right)} \sqrt{b x + a}}{15 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}"," ",0,"2/15*(3*b^4*x^4 - 8*a*b^3*x^3 + 48*a^2*b^2*x^2 + 192*a^3*b*x + 128*a^4)*sqrt(b*x + a)/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)","A",0
159,1,62,0,0.599662," ","integrate(x^3/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} x^{3} - 6 \, a b^{2} x^{2} - 24 \, a^{2} b x - 16 \, a^{3}\right)} \sqrt{b x + a}}{3 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}"," ",0,"2/3*(b^3*x^3 - 6*a*b^2*x^2 - 24*a^2*b*x - 16*a^3)*sqrt(b*x + a)/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)","A",0
160,1,52,0,0.417413," ","integrate(x^2/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} x^{2} + 12 \, a b x + 8 \, a^{2}\right)} \sqrt{b x + a}}{3 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}"," ",0,"2/3*(3*b^2*x^2 + 12*a*b*x + 8*a^2)*sqrt(b*x + a)/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)","A",0
161,1,41,0,0.585343," ","integrate(x/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b x + 2 \, a\right)} \sqrt{b x + a}}{3 \, {\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)}}"," ",0,"-2/3*(3*b*x + 2*a)*sqrt(b*x + a)/(b^4*x^2 + 2*a*b^3*x + a^2*b^2)","A",0
162,1,31,0,0.520930," ","integrate(1/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{b x + a}}{3 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)}}"," ",0,"-2/3*sqrt(b*x + a)/(b^3*x^2 + 2*a*b^2*x + a^2*b)","B",0
163,1,177,0,0.508588," ","integrate(1/x/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{a} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(3 \, a b x + 4 \, a^{2}\right)} \sqrt{b x + a}}{3 \, {\left(a^{3} b^{2} x^{2} + 2 \, a^{4} b x + a^{5}\right)}}, \frac{2 \, {\left(3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(3 \, a b x + 4 \, a^{2}\right)} \sqrt{b x + a}\right)}}{3 \, {\left(a^{3} b^{2} x^{2} + 2 \, a^{4} b x + a^{5}\right)}}\right]"," ",0,"[1/3*(3*(b^2*x^2 + 2*a*b*x + a^2)*sqrt(a)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(3*a*b*x + 4*a^2)*sqrt(b*x + a))/(a^3*b^2*x^2 + 2*a^4*b*x + a^5), 2/3*(3*(b^2*x^2 + 2*a*b*x + a^2)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (3*a*b*x + 4*a^2)*sqrt(b*x + a))/(a^3*b^2*x^2 + 2*a^4*b*x + a^5)]","A",0
164,1,221,0,0.596489," ","integrate(1/x^2/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{3} x^{3} + 2 \, a b^{2} x^{2} + a^{2} b x\right)} \sqrt{a} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, {\left(15 \, a b^{2} x^{2} + 20 \, a^{2} b x + 3 \, a^{3}\right)} \sqrt{b x + a}}{6 \, {\left(a^{4} b^{2} x^{3} + 2 \, a^{5} b x^{2} + a^{6} x\right)}}, -\frac{15 \, {\left(b^{3} x^{3} + 2 \, a b^{2} x^{2} + a^{2} b x\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(15 \, a b^{2} x^{2} + 20 \, a^{2} b x + 3 \, a^{3}\right)} \sqrt{b x + a}}{3 \, {\left(a^{4} b^{2} x^{3} + 2 \, a^{5} b x^{2} + a^{6} x\right)}}\right]"," ",0,"[1/6*(15*(b^3*x^3 + 2*a*b^2*x^2 + a^2*b*x)*sqrt(a)*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*(15*a*b^2*x^2 + 20*a^2*b*x + 3*a^3)*sqrt(b*x + a))/(a^4*b^2*x^3 + 2*a^5*b*x^2 + a^6*x), -1/3*(15*(b^3*x^3 + 2*a*b^2*x^2 + a^2*b*x)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (15*a*b^2*x^2 + 20*a^2*b*x + 3*a^3)*sqrt(b*x + a))/(a^4*b^2*x^3 + 2*a^5*b*x^2 + a^6*x)]","A",0
165,1,255,0,0.568897," ","integrate(1/x^3/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{3} + a^{2} b^{2} x^{2}\right)} \sqrt{a} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(105 \, a b^{3} x^{3} + 140 \, a^{2} b^{2} x^{2} + 21 \, a^{3} b x - 6 \, a^{4}\right)} \sqrt{b x + a}}{24 \, {\left(a^{5} b^{2} x^{4} + 2 \, a^{6} b x^{3} + a^{7} x^{2}\right)}}, \frac{105 \, {\left(b^{4} x^{4} + 2 \, a b^{3} x^{3} + a^{2} b^{2} x^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(105 \, a b^{3} x^{3} + 140 \, a^{2} b^{2} x^{2} + 21 \, a^{3} b x - 6 \, a^{4}\right)} \sqrt{b x + a}}{12 \, {\left(a^{5} b^{2} x^{4} + 2 \, a^{6} b x^{3} + a^{7} x^{2}\right)}}\right]"," ",0,"[1/24*(105*(b^4*x^4 + 2*a*b^3*x^3 + a^2*b^2*x^2)*sqrt(a)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(105*a*b^3*x^3 + 140*a^2*b^2*x^2 + 21*a^3*b*x - 6*a^4)*sqrt(b*x + a))/(a^5*b^2*x^4 + 2*a^6*b*x^3 + a^7*x^2), 1/12*(105*(b^4*x^4 + 2*a*b^3*x^3 + a^2*b^2*x^2)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (105*a*b^3*x^3 + 140*a^2*b^2*x^2 + 21*a^3*b*x - 6*a^4)*sqrt(b*x + a))/(a^5*b^2*x^4 + 2*a^6*b*x^3 + a^7*x^2)]","A",0
166,1,277,0,0.508544," ","integrate(1/x^4/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\left[\frac{315 \, {\left(b^{5} x^{5} + 2 \, a b^{4} x^{4} + a^{2} b^{3} x^{3}\right)} \sqrt{a} \log\left(\frac{b x + 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, {\left(315 \, a b^{4} x^{4} + 420 \, a^{2} b^{3} x^{3} + 63 \, a^{3} b^{2} x^{2} - 18 \, a^{4} b x + 8 \, a^{5}\right)} \sqrt{b x + a}}{48 \, {\left(a^{6} b^{2} x^{5} + 2 \, a^{7} b x^{4} + a^{8} x^{3}\right)}}, -\frac{315 \, {\left(b^{5} x^{5} + 2 \, a b^{4} x^{4} + a^{2} b^{3} x^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(315 \, a b^{4} x^{4} + 420 \, a^{2} b^{3} x^{3} + 63 \, a^{3} b^{2} x^{2} - 18 \, a^{4} b x + 8 \, a^{5}\right)} \sqrt{b x + a}}{24 \, {\left(a^{6} b^{2} x^{5} + 2 \, a^{7} b x^{4} + a^{8} x^{3}\right)}}\right]"," ",0,"[1/48*(315*(b^5*x^5 + 2*a*b^4*x^4 + a^2*b^3*x^3)*sqrt(a)*log((b*x + 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*(315*a*b^4*x^4 + 420*a^2*b^3*x^3 + 63*a^3*b^2*x^2 - 18*a^4*b*x + 8*a^5)*sqrt(b*x + a))/(a^6*b^2*x^5 + 2*a^7*b*x^4 + a^8*x^3), -1/24*(315*(b^5*x^5 + 2*a*b^4*x^4 + a^2*b^3*x^3)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (315*a*b^4*x^4 + 420*a^2*b^3*x^3 + 63*a^3*b^2*x^2 - 18*a^4*b*x + 8*a^5)*sqrt(b*x + a))/(a^6*b^2*x^5 + 2*a^7*b*x^4 + a^8*x^3)]","A",0
167,1,18,0,0.469422," ","integrate(x^(7/2)*arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2}{99} \, {\left(9 \, b x^{5} + 11 \, a x^{4}\right)} \sqrt{x}"," ",0,"2/99*(9*b*x^5 + 11*a*x^4)*sqrt(x)","A",0
168,1,18,0,0.522614," ","integrate(x^(5/2)*arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2}{63} \, {\left(7 \, b x^{4} + 9 \, a x^{3}\right)} \sqrt{x}"," ",0,"2/63*(7*b*x^4 + 9*a*x^3)*sqrt(x)","A",0
169,1,18,0,0.450447," ","integrate(x^(3/2)*arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2}{35} \, {\left(5 \, b x^{3} + 7 \, a x^{2}\right)} \sqrt{x}"," ",0,"2/35*(5*b*x^3 + 7*a*x^2)*sqrt(x)","A",0
170,1,16,0,0.570694," ","integrate(arctanh(tanh(b*x+a))*x^(1/2),x, algorithm=""fricas"")","\frac{2}{15} \, {\left(3 \, b x^{2} + 5 \, a x\right)} \sqrt{x}"," ",0,"2/15*(3*b*x^2 + 5*a*x)*sqrt(x)","A",0
171,1,12,0,0.575634," ","integrate(arctanh(tanh(b*x+a))/x^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, {\left(b x + 3 \, a\right)} \sqrt{x}"," ",0,"2/3*(b*x + 3*a)*sqrt(x)","A",0
172,1,12,0,0.402379," ","integrate(arctanh(tanh(b*x+a))/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b x - a\right)}}{\sqrt{x}}"," ",0,"2*(b*x - a)/sqrt(x)","A",0
173,1,11,0,0.570445," ","integrate(arctanh(tanh(b*x+a))/x^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b x + a\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"-2/3*(3*b*x + a)/x^(3/2)","A",0
174,1,13,0,0.485322," ","integrate(arctanh(tanh(b*x+a))/x^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, b x + 3 \, a\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"-2/15*(5*b*x + 3*a)/x^(5/2)","A",0
175,1,29,0,0.613432," ","integrate(x^(7/2)*arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{2}{1287} \, {\left(99 \, b^{2} x^{6} + 234 \, a b x^{5} + 143 \, a^{2} x^{4}\right)} \sqrt{x}"," ",0,"2/1287*(99*b^2*x^6 + 234*a*b*x^5 + 143*a^2*x^4)*sqrt(x)","A",0
176,1,29,0,0.414207," ","integrate(x^(5/2)*arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{2}{693} \, {\left(63 \, b^{2} x^{5} + 154 \, a b x^{4} + 99 \, a^{2} x^{3}\right)} \sqrt{x}"," ",0,"2/693*(63*b^2*x^5 + 154*a*b*x^4 + 99*a^2*x^3)*sqrt(x)","A",0
177,1,29,0,0.471376," ","integrate(x^(3/2)*arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{2}{315} \, {\left(35 \, b^{2} x^{4} + 90 \, a b x^{3} + 63 \, a^{2} x^{2}\right)} \sqrt{x}"," ",0,"2/315*(35*b^2*x^4 + 90*a*b*x^3 + 63*a^2*x^2)*sqrt(x)","A",0
178,1,27,0,0.535015," ","integrate(arctanh(tanh(b*x+a))^2*x^(1/2),x, algorithm=""fricas"")","\frac{2}{105} \, {\left(15 \, b^{2} x^{3} + 42 \, a b x^{2} + 35 \, a^{2} x\right)} \sqrt{x}"," ",0,"2/105*(15*b^2*x^3 + 42*a*b*x^2 + 35*a^2*x)*sqrt(x)","A",0
179,1,24,0,0.489396," ","integrate(arctanh(tanh(b*x+a))^2/x^(1/2),x, algorithm=""fricas"")","\frac{2}{15} \, {\left(3 \, b^{2} x^{2} + 10 \, a b x + 15 \, a^{2}\right)} \sqrt{x}"," ",0,"2/15*(3*b^2*x^2 + 10*a*b*x + 15*a^2)*sqrt(x)","A",0
180,1,23,0,0.477178," ","integrate(arctanh(tanh(b*x+a))^2/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} x^{2} + 6 \, a b x - 3 \, a^{2}\right)}}{3 \, \sqrt{x}}"," ",0,"2/3*(b^2*x^2 + 6*a*b*x - 3*a^2)/sqrt(x)","A",0
181,1,24,0,0.590883," ","integrate(arctanh(tanh(b*x+a))^2/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{2} x^{2} - 6 \, a b x - a^{2}\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*(3*b^2*x^2 - 6*a*b*x - a^2)/x^(3/2)","A",0
182,1,24,0,0.531716," ","integrate(arctanh(tanh(b*x+a))^2/x^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, b^{2} x^{2} + 10 \, a b x + 3 \, a^{2}\right)}}{15 \, x^{\frac{5}{2}}}"," ",0,"-2/15*(15*b^2*x^2 + 10*a*b*x + 3*a^2)/x^(5/2)","A",0
183,1,40,0,0.427756," ","integrate(x^(7/2)*arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{2}{6435} \, {\left(429 \, b^{3} x^{7} + 1485 \, a b^{2} x^{6} + 1755 \, a^{2} b x^{5} + 715 \, a^{3} x^{4}\right)} \sqrt{x}"," ",0,"2/6435*(429*b^3*x^7 + 1485*a*b^2*x^6 + 1755*a^2*b*x^5 + 715*a^3*x^4)*sqrt(x)","A",0
184,1,40,0,0.494713," ","integrate(x^(5/2)*arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{2}{3003} \, {\left(231 \, b^{3} x^{6} + 819 \, a b^{2} x^{5} + 1001 \, a^{2} b x^{4} + 429 \, a^{3} x^{3}\right)} \sqrt{x}"," ",0,"2/3003*(231*b^3*x^6 + 819*a*b^2*x^5 + 1001*a^2*b*x^4 + 429*a^3*x^3)*sqrt(x)","A",0
185,1,40,0,0.619837," ","integrate(x^(3/2)*arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{2}{1155} \, {\left(105 \, b^{3} x^{5} + 385 \, a b^{2} x^{4} + 495 \, a^{2} b x^{3} + 231 \, a^{3} x^{2}\right)} \sqrt{x}"," ",0,"2/1155*(105*b^3*x^5 + 385*a*b^2*x^4 + 495*a^2*b*x^3 + 231*a^3*x^2)*sqrt(x)","A",0
186,1,38,0,0.677704," ","integrate(arctanh(tanh(b*x+a))^3*x^(1/2),x, algorithm=""fricas"")","\frac{2}{315} \, {\left(35 \, b^{3} x^{4} + 135 \, a b^{2} x^{3} + 189 \, a^{2} b x^{2} + 105 \, a^{3} x\right)} \sqrt{x}"," ",0,"2/315*(35*b^3*x^4 + 135*a*b^2*x^3 + 189*a^2*b*x^2 + 105*a^3*x)*sqrt(x)","A",0
187,1,35,0,0.527295," ","integrate(arctanh(tanh(b*x+a))^3/x^(1/2),x, algorithm=""fricas"")","\frac{2}{35} \, {\left(5 \, b^{3} x^{3} + 21 \, a b^{2} x^{2} + 35 \, a^{2} b x + 35 \, a^{3}\right)} \sqrt{x}"," ",0,"2/35*(5*b^3*x^3 + 21*a*b^2*x^2 + 35*a^2*b*x + 35*a^3)*sqrt(x)","A",0
188,1,34,0,0.630070," ","integrate(arctanh(tanh(b*x+a))^3/x^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} x^{3} + 5 \, a b^{2} x^{2} + 15 \, a^{2} b x - 5 \, a^{3}\right)}}{5 \, \sqrt{x}}"," ",0,"2/5*(b^3*x^3 + 5*a*b^2*x^2 + 15*a^2*b*x - 5*a^3)/sqrt(x)","A",0
189,1,34,0,0.522355," ","integrate(arctanh(tanh(b*x+a))^3/x^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} x^{3} + 9 \, a b^{2} x^{2} - 9 \, a^{2} b x - a^{3}\right)}}{3 \, x^{\frac{3}{2}}}"," ",0,"2/3*(b^3*x^3 + 9*a*b^2*x^2 - 9*a^2*b*x - a^3)/x^(3/2)","A",0
190,1,35,0,0.540438," ","integrate(arctanh(tanh(b*x+a))^3/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, b^{3} x^{3} - 15 \, a b^{2} x^{2} - 5 \, a^{2} b x - a^{3}\right)}}{5 \, x^{\frac{5}{2}}}"," ",0,"2/5*(5*b^3*x^3 - 15*a*b^2*x^2 - 5*a^2*b*x - a^3)/x^(5/2)","A",0
191,1,153,0,0.500954," ","integrate(x^(7/2)/arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\left[\frac{105 \, a^{3} \sqrt{-\frac{a}{b}} \log\left(\frac{b x + 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) + 2 \, {\left(15 \, b^{3} x^{3} - 21 \, a b^{2} x^{2} + 35 \, a^{2} b x - 105 \, a^{3}\right)} \sqrt{x}}{105 \, b^{4}}, \frac{2 \, {\left(105 \, a^{3} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(15 \, b^{3} x^{3} - 21 \, a b^{2} x^{2} + 35 \, a^{2} b x - 105 \, a^{3}\right)} \sqrt{x}\right)}}{105 \, b^{4}}\right]"," ",0,"[1/105*(105*a^3*sqrt(-a/b)*log((b*x + 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) + 2*(15*b^3*x^3 - 21*a*b^2*x^2 + 35*a^2*b*x - 105*a^3)*sqrt(x))/b^4, 2/105*(105*a^3*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (15*b^3*x^3 - 21*a*b^2*x^2 + 35*a^2*b*x - 105*a^3)*sqrt(x))/b^4]","A",0
192,1,132,0,0.483830," ","integrate(x^(5/2)/arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\left[\frac{15 \, a^{2} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) + 2 \, {\left(3 \, b^{2} x^{2} - 5 \, a b x + 15 \, a^{2}\right)} \sqrt{x}}{15 \, b^{3}}, -\frac{2 \, {\left(15 \, a^{2} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) - {\left(3 \, b^{2} x^{2} - 5 \, a b x + 15 \, a^{2}\right)} \sqrt{x}\right)}}{15 \, b^{3}}\right]"," ",0,"[1/15*(15*a^2*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) + 2*(3*b^2*x^2 - 5*a*b*x + 15*a^2)*sqrt(x))/b^3, -2/15*(15*a^2*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) - (3*b^2*x^2 - 5*a*b*x + 15*a^2)*sqrt(x))/b^3]","A",0
193,1,103,0,0.388416," ","integrate(x^(3/2)/arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\left[\frac{3 \, a \sqrt{-\frac{a}{b}} \log\left(\frac{b x + 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) + 2 \, {\left(b x - 3 \, a\right)} \sqrt{x}}{3 \, b^{2}}, \frac{2 \, {\left(3 \, a \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(b x - 3 \, a\right)} \sqrt{x}\right)}}{3 \, b^{2}}\right]"," ",0,"[1/3*(3*a*sqrt(-a/b)*log((b*x + 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) + 2*(b*x - 3*a)*sqrt(x))/b^2, 2/3*(3*a*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (b*x - 3*a)*sqrt(x))/b^2]","A",0
194,1,85,0,0.518269," ","integrate(x^(1/2)/arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) + 2 \, \sqrt{x}}{b}, -\frac{2 \, {\left(\sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) - \sqrt{x}\right)}}{b}\right]"," ",0,"[(sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) + 2*sqrt(x))/b, -2*(sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) - sqrt(x))/b]","A",0
195,1,68,0,0.622305," ","integrate(1/arctanh(tanh(b*x+a))/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right)}{a b}, -\frac{2 \, \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right)}{a b}\right]"," ",0,"[-sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a))/(a*b), -2*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x)))/(a*b)]","A",0
196,1,93,0,0.582623," ","integrate(1/x^(3/2)/arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\left[\frac{x \sqrt{-\frac{b}{a}} \log\left(\frac{b x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) - 2 \, \sqrt{x}}{a x}, \frac{2 \, {\left(x \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - \sqrt{x}\right)}}{a x}\right]"," ",0,"[(x*sqrt(-b/a)*log((b*x - 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) - 2*sqrt(x))/(a*x), 2*(x*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - sqrt(x))/(a*x)]","A",0
197,1,118,0,0.540413," ","integrate(1/x^(5/2)/arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\left[\frac{3 \, b x^{2} \sqrt{-\frac{b}{a}} \log\left(\frac{b x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(3 \, b x - a\right)} \sqrt{x}}{3 \, a^{2} x^{2}}, -\frac{2 \, {\left(3 \, b x^{2} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(3 \, b x - a\right)} \sqrt{x}\right)}}{3 \, a^{2} x^{2}}\right]"," ",0,"[1/3*(3*b*x^2*sqrt(-b/a)*log((b*x + 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(3*b*x - a)*sqrt(x))/(a^2*x^2), -2/3*(3*b*x^2*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (3*b*x - a)*sqrt(x))/(a^2*x^2)]","A",0
198,1,144,0,0.565162," ","integrate(1/x^(7/2)/arctanh(tanh(b*x+a)),x, algorithm=""fricas"")","\left[\frac{15 \, b^{2} x^{3} \sqrt{-\frac{b}{a}} \log\left(\frac{b x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) - 2 \, {\left(15 \, b^{2} x^{2} - 5 \, a b x + 3 \, a^{2}\right)} \sqrt{x}}{15 \, a^{3} x^{3}}, \frac{2 \, {\left(15 \, b^{2} x^{3} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(15 \, b^{2} x^{2} - 5 \, a b x + 3 \, a^{2}\right)} \sqrt{x}\right)}}{15 \, a^{3} x^{3}}\right]"," ",0,"[1/15*(15*b^2*x^3*sqrt(-b/a)*log((b*x - 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) - 2*(15*b^2*x^2 - 5*a*b*x + 3*a^2)*sqrt(x))/(a^3*x^3), 2/15*(15*b^2*x^3*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (15*b^2*x^2 - 5*a*b*x + 3*a^2)*sqrt(x))/(a^3*x^3)]","A",0
199,1,188,0,0.405167," ","integrate(x^(7/2)/arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{2} b x + a^{3}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) + 2 \, {\left(6 \, b^{3} x^{3} - 14 \, a b^{2} x^{2} + 70 \, a^{2} b x + 105 \, a^{3}\right)} \sqrt{x}}{30 \, {\left(b^{5} x + a b^{4}\right)}}, -\frac{105 \, {\left(a^{2} b x + a^{3}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) - {\left(6 \, b^{3} x^{3} - 14 \, a b^{2} x^{2} + 70 \, a^{2} b x + 105 \, a^{3}\right)} \sqrt{x}}{15 \, {\left(b^{5} x + a b^{4}\right)}}\right]"," ",0,"[1/30*(105*(a^2*b*x + a^3)*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) + 2*(6*b^3*x^3 - 14*a*b^2*x^2 + 70*a^2*b*x + 105*a^3)*sqrt(x))/(b^5*x + a*b^4), -1/15*(105*(a^2*b*x + a^3)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) - (6*b^3*x^3 - 14*a*b^2*x^2 + 70*a^2*b*x + 105*a^3)*sqrt(x))/(b^5*x + a*b^4)]","A",0
200,1,161,0,0.516073," ","integrate(x^(5/2)/arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a b x + a^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x + 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) + 2 \, {\left(2 \, b^{2} x^{2} - 10 \, a b x - 15 \, a^{2}\right)} \sqrt{x}}{6 \, {\left(b^{4} x + a b^{3}\right)}}, \frac{15 \, {\left(a b x + a^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(2 \, b^{2} x^{2} - 10 \, a b x - 15 \, a^{2}\right)} \sqrt{x}}{3 \, {\left(b^{4} x + a b^{3}\right)}}\right]"," ",0,"[1/6*(15*(a*b*x + a^2)*sqrt(-a/b)*log((b*x + 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) + 2*(2*b^2*x^2 - 10*a*b*x - 15*a^2)*sqrt(x))/(b^4*x + a*b^3), 1/3*(15*(a*b*x + a^2)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (2*b^2*x^2 - 10*a*b*x - 15*a^2)*sqrt(x))/(b^4*x + a*b^3)]","A",0
201,1,134,0,0.531017," ","integrate(x^(3/2)/arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b x + a\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) + 2 \, {\left(2 \, b x + 3 \, a\right)} \sqrt{x}}{2 \, {\left(b^{3} x + a b^{2}\right)}}, -\frac{3 \, {\left(b x + a\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) - {\left(2 \, b x + 3 \, a\right)} \sqrt{x}}{b^{3} x + a b^{2}}\right]"," ",0,"[1/2*(3*(b*x + a)*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) + 2*(2*b*x + 3*a)*sqrt(x))/(b^3*x + a*b^2), -(3*(b*x + a)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) - (2*b*x + 3*a)*sqrt(x))/(b^3*x + a*b^2)]","A",0
202,1,115,0,0.431699," ","integrate(x^(1/2)/arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a b \sqrt{x} + \sqrt{-a b} {\left(b x + a\right)} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right)}{2 \, {\left(a b^{3} x + a^{2} b^{2}\right)}}, -\frac{a b \sqrt{x} + \sqrt{a b} {\left(b x + a\right)} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right)}{a b^{3} x + a^{2} b^{2}}\right]"," ",0,"[-1/2*(2*a*b*sqrt(x) + sqrt(-a*b)*(b*x + a)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)))/(a*b^3*x + a^2*b^2), -(a*b*sqrt(x) + sqrt(a*b)*(b*x + a)*arctan(sqrt(a*b)/(b*sqrt(x))))/(a*b^3*x + a^2*b^2)]","A",0
203,1,116,0,0.393235," ","integrate(1/arctanh(tanh(b*x+a))^2/x^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a b \sqrt{x} - \sqrt{-a b} {\left(b x + a\right)} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right)}{2 \, {\left(a^{2} b^{2} x + a^{3} b\right)}}, \frac{a b \sqrt{x} - \sqrt{a b} {\left(b x + a\right)} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right)}{a^{2} b^{2} x + a^{3} b}\right]"," ",0,"[1/2*(2*a*b*sqrt(x) - sqrt(-a*b)*(b*x + a)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)))/(a^2*b^2*x + a^3*b), (a*b*sqrt(x) - sqrt(a*b)*(b*x + a)*arctan(sqrt(a*b)/(b*sqrt(x))))/(a^2*b^2*x + a^3*b)]","A",0
204,1,147,0,0.457298," ","integrate(1/x^(3/2)/arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b x^{2} + a x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) - 2 \, {\left(3 \, b x + 2 \, a\right)} \sqrt{x}}{2 \, {\left(a^{2} b x^{2} + a^{3} x\right)}}, \frac{3 \, {\left(b x^{2} + a x\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(3 \, b x + 2 \, a\right)} \sqrt{x}}{a^{2} b x^{2} + a^{3} x}\right]"," ",0,"[1/2*(3*(b*x^2 + a*x)*sqrt(-b/a)*log((b*x - 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) - 2*(3*b*x + 2*a)*sqrt(x))/(a^2*b*x^2 + a^3*x), (3*(b*x^2 + a*x)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (3*b*x + 2*a)*sqrt(x))/(a^2*b*x^2 + a^3*x)]","A",0
205,1,184,0,0.574405," ","integrate(1/x^(5/2)/arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} x^{3} + a b x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(15 \, b^{2} x^{2} + 10 \, a b x - 2 \, a^{2}\right)} \sqrt{x}}{6 \, {\left(a^{3} b x^{3} + a^{4} x^{2}\right)}}, -\frac{15 \, {\left(b^{2} x^{3} + a b x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(15 \, b^{2} x^{2} + 10 \, a b x - 2 \, a^{2}\right)} \sqrt{x}}{3 \, {\left(a^{3} b x^{3} + a^{4} x^{2}\right)}}\right]"," ",0,"[1/6*(15*(b^2*x^3 + a*b*x^2)*sqrt(-b/a)*log((b*x + 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(15*b^2*x^2 + 10*a*b*x - 2*a^2)*sqrt(x))/(a^3*b*x^3 + a^4*x^2), -1/3*(15*(b^2*x^3 + a*b*x^2)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (15*b^2*x^2 + 10*a*b*x - 2*a^2)*sqrt(x))/(a^3*b*x^3 + a^4*x^2)]","A",0
206,1,210,0,0.605535," ","integrate(1/x^(7/2)/arctanh(tanh(b*x+a))^2,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{3} x^{4} + a b^{2} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) - 2 \, {\left(105 \, b^{3} x^{3} + 70 \, a b^{2} x^{2} - 14 \, a^{2} b x + 6 \, a^{3}\right)} \sqrt{x}}{30 \, {\left(a^{4} b x^{4} + a^{5} x^{3}\right)}}, \frac{105 \, {\left(b^{3} x^{4} + a b^{2} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(105 \, b^{3} x^{3} + 70 \, a b^{2} x^{2} - 14 \, a^{2} b x + 6 \, a^{3}\right)} \sqrt{x}}{15 \, {\left(a^{4} b x^{4} + a^{5} x^{3}\right)}}\right]"," ",0,"[1/30*(105*(b^3*x^4 + a*b^2*x^3)*sqrt(-b/a)*log((b*x - 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) - 2*(105*b^3*x^3 + 70*a*b^2*x^2 - 14*a^2*b*x + 6*a^3)*sqrt(x))/(a^4*b*x^4 + a^5*x^3), 1/15*(105*(b^3*x^4 + a*b^2*x^3)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (105*b^3*x^3 + 70*a*b^2*x^2 - 14*a^2*b*x + 6*a^3)*sqrt(x))/(a^4*b*x^4 + a^5*x^3)]","A",0
207,1,227,0,0.571329," ","integrate(x^(7/2)/arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a b^{2} x^{2} + 2 \, a^{2} b x + a^{3}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x + 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) + 2 \, {\left(8 \, b^{3} x^{3} - 56 \, a b^{2} x^{2} - 175 \, a^{2} b x - 105 \, a^{3}\right)} \sqrt{x}}{24 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}, \frac{105 \, {\left(a b^{2} x^{2} + 2 \, a^{2} b x + a^{3}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) + {\left(8 \, b^{3} x^{3} - 56 \, a b^{2} x^{2} - 175 \, a^{2} b x - 105 \, a^{3}\right)} \sqrt{x}}{12 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}\right]"," ",0,"[1/24*(105*(a*b^2*x^2 + 2*a^2*b*x + a^3)*sqrt(-a/b)*log((b*x + 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) + 2*(8*b^3*x^3 - 56*a*b^2*x^2 - 175*a^2*b*x - 105*a^3)*sqrt(x))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4), 1/12*(105*(a*b^2*x^2 + 2*a^2*b*x + a^3)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) + (8*b^3*x^3 - 56*a*b^2*x^2 - 175*a^2*b*x - 105*a^3)*sqrt(x))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)]","A",0
208,1,200,0,0.531062," ","integrate(x^(5/2)/arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{b x - 2 \, b \sqrt{x} \sqrt{-\frac{a}{b}} - a}{b x + a}\right) + 2 \, {\left(8 \, b^{2} x^{2} + 25 \, a b x + 15 \, a^{2}\right)} \sqrt{x}}{8 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}, -\frac{15 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{b \sqrt{x} \sqrt{\frac{a}{b}}}{a}\right) - {\left(8 \, b^{2} x^{2} + 25 \, a b x + 15 \, a^{2}\right)} \sqrt{x}}{4 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}\right]"," ",0,"[1/8*(15*(b^2*x^2 + 2*a*b*x + a^2)*sqrt(-a/b)*log((b*x - 2*b*sqrt(x)*sqrt(-a/b) - a)/(b*x + a)) + 2*(8*b^2*x^2 + 25*a*b*x + 15*a^2)*sqrt(x))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3), -1/4*(15*(b^2*x^2 + 2*a*b*x + a^2)*sqrt(a/b)*arctan(b*sqrt(x)*sqrt(a/b)/a) - (8*b^2*x^2 + 25*a*b*x + 15*a^2)*sqrt(x))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)]","A",0
209,1,185,0,0.497185," ","integrate(x^(3/2)/arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) + 2 \, {\left(5 \, a b^{2} x + 3 \, a^{2} b\right)} \sqrt{x}}{8 \, {\left(a b^{5} x^{2} + 2 \, a^{2} b^{4} x + a^{3} b^{3}\right)}}, -\frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) + {\left(5 \, a b^{2} x + 3 \, a^{2} b\right)} \sqrt{x}}{4 \, {\left(a b^{5} x^{2} + 2 \, a^{2} b^{4} x + a^{3} b^{3}\right)}}\right]"," ",0,"[-1/8*(3*(b^2*x^2 + 2*a*b*x + a^2)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) + 2*(5*a*b^2*x + 3*a^2*b)*sqrt(x))/(a*b^5*x^2 + 2*a^2*b^4*x + a^3*b^3), -1/4*(3*(b^2*x^2 + 2*a*b*x + a^2)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) + (5*a*b^2*x + 3*a^2*b)*sqrt(x))/(a*b^5*x^2 + 2*a^2*b^4*x + a^3*b^3)]","A",0
210,1,186,0,0.515595," ","integrate(x^(1/2)/arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) - 2 \, {\left(a b^{2} x - a^{2} b\right)} \sqrt{x}}{8 \, {\left(a^{2} b^{4} x^{2} + 2 \, a^{3} b^{3} x + a^{4} b^{2}\right)}}, -\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) - {\left(a b^{2} x - a^{2} b\right)} \sqrt{x}}{4 \, {\left(a^{2} b^{4} x^{2} + 2 \, a^{3} b^{3} x + a^{4} b^{2}\right)}}\right]"," ",0,"[-1/8*((b^2*x^2 + 2*a*b*x + a^2)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) - 2*(a*b^2*x - a^2*b)*sqrt(x))/(a^2*b^4*x^2 + 2*a^3*b^3*x + a^4*b^2), -1/4*((b^2*x^2 + 2*a*b*x + a^2)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) - (a*b^2*x - a^2*b)*sqrt(x))/(a^2*b^4*x^2 + 2*a^3*b^3*x + a^4*b^2)]","A",0
211,1,186,0,0.506259," ","integrate(1/arctanh(tanh(b*x+a))^3/x^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{-a b} \log\left(\frac{b x - a - 2 \, \sqrt{-a b} \sqrt{x}}{b x + a}\right) - 2 \, {\left(3 \, a b^{2} x + 5 \, a^{2} b\right)} \sqrt{x}}{8 \, {\left(a^{3} b^{3} x^{2} + 2 \, a^{4} b^{2} x + a^{5} b\right)}}, -\frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b}}{b \sqrt{x}}\right) - {\left(3 \, a b^{2} x + 5 \, a^{2} b\right)} \sqrt{x}}{4 \, {\left(a^{3} b^{3} x^{2} + 2 \, a^{4} b^{2} x + a^{5} b\right)}}\right]"," ",0,"[-1/8*(3*(b^2*x^2 + 2*a*b*x + a^2)*sqrt(-a*b)*log((b*x - a - 2*sqrt(-a*b)*sqrt(x))/(b*x + a)) - 2*(3*a*b^2*x + 5*a^2*b)*sqrt(x))/(a^3*b^3*x^2 + 2*a^4*b^2*x + a^5*b), -1/4*(3*(b^2*x^2 + 2*a*b*x + a^2)*sqrt(a*b)*arctan(sqrt(a*b)/(b*sqrt(x))) - (3*a*b^2*x + 5*a^2*b)*sqrt(x))/(a^3*b^3*x^2 + 2*a^4*b^2*x + a^5*b)]","A",0
212,1,214,0,0.469377," ","integrate(1/x^(3/2)/arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} x^{3} + 2 \, a b x^{2} + a^{2} x\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) - 2 \, {\left(15 \, b^{2} x^{2} + 25 \, a b x + 8 \, a^{2}\right)} \sqrt{x}}{8 \, {\left(a^{3} b^{2} x^{3} + 2 \, a^{4} b x^{2} + a^{5} x\right)}}, \frac{15 \, {\left(b^{2} x^{3} + 2 \, a b x^{2} + a^{2} x\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(15 \, b^{2} x^{2} + 25 \, a b x + 8 \, a^{2}\right)} \sqrt{x}}{4 \, {\left(a^{3} b^{2} x^{3} + 2 \, a^{4} b x^{2} + a^{5} x\right)}}\right]"," ",0,"[1/8*(15*(b^2*x^3 + 2*a*b*x^2 + a^2*x)*sqrt(-b/a)*log((b*x - 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) - 2*(15*b^2*x^2 + 25*a*b*x + 8*a^2)*sqrt(x))/(a^3*b^2*x^3 + 2*a^4*b*x^2 + a^5*x), 1/4*(15*(b^2*x^3 + 2*a*b*x^2 + a^2*x)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (15*b^2*x^2 + 25*a*b*x + 8*a^2)*sqrt(x))/(a^3*b^2*x^3 + 2*a^4*b*x^2 + a^5*x)]","A",0
213,1,250,0,0.539694," ","integrate(1/x^(5/2)/arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(b^{3} x^{4} + 2 \, a b^{2} x^{3} + a^{2} b x^{2}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x + 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) + 2 \, {\left(105 \, b^{3} x^{3} + 175 \, a b^{2} x^{2} + 56 \, a^{2} b x - 8 \, a^{3}\right)} \sqrt{x}}{24 \, {\left(a^{4} b^{2} x^{4} + 2 \, a^{5} b x^{3} + a^{6} x^{2}\right)}}, -\frac{105 \, {\left(b^{3} x^{4} + 2 \, a b^{2} x^{3} + a^{2} b x^{2}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(105 \, b^{3} x^{3} + 175 \, a b^{2} x^{2} + 56 \, a^{2} b x - 8 \, a^{3}\right)} \sqrt{x}}{12 \, {\left(a^{4} b^{2} x^{4} + 2 \, a^{5} b x^{3} + a^{6} x^{2}\right)}}\right]"," ",0,"[1/24*(105*(b^3*x^4 + 2*a*b^2*x^3 + a^2*b*x^2)*sqrt(-b/a)*log((b*x + 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) + 2*(105*b^3*x^3 + 175*a*b^2*x^2 + 56*a^2*b*x - 8*a^3)*sqrt(x))/(a^4*b^2*x^4 + 2*a^5*b*x^3 + a^6*x^2), -1/12*(105*(b^3*x^4 + 2*a*b^2*x^3 + a^2*b*x^2)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (105*b^3*x^3 + 175*a*b^2*x^2 + 56*a^2*b*x - 8*a^3)*sqrt(x))/(a^4*b^2*x^4 + 2*a^5*b*x^3 + a^6*x^2)]","A",0
214,1,276,0,0.647202," ","integrate(1/x^(7/2)/arctanh(tanh(b*x+a))^3,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(b^{4} x^{5} + 2 \, a b^{3} x^{4} + a^{2} b^{2} x^{3}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b x - 2 \, a \sqrt{x} \sqrt{-\frac{b}{a}} - a}{b x + a}\right) - 2 \, {\left(315 \, b^{4} x^{4} + 525 \, a b^{3} x^{3} + 168 \, a^{2} b^{2} x^{2} - 24 \, a^{3} b x + 8 \, a^{4}\right)} \sqrt{x}}{40 \, {\left(a^{5} b^{2} x^{5} + 2 \, a^{6} b x^{4} + a^{7} x^{3}\right)}}, \frac{315 \, {\left(b^{4} x^{5} + 2 \, a b^{3} x^{4} + a^{2} b^{2} x^{3}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{a \sqrt{\frac{b}{a}}}{b \sqrt{x}}\right) - {\left(315 \, b^{4} x^{4} + 525 \, a b^{3} x^{3} + 168 \, a^{2} b^{2} x^{2} - 24 \, a^{3} b x + 8 \, a^{4}\right)} \sqrt{x}}{20 \, {\left(a^{5} b^{2} x^{5} + 2 \, a^{6} b x^{4} + a^{7} x^{3}\right)}}\right]"," ",0,"[1/40*(315*(b^4*x^5 + 2*a*b^3*x^4 + a^2*b^2*x^3)*sqrt(-b/a)*log((b*x - 2*a*sqrt(x)*sqrt(-b/a) - a)/(b*x + a)) - 2*(315*b^4*x^4 + 525*a*b^3*x^3 + 168*a^2*b^2*x^2 - 24*a^3*b*x + 8*a^4)*sqrt(x))/(a^5*b^2*x^5 + 2*a^6*b*x^4 + a^7*x^3), 1/20*(315*(b^4*x^5 + 2*a*b^3*x^4 + a^2*b^2*x^3)*sqrt(b/a)*arctan(a*sqrt(b/a)/(b*sqrt(x))) - (315*b^4*x^4 + 525*a*b^3*x^3 + 168*a^2*b^2*x^2 - 24*a^3*b*x + 8*a^4)*sqrt(x))/(a^5*b^2*x^5 + 2*a^6*b*x^4 + a^7*x^3)]","A",0
215,1,141,0,0.673663," ","integrate(x^(3/2)*arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{3} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(8 \, b^{3} x^{2} + 2 \, a b^{2} x - 3 \, a^{2} b\right)} \sqrt{b x + a} \sqrt{x}}{48 \, b^{3}}, -\frac{3 \, a^{3} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(8 \, b^{3} x^{2} + 2 \, a b^{2} x - 3 \, a^{2} b\right)} \sqrt{b x + a} \sqrt{x}}{24 \, b^{3}}\right]"," ",0,"[1/48*(3*a^3*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(8*b^3*x^2 + 2*a*b^2*x - 3*a^2*b)*sqrt(b*x + a)*sqrt(x))/b^3, -1/24*(3*a^3*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (8*b^3*x^2 + 2*a*b^2*x - 3*a^2*b)*sqrt(b*x + a)*sqrt(x))/b^3]","A",0
216,1,114,0,0.552080," ","integrate(x^(1/2)*arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{a^{2} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(2 \, b^{2} x + a b\right)} \sqrt{b x + a} \sqrt{x}}{8 \, b^{2}}, \frac{a^{2} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(2 \, b^{2} x + a b\right)} \sqrt{b x + a} \sqrt{x}}{4 \, b^{2}}\right]"," ",0,"[1/8*(a^2*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(2*b^2*x + a*b)*sqrt(b*x + a)*sqrt(x))/b^2, 1/4*(a^2*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (2*b^2*x + a*b)*sqrt(b*x + a)*sqrt(x))/b^2]","A",0
217,1,93,0,0.488961," ","integrate(arctanh(tanh(b*x+a))^(1/2)/x^(1/2),x, algorithm=""fricas"")","\left[\frac{a \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, \sqrt{b x + a} b \sqrt{x}}{2 \, b}, -\frac{a \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - \sqrt{b x + a} b \sqrt{x}}{b}\right]"," ",0,"[1/2*(a*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*sqrt(b*x + a)*b*sqrt(x))/b, -(a*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - sqrt(b*x + a)*b*sqrt(x))/b]","A",0
218,1,89,0,0.557173," ","integrate(arctanh(tanh(b*x+a))^(1/2)/x^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b} x \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, \sqrt{b x + a} \sqrt{x}}{x}, -\frac{2 \, {\left(\sqrt{-b} x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + \sqrt{b x + a} \sqrt{x}\right)}}{x}\right]"," ",0,"[(sqrt(b)*x*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*sqrt(b*x + a)*sqrt(x))/x, -2*(sqrt(-b)*x*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + sqrt(b*x + a)*sqrt(x))/x]","A",0
219,1,15,0,0.529609," ","integrate(arctanh(tanh(b*x+a))^(1/2)/x^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(b x + a\right)}^{\frac{3}{2}}}{3 \, a x^{\frac{3}{2}}}"," ",0,"-2/3*(b*x + a)^(3/2)/(a*x^(3/2))","A",0
220,1,34,0,0.565074," ","integrate(arctanh(tanh(b*x+a))^(1/2)/x^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, b^{2} x^{2} - a b x - 3 \, a^{2}\right)} \sqrt{b x + a}}{15 \, a^{2} x^{\frac{5}{2}}}"," ",0,"2/15*(2*b^2*x^2 - a*b*x - 3*a^2)*sqrt(b*x + a)/(a^2*x^(5/2))","A",0
221,1,45,0,0.601460," ","integrate(arctanh(tanh(b*x+a))^(1/2)/x^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, b^{3} x^{3} - 4 \, a b^{2} x^{2} + 3 \, a^{2} b x + 15 \, a^{3}\right)} \sqrt{b x + a}}{105 \, a^{3} x^{\frac{7}{2}}}"," ",0,"-2/105*(8*b^3*x^3 - 4*a*b^2*x^2 + 3*a^2*b*x + 15*a^3)*sqrt(b*x + a)/(a^3*x^(7/2))","A",0
222,1,56,0,0.745751," ","integrate(arctanh(tanh(b*x+a))^(1/2)/x^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, b^{4} x^{4} - 8 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} - 5 \, a^{3} b x - 35 \, a^{4}\right)} \sqrt{b x + a}}{315 \, a^{4} x^{\frac{9}{2}}}"," ",0,"2/315*(16*b^4*x^4 - 8*a*b^3*x^3 + 6*a^2*b^2*x^2 - 5*a^3*b*x - 35*a^4)*sqrt(b*x + a)/(a^4*x^(9/2))","A",0
223,1,163,0,0.514802," ","integrate(x^(3/2)*arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{4} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(16 \, b^{4} x^{3} + 24 \, a b^{3} x^{2} + 2 \, a^{2} b^{2} x - 3 \, a^{3} b\right)} \sqrt{b x + a} \sqrt{x}}{128 \, b^{3}}, -\frac{3 \, a^{4} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(16 \, b^{4} x^{3} + 24 \, a b^{3} x^{2} + 2 \, a^{2} b^{2} x - 3 \, a^{3} b\right)} \sqrt{b x + a} \sqrt{x}}{64 \, b^{3}}\right]"," ",0,"[1/128*(3*a^4*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(16*b^4*x^3 + 24*a*b^3*x^2 + 2*a^2*b^2*x - 3*a^3*b)*sqrt(b*x + a)*sqrt(x))/b^3, -1/64*(3*a^4*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (16*b^4*x^3 + 24*a*b^3*x^2 + 2*a^2*b^2*x - 3*a^3*b)*sqrt(b*x + a)*sqrt(x))/b^3]","A",0
224,1,140,0,0.484572," ","integrate(x^(1/2)*arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{3} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(8 \, b^{3} x^{2} + 14 \, a b^{2} x + 3 \, a^{2} b\right)} \sqrt{b x + a} \sqrt{x}}{48 \, b^{2}}, \frac{3 \, a^{3} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(8 \, b^{3} x^{2} + 14 \, a b^{2} x + 3 \, a^{2} b\right)} \sqrt{b x + a} \sqrt{x}}{24 \, b^{2}}\right]"," ",0,"[1/48*(3*a^3*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(8*b^3*x^2 + 14*a*b^2*x + 3*a^2*b)*sqrt(b*x + a)*sqrt(x))/b^2, 1/24*(3*a^3*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (8*b^3*x^2 + 14*a*b^2*x + 3*a^2*b)*sqrt(b*x + a)*sqrt(x))/b^2]","A",0
225,1,119,0,0.562983," ","integrate(arctanh(tanh(b*x+a))^(3/2)/x^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(2 \, b^{2} x + 5 \, a b\right)} \sqrt{b x + a} \sqrt{x}}{8 \, b}, -\frac{3 \, a^{2} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(2 \, b^{2} x + 5 \, a b\right)} \sqrt{b x + a} \sqrt{x}}{4 \, b}\right]"," ",0,"[1/8*(3*a^2*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(2*b^2*x + 5*a*b)*sqrt(b*x + a)*sqrt(x))/b, -1/4*(3*a^2*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (2*b^2*x + 5*a*b)*sqrt(b*x + a)*sqrt(x))/b]","A",0
226,1,109,0,0.495143," ","integrate(arctanh(tanh(b*x+a))^(3/2)/x^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, a \sqrt{b} x \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, \sqrt{b x + a} {\left(b x - 2 \, a\right)} \sqrt{x}}{2 \, x}, -\frac{3 \, a \sqrt{-b} x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - \sqrt{b x + a} {\left(b x - 2 \, a\right)} \sqrt{x}}{x}\right]"," ",0,"[1/2*(3*a*sqrt(b)*x*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*sqrt(b*x + a)*(b*x - 2*a)*sqrt(x))/x, -(3*a*sqrt(-b)*x*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - sqrt(b*x + a)*(b*x - 2*a)*sqrt(x))/x]","A",0
227,1,109,0,0.578439," ","integrate(arctanh(tanh(b*x+a))^(3/2)/x^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, b^{\frac{3}{2}} x^{2} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(4 \, b x + a\right)} \sqrt{b x + a} \sqrt{x}}{3 \, x^{2}}, -\frac{2 \, {\left(3 \, \sqrt{-b} b x^{2} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(4 \, b x + a\right)} \sqrt{b x + a} \sqrt{x}\right)}}{3 \, x^{2}}\right]"," ",0,"[1/3*(3*b^(3/2)*x^2*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(4*b*x + a)*sqrt(b*x + a)*sqrt(x))/x^2, -2/3*(3*sqrt(-b)*b*x^2*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (4*b*x + a)*sqrt(b*x + a)*sqrt(x))/x^2]","A",0
228,1,31,0,0.440647," ","integrate(arctanh(tanh(b*x+a))^(3/2)/x^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{b x + a}}{5 \, a x^{\frac{5}{2}}}"," ",0,"-2/5*(b^2*x^2 + 2*a*b*x + a^2)*sqrt(b*x + a)/(a*x^(5/2))","A",0
229,1,45,0,0.497964," ","integrate(arctanh(tanh(b*x+a))^(3/2)/x^(9/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, b^{3} x^{3} - a b^{2} x^{2} - 8 \, a^{2} b x - 5 \, a^{3}\right)} \sqrt{b x + a}}{35 \, a^{2} x^{\frac{7}{2}}}"," ",0,"2/35*(2*b^3*x^3 - a*b^2*x^2 - 8*a^2*b*x - 5*a^3)*sqrt(b*x + a)/(a^2*x^(7/2))","A",0
230,1,56,0,0.528231," ","integrate(arctanh(tanh(b*x+a))^(3/2)/x^(11/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, b^{4} x^{4} - 4 \, a b^{3} x^{3} + 3 \, a^{2} b^{2} x^{2} + 50 \, a^{3} b x + 35 \, a^{4}\right)} \sqrt{b x + a}}{315 \, a^{3} x^{\frac{9}{2}}}"," ",0,"-2/315*(8*b^4*x^4 - 4*a*b^3*x^3 + 3*a^2*b^2*x^2 + 50*a^3*b*x + 35*a^4)*sqrt(b*x + a)/(a^3*x^(9/2))","A",0
231,1,67,0,0.509411," ","integrate(arctanh(tanh(b*x+a))^(3/2)/x^(13/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, b^{5} x^{5} - 8 \, a b^{4} x^{4} + 6 \, a^{2} b^{3} x^{3} - 5 \, a^{3} b^{2} x^{2} - 140 \, a^{4} b x - 105 \, a^{5}\right)} \sqrt{b x + a}}{1155 \, a^{4} x^{\frac{11}{2}}}"," ",0,"2/1155*(16*b^5*x^5 - 8*a*b^4*x^4 + 6*a^2*b^3*x^3 - 5*a^3*b^2*x^2 - 140*a^4*b*x - 105*a^5)*sqrt(b*x + a)/(a^4*x^(11/2))","A",0
232,1,162,0,0.404992," ","integrate(x^(1/2)*arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{4} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(48 \, b^{4} x^{3} + 136 \, a b^{3} x^{2} + 118 \, a^{2} b^{2} x + 15 \, a^{3} b\right)} \sqrt{b x + a} \sqrt{x}}{384 \, b^{2}}, \frac{15 \, a^{4} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(48 \, b^{4} x^{3} + 136 \, a b^{3} x^{2} + 118 \, a^{2} b^{2} x + 15 \, a^{3} b\right)} \sqrt{b x + a} \sqrt{x}}{192 \, b^{2}}\right]"," ",0,"[1/384*(15*a^4*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(48*b^4*x^3 + 136*a*b^3*x^2 + 118*a^2*b^2*x + 15*a^3*b)*sqrt(b*x + a)*sqrt(x))/b^2, 1/192*(15*a^4*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (48*b^4*x^3 + 136*a*b^3*x^2 + 118*a^2*b^2*x + 15*a^3*b)*sqrt(b*x + a)*sqrt(x))/b^2]","A",0
233,1,141,0,0.561618," ","integrate(arctanh(tanh(b*x+a))^(5/2)/x^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{3} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(8 \, b^{3} x^{2} + 26 \, a b^{2} x + 33 \, a^{2} b\right)} \sqrt{b x + a} \sqrt{x}}{48 \, b}, -\frac{15 \, a^{3} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(8 \, b^{3} x^{2} + 26 \, a b^{2} x + 33 \, a^{2} b\right)} \sqrt{b x + a} \sqrt{x}}{24 \, b}\right]"," ",0,"[1/48*(15*a^3*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(8*b^3*x^2 + 26*a*b^2*x + 33*a^2*b)*sqrt(b*x + a)*sqrt(x))/b, -1/24*(15*a^3*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (8*b^3*x^2 + 26*a*b^2*x + 33*a^2*b)*sqrt(b*x + a)*sqrt(x))/b]","A",0
234,1,137,0,0.478464," ","integrate(arctanh(tanh(b*x+a))^(5/2)/x^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{2} \sqrt{b} x \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(2 \, b^{2} x^{2} + 9 \, a b x - 8 \, a^{2}\right)} \sqrt{b x + a} \sqrt{x}}{8 \, x}, -\frac{15 \, a^{2} \sqrt{-b} x \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(2 \, b^{2} x^{2} + 9 \, a b x - 8 \, a^{2}\right)} \sqrt{b x + a} \sqrt{x}}{4 \, x}\right]"," ",0,"[1/8*(15*a^2*sqrt(b)*x*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(2*b^2*x^2 + 9*a*b*x - 8*a^2)*sqrt(b*x + a)*sqrt(x))/x, -1/4*(15*a^2*sqrt(-b)*x*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (2*b^2*x^2 + 9*a*b*x - 8*a^2)*sqrt(b*x + a)*sqrt(x))/x]","A",0
235,1,138,0,0.483246," ","integrate(arctanh(tanh(b*x+a))^(5/2)/x^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, a b^{\frac{3}{2}} x^{2} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(3 \, b^{2} x^{2} - 14 \, a b x - 2 \, a^{2}\right)} \sqrt{b x + a} \sqrt{x}}{6 \, x^{2}}, -\frac{15 \, a \sqrt{-b} b x^{2} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(3 \, b^{2} x^{2} - 14 \, a b x - 2 \, a^{2}\right)} \sqrt{b x + a} \sqrt{x}}{3 \, x^{2}}\right]"," ",0,"[1/6*(15*a*b^(3/2)*x^2*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(3*b^2*x^2 - 14*a*b*x - 2*a^2)*sqrt(b*x + a)*sqrt(x))/x^2, -1/3*(15*a*sqrt(-b)*b*x^2*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (3*b^2*x^2 - 14*a*b*x - 2*a^2)*sqrt(b*x + a)*sqrt(x))/x^2]","A",0
236,1,137,0,0.899108," ","integrate(arctanh(tanh(b*x+a))^(5/2)/x^(7/2),x, algorithm=""fricas"")","\left[\frac{15 \, b^{\frac{5}{2}} x^{3} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(23 \, b^{2} x^{2} + 11 \, a b x + 3 \, a^{2}\right)} \sqrt{b x + a} \sqrt{x}}{15 \, x^{3}}, -\frac{2 \, {\left(15 \, \sqrt{-b} b^{2} x^{3} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(23 \, b^{2} x^{2} + 11 \, a b x + 3 \, a^{2}\right)} \sqrt{b x + a} \sqrt{x}\right)}}{15 \, x^{3}}\right]"," ",0,"[1/15*(15*b^(5/2)*x^3*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(23*b^2*x^2 + 11*a*b*x + 3*a^2)*sqrt(b*x + a)*sqrt(x))/x^3, -2/15*(15*sqrt(-b)*b^2*x^3*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (23*b^2*x^2 + 11*a*b*x + 3*a^2)*sqrt(b*x + a)*sqrt(x))/x^3]","A",0
237,1,42,0,0.418060," ","integrate(arctanh(tanh(b*x+a))^(5/2)/x^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right)} \sqrt{b x + a}}{7 \, a x^{\frac{7}{2}}}"," ",0,"-2/7*(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*sqrt(b*x + a)/(a*x^(7/2))","A",0
238,1,56,0,0.452776," ","integrate(arctanh(tanh(b*x+a))^(5/2)/x^(11/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, b^{4} x^{4} - a b^{3} x^{3} - 15 \, a^{2} b^{2} x^{2} - 19 \, a^{3} b x - 7 \, a^{4}\right)} \sqrt{b x + a}}{63 \, a^{2} x^{\frac{9}{2}}}"," ",0,"2/63*(2*b^4*x^4 - a*b^3*x^3 - 15*a^2*b^2*x^2 - 19*a^3*b*x - 7*a^4)*sqrt(b*x + a)/(a^2*x^(9/2))","A",0
239,1,67,0,0.565342," ","integrate(arctanh(tanh(b*x+a))^(5/2)/x^(13/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, b^{5} x^{5} - 4 \, a b^{4} x^{4} + 3 \, a^{2} b^{3} x^{3} + 113 \, a^{3} b^{2} x^{2} + 161 \, a^{4} b x + 63 \, a^{5}\right)} \sqrt{b x + a}}{693 \, a^{3} x^{\frac{11}{2}}}"," ",0,"-2/693*(8*b^5*x^5 - 4*a*b^4*x^4 + 3*a^2*b^3*x^3 + 113*a^3*b^2*x^2 + 161*a^4*b*x + 63*a^5)*sqrt(b*x + a)/(a^3*x^(11/2))","A",0
240,1,78,0,0.489681," ","integrate(arctanh(tanh(b*x+a))^(5/2)/x^(15/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, b^{6} x^{6} - 8 \, a b^{5} x^{5} + 6 \, a^{2} b^{4} x^{4} - 5 \, a^{3} b^{3} x^{3} - 371 \, a^{4} b^{2} x^{2} - 567 \, a^{5} b x - 231 \, a^{6}\right)} \sqrt{b x + a}}{3003 \, a^{4} x^{\frac{13}{2}}}"," ",0,"2/3003*(16*b^6*x^6 - 8*a*b^5*x^5 + 6*a^2*b^4*x^4 - 5*a^3*b^3*x^3 - 371*a^4*b^2*x^2 - 567*a^5*b*x - 231*a^6)*sqrt(b*x + a)/(a^4*x^(13/2))","A",0
241,1,140,0,0.636567," ","integrate(x^(5/2)/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, a^{3} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(8 \, b^{3} x^{2} - 10 \, a b^{2} x + 15 \, a^{2} b\right)} \sqrt{b x + a} \sqrt{x}}{48 \, b^{4}}, \frac{15 \, a^{3} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(8 \, b^{3} x^{2} - 10 \, a b^{2} x + 15 \, a^{2} b\right)} \sqrt{b x + a} \sqrt{x}}{24 \, b^{4}}\right]"," ",0,"[1/48*(15*a^3*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(8*b^3*x^2 - 10*a*b^2*x + 15*a^2*b)*sqrt(b*x + a)*sqrt(x))/b^4, 1/24*(15*a^3*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (8*b^3*x^2 - 10*a*b^2*x + 15*a^2*b)*sqrt(b*x + a)*sqrt(x))/b^4]","A",0
242,1,119,0,0.586505," ","integrate(x^(3/2)/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, a^{2} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(2 \, b^{2} x - 3 \, a b\right)} \sqrt{b x + a} \sqrt{x}}{8 \, b^{3}}, -\frac{3 \, a^{2} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(2 \, b^{2} x - 3 \, a b\right)} \sqrt{b x + a} \sqrt{x}}{4 \, b^{3}}\right]"," ",0,"[1/8*(3*a^2*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(2*b^2*x - 3*a*b)*sqrt(b*x + a)*sqrt(x))/b^3, -1/4*(3*a^2*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (2*b^2*x - 3*a*b)*sqrt(b*x + a)*sqrt(x))/b^3]","A",0
243,1,91,0,0.465423," ","integrate(x^(1/2)/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{a \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, \sqrt{b x + a} b \sqrt{x}}{2 \, b^{2}}, \frac{a \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + \sqrt{b x + a} b \sqrt{x}}{b^{2}}\right]"," ",0,"[1/2*(a*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*sqrt(b*x + a)*b*sqrt(x))/b^2, (a*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + sqrt(b*x + a)*b*sqrt(x))/b^2]","A",0
244,1,57,0,0.766576," ","integrate(1/x^(1/2)/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right)}{\sqrt{b}}, -\frac{2 \, \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right)}{b}\right]"," ",0,"[log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a)/sqrt(b), -2*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x)))/b]","A",0
245,1,15,0,0.491929," ","integrate(1/x^(3/2)/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{b x + a}}{a \sqrt{x}}"," ",0,"-2*sqrt(b*x + a)/(a*sqrt(x))","A",0
246,1,23,0,0.562156," ","integrate(1/x^(5/2)/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, b x - a\right)} \sqrt{b x + a}}{3 \, a^{2} x^{\frac{3}{2}}}"," ",0,"2/3*(2*b*x - a)*sqrt(b*x + a)/(a^2*x^(3/2))","A",0
247,1,34,0,0.468584," ","integrate(1/x^(7/2)/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, b^{2} x^{2} - 4 \, a b x + 3 \, a^{2}\right)} \sqrt{b x + a}}{15 \, a^{3} x^{\frac{5}{2}}}"," ",0,"-2/15*(8*b^2*x^2 - 4*a*b*x + 3*a^2)*sqrt(b*x + a)/(a^3*x^(5/2))","A",0
248,1,45,0,0.711930," ","integrate(1/x^(9/2)/arctanh(tanh(b*x+a))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, b^{3} x^{3} - 8 \, a b^{2} x^{2} + 6 \, a^{2} b x - 5 \, a^{3}\right)} \sqrt{b x + a}}{35 \, a^{4} x^{\frac{7}{2}}}"," ",0,"2/35*(16*b^3*x^3 - 8*a*b^2*x^2 + 6*a^2*b*x - 5*a^3)*sqrt(b*x + a)/(a^4*x^(7/2))","A",0
249,1,196,0,0.508938," ","integrate(x^(7/2)/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{3} b x + a^{4}\right)} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(8 \, b^{4} x^{3} - 14 \, a b^{3} x^{2} + 35 \, a^{2} b^{2} x + 105 \, a^{3} b\right)} \sqrt{b x + a} \sqrt{x}}{48 \, {\left(b^{6} x + a b^{5}\right)}}, \frac{105 \, {\left(a^{3} b x + a^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(8 \, b^{4} x^{3} - 14 \, a b^{3} x^{2} + 35 \, a^{2} b^{2} x + 105 \, a^{3} b\right)} \sqrt{b x + a} \sqrt{x}}{24 \, {\left(b^{6} x + a b^{5}\right)}}\right]"," ",0,"[1/48*(105*(a^3*b*x + a^4)*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(8*b^4*x^3 - 14*a*b^3*x^2 + 35*a^2*b^2*x + 105*a^3*b)*sqrt(b*x + a)*sqrt(x))/(b^6*x + a*b^5), 1/24*(105*(a^3*b*x + a^4)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (8*b^4*x^3 - 14*a*b^3*x^2 + 35*a^2*b^2*x + 105*a^3*b)*sqrt(b*x + a)*sqrt(x))/(b^6*x + a*b^5)]","A",0
250,1,175,0,0.566756," ","integrate(x^(5/2)/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{2} b x + a^{3}\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(2 \, b^{3} x^{2} - 5 \, a b^{2} x - 15 \, a^{2} b\right)} \sqrt{b x + a} \sqrt{x}}{8 \, {\left(b^{5} x + a b^{4}\right)}}, -\frac{15 \, {\left(a^{2} b x + a^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(2 \, b^{3} x^{2} - 5 \, a b^{2} x - 15 \, a^{2} b\right)} \sqrt{b x + a} \sqrt{x}}{4 \, {\left(b^{5} x + a b^{4}\right)}}\right]"," ",0,"[1/8*(15*(a^2*b*x + a^3)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(2*b^3*x^2 - 5*a*b^2*x - 15*a^2*b)*sqrt(b*x + a)*sqrt(x))/(b^5*x + a*b^4), -1/4*(15*(a^2*b*x + a^3)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (2*b^3*x^2 - 5*a*b^2*x - 15*a^2*b)*sqrt(b*x + a)*sqrt(x))/(b^5*x + a*b^4)]","A",0
251,1,145,0,0.576284," ","integrate(x^(3/2)/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b x + a^{2}\right)} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(b^{2} x + 3 \, a b\right)} \sqrt{b x + a} \sqrt{x}}{2 \, {\left(b^{4} x + a b^{3}\right)}}, \frac{3 \, {\left(a b x + a^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(b^{2} x + 3 \, a b\right)} \sqrt{b x + a} \sqrt{x}}{b^{4} x + a b^{3}}\right]"," ",0,"[1/2*(3*(a*b*x + a^2)*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(b^2*x + 3*a*b)*sqrt(b*x + a)*sqrt(x))/(b^4*x + a*b^3), (3*(a*b*x + a^2)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (b^2*x + 3*a*b)*sqrt(b*x + a)*sqrt(x))/(b^4*x + a*b^3)]","A",0
252,1,119,0,0.474060," ","integrate(x^(1/2)/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(b x + a\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, \sqrt{b x + a} b \sqrt{x}}{b^{3} x + a b^{2}}, -\frac{2 \, {\left({\left(b x + a\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + \sqrt{b x + a} b \sqrt{x}\right)}}{b^{3} x + a b^{2}}\right]"," ",0,"[((b*x + a)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*sqrt(b*x + a)*b*sqrt(x))/(b^3*x + a*b^2), -2*((b*x + a)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + sqrt(b*x + a)*b*sqrt(x))/(b^3*x + a*b^2)]","A",0
253,1,22,0,0.506223," ","integrate(1/x^(1/2)/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{b x + a} \sqrt{x}}{a b x + a^{2}}"," ",0,"2*sqrt(b*x + a)*sqrt(x)/(a*b*x + a^2)","A",0
254,1,34,0,0.427189," ","integrate(1/x^(3/2)/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, b x + a\right)} \sqrt{b x + a} \sqrt{x}}{a^{2} b x^{2} + a^{3} x}"," ",0,"-2*(2*b*x + a)*sqrt(b*x + a)*sqrt(x)/(a^2*b*x^2 + a^3*x)","A",0
255,1,49,0,0.575448," ","integrate(1/x^(5/2)/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, b^{2} x^{2} + 4 \, a b x - a^{2}\right)} \sqrt{b x + a} \sqrt{x}}{3 \, {\left(a^{3} b x^{3} + a^{4} x^{2}\right)}}"," ",0,"2/3*(8*b^2*x^2 + 4*a*b*x - a^2)*sqrt(b*x + a)*sqrt(x)/(a^3*b*x^3 + a^4*x^2)","A",0
256,1,58,0,0.582949," ","integrate(1/x^(7/2)/arctanh(tanh(b*x+a))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(16 \, b^{3} x^{3} + 8 \, a b^{2} x^{2} - 2 \, a^{2} b x + a^{3}\right)} \sqrt{b x + a} \sqrt{x}}{5 \, {\left(a^{4} b x^{4} + a^{5} x^{3}\right)}}"," ",0,"-2/5*(16*b^3*x^3 + 8*a*b^2*x^2 - 2*a^2*b*x + a^3)*sqrt(b*x + a)*sqrt(x)/(a^4*b*x^4 + a^5*x^3)","A",0
257,1,241,0,0.525794," ","integrate(x^(7/2)/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{2} b^{2} x^{2} + 2 \, a^{3} b x + a^{4}\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(6 \, b^{4} x^{3} - 21 \, a b^{3} x^{2} - 140 \, a^{2} b^{2} x - 105 \, a^{3} b\right)} \sqrt{b x + a} \sqrt{x}}{24 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}, -\frac{105 \, {\left(a^{2} b^{2} x^{2} + 2 \, a^{3} b x + a^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) - {\left(6 \, b^{4} x^{3} - 21 \, a b^{3} x^{2} - 140 \, a^{2} b^{2} x - 105 \, a^{3} b\right)} \sqrt{b x + a} \sqrt{x}}{12 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}\right]"," ",0,"[1/24*(105*(a^2*b^2*x^2 + 2*a^3*b*x + a^4)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(6*b^4*x^3 - 21*a*b^3*x^2 - 140*a^2*b^2*x - 105*a^3*b)*sqrt(b*x + a)*sqrt(x))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5), -1/12*(105*(a^2*b^2*x^2 + 2*a^3*b*x + a^4)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) - (6*b^4*x^3 - 21*a*b^3*x^2 - 140*a^2*b^2*x - 105*a^3*b)*sqrt(b*x + a)*sqrt(x))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)]","A",0
258,1,214,0,0.804129," ","integrate(x^(5/2)/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a b^{2} x^{2} + 2 \, a^{2} b x + a^{3}\right)} \sqrt{b} \log\left(2 \, b x - 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) + 2 \, {\left(3 \, b^{3} x^{2} + 20 \, a b^{2} x + 15 \, a^{2} b\right)} \sqrt{b x + a} \sqrt{x}}{6 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}, \frac{15 \, {\left(a b^{2} x^{2} + 2 \, a^{2} b x + a^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(3 \, b^{3} x^{2} + 20 \, a b^{2} x + 15 \, a^{2} b\right)} \sqrt{b x + a} \sqrt{x}}{3 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}\right]"," ",0,"[1/6*(15*(a*b^2*x^2 + 2*a^2*b*x + a^3)*sqrt(b)*log(2*b*x - 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) + 2*(3*b^3*x^2 + 20*a*b^2*x + 15*a^2*b)*sqrt(b*x + a)*sqrt(x))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4), 1/3*(15*(a*b^2*x^2 + 2*a^2*b*x + a^3)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (3*b^3*x^2 + 20*a*b^2*x + 15*a^2*b)*sqrt(b*x + a)*sqrt(x))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)]","A",0
259,1,186,0,0.515392," ","integrate(x^(3/2)/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{b} \log\left(2 \, b x + 2 \, \sqrt{b x + a} \sqrt{b} \sqrt{x} + a\right) - 2 \, {\left(4 \, b^{2} x + 3 \, a b\right)} \sqrt{b x + a} \sqrt{x}}{3 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}, -\frac{2 \, {\left(3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-b}}{b \sqrt{x}}\right) + {\left(4 \, b^{2} x + 3 \, a b\right)} \sqrt{b x + a} \sqrt{x}\right)}}{3 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}\right]"," ",0,"[1/3*(3*(b^2*x^2 + 2*a*b*x + a^2)*sqrt(b)*log(2*b*x + 2*sqrt(b*x + a)*sqrt(b)*sqrt(x) + a) - 2*(4*b^2*x + 3*a*b)*sqrt(b*x + a)*sqrt(x))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3), -2/3*(3*(b^2*x^2 + 2*a*b*x + a^2)*sqrt(-b)*arctan(sqrt(b*x + a)*sqrt(-b)/(b*sqrt(x))) + (4*b^2*x + 3*a*b)*sqrt(b*x + a)*sqrt(x))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)]","A",0
260,1,33,0,0.550057," ","integrate(x^(1/2)/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{b x + a} x^{\frac{3}{2}}}{3 \, {\left(a b^{2} x^{2} + 2 \, a^{2} b x + a^{3}\right)}}"," ",0,"2/3*sqrt(b*x + a)*x^(3/2)/(a*b^2*x^2 + 2*a^2*b*x + a^3)","A",0
261,1,43,0,0.457855," ","integrate(1/x^(1/2)/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, b x + 3 \, a\right)} \sqrt{b x + a} \sqrt{x}}{3 \, {\left(a^{2} b^{2} x^{2} + 2 \, a^{3} b x + a^{4}\right)}}"," ",0,"2/3*(2*b*x + 3*a)*sqrt(b*x + a)*sqrt(x)/(a^2*b^2*x^2 + 2*a^3*b*x + a^4)","A",0
262,1,58,0,0.382098," ","integrate(1/x^(3/2)/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, b^{2} x^{2} + 12 \, a b x + 3 \, a^{2}\right)} \sqrt{b x + a} \sqrt{x}}{3 \, {\left(a^{3} b^{2} x^{3} + 2 \, a^{4} b x^{2} + a^{5} x\right)}}"," ",0,"-2/3*(8*b^2*x^2 + 12*a*b*x + 3*a^2)*sqrt(b*x + a)*sqrt(x)/(a^3*b^2*x^3 + 2*a^4*b*x^2 + a^5*x)","A",0
263,1,71,0,0.397382," ","integrate(1/x^(5/2)/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, b^{3} x^{3} + 24 \, a b^{2} x^{2} + 6 \, a^{2} b x - a^{3}\right)} \sqrt{b x + a} \sqrt{x}}{3 \, {\left(a^{4} b^{2} x^{4} + 2 \, a^{5} b x^{3} + a^{6} x^{2}\right)}}"," ",0,"2/3*(16*b^3*x^3 + 24*a*b^2*x^2 + 6*a^2*b*x - a^3)*sqrt(b*x + a)*sqrt(x)/(a^4*b^2*x^4 + 2*a^5*b*x^3 + a^6*x^2)","A",0
264,1,82,0,0.734935," ","integrate(1/x^(7/2)/arctanh(tanh(b*x+a))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(128 \, b^{4} x^{4} + 192 \, a b^{3} x^{3} + 48 \, a^{2} b^{2} x^{2} - 8 \, a^{3} b x + 3 \, a^{4}\right)} \sqrt{b x + a} \sqrt{x}}{15 \, {\left(a^{5} b^{2} x^{5} + 2 \, a^{6} b x^{4} + a^{7} x^{3}\right)}}"," ",0,"-2/15*(128*b^4*x^4 + 192*a*b^3*x^3 + 48*a^2*b^2*x^2 - 8*a^3*b*x + 3*a^4)*sqrt(b*x + a)*sqrt(x)/(a^5*b^2*x^5 + 2*a^6*b*x^4 + a^7*x^3)","A",0
265,0,0,0,0.466477," ","integrate(x^m*arctanh(tanh(b*x+a))^n,x, algorithm=""fricas"")","{\rm integral}\left(x^{m} \operatorname{artanh}\left(\tanh\left(b x + a\right)\right)^{n}, x\right)"," ",0,"integral(x^m*arctanh(tanh(b*x + a))^n, x)","F",0
266,1,374,0,0.403241," ","integrate(x^4*arctanh(tanh(b*x+a))^n,x, algorithm=""fricas"")","-\frac{{\left(24 \, a^{4} b n x - {\left(b^{5} n^{4} + 10 \, b^{5} n^{3} + 35 \, b^{5} n^{2} + 50 \, b^{5} n + 24 \, b^{5}\right)} x^{5} - 24 \, a^{5} - {\left(a b^{4} n^{4} + 6 \, a b^{4} n^{3} + 11 \, a b^{4} n^{2} + 6 \, a b^{4} n\right)} x^{4} + 4 \, {\left(a^{2} b^{3} n^{3} + 3 \, a^{2} b^{3} n^{2} + 2 \, a^{2} b^{3} n\right)} x^{3} - 12 \, {\left(a^{3} b^{2} n^{2} + a^{3} b^{2} n\right)} x^{2}\right)} \cosh\left(n \log\left(b x + a\right)\right) + {\left(24 \, a^{4} b n x - {\left(b^{5} n^{4} + 10 \, b^{5} n^{3} + 35 \, b^{5} n^{2} + 50 \, b^{5} n + 24 \, b^{5}\right)} x^{5} - 24 \, a^{5} - {\left(a b^{4} n^{4} + 6 \, a b^{4} n^{3} + 11 \, a b^{4} n^{2} + 6 \, a b^{4} n\right)} x^{4} + 4 \, {\left(a^{2} b^{3} n^{3} + 3 \, a^{2} b^{3} n^{2} + 2 \, a^{2} b^{3} n\right)} x^{3} - 12 \, {\left(a^{3} b^{2} n^{2} + a^{3} b^{2} n\right)} x^{2}\right)} \sinh\left(n \log\left(b x + a\right)\right)}{b^{5} n^{5} + 15 \, b^{5} n^{4} + 85 \, b^{5} n^{3} + 225 \, b^{5} n^{2} + 274 \, b^{5} n + 120 \, b^{5}}"," ",0,"-((24*a^4*b*n*x - (b^5*n^4 + 10*b^5*n^3 + 35*b^5*n^2 + 50*b^5*n + 24*b^5)*x^5 - 24*a^5 - (a*b^4*n^4 + 6*a*b^4*n^3 + 11*a*b^4*n^2 + 6*a*b^4*n)*x^4 + 4*(a^2*b^3*n^3 + 3*a^2*b^3*n^2 + 2*a^2*b^3*n)*x^3 - 12*(a^3*b^2*n^2 + a^3*b^2*n)*x^2)*cosh(n*log(b*x + a)) + (24*a^4*b*n*x - (b^5*n^4 + 10*b^5*n^3 + 35*b^5*n^2 + 50*b^5*n + 24*b^5)*x^5 - 24*a^5 - (a*b^4*n^4 + 6*a*b^4*n^3 + 11*a*b^4*n^2 + 6*a*b^4*n)*x^4 + 4*(a^2*b^3*n^3 + 3*a^2*b^3*n^2 + 2*a^2*b^3*n)*x^3 - 12*(a^3*b^2*n^2 + a^3*b^2*n)*x^2)*sinh(n*log(b*x + a)))/(b^5*n^5 + 15*b^5*n^4 + 85*b^5*n^3 + 225*b^5*n^2 + 274*b^5*n + 120*b^5)","B",0
267,1,255,0,0.507997," ","integrate(x^3*arctanh(tanh(b*x+a))^n,x, algorithm=""fricas"")","\frac{{\left(6 \, a^{3} b n x + {\left(b^{4} n^{3} + 6 \, b^{4} n^{2} + 11 \, b^{4} n + 6 \, b^{4}\right)} x^{4} - 6 \, a^{4} + {\left(a b^{3} n^{3} + 3 \, a b^{3} n^{2} + 2 \, a b^{3} n\right)} x^{3} - 3 \, {\left(a^{2} b^{2} n^{2} + a^{2} b^{2} n\right)} x^{2}\right)} \cosh\left(n \log\left(b x + a\right)\right) + {\left(6 \, a^{3} b n x + {\left(b^{4} n^{3} + 6 \, b^{4} n^{2} + 11 \, b^{4} n + 6 \, b^{4}\right)} x^{4} - 6 \, a^{4} + {\left(a b^{3} n^{3} + 3 \, a b^{3} n^{2} + 2 \, a b^{3} n\right)} x^{3} - 3 \, {\left(a^{2} b^{2} n^{2} + a^{2} b^{2} n\right)} x^{2}\right)} \sinh\left(n \log\left(b x + a\right)\right)}{b^{4} n^{4} + 10 \, b^{4} n^{3} + 35 \, b^{4} n^{2} + 50 \, b^{4} n + 24 \, b^{4}}"," ",0,"((6*a^3*b*n*x + (b^4*n^3 + 6*b^4*n^2 + 11*b^4*n + 6*b^4)*x^4 - 6*a^4 + (a*b^3*n^3 + 3*a*b^3*n^2 + 2*a*b^3*n)*x^3 - 3*(a^2*b^2*n^2 + a^2*b^2*n)*x^2)*cosh(n*log(b*x + a)) + (6*a^3*b*n*x + (b^4*n^3 + 6*b^4*n^2 + 11*b^4*n + 6*b^4)*x^4 - 6*a^4 + (a*b^3*n^3 + 3*a*b^3*n^2 + 2*a*b^3*n)*x^3 - 3*(a^2*b^2*n^2 + a^2*b^2*n)*x^2)*sinh(n*log(b*x + a)))/(b^4*n^4 + 10*b^4*n^3 + 35*b^4*n^2 + 50*b^4*n + 24*b^4)","B",0
268,1,168,0,0.666677," ","integrate(x^2*arctanh(tanh(b*x+a))^n,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{2} b n x - {\left(b^{3} n^{2} + 3 \, b^{3} n + 2 \, b^{3}\right)} x^{3} - 2 \, a^{3} - {\left(a b^{2} n^{2} + a b^{2} n\right)} x^{2}\right)} \cosh\left(n \log\left(b x + a\right)\right) + {\left(2 \, a^{2} b n x - {\left(b^{3} n^{2} + 3 \, b^{3} n + 2 \, b^{3}\right)} x^{3} - 2 \, a^{3} - {\left(a b^{2} n^{2} + a b^{2} n\right)} x^{2}\right)} \sinh\left(n \log\left(b x + a\right)\right)}{b^{3} n^{3} + 6 \, b^{3} n^{2} + 11 \, b^{3} n + 6 \, b^{3}}"," ",0,"-((2*a^2*b*n*x - (b^3*n^2 + 3*b^3*n + 2*b^3)*x^3 - 2*a^3 - (a*b^2*n^2 + a*b^2*n)*x^2)*cosh(n*log(b*x + a)) + (2*a^2*b*n*x - (b^3*n^2 + 3*b^3*n + 2*b^3)*x^3 - 2*a^3 - (a*b^2*n^2 + a*b^2*n)*x^2)*sinh(n*log(b*x + a)))/(b^3*n^3 + 6*b^3*n^2 + 11*b^3*n + 6*b^3)","B",0
269,1,91,0,0.559255," ","integrate(x*arctanh(tanh(b*x+a))^n,x, algorithm=""fricas"")","\frac{{\left(a b n x + {\left(b^{2} n + b^{2}\right)} x^{2} - a^{2}\right)} \cosh\left(n \log\left(b x + a\right)\right) + {\left(a b n x + {\left(b^{2} n + b^{2}\right)} x^{2} - a^{2}\right)} \sinh\left(n \log\left(b x + a\right)\right)}{b^{2} n^{2} + 3 \, b^{2} n + 2 \, b^{2}}"," ",0,"((a*b*n*x + (b^2*n + b^2)*x^2 - a^2)*cosh(n*log(b*x + a)) + (a*b*n*x + (b^2*n + b^2)*x^2 - a^2)*sinh(n*log(b*x + a)))/(b^2*n^2 + 3*b^2*n + 2*b^2)","A",0
270,1,39,0,0.505808," ","integrate(arctanh(tanh(b*x+a))^n,x, algorithm=""fricas"")","\frac{{\left(b x + a\right)} \cosh\left(n \log\left(b x + a\right)\right) + {\left(b x + a\right)} \sinh\left(n \log\left(b x + a\right)\right)}{b n + b}"," ",0,"((b*x + a)*cosh(n*log(b*x + a)) + (b*x + a)*sinh(n*log(b*x + a)))/(b*n + b)","A",0
271,0,0,0,0.686877," ","integrate(arctanh(tanh(b*x+a))^n/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(\tanh\left(b x + a\right)\right)^{n}}{x}, x\right)"," ",0,"integral(arctanh(tanh(b*x + a))^n/x, x)","F",0
272,0,0,0,1.755349," ","integrate(arctanh(tanh(b*x+a))^n/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(\tanh\left(b x + a\right)\right)^{n}}{x^{2}}, x\right)"," ",0,"integral(arctanh(tanh(b*x + a))^n/x^2, x)","F",0
273,0,0,0,0.487765," ","integrate(arctanh(tanh(b*x+a))^n/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(\tanh\left(b x + a\right)\right)^{n}}{x^{3}}, x\right)"," ",0,"integral(arctanh(tanh(b*x + a))^n/x^3, x)","F",0
274,1,33,0,0.453642," ","integrate(x^m*arccoth(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{{\left({\left(b m + b\right)} x^{2} + {\left(a m + 2 \, a\right)} x\right)} x^{m}}{m^{2} + 3 \, m + 2}"," ",0,"((b*m + b)*x^2 + (a*m + 2*a)*x)*x^m/(m^2 + 3*m + 2)","A",0
275,1,13,0,0.688153," ","integrate(x^2*arctanh(coth(b*x+a)),x, algorithm=""fricas"")","\frac{1}{4} \, b x^{4} + \frac{1}{3} \, a x^{3}"," ",0,"1/4*b*x^4 + 1/3*a*x^3","A",0
276,1,13,0,0.601571," ","integrate(x*arctanh(coth(b*x+a)),x, algorithm=""fricas"")","\frac{1}{3} \, b x^{3} + \frac{1}{2} \, a x^{2}"," ",0,"1/3*b*x^3 + 1/2*a*x^2","A",0
277,1,10,0,0.492684," ","integrate(arctanh(coth(b*x+a)),x, algorithm=""fricas"")","\frac{1}{2} \, b x^{2} + a x"," ",0,"1/2*b*x^2 + a*x","A",0
278,1,8,0,0.706329," ","integrate(arctanh(coth(b*x+a))/x,x, algorithm=""fricas"")","b x + a \log\left(x\right)"," ",0,"b*x + a*log(x)","A",0
279,1,13,0,0.615146," ","integrate(arctanh(coth(b*x+a))/x^2,x, algorithm=""fricas"")","\frac{b x \log\left(x\right) - a}{x}"," ",0,"(b*x*log(x) - a)/x","A",0
280,1,11,0,0.472959," ","integrate(arctanh(coth(b*x+a))/x^3,x, algorithm=""fricas"")","-\frac{2 \, b x + a}{2 \, x^{2}}"," ",0,"-1/2*(2*b*x + a)/x^2","A",0
281,1,58,0,0.609126," ","integrate(arctanh(cosh(x)),x, algorithm=""fricas"")","\frac{1}{2} \, x \log\left(-\frac{\cosh\left(x\right) + 1}{\cosh\left(x\right) - 1}\right) - x \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + x \log\left(-\cosh\left(x\right) - \sinh\left(x\right) + 1\right) + {\rm Li}_2\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - {\rm Li}_2\left(-\cosh\left(x\right) - \sinh\left(x\right)\right)"," ",0,"1/2*x*log(-(cosh(x) + 1)/(cosh(x) - 1)) - x*log(cosh(x) + sinh(x) + 1) + x*log(-cosh(x) - sinh(x) + 1) + dilog(cosh(x) + sinh(x)) - dilog(-cosh(x) - sinh(x))","B",0
282,1,88,0,0.405367," ","integrate(x*arctanh(cosh(x)),x, algorithm=""fricas"")","\frac{1}{4} \, x^{2} \log\left(-\frac{\cosh\left(x\right) + 1}{\cosh\left(x\right) - 1}\right) - \frac{1}{2} \, x^{2} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + \frac{1}{2} \, x^{2} \log\left(-\cosh\left(x\right) - \sinh\left(x\right) + 1\right) + x {\rm Li}_2\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - x {\rm Li}_2\left(-\cosh\left(x\right) - \sinh\left(x\right)\right) - {\rm polylog}\left(3, \cosh\left(x\right) + \sinh\left(x\right)\right) + {\rm polylog}\left(3, -\cosh\left(x\right) - \sinh\left(x\right)\right)"," ",0,"1/4*x^2*log(-(cosh(x) + 1)/(cosh(x) - 1)) - 1/2*x^2*log(cosh(x) + sinh(x) + 1) + 1/2*x^2*log(-cosh(x) - sinh(x) + 1) + x*dilog(cosh(x) + sinh(x)) - x*dilog(-cosh(x) - sinh(x)) - polylog(3, cosh(x) + sinh(x)) + polylog(3, -cosh(x) - sinh(x))","C",0
283,1,118,0,0.833464," ","integrate(x^2*arctanh(cosh(x)),x, algorithm=""fricas"")","\frac{1}{6} \, x^{3} \log\left(-\frac{\cosh\left(x\right) + 1}{\cosh\left(x\right) - 1}\right) - \frac{1}{3} \, x^{3} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + \frac{1}{3} \, x^{3} \log\left(-\cosh\left(x\right) - \sinh\left(x\right) + 1\right) + x^{2} {\rm Li}_2\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - x^{2} {\rm Li}_2\left(-\cosh\left(x\right) - \sinh\left(x\right)\right) - 2 \, x {\rm polylog}\left(3, \cosh\left(x\right) + \sinh\left(x\right)\right) + 2 \, x {\rm polylog}\left(3, -\cosh\left(x\right) - \sinh\left(x\right)\right) + 2 \, {\rm polylog}\left(4, \cosh\left(x\right) + \sinh\left(x\right)\right) - 2 \, {\rm polylog}\left(4, -\cosh\left(x\right) - \sinh\left(x\right)\right)"," ",0,"1/6*x^3*log(-(cosh(x) + 1)/(cosh(x) - 1)) - 1/3*x^3*log(cosh(x) + sinh(x) + 1) + 1/3*x^3*log(-cosh(x) - sinh(x) + 1) + x^2*dilog(cosh(x) + sinh(x)) - x^2*dilog(-cosh(x) - sinh(x)) - 2*x*polylog(3, cosh(x) + sinh(x)) + 2*x*polylog(3, -cosh(x) - sinh(x)) + 2*polylog(4, cosh(x) + sinh(x)) - 2*polylog(4, -cosh(x) - sinh(x))","C",0
284,1,900,0,0.474115," ","integrate(x^2*arctanh(c+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b^{3} x^{3} \log\left(-\frac{{\left(c + 1\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{{\left(c - 1\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 3 \, b^{2} x^{2} {\rm Li}_2\left(\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 \, b^{2} x^{2} {\rm Li}_2\left(-\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 3 \, b^{2} x^{2} {\rm Li}_2\left(\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 3 \, b^{2} x^{2} {\rm Li}_2\left(-\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + a^{3} \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d + 1\right)} \sqrt{-\frac{c + d + 1}{c - d + 1}}\right) + a^{3} \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d + 1\right)} \sqrt{-\frac{c + d + 1}{c - d + 1}}\right) - a^{3} \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d - 1\right)} \sqrt{-\frac{c + d - 1}{c - d - 1}}\right) - a^{3} \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d - 1\right)} \sqrt{-\frac{c + d - 1}{c - d - 1}}\right) + 6 \, b x {\rm polylog}\left(3, \sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, b x {\rm polylog}\left(3, -\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b x {\rm polylog}\left(3, \sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b x {\rm polylog}\left(3, -\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 6 \, {\rm polylog}\left(4, \sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, {\rm polylog}\left(4, -\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, {\rm polylog}\left(4, \sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, {\rm polylog}\left(4, -\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{6 \, b^{3}}"," ",0,"1/6*(b^3*x^3*log(-((c + 1)*cosh(b*x + a) + d*sinh(b*x + a))/((c - 1)*cosh(b*x + a) + d*sinh(b*x + a))) - 3*b^2*x^2*dilog(sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 3*b^2*x^2*dilog(-sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 3*b^2*x^2*dilog(sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + 3*b^2*x^2*dilog(-sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + a^3*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) + 2*(c - d + 1)*sqrt(-(c + d + 1)/(c - d + 1))) + a^3*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) - 2*(c - d + 1)*sqrt(-(c + d + 1)/(c - d + 1))) - a^3*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) + 2*(c - d - 1)*sqrt(-(c + d - 1)/(c - d - 1))) - a^3*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) - 2*(c - d - 1)*sqrt(-(c + d - 1)/(c - d - 1))) + 6*b*x*polylog(3, sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*b*x*polylog(3, -sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*b*x*polylog(3, sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*b*x*polylog(3, -sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) - (b^3*x^3 + a^3)*log(sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b^3*x^3 + a^3)*log(-sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b^3*x^3 + a^3)*log(sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b^3*x^3 + a^3)*log(-sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 6*polylog(4, sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*polylog(4, -sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*polylog(4, sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*polylog(4, -sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
285,1,746,0,0.580886," ","integrate(x*arctanh(c+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} \log\left(-\frac{{\left(c + 1\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{{\left(c - 1\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 2 \, b x {\rm Li}_2\left(\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, b x {\rm Li}_2\left(-\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, b x {\rm Li}_2\left(\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, b x {\rm Li}_2\left(-\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - a^{2} \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d + 1\right)} \sqrt{-\frac{c + d + 1}{c - d + 1}}\right) - a^{2} \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d + 1\right)} \sqrt{-\frac{c + d + 1}{c - d + 1}}\right) + a^{2} \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d - 1\right)} \sqrt{-\frac{c + d - 1}{c - d - 1}}\right) + a^{2} \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d - 1\right)} \sqrt{-\frac{c + d - 1}{c - d - 1}}\right) - {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 2 \, {\rm polylog}\left(3, \sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, {\rm polylog}\left(3, -\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, {\rm polylog}\left(3, \sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, {\rm polylog}\left(3, -\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{4 \, b^{2}}"," ",0,"1/4*(b^2*x^2*log(-((c + 1)*cosh(b*x + a) + d*sinh(b*x + a))/((c - 1)*cosh(b*x + a) + d*sinh(b*x + a))) - 2*b*x*dilog(sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*b*x*dilog(-sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*b*x*dilog(sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*b*x*dilog(-sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) - a^2*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) + 2*(c - d + 1)*sqrt(-(c + d + 1)/(c - d + 1))) - a^2*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) - 2*(c - d + 1)*sqrt(-(c + d + 1)/(c - d + 1))) + a^2*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) + 2*(c - d - 1)*sqrt(-(c + d - 1)/(c - d - 1))) + a^2*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) - 2*(c - d - 1)*sqrt(-(c + d - 1)/(c - d - 1))) - (b^2*x^2 - a^2)*log(sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b^2*x^2 - a^2)*log(-sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b^2*x^2 - a^2)*log(sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b^2*x^2 - a^2)*log(-sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 2*polylog(3, sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*polylog(3, -sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*polylog(3, sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*polylog(3, -sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
286,1,552,0,0.936828," ","integrate(arctanh(c+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b x \log\left(-\frac{{\left(c + 1\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{{\left(c - 1\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) + a \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d + 1\right)} \sqrt{-\frac{c + d + 1}{c - d + 1}}\right) + a \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d + 1\right)} \sqrt{-\frac{c + d + 1}{c - d + 1}}\right) - a \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d - 1\right)} \sqrt{-\frac{c + d - 1}{c - d - 1}}\right) - a \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d - 1\right)} \sqrt{-\frac{c + d - 1}{c - d - 1}}\right) - {\left(b x + a\right)} \log\left(\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b x + a\right)} \log\left(-\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b x + a\right)} \log\left(\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b x + a\right)} \log\left(-\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\rm Li}_2\left(\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - {\rm Li}_2\left(-\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\rm Li}_2\left(\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\rm Li}_2\left(-\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(b*x*log(-((c + 1)*cosh(b*x + a) + d*sinh(b*x + a))/((c - 1)*cosh(b*x + a) + d*sinh(b*x + a))) + a*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) + 2*(c - d + 1)*sqrt(-(c + d + 1)/(c - d + 1))) + a*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) - 2*(c - d + 1)*sqrt(-(c + d + 1)/(c - d + 1))) - a*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) + 2*(c - d - 1)*sqrt(-(c + d - 1)/(c - d - 1))) - a*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) - 2*(c - d - 1)*sqrt(-(c + d - 1)/(c - d - 1))) - (b*x + a)*log(sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b*x + a)*log(-sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b*x + a)*log(sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b*x + a)*log(-sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - dilog(sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - dilog(-sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + dilog(sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + dilog(-sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
287,0,0,0,0.532615," ","integrate(arctanh(c+d*tanh(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(d \tanh\left(b x + a\right) + c\right)}{x}, x\right)"," ",0,"integral(arctanh(d*tanh(b*x + a) + c)/x, x)","F",0
288,1,451,0,0.586233," ","integrate(x^3*arctanh(1+d+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{5} x^{5} + 5 \, b^{4} x^{4} \log\left(-\frac{{\left(d + 2\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 20 \, b^{3} x^{3} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 20 \, b^{3} x^{3} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 5 \, a^{4} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) + \sqrt{-4 \, d - 4}\right) - 5 \, a^{4} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) - \sqrt{-4 \, d - 4}\right) + 60 \, b^{2} x^{2} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 60 \, b^{2} x^{2} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 120 \, b x {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 120 \, b x {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 5 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 5 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 120 \, {\rm polylog}\left(5, \frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 120 \, {\rm polylog}\left(5, -\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{40 \, b^{4}}"," ",0,"1/40*(2*b^5*x^5 + 5*b^4*x^4*log(-((d + 2)*cosh(b*x + a) + d*sinh(b*x + a))/(d*cosh(b*x + a) + d*sinh(b*x + a))) - 20*b^3*x^3*dilog(1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 20*b^3*x^3*dilog(-1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 5*a^4*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) + sqrt(-4*d - 4)) - 5*a^4*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) - sqrt(-4*d - 4)) + 60*b^2*x^2*polylog(3, 1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) + 60*b^2*x^2*polylog(3, -1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 120*b*x*polylog(4, 1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 120*b*x*polylog(4, -1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 5*(b^4*x^4 - a^4)*log(1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 5*(b^4*x^4 - a^4)*log(-1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 120*polylog(5, 1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) + 120*polylog(5, -1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))))/b^4","C",0
289,1,382,0,0.839951," ","integrate(x^2*arctanh(1+d+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b^{4} x^{4} + 2 \, b^{3} x^{3} \log\left(-\frac{{\left(d + 2\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, a^{3} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) + \sqrt{-4 \, d - 4}\right) + 2 \, a^{3} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) - \sqrt{-4 \, d - 4}\right) + 12 \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 12 \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 12 \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 12 \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(b^4*x^4 + 2*b^3*x^3*log(-((d + 2)*cosh(b*x + a) + d*sinh(b*x + a))/(d*cosh(b*x + a) + d*sinh(b*x + a))) - 6*b^2*x^2*dilog(1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 6*b^2*x^2*dilog(-1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) + 2*a^3*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) + sqrt(-4*d - 4)) + 2*a^3*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) - sqrt(-4*d - 4)) + 12*b*x*polylog(3, 1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) + 12*b*x*polylog(3, -1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 2*(b^3*x^3 + a^3)*log(1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 2*(b^3*x^3 + a^3)*log(-1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 12*polylog(4, 1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 12*polylog(4, -1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
290,1,323,0,0.639594," ","integrate(x*arctanh(1+d+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} + 3 \, b^{2} x^{2} \log\left(-\frac{{\left(d + 2\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 6 \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 \, a^{2} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) + \sqrt{-4 \, d - 4}\right) - 3 \, a^{2} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) - \sqrt{-4 \, d - 4}\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 6 \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*b^3*x^3 + 3*b^2*x^2*log(-((d + 2)*cosh(b*x + a) + d*sinh(b*x + a))/(d*cosh(b*x + a) + d*sinh(b*x + a))) - 6*b*x*dilog(1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 6*b*x*dilog(-1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 3*a^2*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) + sqrt(-4*d - 4)) - 3*a^2*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) - sqrt(-4*d - 4)) - 3*(b^2*x^2 - a^2)*log(1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 3*(b^2*x^2 - a^2)*log(-1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 6*polylog(3, 1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) + 6*polylog(3, -1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
291,1,239,0,0.575868," ","integrate(arctanh(1+d+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} + b x \log\left(-\frac{{\left(d + 2\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) + a \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) + \sqrt{-4 \, d - 4}\right) + a \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) - \sqrt{-4 \, d - 4}\right) - {\left(b x + a\right)} \log\left(\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b x + a\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(b^2*x^2 + b*x*log(-((d + 2)*cosh(b*x + a) + d*sinh(b*x + a))/(d*cosh(b*x + a) + d*sinh(b*x + a))) + a*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) + sqrt(-4*d - 4)) + a*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) - sqrt(-4*d - 4)) - (b*x + a)*log(1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b*x + a)*log(-1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - dilog(1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - dilog(-1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
292,0,0,0,0.540799," ","integrate(arctanh(1+d+d*tanh(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(d \tanh\left(b x + a\right) + d + 1\right)}{x}, x\right)"," ",0,"integral(arctanh(d*tanh(b*x + a) + d + 1)/x, x)","F",0
293,1,424,0,0.631662," ","integrate(-x^3*arctanh(-1+d+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{5} x^{5} - 5 \, b^{4} x^{4} \log\left(-\frac{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{{\left(d - 2\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 20 \, b^{3} x^{3} {\rm Li}_2\left(\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 20 \, b^{3} x^{3} {\rm Li}_2\left(-\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 5 \, a^{4} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) + 2 \, \sqrt{d - 1}\right) - 5 \, a^{4} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) - 2 \, \sqrt{d - 1}\right) + 60 \, b^{2} x^{2} {\rm polylog}\left(3, \sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 60 \, b^{2} x^{2} {\rm polylog}\left(3, -\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 120 \, b x {\rm polylog}\left(4, \sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 120 \, b x {\rm polylog}\left(4, -\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 5 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 5 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(-\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 120 \, {\rm polylog}\left(5, \sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 120 \, {\rm polylog}\left(5, -\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{40 \, b^{4}}"," ",0,"1/40*(2*b^5*x^5 - 5*b^4*x^4*log(-(d*cosh(b*x + a) + d*sinh(b*x + a))/((d - 2)*cosh(b*x + a) + d*sinh(b*x + a))) - 20*b^3*x^3*dilog(sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 20*b^3*x^3*dilog(-sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 5*a^4*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) + 2*sqrt(d - 1)) - 5*a^4*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) - 2*sqrt(d - 1)) + 60*b^2*x^2*polylog(3, sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) + 60*b^2*x^2*polylog(3, -sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 120*b*x*polylog(4, sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 120*b*x*polylog(4, -sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 5*(b^4*x^4 - a^4)*log(sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 5*(b^4*x^4 - a^4)*log(-sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 120*polylog(5, sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) + 120*polylog(5, -sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))))/b^4","C",0
294,1,360,0,0.733830," ","integrate(-x^2*arctanh(-1+d+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b^{4} x^{4} - 2 \, b^{3} x^{3} \log\left(-\frac{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{{\left(d - 2\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(-\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, a^{3} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) + 2 \, \sqrt{d - 1}\right) + 2 \, a^{3} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) - 2 \, \sqrt{d - 1}\right) + 12 \, b x {\rm polylog}\left(3, \sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 12 \, b x {\rm polylog}\left(3, -\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 12 \, {\rm polylog}\left(4, \sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 12 \, {\rm polylog}\left(4, -\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(b^4*x^4 - 2*b^3*x^3*log(-(d*cosh(b*x + a) + d*sinh(b*x + a))/((d - 2)*cosh(b*x + a) + d*sinh(b*x + a))) - 6*b^2*x^2*dilog(sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 6*b^2*x^2*dilog(-sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) + 2*a^3*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) + 2*sqrt(d - 1)) + 2*a^3*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) - 2*sqrt(d - 1)) + 12*b*x*polylog(3, sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) + 12*b*x*polylog(3, -sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 2*(b^3*x^3 + a^3)*log(sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 2*(b^3*x^3 + a^3)*log(-sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 12*polylog(4, sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 12*polylog(4, -sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
295,1,306,0,0.558663," ","integrate(-x*arctanh(-1+d+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} - 3 \, b^{2} x^{2} \log\left(-\frac{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{{\left(d - 2\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 6 \, b x {\rm Li}_2\left(\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b x {\rm Li}_2\left(-\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 \, a^{2} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) + 2 \, \sqrt{d - 1}\right) - 3 \, a^{2} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) - 2 \, \sqrt{d - 1}\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 6 \, {\rm polylog}\left(3, \sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, {\rm polylog}\left(3, -\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*b^3*x^3 - 3*b^2*x^2*log(-(d*cosh(b*x + a) + d*sinh(b*x + a))/((d - 2)*cosh(b*x + a) + d*sinh(b*x + a))) - 6*b*x*dilog(sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 6*b*x*dilog(-sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 3*a^2*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) + 2*sqrt(d - 1)) - 3*a^2*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) - 2*sqrt(d - 1)) - 3*(b^2*x^2 - a^2)*log(sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 3*(b^2*x^2 - a^2)*log(-sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 6*polylog(3, sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) + 6*polylog(3, -sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
296,1,228,0,0.497131," ","integrate(-arctanh(-1+d+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} - b x \log\left(-\frac{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{{\left(d - 2\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) + a \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) + 2 \, \sqrt{d - 1}\right) + a \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) - 2 \, \sqrt{d - 1}\right) - {\left(b x + a\right)} \log\left(\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b x + a\right)} \log\left(-\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\rm Li}_2\left(\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - {\rm Li}_2\left(-\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(b^2*x^2 - b*x*log(-(d*cosh(b*x + a) + d*sinh(b*x + a))/((d - 2)*cosh(b*x + a) + d*sinh(b*x + a))) + a*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) + 2*sqrt(d - 1)) + a*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) - 2*sqrt(d - 1)) - (b*x + a)*log(sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b*x + a)*log(-sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - dilog(sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - dilog(-sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
297,0,0,0,0.450030," ","integrate(-arctanh(-1+d+d*tanh(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(d \tanh\left(b x + a\right) + d - 1\right)}{x}, x\right)"," ",0,"integral(-arctanh(d*tanh(b*x + a) + d - 1)/x, x)","F",0
298,1,880,0,0.916688," ","integrate(x^2*arctanh(c+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{b^{3} x^{3} \log\left(-\frac{d \cosh\left(b x + a\right) + {\left(c + 1\right)} \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + {\left(c - 1\right)} \sinh\left(b x + a\right)}\right) - 3 \, b^{2} x^{2} {\rm Li}_2\left(\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 \, b^{2} x^{2} {\rm Li}_2\left(-\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 3 \, b^{2} x^{2} {\rm Li}_2\left(\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 3 \, b^{2} x^{2} {\rm Li}_2\left(-\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + a^{3} \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d + 1\right)} \sqrt{\frac{c + d + 1}{c - d + 1}}\right) + a^{3} \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d + 1\right)} \sqrt{\frac{c + d + 1}{c - d + 1}}\right) - a^{3} \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d - 1\right)} \sqrt{\frac{c + d - 1}{c - d - 1}}\right) - a^{3} \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d - 1\right)} \sqrt{\frac{c + d - 1}{c - d - 1}}\right) + 6 \, b x {\rm polylog}\left(3, \sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, b x {\rm polylog}\left(3, -\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b x {\rm polylog}\left(3, \sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b x {\rm polylog}\left(3, -\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 6 \, {\rm polylog}\left(4, \sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, {\rm polylog}\left(4, -\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, {\rm polylog}\left(4, \sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, {\rm polylog}\left(4, -\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{6 \, b^{3}}"," ",0,"1/6*(b^3*x^3*log(-(d*cosh(b*x + a) + (c + 1)*sinh(b*x + a))/(d*cosh(b*x + a) + (c - 1)*sinh(b*x + a))) - 3*b^2*x^2*dilog(sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 3*b^2*x^2*dilog(-sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 3*b^2*x^2*dilog(sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + 3*b^2*x^2*dilog(-sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + a^3*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) + 2*(c - d + 1)*sqrt((c + d + 1)/(c - d + 1))) + a^3*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) - 2*(c - d + 1)*sqrt((c + d + 1)/(c - d + 1))) - a^3*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) + 2*(c - d - 1)*sqrt((c + d - 1)/(c - d - 1))) - a^3*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) - 2*(c - d - 1)*sqrt((c + d - 1)/(c - d - 1))) + 6*b*x*polylog(3, sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*b*x*polylog(3, -sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*b*x*polylog(3, sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*b*x*polylog(3, -sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) - (b^3*x^3 + a^3)*log(sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b^3*x^3 + a^3)*log(-sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b^3*x^3 + a^3)*log(sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b^3*x^3 + a^3)*log(-sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 6*polylog(4, sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*polylog(4, -sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*polylog(4, sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*polylog(4, -sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
299,1,730,0,0.778349," ","integrate(x*arctanh(c+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} \log\left(-\frac{d \cosh\left(b x + a\right) + {\left(c + 1\right)} \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + {\left(c - 1\right)} \sinh\left(b x + a\right)}\right) - 2 \, b x {\rm Li}_2\left(\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, b x {\rm Li}_2\left(-\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, b x {\rm Li}_2\left(\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, b x {\rm Li}_2\left(-\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - a^{2} \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d + 1\right)} \sqrt{\frac{c + d + 1}{c - d + 1}}\right) - a^{2} \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d + 1\right)} \sqrt{\frac{c + d + 1}{c - d + 1}}\right) + a^{2} \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d - 1\right)} \sqrt{\frac{c + d - 1}{c - d - 1}}\right) + a^{2} \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d - 1\right)} \sqrt{\frac{c + d - 1}{c - d - 1}}\right) - {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 2 \, {\rm polylog}\left(3, \sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, {\rm polylog}\left(3, -\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, {\rm polylog}\left(3, \sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, {\rm polylog}\left(3, -\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{4 \, b^{2}}"," ",0,"1/4*(b^2*x^2*log(-(d*cosh(b*x + a) + (c + 1)*sinh(b*x + a))/(d*cosh(b*x + a) + (c - 1)*sinh(b*x + a))) - 2*b*x*dilog(sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*b*x*dilog(-sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*b*x*dilog(sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*b*x*dilog(-sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) - a^2*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) + 2*(c - d + 1)*sqrt((c + d + 1)/(c - d + 1))) - a^2*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) - 2*(c - d + 1)*sqrt((c + d + 1)/(c - d + 1))) + a^2*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) + 2*(c - d - 1)*sqrt((c + d - 1)/(c - d - 1))) + a^2*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) - 2*(c - d - 1)*sqrt((c + d - 1)/(c - d - 1))) - (b^2*x^2 - a^2)*log(sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b^2*x^2 - a^2)*log(-sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b^2*x^2 - a^2)*log(sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b^2*x^2 - a^2)*log(-sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 2*polylog(3, sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*polylog(3, -sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*polylog(3, sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*polylog(3, -sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
300,1,540,0,0.468603," ","integrate(arctanh(c+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{b x \log\left(-\frac{d \cosh\left(b x + a\right) + {\left(c + 1\right)} \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + {\left(c - 1\right)} \sinh\left(b x + a\right)}\right) + a \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d + 1\right)} \sqrt{\frac{c + d + 1}{c - d + 1}}\right) + a \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d + 1\right)} \sqrt{\frac{c + d + 1}{c - d + 1}}\right) - a \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d - 1\right)} \sqrt{\frac{c + d - 1}{c - d - 1}}\right) - a \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d - 1\right)} \sqrt{\frac{c + d - 1}{c - d - 1}}\right) - {\left(b x + a\right)} \log\left(\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b x + a\right)} \log\left(-\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b x + a\right)} \log\left(\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b x + a\right)} \log\left(-\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\rm Li}_2\left(\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - {\rm Li}_2\left(-\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\rm Li}_2\left(\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\rm Li}_2\left(-\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(b*x*log(-(d*cosh(b*x + a) + (c + 1)*sinh(b*x + a))/(d*cosh(b*x + a) + (c - 1)*sinh(b*x + a))) + a*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) + 2*(c - d + 1)*sqrt((c + d + 1)/(c - d + 1))) + a*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) - 2*(c - d + 1)*sqrt((c + d + 1)/(c - d + 1))) - a*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) + 2*(c - d - 1)*sqrt((c + d - 1)/(c - d - 1))) - a*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) - 2*(c - d - 1)*sqrt((c + d - 1)/(c - d - 1))) - (b*x + a)*log(sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b*x + a)*log(-sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b*x + a)*log(sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b*x + a)*log(-sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - dilog(sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - dilog(-sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + dilog(sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + dilog(-sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
301,0,0,0,0.733559," ","integrate(arctanh(c+d*coth(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(d \coth\left(b x + a\right) + c\right)}{x}, x\right)"," ",0,"integral(arctanh(d*coth(b*x + a) + c)/x, x)","F",0
302,1,424,0,1.527572," ","integrate(x^3*arctanh(1+d+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{5} x^{5} + 5 \, b^{4} x^{4} \log\left(-\frac{d \cosh\left(b x + a\right) + {\left(d + 2\right)} \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 20 \, b^{3} x^{3} {\rm Li}_2\left(\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 20 \, b^{3} x^{3} {\rm Li}_2\left(-\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 5 \, a^{4} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) + 2 \, \sqrt{d + 1}\right) - 5 \, a^{4} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) - 2 \, \sqrt{d + 1}\right) + 60 \, b^{2} x^{2} {\rm polylog}\left(3, \sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 60 \, b^{2} x^{2} {\rm polylog}\left(3, -\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 120 \, b x {\rm polylog}\left(4, \sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 120 \, b x {\rm polylog}\left(4, -\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 5 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 5 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(-\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 120 \, {\rm polylog}\left(5, \sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 120 \, {\rm polylog}\left(5, -\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{40 \, b^{4}}"," ",0,"1/40*(2*b^5*x^5 + 5*b^4*x^4*log(-(d*cosh(b*x + a) + (d + 2)*sinh(b*x + a))/(d*cosh(b*x + a) + d*sinh(b*x + a))) - 20*b^3*x^3*dilog(sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 20*b^3*x^3*dilog(-sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 5*a^4*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) + 2*sqrt(d + 1)) - 5*a^4*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) - 2*sqrt(d + 1)) + 60*b^2*x^2*polylog(3, sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) + 60*b^2*x^2*polylog(3, -sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 120*b*x*polylog(4, sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 120*b*x*polylog(4, -sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 5*(b^4*x^4 - a^4)*log(sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 5*(b^4*x^4 - a^4)*log(-sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 120*polylog(5, sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) + 120*polylog(5, -sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))))/b^4","C",0
303,1,360,0,0.995376," ","integrate(x^2*arctanh(1+d+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{b^{4} x^{4} + 2 \, b^{3} x^{3} \log\left(-\frac{d \cosh\left(b x + a\right) + {\left(d + 2\right)} \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(-\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, a^{3} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) + 2 \, \sqrt{d + 1}\right) + 2 \, a^{3} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) - 2 \, \sqrt{d + 1}\right) + 12 \, b x {\rm polylog}\left(3, \sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 12 \, b x {\rm polylog}\left(3, -\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 12 \, {\rm polylog}\left(4, \sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 12 \, {\rm polylog}\left(4, -\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(b^4*x^4 + 2*b^3*x^3*log(-(d*cosh(b*x + a) + (d + 2)*sinh(b*x + a))/(d*cosh(b*x + a) + d*sinh(b*x + a))) - 6*b^2*x^2*dilog(sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 6*b^2*x^2*dilog(-sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) + 2*a^3*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) + 2*sqrt(d + 1)) + 2*a^3*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) - 2*sqrt(d + 1)) + 12*b*x*polylog(3, sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) + 12*b*x*polylog(3, -sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 2*(b^3*x^3 + a^3)*log(sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 2*(b^3*x^3 + a^3)*log(-sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 12*polylog(4, sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 12*polylog(4, -sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
304,1,306,0,0.583062," ","integrate(x*arctanh(1+d+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} + 3 \, b^{2} x^{2} \log\left(-\frac{d \cosh\left(b x + a\right) + {\left(d + 2\right)} \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 6 \, b x {\rm Li}_2\left(\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b x {\rm Li}_2\left(-\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 \, a^{2} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) + 2 \, \sqrt{d + 1}\right) - 3 \, a^{2} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) - 2 \, \sqrt{d + 1}\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 6 \, {\rm polylog}\left(3, \sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, {\rm polylog}\left(3, -\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*b^3*x^3 + 3*b^2*x^2*log(-(d*cosh(b*x + a) + (d + 2)*sinh(b*x + a))/(d*cosh(b*x + a) + d*sinh(b*x + a))) - 6*b*x*dilog(sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 6*b*x*dilog(-sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 3*a^2*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) + 2*sqrt(d + 1)) - 3*a^2*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) - 2*sqrt(d + 1)) - 3*(b^2*x^2 - a^2)*log(sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 3*(b^2*x^2 - a^2)*log(-sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 6*polylog(3, sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) + 6*polylog(3, -sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
305,1,227,0,0.486179," ","integrate(arctanh(1+d+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} + b x \log\left(-\frac{d \cosh\left(b x + a\right) + {\left(d + 2\right)} \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) + a \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) + 2 \, \sqrt{d + 1}\right) + a \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) - 2 \, \sqrt{d + 1}\right) - {\left(b x + a\right)} \log\left(\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b x + a\right)} \log\left(-\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\rm Li}_2\left(\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - {\rm Li}_2\left(-\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(b^2*x^2 + b*x*log(-(d*cosh(b*x + a) + (d + 2)*sinh(b*x + a))/(d*cosh(b*x + a) + d*sinh(b*x + a))) + a*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) + 2*sqrt(d + 1)) + a*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) - 2*sqrt(d + 1)) - (b*x + a)*log(sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b*x + a)*log(-sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - dilog(sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - dilog(-sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
306,0,0,0,0.790256," ","integrate(arctanh(1+d+d*coth(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(d \coth\left(b x + a\right) + d + 1\right)}{x}, x\right)"," ",0,"integral(arctanh(d*coth(b*x + a) + d + 1)/x, x)","F",0
307,1,451,0,0.528784," ","integrate(-x^3*arctanh(-1+d+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{5} x^{5} - 5 \, b^{4} x^{4} \log\left(-\frac{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + {\left(d - 2\right)} \sinh\left(b x + a\right)}\right) - 20 \, b^{3} x^{3} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 20 \, b^{3} x^{3} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 5 \, a^{4} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) + \sqrt{-4 \, d + 4}\right) - 5 \, a^{4} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) - \sqrt{-4 \, d + 4}\right) + 60 \, b^{2} x^{2} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 60 \, b^{2} x^{2} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 120 \, b x {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 120 \, b x {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 5 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 5 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 120 \, {\rm polylog}\left(5, \frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 120 \, {\rm polylog}\left(5, -\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{40 \, b^{4}}"," ",0,"1/40*(2*b^5*x^5 - 5*b^4*x^4*log(-(d*cosh(b*x + a) + d*sinh(b*x + a))/(d*cosh(b*x + a) + (d - 2)*sinh(b*x + a))) - 20*b^3*x^3*dilog(1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 20*b^3*x^3*dilog(-1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 5*a^4*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) + sqrt(-4*d + 4)) - 5*a^4*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) - sqrt(-4*d + 4)) + 60*b^2*x^2*polylog(3, 1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) + 60*b^2*x^2*polylog(3, -1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 120*b*x*polylog(4, 1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 120*b*x*polylog(4, -1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 5*(b^4*x^4 - a^4)*log(1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 5*(b^4*x^4 - a^4)*log(-1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 120*polylog(5, 1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) + 120*polylog(5, -1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))))/b^4","C",0
308,1,382,0,0.530523," ","integrate(-x^2*arctanh(-1+d+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{b^{4} x^{4} - 2 \, b^{3} x^{3} \log\left(-\frac{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + {\left(d - 2\right)} \sinh\left(b x + a\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, a^{3} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) + \sqrt{-4 \, d + 4}\right) + 2 \, a^{3} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) - \sqrt{-4 \, d + 4}\right) + 12 \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 12 \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 12 \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 12 \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(b^4*x^4 - 2*b^3*x^3*log(-(d*cosh(b*x + a) + d*sinh(b*x + a))/(d*cosh(b*x + a) + (d - 2)*sinh(b*x + a))) - 6*b^2*x^2*dilog(1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 6*b^2*x^2*dilog(-1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) + 2*a^3*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) + sqrt(-4*d + 4)) + 2*a^3*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) - sqrt(-4*d + 4)) + 12*b*x*polylog(3, 1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) + 12*b*x*polylog(3, -1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 2*(b^3*x^3 + a^3)*log(1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 2*(b^3*x^3 + a^3)*log(-1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 12*polylog(4, 1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 12*polylog(4, -1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
309,1,323,0,0.634213," ","integrate(-x*arctanh(-1+d+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} - 3 \, b^{2} x^{2} \log\left(-\frac{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + {\left(d - 2\right)} \sinh\left(b x + a\right)}\right) - 6 \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 \, a^{2} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) + \sqrt{-4 \, d + 4}\right) - 3 \, a^{2} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) - \sqrt{-4 \, d + 4}\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 6 \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*b^3*x^3 - 3*b^2*x^2*log(-(d*cosh(b*x + a) + d*sinh(b*x + a))/(d*cosh(b*x + a) + (d - 2)*sinh(b*x + a))) - 6*b*x*dilog(1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 6*b*x*dilog(-1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 3*a^2*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) + sqrt(-4*d + 4)) - 3*a^2*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) - sqrt(-4*d + 4)) - 3*(b^2*x^2 - a^2)*log(1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 3*(b^2*x^2 - a^2)*log(-1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 6*polylog(3, 1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) + 6*polylog(3, -1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
310,1,240,0,0.539626," ","integrate(-arctanh(-1+d+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} - b x \log\left(-\frac{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + {\left(d - 2\right)} \sinh\left(b x + a\right)}\right) + a \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) + \sqrt{-4 \, d + 4}\right) + a \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) - \sqrt{-4 \, d + 4}\right) - {\left(b x + a\right)} \log\left(\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b x + a\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(b^2*x^2 - b*x*log(-(d*cosh(b*x + a) + d*sinh(b*x + a))/(d*cosh(b*x + a) + (d - 2)*sinh(b*x + a))) + a*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) + sqrt(-4*d + 4)) + a*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) - sqrt(-4*d + 4)) - (b*x + a)*log(1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b*x + a)*log(-1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - dilog(1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - dilog(-1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
311,0,0,0,0.388026," ","integrate(-arctanh(-1+d+d*coth(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(d \coth\left(b x + a\right) + d - 1\right)}{x}, x\right)"," ",0,"integral(-arctanh(d*coth(b*x + a) + d - 1)/x, x)","F",0
312,1,1809,0,1.236602," ","integrate((f*x+e)^3*arctanh(tan(b*x+a)),x, algorithm=""fricas"")","-\frac{3 \, f^{3} {\rm polylog}\left(5, \frac{i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) - 3 \, f^{3} {\rm polylog}\left(5, \frac{i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) + 3 \, f^{3} {\rm polylog}\left(5, \frac{-i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) - 3 \, f^{3} {\rm polylog}\left(5, \frac{-i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) - {\left(4 i \, b^{3} f^{3} x^{3} + 12 i \, b^{3} e f^{2} x^{2} + 12 i \, b^{3} e^{2} f x + 4 i \, b^{3} e^{3}\right)} {\rm Li}_2\left(-\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - {\left(4 i \, b^{3} f^{3} x^{3} + 12 i \, b^{3} e f^{2} x^{2} + 12 i \, b^{3} e^{2} f x + 4 i \, b^{3} e^{3}\right)} {\rm Li}_2\left(-\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - {\left(-4 i \, b^{3} f^{3} x^{3} - 12 i \, b^{3} e f^{2} x^{2} - 12 i \, b^{3} e^{2} f x - 4 i \, b^{3} e^{3}\right)} {\rm Li}_2\left(-\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - {\left(-4 i \, b^{3} f^{3} x^{3} - 12 i \, b^{3} e f^{2} x^{2} - 12 i \, b^{3} e^{2} f x - 4 i \, b^{3} e^{3}\right)} {\rm Li}_2\left(-\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + 2 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x + 4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) + i - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) + i - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x + 4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x + 4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x + 4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\frac{\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\frac{\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x\right)} \log\left(-\frac{\tan\left(b x + a\right) + 1}{\tan\left(b x + a\right) - 1}\right) - {\left(6 i \, b f^{3} x + 6 i \, b e f^{2}\right)} {\rm polylog}\left(4, \frac{i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) - {\left(6 i \, b f^{3} x + 6 i \, b e f^{2}\right)} {\rm polylog}\left(4, \frac{i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) - {\left(-6 i \, b f^{3} x - 6 i \, b e f^{2}\right)} {\rm polylog}\left(4, \frac{-i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) - {\left(-6 i \, b f^{3} x - 6 i \, b e f^{2}\right)} {\rm polylog}\left(4, \frac{-i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 \, {\left(b^{2} f^{3} x^{2} + 2 \, b^{2} e f^{2} x + b^{2} e^{2} f\right)} {\rm polylog}\left(3, \frac{i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) + 6 \, {\left(b^{2} f^{3} x^{2} + 2 \, b^{2} e f^{2} x + b^{2} e^{2} f\right)} {\rm polylog}\left(3, \frac{i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 \, {\left(b^{2} f^{3} x^{2} + 2 \, b^{2} e f^{2} x + b^{2} e^{2} f\right)} {\rm polylog}\left(3, \frac{-i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) + 6 \, {\left(b^{2} f^{3} x^{2} + 2 \, b^{2} e f^{2} x + b^{2} e^{2} f\right)} {\rm polylog}\left(3, \frac{-i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right)}{32 \, b^{4}}"," ",0,"-1/32*(3*f^3*polylog(5, (I*tan(b*x + a)^2 + 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) - 3*f^3*polylog(5, (I*tan(b*x + a)^2 - 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) + 3*f^3*polylog(5, (-I*tan(b*x + a)^2 + 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) - 3*f^3*polylog(5, (-I*tan(b*x + a)^2 - 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) - (4*I*b^3*f^3*x^3 + 12*I*b^3*e*f^2*x^2 + 12*I*b^3*e^2*f*x + 4*I*b^3*e^3)*dilog(-((I + 1)*tan(b*x + a)^2 + 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1) + 1) - (4*I*b^3*f^3*x^3 + 12*I*b^3*e*f^2*x^2 + 12*I*b^3*e^2*f*x + 4*I*b^3*e^3)*dilog(-((I + 1)*tan(b*x + a)^2 - 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1) + 1) - (-4*I*b^3*f^3*x^3 - 12*I*b^3*e*f^2*x^2 - 12*I*b^3*e^2*f*x - 4*I*b^3*e^3)*dilog(-(-(I - 1)*tan(b*x + a)^2 + 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1) + 1) - (-4*I*b^3*f^3*x^3 - 12*I*b^3*e*f^2*x^2 - 12*I*b^3*e^2*f*x - 4*I*b^3*e^3)*dilog(-(-(I - 1)*tan(b*x + a)^2 - 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1) + 1) + 2*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x + 4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(((I + 1)*tan(b*x + a)^2 + 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1)) - 2*(4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(((I + 1)*tan(b*x + a)^2 + 2*I*tan(b*x + a) + I - 1)/(tan(b*x + a)^2 + 1)) + 2*(4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(((I + 1)*tan(b*x + a)^2 - 2*I*tan(b*x + a) + I - 1)/(tan(b*x + a)^2 + 1)) - 2*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x + 4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(((I + 1)*tan(b*x + a)^2 - 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1)) + 2*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x + 4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log((-(I - 1)*tan(b*x + a)^2 + 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) - 2*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x + 4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log((-(I - 1)*tan(b*x + a)^2 - 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) - 2*(4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(((I - 1)*tan(b*x + a)^2 + 2*I*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 2*(4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(((I - 1)*tan(b*x + a)^2 - 2*I*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) - 4*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x)*log(-(tan(b*x + a) + 1)/(tan(b*x + a) - 1)) - (6*I*b*f^3*x + 6*I*b*e*f^2)*polylog(4, (I*tan(b*x + a)^2 + 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) - (6*I*b*f^3*x + 6*I*b*e*f^2)*polylog(4, (I*tan(b*x + a)^2 - 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) - (-6*I*b*f^3*x - 6*I*b*e*f^2)*polylog(4, (-I*tan(b*x + a)^2 + 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) - (-6*I*b*f^3*x - 6*I*b*e*f^2)*polylog(4, (-I*tan(b*x + a)^2 - 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) - 6*(b^2*f^3*x^2 + 2*b^2*e*f^2*x + b^2*e^2*f)*polylog(3, (I*tan(b*x + a)^2 + 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) + 6*(b^2*f^3*x^2 + 2*b^2*e*f^2*x + b^2*e^2*f)*polylog(3, (I*tan(b*x + a)^2 - 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) - 6*(b^2*f^3*x^2 + 2*b^2*e*f^2*x + b^2*e^2*f)*polylog(3, (-I*tan(b*x + a)^2 + 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) + 6*(b^2*f^3*x^2 + 2*b^2*e*f^2*x + b^2*e^2*f)*polylog(3, (-I*tan(b*x + a)^2 - 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)))/b^4","C",0
313,1,1279,0,0.613050," ","integrate((f*x+e)^2*arctanh(tan(b*x+a)),x, algorithm=""fricas"")","\frac{3 i \, f^{2} {\rm polylog}\left(4, \frac{i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) + 3 i \, f^{2} {\rm polylog}\left(4, \frac{i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) - 3 i \, f^{2} {\rm polylog}\left(4, \frac{-i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) - 3 i \, f^{2} {\rm polylog}\left(4, \frac{-i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) + {\left(6 i \, b^{2} f^{2} x^{2} + 12 i \, b^{2} e f x + 6 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + {\left(6 i \, b^{2} f^{2} x^{2} + 12 i \, b^{2} e f x + 6 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + {\left(-6 i \, b^{2} f^{2} x^{2} - 12 i \, b^{2} e f x - 6 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + {\left(-6 i \, b^{2} f^{2} x^{2} - 12 i \, b^{2} e f x - 6 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - 4 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x + 3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 \, {\left(3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) + i - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 \, {\left(3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) + i - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x + 3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x + 3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x + 3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 \, {\left(3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\frac{\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 \, {\left(3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\frac{\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 8 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x\right)} \log\left(-\frac{\tan\left(b x + a\right) + 1}{\tan\left(b x + a\right) - 1}\right) + 6 \, {\left(b f^{2} x + b e f\right)} {\rm polylog}\left(3, \frac{i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 \, {\left(b f^{2} x + b e f\right)} {\rm polylog}\left(3, \frac{i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) + 6 \, {\left(b f^{2} x + b e f\right)} {\rm polylog}\left(3, \frac{-i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 \, {\left(b f^{2} x + b e f\right)} {\rm polylog}\left(3, \frac{-i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right)}{48 \, b^{3}}"," ",0,"1/48*(3*I*f^2*polylog(4, (I*tan(b*x + a)^2 + 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) + 3*I*f^2*polylog(4, (I*tan(b*x + a)^2 - 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) - 3*I*f^2*polylog(4, (-I*tan(b*x + a)^2 + 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) - 3*I*f^2*polylog(4, (-I*tan(b*x + a)^2 - 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) + (6*I*b^2*f^2*x^2 + 12*I*b^2*e*f*x + 6*I*b^2*e^2)*dilog(-((I + 1)*tan(b*x + a)^2 + 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1) + 1) + (6*I*b^2*f^2*x^2 + 12*I*b^2*e*f*x + 6*I*b^2*e^2)*dilog(-((I + 1)*tan(b*x + a)^2 - 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1) + 1) + (-6*I*b^2*f^2*x^2 - 12*I*b^2*e*f*x - 6*I*b^2*e^2)*dilog(-(-(I - 1)*tan(b*x + a)^2 + 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1) + 1) + (-6*I*b^2*f^2*x^2 - 12*I*b^2*e*f*x - 6*I*b^2*e^2)*dilog(-(-(I - 1)*tan(b*x + a)^2 - 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1) + 1) - 4*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x + 3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(((I + 1)*tan(b*x + a)^2 + 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1)) + 4*(3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(((I + 1)*tan(b*x + a)^2 + 2*I*tan(b*x + a) + I - 1)/(tan(b*x + a)^2 + 1)) - 4*(3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(((I + 1)*tan(b*x + a)^2 - 2*I*tan(b*x + a) + I - 1)/(tan(b*x + a)^2 + 1)) + 4*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x + 3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(((I + 1)*tan(b*x + a)^2 - 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1)) - 4*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x + 3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log((-(I - 1)*tan(b*x + a)^2 + 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 4*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x + 3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log((-(I - 1)*tan(b*x + a)^2 - 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 4*(3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(((I - 1)*tan(b*x + a)^2 + 2*I*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) - 4*(3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(((I - 1)*tan(b*x + a)^2 - 2*I*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 8*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x)*log(-(tan(b*x + a) + 1)/(tan(b*x + a) - 1)) + 6*(b*f^2*x + b*e*f)*polylog(3, (I*tan(b*x + a)^2 + 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) - 6*(b*f^2*x + b*e*f)*polylog(3, (I*tan(b*x + a)^2 - 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) + 6*(b*f^2*x + b*e*f)*polylog(3, (-I*tan(b*x + a)^2 + 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) - 6*(b*f^2*x + b*e*f)*polylog(3, (-I*tan(b*x + a)^2 - 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)))/b^3","C",0
314,1,831,0,0.770992," ","integrate((f*x+e)*arctanh(tan(b*x+a)),x, algorithm=""fricas"")","\frac{{\left(2 i \, b f x + 2 i \, b e\right)} {\rm Li}_2\left(-\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + {\left(2 i \, b f x + 2 i \, b e\right)} {\rm Li}_2\left(-\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + {\left(-2 i \, b f x - 2 i \, b e\right)} {\rm Li}_2\left(-\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + {\left(-2 i \, b f x - 2 i \, b e\right)} {\rm Li}_2\left(-\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - 2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x + 2 \, a b e - a^{2} f\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(2 \, a b e - a^{2} f\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) + i - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(2 \, a b e - a^{2} f\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) + i - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x + 2 \, a b e - a^{2} f\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x + 2 \, a b e - a^{2} f\right)} \log\left(\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x + 2 \, a b e - a^{2} f\right)} \log\left(\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(2 \, a b e - a^{2} f\right)} \log\left(\frac{\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(2 \, a b e - a^{2} f\right)} \log\left(\frac{\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x\right)} \log\left(-\frac{\tan\left(b x + a\right) + 1}{\tan\left(b x + a\right) - 1}\right) + f {\rm polylog}\left(3, \frac{i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) - f {\rm polylog}\left(3, \frac{i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) + f {\rm polylog}\left(3, \frac{-i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) - f {\rm polylog}\left(3, \frac{-i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right)}{16 \, b^{2}}"," ",0,"1/16*((2*I*b*f*x + 2*I*b*e)*dilog(-((I + 1)*tan(b*x + a)^2 + 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1) + 1) + (2*I*b*f*x + 2*I*b*e)*dilog(-((I + 1)*tan(b*x + a)^2 - 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1) + 1) + (-2*I*b*f*x - 2*I*b*e)*dilog(-(-(I - 1)*tan(b*x + a)^2 + 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1) + 1) + (-2*I*b*f*x - 2*I*b*e)*dilog(-(-(I - 1)*tan(b*x + a)^2 - 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1) + 1) - 2*(b^2*f*x^2 + 2*b^2*e*x + 2*a*b*e - a^2*f)*log(((I + 1)*tan(b*x + a)^2 + 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1)) + 2*(2*a*b*e - a^2*f)*log(((I + 1)*tan(b*x + a)^2 + 2*I*tan(b*x + a) + I - 1)/(tan(b*x + a)^2 + 1)) - 2*(2*a*b*e - a^2*f)*log(((I + 1)*tan(b*x + a)^2 - 2*I*tan(b*x + a) + I - 1)/(tan(b*x + a)^2 + 1)) + 2*(b^2*f*x^2 + 2*b^2*e*x + 2*a*b*e - a^2*f)*log(((I + 1)*tan(b*x + a)^2 - 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1)) - 2*(b^2*f*x^2 + 2*b^2*e*x + 2*a*b*e - a^2*f)*log((-(I - 1)*tan(b*x + a)^2 + 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 2*(b^2*f*x^2 + 2*b^2*e*x + 2*a*b*e - a^2*f)*log((-(I - 1)*tan(b*x + a)^2 - 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 2*(2*a*b*e - a^2*f)*log(((I - 1)*tan(b*x + a)^2 + 2*I*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) - 2*(2*a*b*e - a^2*f)*log(((I - 1)*tan(b*x + a)^2 - 2*I*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 4*(b^2*f*x^2 + 2*b^2*e*x)*log(-(tan(b*x + a) + 1)/(tan(b*x + a) - 1)) + f*polylog(3, (I*tan(b*x + a)^2 + 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) - f*polylog(3, (I*tan(b*x + a)^2 - 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) + f*polylog(3, (-I*tan(b*x + a)^2 + 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) - f*polylog(3, (-I*tan(b*x + a)^2 - 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)))/b^2","C",0
315,1,499,0,0.694116," ","integrate(arctanh(tan(b*x+a)),x, algorithm=""fricas"")","\frac{4 \, b x \log\left(-\frac{\tan\left(b x + a\right) + 1}{\tan\left(b x + a\right) - 1}\right) - 2 \, {\left(b x + a\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, a \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) + i - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, a \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) + i - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(b x + a\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(b x + a\right)} \log\left(\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(b x + a\right)} \log\left(\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, a \log\left(\frac{\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, a \log\left(\frac{\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + i \, {\rm Li}_2\left(-\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + i \, {\rm Li}_2\left(-\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - i \, {\rm Li}_2\left(-\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - i \, {\rm Li}_2\left(-\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right)}{8 \, b}"," ",0,"1/8*(4*b*x*log(-(tan(b*x + a) + 1)/(tan(b*x + a) - 1)) - 2*(b*x + a)*log(((I + 1)*tan(b*x + a)^2 + 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1)) + 2*a*log(((I + 1)*tan(b*x + a)^2 + 2*I*tan(b*x + a) + I - 1)/(tan(b*x + a)^2 + 1)) - 2*a*log(((I + 1)*tan(b*x + a)^2 - 2*I*tan(b*x + a) + I - 1)/(tan(b*x + a)^2 + 1)) + 2*(b*x + a)*log(((I + 1)*tan(b*x + a)^2 - 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1)) - 2*(b*x + a)*log((-(I - 1)*tan(b*x + a)^2 + 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 2*(b*x + a)*log((-(I - 1)*tan(b*x + a)^2 - 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 2*a*log(((I - 1)*tan(b*x + a)^2 + 2*I*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) - 2*a*log(((I - 1)*tan(b*x + a)^2 - 2*I*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + I*dilog(-((I + 1)*tan(b*x + a)^2 + 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1) + 1) + I*dilog(-((I + 1)*tan(b*x + a)^2 - 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1) + 1) - I*dilog(-(-(I - 1)*tan(b*x + a)^2 + 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1) + 1) - I*dilog(-(-(I - 1)*tan(b*x + a)^2 - 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1) + 1))/b","B",0
316,0,0,0,0.634232," ","integrate(arctanh(tan(b*x+a))/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(\tan\left(b x + a\right)\right)}{f x + e}, x\right)"," ",0,"integral(arctanh(tan(b*x + a))/(f*x + e), x)","F",0
317,1,2161,0,0.754236," ","integrate(x^2*arctanh(c+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{8 \, b^{3} x^{3} \log\left(-\frac{d \tan\left(b x + a\right) + c + 1}{d \tan\left(b x + a\right) + c - 1}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{{\left(2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} - 2 i \, {\left(c + 1\right)} d + {\left(2 i \, c^{2} + 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1} + 1\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{{\left(-2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} + 2 i \, {\left(c + 1\right)} d + {\left(-2 i \, c^{2} + 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1} + 1\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{2 \, {\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, {\left(c - 1\right)} d - {\left(-2 i \, c^{2} + 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1} + 1\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{2 \, {\left(-i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, {\left(c - 1\right)} d - {\left(2 i \, c^{2} + 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1} + 1\right) + 4 \, a^{3} \log\left(\frac{{\left(i \, {\left(c + 1\right)} d + d^{2}\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, {\left(c + 1\right)} d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 \, a^{3} \log\left(\frac{{\left(i \, {\left(c + 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, {\left(c + 1\right)} d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \tan\left(b x + a\right) + 2 \, c + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 \, a^{3} \log\left(\frac{{\left(i \, {\left(c - 1\right)} d + d^{2}\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, {\left(c - 1\right)} d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 \, a^{3} \log\left(\frac{{\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, {\left(c - 1\right)} d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \tan\left(b x + a\right) - 2 \, c + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, {\left(c + 1\right)} d + d^{2} + {\left(2 i \, c^{2} - 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) - 6 \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, {\left(c + 1\right)} d + d^{2} + {\left(-2 i \, c^{2} - 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) + 6 \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, {\left(c - 1\right)} d + d^{2} + {\left(2 i \, c^{2} - 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) + 6 \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, {\left(c - 1\right)} d + d^{2} + {\left(-2 i \, c^{2} - 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) - 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{{\left(2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} - 2 i \, {\left(c + 1\right)} d + {\left(2 i \, c^{2} + 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) - 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{{\left(-2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} + 2 i \, {\left(c + 1\right)} d + {\left(-2 i \, c^{2} + 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) + 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\frac{2 \, {\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, {\left(c - 1\right)} d - {\left(-2 i \, c^{2} + 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) + 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\frac{2 \, {\left(-i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, {\left(c - 1\right)} d - {\left(2 i \, c^{2} + 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) + 3 i \, {\rm polylog}\left(4, \frac{{\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, {\left(c + 1\right)} d + d^{2} + {\left(2 i \, c^{2} - 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) - 3 i \, {\rm polylog}\left(4, \frac{{\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, {\left(c + 1\right)} d + d^{2} + {\left(-2 i \, c^{2} - 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) - 3 i \, {\rm polylog}\left(4, \frac{{\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, {\left(c - 1\right)} d + d^{2} + {\left(2 i \, c^{2} - 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) + 3 i \, {\rm polylog}\left(4, \frac{{\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, {\left(c - 1\right)} d + d^{2} + {\left(-2 i \, c^{2} - 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right)}{48 \, b^{3}}"," ",0,"1/48*(8*b^3*x^3*log(-(d*tan(b*x + a) + c + 1)/(d*tan(b*x + a) + c - 1)) + 6*I*b^2*x^2*dilog(-((2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 - 2*I*(c + 1)*d + (2*I*c^2 + 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1) + 1) - 6*I*b^2*x^2*dilog(-((-2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 + 2*I*(c + 1)*d + (-2*I*c^2 + 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1) + 1) + 6*I*b^2*x^2*dilog((2*(I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 - 2*I*(c - 1)*d - (-2*I*c^2 + 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1) + 1) - 6*I*b^2*x^2*dilog((2*(-I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 + 2*I*(c - 1)*d - (2*I*c^2 + 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1) + 1) + 4*a^3*log(((I*(c + 1)*d + d^2)*tan(b*x + a)^2 - c^2 + I*(c + 1)*d + (I*c^2 + I*d^2 + 2*I*c + I)*tan(b*x + a) - 2*c - 1)/(tan(b*x + a)^2 + 1)) + 4*a^3*log(((I*(c + 1)*d - d^2)*tan(b*x + a)^2 + c^2 + I*(c + 1)*d + (I*c^2 + I*d^2 + 2*I*c + I)*tan(b*x + a) + 2*c + 1)/(tan(b*x + a)^2 + 1)) - 4*a^3*log(((I*(c - 1)*d + d^2)*tan(b*x + a)^2 - c^2 + I*(c - 1)*d + (I*c^2 + I*d^2 - 2*I*c + I)*tan(b*x + a) + 2*c - 1)/(tan(b*x + a)^2 + 1)) - 4*a^3*log(((I*(c - 1)*d - d^2)*tan(b*x + a)^2 + c^2 + I*(c - 1)*d + (I*c^2 + I*d^2 - 2*I*c + I)*tan(b*x + a) - 2*c + 1)/(tan(b*x + a)^2 + 1)) - 6*b*x*polylog(3, ((c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*tan(b*x + a)^2 - c^2 - 2*I*(c + 1)*d + d^2 + (2*I*c^2 - 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) - 2*c - 1)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) - 6*b*x*polylog(3, ((c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*tan(b*x + a)^2 - c^2 + 2*I*(c + 1)*d + d^2 + (-2*I*c^2 - 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) - 2*c - 1)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) + 6*b*x*polylog(3, ((c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*tan(b*x + a)^2 - c^2 - 2*I*(c - 1)*d + d^2 + (2*I*c^2 - 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 2*c - 1)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) + 6*b*x*polylog(3, ((c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*tan(b*x + a)^2 - c^2 + 2*I*(c - 1)*d + d^2 + (-2*I*c^2 - 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 2*c - 1)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) - 4*(b^3*x^3 + a^3)*log(((2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 - 2*I*(c + 1)*d + (2*I*c^2 + 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) - 4*(b^3*x^3 + a^3)*log(((-2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 + 2*I*(c + 1)*d + (-2*I*c^2 + 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) + 4*(b^3*x^3 + a^3)*log(-(2*(I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 - 2*I*(c - 1)*d - (-2*I*c^2 + 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) + 4*(b^3*x^3 + a^3)*log(-(2*(-I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 + 2*I*(c - 1)*d - (2*I*c^2 + 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) + 3*I*polylog(4, ((c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*tan(b*x + a)^2 - c^2 - 2*I*(c + 1)*d + d^2 + (2*I*c^2 - 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) - 2*c - 1)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) - 3*I*polylog(4, ((c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*tan(b*x + a)^2 - c^2 + 2*I*(c + 1)*d + d^2 + (-2*I*c^2 - 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) - 2*c - 1)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) - 3*I*polylog(4, ((c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*tan(b*x + a)^2 - c^2 - 2*I*(c - 1)*d + d^2 + (2*I*c^2 - 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 2*c - 1)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) + 3*I*polylog(4, ((c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*tan(b*x + a)^2 - c^2 + 2*I*(c - 1)*d + d^2 + (-2*I*c^2 - 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 2*c - 1)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)))/b^3","C",0
318,1,1689,0,1.063593," ","integrate(x*arctanh(c+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{4 \, b^{2} x^{2} \log\left(-\frac{d \tan\left(b x + a\right) + c + 1}{d \tan\left(b x + a\right) + c - 1}\right) + 2 i \, b x {\rm Li}_2\left(-\frac{{\left(2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} - 2 i \, {\left(c + 1\right)} d + {\left(2 i \, c^{2} + 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1} + 1\right) - 2 i \, b x {\rm Li}_2\left(-\frac{{\left(-2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} + 2 i \, {\left(c + 1\right)} d + {\left(-2 i \, c^{2} + 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1} + 1\right) + 2 i \, b x {\rm Li}_2\left(\frac{2 \, {\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, {\left(c - 1\right)} d - {\left(-2 i \, c^{2} + 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1} + 1\right) - 2 i \, b x {\rm Li}_2\left(\frac{2 \, {\left(-i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, {\left(c - 1\right)} d - {\left(2 i \, c^{2} + 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1} + 1\right) - 2 \, a^{2} \log\left(\frac{{\left(i \, {\left(c + 1\right)} d + d^{2}\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, {\left(c + 1\right)} d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, a^{2} \log\left(\frac{{\left(i \, {\left(c + 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, {\left(c + 1\right)} d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \tan\left(b x + a\right) + 2 \, c + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, a^{2} \log\left(\frac{{\left(i \, {\left(c - 1\right)} d + d^{2}\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, {\left(c - 1\right)} d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, a^{2} \log\left(\frac{{\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, {\left(c - 1\right)} d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \tan\left(b x + a\right) - 2 \, c + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{{\left(2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} - 2 i \, {\left(c + 1\right)} d + {\left(2 i \, c^{2} + 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) - 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{{\left(-2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} + 2 i \, {\left(c + 1\right)} d + {\left(-2 i \, c^{2} + 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) + 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\frac{2 \, {\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, {\left(c - 1\right)} d - {\left(-2 i \, c^{2} + 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) + 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\frac{2 \, {\left(-i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, {\left(c - 1\right)} d - {\left(2 i \, c^{2} + 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) - {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, {\left(c + 1\right)} d + d^{2} + {\left(2 i \, c^{2} - 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) - {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, {\left(c + 1\right)} d + d^{2} + {\left(-2 i \, c^{2} - 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) + {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, {\left(c - 1\right)} d + d^{2} + {\left(2 i \, c^{2} - 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) + {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, {\left(c - 1\right)} d + d^{2} + {\left(-2 i \, c^{2} - 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right)}{16 \, b^{2}}"," ",0,"1/16*(4*b^2*x^2*log(-(d*tan(b*x + a) + c + 1)/(d*tan(b*x + a) + c - 1)) + 2*I*b*x*dilog(-((2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 - 2*I*(c + 1)*d + (2*I*c^2 + 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1) + 1) - 2*I*b*x*dilog(-((-2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 + 2*I*(c + 1)*d + (-2*I*c^2 + 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1) + 1) + 2*I*b*x*dilog((2*(I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 - 2*I*(c - 1)*d - (-2*I*c^2 + 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1) + 1) - 2*I*b*x*dilog((2*(-I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 + 2*I*(c - 1)*d - (2*I*c^2 + 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1) + 1) - 2*a^2*log(((I*(c + 1)*d + d^2)*tan(b*x + a)^2 - c^2 + I*(c + 1)*d + (I*c^2 + I*d^2 + 2*I*c + I)*tan(b*x + a) - 2*c - 1)/(tan(b*x + a)^2 + 1)) - 2*a^2*log(((I*(c + 1)*d - d^2)*tan(b*x + a)^2 + c^2 + I*(c + 1)*d + (I*c^2 + I*d^2 + 2*I*c + I)*tan(b*x + a) + 2*c + 1)/(tan(b*x + a)^2 + 1)) + 2*a^2*log(((I*(c - 1)*d + d^2)*tan(b*x + a)^2 - c^2 + I*(c - 1)*d + (I*c^2 + I*d^2 - 2*I*c + I)*tan(b*x + a) + 2*c - 1)/(tan(b*x + a)^2 + 1)) + 2*a^2*log(((I*(c - 1)*d - d^2)*tan(b*x + a)^2 + c^2 + I*(c - 1)*d + (I*c^2 + I*d^2 - 2*I*c + I)*tan(b*x + a) - 2*c + 1)/(tan(b*x + a)^2 + 1)) - 2*(b^2*x^2 - a^2)*log(((2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 - 2*I*(c + 1)*d + (2*I*c^2 + 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) - 2*(b^2*x^2 - a^2)*log(((-2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 + 2*I*(c + 1)*d + (-2*I*c^2 + 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) + 2*(b^2*x^2 - a^2)*log(-(2*(I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 - 2*I*(c - 1)*d - (-2*I*c^2 + 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) + 2*(b^2*x^2 - a^2)*log(-(2*(-I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 + 2*I*(c - 1)*d - (2*I*c^2 + 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) - polylog(3, ((c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*tan(b*x + a)^2 - c^2 - 2*I*(c + 1)*d + d^2 + (2*I*c^2 - 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) - 2*c - 1)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) - polylog(3, ((c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*tan(b*x + a)^2 - c^2 + 2*I*(c + 1)*d + d^2 + (-2*I*c^2 - 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) - 2*c - 1)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) + polylog(3, ((c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*tan(b*x + a)^2 - c^2 - 2*I*(c - 1)*d + d^2 + (2*I*c^2 - 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 2*c - 1)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) + polylog(3, ((c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*tan(b*x + a)^2 - c^2 + 2*I*(c - 1)*d + d^2 + (-2*I*c^2 - 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 2*c - 1)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)))/b^2","C",0
319,1,1189,0,0.654837," ","integrate(arctanh(c+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{4 \, b x \log\left(-\frac{d \tan\left(b x + a\right) + c + 1}{d \tan\left(b x + a\right) + c - 1}\right) - 2 \, {\left(b x + a\right)} \log\left(\frac{{\left(2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} - 2 i \, {\left(c + 1\right)} d + {\left(2 i \, c^{2} + 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) - 2 \, {\left(b x + a\right)} \log\left(\frac{{\left(-2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} + 2 i \, {\left(c + 1\right)} d + {\left(-2 i \, c^{2} + 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) + 2 \, {\left(b x + a\right)} \log\left(-\frac{2 \, {\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, {\left(c - 1\right)} d - {\left(-2 i \, c^{2} + 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) + 2 \, {\left(b x + a\right)} \log\left(-\frac{2 \, {\left(-i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, {\left(c - 1\right)} d - {\left(2 i \, c^{2} + 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) + 2 \, a \log\left(\frac{{\left(i \, {\left(c + 1\right)} d + d^{2}\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, {\left(c + 1\right)} d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, a \log\left(\frac{{\left(i \, {\left(c + 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, {\left(c + 1\right)} d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \tan\left(b x + a\right) + 2 \, c + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, a \log\left(\frac{{\left(i \, {\left(c - 1\right)} d + d^{2}\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, {\left(c - 1\right)} d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, a \log\left(\frac{{\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, {\left(c - 1\right)} d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \tan\left(b x + a\right) - 2 \, c + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + i \, {\rm Li}_2\left(-\frac{{\left(2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} - 2 i \, {\left(c + 1\right)} d + {\left(2 i \, c^{2} + 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1} + 1\right) - i \, {\rm Li}_2\left(-\frac{{\left(-2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} + 2 i \, {\left(c + 1\right)} d + {\left(-2 i \, c^{2} + 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1} + 1\right) + i \, {\rm Li}_2\left(\frac{2 \, {\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, {\left(c - 1\right)} d - {\left(-2 i \, c^{2} + 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1} + 1\right) - i \, {\rm Li}_2\left(\frac{2 \, {\left(-i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, {\left(c - 1\right)} d - {\left(2 i \, c^{2} + 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1} + 1\right)}{8 \, b}"," ",0,"1/8*(4*b*x*log(-(d*tan(b*x + a) + c + 1)/(d*tan(b*x + a) + c - 1)) - 2*(b*x + a)*log(((2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 - 2*I*(c + 1)*d + (2*I*c^2 + 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) - 2*(b*x + a)*log(((-2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 + 2*I*(c + 1)*d + (-2*I*c^2 + 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) + 2*(b*x + a)*log(-(2*(I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 - 2*I*(c - 1)*d - (-2*I*c^2 + 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) + 2*(b*x + a)*log(-(2*(-I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 + 2*I*(c - 1)*d - (2*I*c^2 + 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) + 2*a*log(((I*(c + 1)*d + d^2)*tan(b*x + a)^2 - c^2 + I*(c + 1)*d + (I*c^2 + I*d^2 + 2*I*c + I)*tan(b*x + a) - 2*c - 1)/(tan(b*x + a)^2 + 1)) + 2*a*log(((I*(c + 1)*d - d^2)*tan(b*x + a)^2 + c^2 + I*(c + 1)*d + (I*c^2 + I*d^2 + 2*I*c + I)*tan(b*x + a) + 2*c + 1)/(tan(b*x + a)^2 + 1)) - 2*a*log(((I*(c - 1)*d + d^2)*tan(b*x + a)^2 - c^2 + I*(c - 1)*d + (I*c^2 + I*d^2 - 2*I*c + I)*tan(b*x + a) + 2*c - 1)/(tan(b*x + a)^2 + 1)) - 2*a*log(((I*(c - 1)*d - d^2)*tan(b*x + a)^2 + c^2 + I*(c - 1)*d + (I*c^2 + I*d^2 - 2*I*c + I)*tan(b*x + a) - 2*c + 1)/(tan(b*x + a)^2 + 1)) + I*dilog(-((2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 - 2*I*(c + 1)*d + (2*I*c^2 + 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1) + 1) - I*dilog(-((-2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 + 2*I*(c + 1)*d + (-2*I*c^2 + 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1) + 1) + I*dilog((2*(I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 - 2*I*(c - 1)*d - (-2*I*c^2 + 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1) + 1) - I*dilog((2*(-I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 + 2*I*(c - 1)*d - (2*I*c^2 + 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1) + 1))/b","B",0
320,0,0,0,0.501114," ","integrate(arctanh(c+d*tan(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(d \tan\left(b x + a\right) + c\right)}{x}, x\right)"," ",0,"integral(arctanh(d*tan(b*x + a) + c)/x, x)","F",0
321,1,349,0,0.625260," ","integrate(x^2*arctanh(1-I*d+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{i \, b^{4} x^{4} + 2 \, b^{3} x^{3} \log\left(-\frac{{\left({\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{d}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - i \, a^{4} + 2 \, a^{3} \log\left(\frac{{\left(2 \, d + 2 i\right)} e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{4 i \, d - 4}}{2 \, d + 2 i}\right) + 2 \, a^{3} \log\left(\frac{{\left(2 \, d + 2 i\right)} e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{4 i \, d - 4}}{2 \, d + 2 i}\right) - 12 \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 12 \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - 12 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 12 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(I*b^4*x^4 + 2*b^3*x^3*log(-((d + I)*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/d) + 6*I*b^2*x^2*dilog(1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) + 6*I*b^2*x^2*dilog(-1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) - I*a^4 + 2*a^3*log(((2*d + 2*I)*e^(I*b*x + I*a) + I*sqrt(4*I*d - 4))/(2*d + 2*I)) + 2*a^3*log(((2*d + 2*I)*e^(I*b*x + I*a) - I*sqrt(4*I*d - 4))/(2*d + 2*I)) - 12*b*x*polylog(3, 1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) - 12*b*x*polylog(3, -1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) - 2*(b^3*x^3 + a^3)*log(1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a) + 1) - 2*(b^3*x^3 + a^3)*log(-1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a) + 1) - 12*I*polylog(4, 1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) - 12*I*polylog(4, -1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)))/b^3","C",0
322,1,297,0,0.504856," ","integrate(x*arctanh(1-I*d+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{2 i \, b^{3} x^{3} + 3 \, b^{2} x^{2} \log\left(-\frac{{\left({\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{d}\right) + 2 i \, a^{3} + 6 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) + 6 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 3 \, a^{2} \log\left(\frac{{\left(2 \, d + 2 i\right)} e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{4 i \, d - 4}}{2 \, d + 2 i}\right) - 3 \, a^{2} \log\left(\frac{{\left(2 \, d + 2 i\right)} e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{4 i \, d - 4}}{2 \, d + 2 i}\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - 6 \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 6 \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*I*b^3*x^3 + 3*b^2*x^2*log(-((d + I)*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/d) + 2*I*a^3 + 6*I*b*x*dilog(1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) + 6*I*b*x*dilog(-1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) - 3*a^2*log(((2*d + 2*I)*e^(I*b*x + I*a) + I*sqrt(4*I*d - 4))/(2*d + 2*I)) - 3*a^2*log(((2*d + 2*I)*e^(I*b*x + I*a) - I*sqrt(4*I*d - 4))/(2*d + 2*I)) - 3*(b^2*x^2 - a^2)*log(1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a) + 1) - 3*(b^2*x^2 - a^2)*log(-1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a) + 1) - 6*polylog(3, 1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) - 6*polylog(3, -1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)))/b^2","C",0
323,1,222,0,1.009547," ","integrate(arctanh(1-I*d+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{i \, b^{2} x^{2} + b x \log\left(-\frac{{\left({\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{d}\right) - i \, a^{2} - {\left(b x + a\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - {\left(b x + a\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) + a \log\left(\frac{{\left(2 \, d + 2 i\right)} e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{4 i \, d - 4}}{2 \, d + 2 i}\right) + a \log\left(\frac{{\left(2 \, d + 2 i\right)} e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{4 i \, d - 4}}{2 \, d + 2 i}\right) + i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) + i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right)}{2 \, b}"," ",0,"1/2*(I*b^2*x^2 + b*x*log(-((d + I)*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/d) - I*a^2 - (b*x + a)*log(1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a) + 1) - (b*x + a)*log(-1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a) + 1) + a*log(((2*d + 2*I)*e^(I*b*x + I*a) + I*sqrt(4*I*d - 4))/(2*d + 2*I)) + a*log(((2*d + 2*I)*e^(I*b*x + I*a) - I*sqrt(4*I*d - 4))/(2*d + 2*I)) + I*dilog(1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) + I*dilog(-1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)))/b","B",0
324,0,0,0,0.518971," ","integrate(arctanh(1-I*d+d*tan(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(-\frac{{\left({\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{d}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*log(-((d + I)*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/d)/x, x)","F",0
325,1,349,0,0.581863," ","integrate(-x^2*arctanh(-1-I*d+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{i \, b^{4} x^{4} - 2 \, b^{3} x^{3} \log\left(-\frac{d e^{\left(2 i \, b x + 2 i \, a\right)}}{{\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - i \, a^{4} + 2 \, a^{3} \log\left(\frac{{\left(2 \, d - 2 i\right)} e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{-4 i \, d - 4}}{2 \, d - 2 i}\right) + 2 \, a^{3} \log\left(\frac{{\left(2 \, d - 2 i\right)} e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{-4 i \, d - 4}}{2 \, d - 2 i}\right) - 12 \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 12 \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - 12 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 12 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(I*b^4*x^4 - 2*b^3*x^3*log(-d*e^(2*I*b*x + 2*I*a)/((d - I)*e^(2*I*b*x + 2*I*a) - I)) + 6*I*b^2*x^2*dilog(1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) + 6*I*b^2*x^2*dilog(-1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) - I*a^4 + 2*a^3*log(((2*d - 2*I)*e^(I*b*x + I*a) + I*sqrt(-4*I*d - 4))/(2*d - 2*I)) + 2*a^3*log(((2*d - 2*I)*e^(I*b*x + I*a) - I*sqrt(-4*I*d - 4))/(2*d - 2*I)) - 12*b*x*polylog(3, 1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) - 12*b*x*polylog(3, -1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) - 2*(b^3*x^3 + a^3)*log(1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a) + 1) - 2*(b^3*x^3 + a^3)*log(-1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a) + 1) - 12*I*polylog(4, 1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) - 12*I*polylog(4, -1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)))/b^3","C",0
326,1,297,0,0.470980," ","integrate(-x*arctanh(-1-I*d+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{2 i \, b^{3} x^{3} - 3 \, b^{2} x^{2} \log\left(-\frac{d e^{\left(2 i \, b x + 2 i \, a\right)}}{{\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) + 2 i \, a^{3} + 6 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) + 6 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 3 \, a^{2} \log\left(\frac{{\left(2 \, d - 2 i\right)} e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{-4 i \, d - 4}}{2 \, d - 2 i}\right) - 3 \, a^{2} \log\left(\frac{{\left(2 \, d - 2 i\right)} e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{-4 i \, d - 4}}{2 \, d - 2 i}\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - 6 \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 6 \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*I*b^3*x^3 - 3*b^2*x^2*log(-d*e^(2*I*b*x + 2*I*a)/((d - I)*e^(2*I*b*x + 2*I*a) - I)) + 2*I*a^3 + 6*I*b*x*dilog(1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) + 6*I*b*x*dilog(-1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) - 3*a^2*log(((2*d - 2*I)*e^(I*b*x + I*a) + I*sqrt(-4*I*d - 4))/(2*d - 2*I)) - 3*a^2*log(((2*d - 2*I)*e^(I*b*x + I*a) - I*sqrt(-4*I*d - 4))/(2*d - 2*I)) - 3*(b^2*x^2 - a^2)*log(1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a) + 1) - 3*(b^2*x^2 - a^2)*log(-1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a) + 1) - 6*polylog(3, 1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) - 6*polylog(3, -1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)))/b^2","C",0
327,1,223,0,0.707812," ","integrate(-arctanh(-1-I*d+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{i \, b^{2} x^{2} - b x \log\left(-\frac{d e^{\left(2 i \, b x + 2 i \, a\right)}}{{\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) - i \, a^{2} - {\left(b x + a\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - {\left(b x + a\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) + a \log\left(\frac{{\left(2 \, d - 2 i\right)} e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{-4 i \, d - 4}}{2 \, d - 2 i}\right) + a \log\left(\frac{{\left(2 \, d - 2 i\right)} e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{-4 i \, d - 4}}{2 \, d - 2 i}\right) + i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) + i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right)}{2 \, b}"," ",0,"1/2*(I*b^2*x^2 - b*x*log(-d*e^(2*I*b*x + 2*I*a)/((d - I)*e^(2*I*b*x + 2*I*a) - I)) - I*a^2 - (b*x + a)*log(1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a) + 1) - (b*x + a)*log(-1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a) + 1) + a*log(((2*d - 2*I)*e^(I*b*x + I*a) + I*sqrt(-4*I*d - 4))/(2*d - 2*I)) + a*log(((2*d - 2*I)*e^(I*b*x + I*a) - I*sqrt(-4*I*d - 4))/(2*d - 2*I)) + I*dilog(1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) + I*dilog(-1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)))/b","B",0
328,0,0,0,1.408589," ","integrate(-arctanh(-1-I*d+d*tan(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\log\left(-\frac{d e^{\left(2 i \, b x + 2 i \, a\right)}}{{\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right)}{2 \, x}, x\right)"," ",0,"integral(-1/2*log(-d*e^(2*I*b*x + 2*I*a)/((d - I)*e^(2*I*b*x + 2*I*a) - I))/x, x)","F",0
329,1,1567,0,0.674021," ","integrate((f*x+e)^3*arctanh(cot(b*x+a)),x, algorithm=""fricas"")","-\frac{3 \, f^{3} {\rm polylog}\left(5, i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - 3 \, f^{3} {\rm polylog}\left(5, i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + 3 \, f^{3} {\rm polylog}\left(5, -i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - 3 \, f^{3} {\rm polylog}\left(5, -i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) - {\left(4 i \, b^{3} f^{3} x^{3} + 12 i \, b^{3} e f^{2} x^{2} + 12 i \, b^{3} e^{2} f x + 4 i \, b^{3} e^{3}\right)} {\rm Li}_2\left(i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - {\left(4 i \, b^{3} f^{3} x^{3} + 12 i \, b^{3} e f^{2} x^{2} + 12 i \, b^{3} e^{2} f x + 4 i \, b^{3} e^{3}\right)} {\rm Li}_2\left(i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) - {\left(-4 i \, b^{3} f^{3} x^{3} - 12 i \, b^{3} e f^{2} x^{2} - 12 i \, b^{3} e^{2} f x - 4 i \, b^{3} e^{3}\right)} {\rm Li}_2\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - {\left(-4 i \, b^{3} f^{3} x^{3} - 12 i \, b^{3} e f^{2} x^{2} - 12 i \, b^{3} e^{2} f x - 4 i \, b^{3} e^{3}\right)} {\rm Li}_2\left(-i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) - 4 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x\right)} \log\left(-\frac{\cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1}{\cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1}\right) - 2 \, {\left(4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) + 2 \, {\left(4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) + 2 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x + 4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1\right) - 2 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x + 4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x + 4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1\right) - 2 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x + 4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(-i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1\right) - 2 \, {\left(4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) + 2 \, {\left(4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - {\left(-6 i \, b f^{3} x - 6 i \, b e f^{2}\right)} {\rm polylog}\left(4, i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - {\left(-6 i \, b f^{3} x - 6 i \, b e f^{2}\right)} {\rm polylog}\left(4, i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) - {\left(6 i \, b f^{3} x + 6 i \, b e f^{2}\right)} {\rm polylog}\left(4, -i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - {\left(6 i \, b f^{3} x + 6 i \, b e f^{2}\right)} {\rm polylog}\left(4, -i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) - 6 \, {\left(b^{2} f^{3} x^{2} + 2 \, b^{2} e f^{2} x + b^{2} e^{2} f\right)} {\rm polylog}\left(3, i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) + 6 \, {\left(b^{2} f^{3} x^{2} + 2 \, b^{2} e f^{2} x + b^{2} e^{2} f\right)} {\rm polylog}\left(3, i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) - 6 \, {\left(b^{2} f^{3} x^{2} + 2 \, b^{2} e f^{2} x + b^{2} e^{2} f\right)} {\rm polylog}\left(3, -i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) + 6 \, {\left(b^{2} f^{3} x^{2} + 2 \, b^{2} e f^{2} x + b^{2} e^{2} f\right)} {\rm polylog}\left(3, -i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)}{32 \, b^{4}}"," ",0,"-1/32*(3*f^3*polylog(5, I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - 3*f^3*polylog(5, I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + 3*f^3*polylog(5, -I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - 3*f^3*polylog(5, -I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) - (4*I*b^3*f^3*x^3 + 12*I*b^3*e*f^2*x^2 + 12*I*b^3*e^2*f*x + 4*I*b^3*e^3)*dilog(I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - (4*I*b^3*f^3*x^3 + 12*I*b^3*e*f^2*x^2 + 12*I*b^3*e^2*f*x + 4*I*b^3*e^3)*dilog(I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) - (-4*I*b^3*f^3*x^3 - 12*I*b^3*e*f^2*x^2 - 12*I*b^3*e^2*f*x - 4*I*b^3*e^3)*dilog(-I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - (-4*I*b^3*f^3*x^3 - 12*I*b^3*e*f^2*x^2 - 12*I*b^3*e^2*f*x - 4*I*b^3*e^3)*dilog(-I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) - 4*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x)*log(-(cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1)/(cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1)) - 2*(4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + I) + 2*(4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + I) + 2*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x + 4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1) - 2*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x + 4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1) + 2*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x + 4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(-I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1) - 2*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x + 4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(-I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1) - 2*(4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + I) + 2*(4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + I) - (-6*I*b*f^3*x - 6*I*b*e*f^2)*polylog(4, I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - (-6*I*b*f^3*x - 6*I*b*e*f^2)*polylog(4, I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) - (6*I*b*f^3*x + 6*I*b*e*f^2)*polylog(4, -I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - (6*I*b*f^3*x + 6*I*b*e*f^2)*polylog(4, -I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) - 6*(b^2*f^3*x^2 + 2*b^2*e*f^2*x + b^2*e^2*f)*polylog(3, I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) + 6*(b^2*f^3*x^2 + 2*b^2*e*f^2*x + b^2*e^2*f)*polylog(3, I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) - 6*(b^2*f^3*x^2 + 2*b^2*e*f^2*x + b^2*e^2*f)*polylog(3, -I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) + 6*(b^2*f^3*x^2 + 2*b^2*e*f^2*x + b^2*e^2*f)*polylog(3, -I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)))/b^4","C",0
330,1,1081,0,0.973953," ","integrate((f*x+e)^2*arctanh(cot(b*x+a)),x, algorithm=""fricas"")","\frac{-3 i \, f^{2} {\rm polylog}\left(4, i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - 3 i \, f^{2} {\rm polylog}\left(4, i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + 3 i \, f^{2} {\rm polylog}\left(4, -i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) + 3 i \, f^{2} {\rm polylog}\left(4, -i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(6 i \, b^{2} f^{2} x^{2} + 12 i \, b^{2} e f x + 6 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(6 i \, b^{2} f^{2} x^{2} + 12 i \, b^{2} e f x + 6 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(-6 i \, b^{2} f^{2} x^{2} - 12 i \, b^{2} e f x - 6 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(-6 i \, b^{2} f^{2} x^{2} - 12 i \, b^{2} e f x - 6 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + 8 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x\right)} \log\left(-\frac{\cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1}{\cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1}\right) + 4 \, {\left(3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 4 \, {\left(3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 4 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x + 3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 4 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x + 3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1\right) - 4 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x + 3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 4 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x + 3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(-i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 4 \, {\left(3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 4 \, {\left(3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) + 6 \, {\left(b f^{2} x + b e f\right)} {\rm polylog}\left(3, i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - 6 \, {\left(b f^{2} x + b e f\right)} {\rm polylog}\left(3, i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + 6 \, {\left(b f^{2} x + b e f\right)} {\rm polylog}\left(3, -i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - 6 \, {\left(b f^{2} x + b e f\right)} {\rm polylog}\left(3, -i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)}{48 \, b^{3}}"," ",0,"1/48*(-3*I*f^2*polylog(4, I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - 3*I*f^2*polylog(4, I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + 3*I*f^2*polylog(4, -I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) + 3*I*f^2*polylog(4, -I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + (6*I*b^2*f^2*x^2 + 12*I*b^2*e*f*x + 6*I*b^2*e^2)*dilog(I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) + (6*I*b^2*f^2*x^2 + 12*I*b^2*e*f*x + 6*I*b^2*e^2)*dilog(I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + (-6*I*b^2*f^2*x^2 - 12*I*b^2*e*f*x - 6*I*b^2*e^2)*dilog(-I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) + (-6*I*b^2*f^2*x^2 - 12*I*b^2*e*f*x - 6*I*b^2*e^2)*dilog(-I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + 8*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x)*log(-(cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1)/(cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1)) + 4*(3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + I) - 4*(3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + I) - 4*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x + 3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1) + 4*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x + 3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1) - 4*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x + 3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(-I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1) + 4*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x + 3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(-I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1) + 4*(3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + I) - 4*(3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + I) + 6*(b*f^2*x + b*e*f)*polylog(3, I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - 6*(b*f^2*x + b*e*f)*polylog(3, I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + 6*(b*f^2*x + b*e*f)*polylog(3, -I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - 6*(b*f^2*x + b*e*f)*polylog(3, -I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)))/b^3","C",0
331,1,677,0,0.736792," ","integrate((f*x+e)*arctanh(cot(b*x+a)),x, algorithm=""fricas"")","\frac{{\left(2 i \, b f x + 2 i \, b e\right)} {\rm Li}_2\left(i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(2 i \, b f x + 2 i \, b e\right)} {\rm Li}_2\left(i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(-2 i \, b f x - 2 i \, b e\right)} {\rm Li}_2\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(-2 i \, b f x - 2 i \, b e\right)} {\rm Li}_2\left(-i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + 4 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x\right)} \log\left(-\frac{\cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1}{\cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1}\right) + 2 \, {\left(2 \, a b e - a^{2} f\right)} \log\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 2 \, {\left(2 \, a b e - a^{2} f\right)} \log\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x + 2 \, a b e - a^{2} f\right)} \log\left(i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x + 2 \, a b e - a^{2} f\right)} \log\left(i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1\right) - 2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x + 2 \, a b e - a^{2} f\right)} \log\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x + 2 \, a b e - a^{2} f\right)} \log\left(-i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(2 \, a b e - a^{2} f\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 2 \, {\left(2 \, a b e - a^{2} f\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) + f {\rm polylog}\left(3, i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - f {\rm polylog}\left(3, i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + f {\rm polylog}\left(3, -i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - f {\rm polylog}\left(3, -i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)}{16 \, b^{2}}"," ",0,"1/16*((2*I*b*f*x + 2*I*b*e)*dilog(I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) + (2*I*b*f*x + 2*I*b*e)*dilog(I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + (-2*I*b*f*x - 2*I*b*e)*dilog(-I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) + (-2*I*b*f*x - 2*I*b*e)*dilog(-I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + 4*(b^2*f*x^2 + 2*b^2*e*x)*log(-(cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1)/(cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1)) + 2*(2*a*b*e - a^2*f)*log(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + I) - 2*(2*a*b*e - a^2*f)*log(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + I) - 2*(b^2*f*x^2 + 2*b^2*e*x + 2*a*b*e - a^2*f)*log(I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1) + 2*(b^2*f*x^2 + 2*b^2*e*x + 2*a*b*e - a^2*f)*log(I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1) - 2*(b^2*f*x^2 + 2*b^2*e*x + 2*a*b*e - a^2*f)*log(-I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1) + 2*(b^2*f*x^2 + 2*b^2*e*x + 2*a*b*e - a^2*f)*log(-I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1) + 2*(2*a*b*e - a^2*f)*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + I) - 2*(2*a*b*e - a^2*f)*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + I) + f*polylog(3, I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - f*polylog(3, I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + f*polylog(3, -I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - f*polylog(3, -I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)))/b^2","C",0
332,1,389,0,0.609340," ","integrate(arctanh(cot(b*x+a)),x, algorithm=""fricas"")","\frac{4 \, b x \log\left(-\frac{\cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1}{\cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1}\right) + 2 \, a \log\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 2 \, a \log\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 2 \, {\left(b x + a\right)} \log\left(i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(b x + a\right)} \log\left(i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1\right) - 2 \, {\left(b x + a\right)} \log\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(b x + a\right)} \log\left(-i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, a \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 2 \, a \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) + i \, {\rm Li}_2\left(i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) + i \, {\rm Li}_2\left(i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) - i \, {\rm Li}_2\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - i \, {\rm Li}_2\left(-i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)}{8 \, b}"," ",0,"1/8*(4*b*x*log(-(cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1)/(cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1)) + 2*a*log(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + I) - 2*a*log(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + I) - 2*(b*x + a)*log(I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1) + 2*(b*x + a)*log(I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1) - 2*(b*x + a)*log(-I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1) + 2*(b*x + a)*log(-I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1) + 2*a*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + I) - 2*a*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + I) + I*dilog(I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) + I*dilog(I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) - I*dilog(-I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - I*dilog(-I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)))/b","B",0
333,0,0,0,0.436426," ","integrate(arctanh(cot(b*x+a))/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(\cot\left(b x + a\right)\right)}{f x + e}, x\right)"," ",0,"integral(arctanh(cot(b*x + a))/(f*x + e), x)","F",0
334,1,1799,0,1.023102," ","integrate(x^2*arctanh(c+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{8 \, b^{3} x^{3} \log\left(-\frac{d \cos\left(2 \, b x + 2 \, a\right) + {\left(c + 1\right)} \sin\left(2 \, b x + 2 \, a\right) + d}{d \cos\left(2 \, b x + 2 \, a\right) + {\left(c - 1\right)} \sin\left(2 \, b x + 2 \, a\right) + d}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1} + 1\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1} + 1\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1} + 1\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1} + 1\right) + 4 \, a^{3} \log\left(\frac{1}{2} \, c^{2} + i \, {\left(c + 1\right)} d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + c + \frac{1}{2}\right) - 4 \, a^{3} \log\left(\frac{1}{2} \, c^{2} + i \, {\left(c - 1\right)} d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - c + \frac{1}{2}\right) + 4 \, a^{3} \log\left(-\frac{1}{2} \, c^{2} + i \, {\left(c + 1\right)} d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - c - \frac{1}{2}\right) - 4 \, a^{3} \log\left(-\frac{1}{2} \, c^{2} + i \, {\left(c - 1\right)} d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + c - \frac{1}{2}\right) - 6 \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, c + 1}\right) - 6 \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, c + 1}\right) + 6 \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, c + 1}\right) + 6 \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, c + 1}\right) - 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1}\right) - 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1}\right) + 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1}\right) + 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1}\right) - 3 i \, {\rm polylog}\left(4, \frac{{\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, c + 1}\right) + 3 i \, {\rm polylog}\left(4, \frac{{\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, c + 1}\right) + 3 i \, {\rm polylog}\left(4, \frac{{\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, c + 1}\right) - 3 i \, {\rm polylog}\left(4, \frac{{\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, c + 1}\right)}{48 \, b^{3}}"," ",0,"1/48*(8*b^3*x^3*log(-(d*cos(2*b*x + 2*a) + (c + 1)*sin(2*b*x + 2*a) + d)/(d*cos(2*b*x + 2*a) + (c - 1)*sin(2*b*x + 2*a) + d)) + 6*I*b^2*x^2*dilog(-(c^2 + d^2 - (c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1) + 1) - 6*I*b^2*x^2*dilog(-(c^2 + d^2 - (c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1) + 1) - 6*I*b^2*x^2*dilog(-(c^2 + d^2 - (c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1) + 1) + 6*I*b^2*x^2*dilog(-(c^2 + d^2 - (c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1) + 1) + 4*a^3*log(1/2*c^2 + I*(c + 1)*d - 1/2*d^2 - 1/2*(c^2 + d^2 + 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + c + 1/2) - 4*a^3*log(1/2*c^2 + I*(c - 1)*d - 1/2*d^2 - 1/2*(c^2 + d^2 - 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - c + 1/2) + 4*a^3*log(-1/2*c^2 + I*(c + 1)*d + 1/2*d^2 + 1/2*(c^2 + d^2 + 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) - c - 1/2) - 4*a^3*log(-1/2*c^2 + I*(c - 1)*d + 1/2*d^2 + 1/2*(c^2 + d^2 - 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) + c - 1/2) - 6*b*x*polylog(3, ((c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*c + 1)) - 6*b*x*polylog(3, ((c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*c + 1)) + 6*b*x*polylog(3, ((c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*c + 1)) + 6*b*x*polylog(3, ((c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*c + 1)) - 4*(b^3*x^3 + a^3)*log((c^2 + d^2 - (c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1)) - 4*(b^3*x^3 + a^3)*log((c^2 + d^2 - (c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1)) + 4*(b^3*x^3 + a^3)*log((c^2 + d^2 - (c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1)) + 4*(b^3*x^3 + a^3)*log((c^2 + d^2 - (c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1)) - 3*I*polylog(4, ((c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*c + 1)) + 3*I*polylog(4, ((c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*c + 1)) + 3*I*polylog(4, ((c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*c + 1)) - 3*I*polylog(4, ((c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*c + 1)))/b^3","C",0
335,1,1463,0,0.636073," ","integrate(x*arctanh(c+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{4 \, b^{2} x^{2} \log\left(-\frac{d \cos\left(2 \, b x + 2 \, a\right) + {\left(c + 1\right)} \sin\left(2 \, b x + 2 \, a\right) + d}{d \cos\left(2 \, b x + 2 \, a\right) + {\left(c - 1\right)} \sin\left(2 \, b x + 2 \, a\right) + d}\right) + 2 i \, b x {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1} + 1\right) - 2 i \, b x {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1} + 1\right) - 2 i \, b x {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1} + 1\right) + 2 i \, b x {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1} + 1\right) - 2 \, a^{2} \log\left(\frac{1}{2} \, c^{2} + i \, {\left(c + 1\right)} d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + c + \frac{1}{2}\right) + 2 \, a^{2} \log\left(\frac{1}{2} \, c^{2} + i \, {\left(c - 1\right)} d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - c + \frac{1}{2}\right) - 2 \, a^{2} \log\left(-\frac{1}{2} \, c^{2} + i \, {\left(c + 1\right)} d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - c - \frac{1}{2}\right) + 2 \, a^{2} \log\left(-\frac{1}{2} \, c^{2} + i \, {\left(c - 1\right)} d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + c - \frac{1}{2}\right) - 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1}\right) - 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1}\right) + 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1}\right) + 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1}\right) - {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, c + 1}\right) - {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, c + 1}\right) + {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, c + 1}\right) + {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, c + 1}\right)}{16 \, b^{2}}"," ",0,"1/16*(4*b^2*x^2*log(-(d*cos(2*b*x + 2*a) + (c + 1)*sin(2*b*x + 2*a) + d)/(d*cos(2*b*x + 2*a) + (c - 1)*sin(2*b*x + 2*a) + d)) + 2*I*b*x*dilog(-(c^2 + d^2 - (c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1) + 1) - 2*I*b*x*dilog(-(c^2 + d^2 - (c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1) + 1) - 2*I*b*x*dilog(-(c^2 + d^2 - (c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1) + 1) + 2*I*b*x*dilog(-(c^2 + d^2 - (c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1) + 1) - 2*a^2*log(1/2*c^2 + I*(c + 1)*d - 1/2*d^2 - 1/2*(c^2 + d^2 + 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + c + 1/2) + 2*a^2*log(1/2*c^2 + I*(c - 1)*d - 1/2*d^2 - 1/2*(c^2 + d^2 - 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - c + 1/2) - 2*a^2*log(-1/2*c^2 + I*(c + 1)*d + 1/2*d^2 + 1/2*(c^2 + d^2 + 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) - c - 1/2) + 2*a^2*log(-1/2*c^2 + I*(c - 1)*d + 1/2*d^2 + 1/2*(c^2 + d^2 - 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) + c - 1/2) - 2*(b^2*x^2 - a^2)*log((c^2 + d^2 - (c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1)) - 2*(b^2*x^2 - a^2)*log((c^2 + d^2 - (c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1)) + 2*(b^2*x^2 - a^2)*log((c^2 + d^2 - (c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1)) + 2*(b^2*x^2 - a^2)*log((c^2 + d^2 - (c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1)) - polylog(3, ((c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*c + 1)) - polylog(3, ((c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*c + 1)) + polylog(3, ((c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*c + 1)) + polylog(3, ((c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*c + 1)))/b^2","C",0
336,1,1099,0,0.995814," ","integrate(arctanh(c+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{4 \, b x \log\left(-\frac{d \cos\left(2 \, b x + 2 \, a\right) + {\left(c + 1\right)} \sin\left(2 \, b x + 2 \, a\right) + d}{d \cos\left(2 \, b x + 2 \, a\right) + {\left(c - 1\right)} \sin\left(2 \, b x + 2 \, a\right) + d}\right) + 2 \, a \log\left(\frac{1}{2} \, c^{2} + i \, {\left(c + 1\right)} d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + c + \frac{1}{2}\right) - 2 \, a \log\left(\frac{1}{2} \, c^{2} + i \, {\left(c - 1\right)} d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - c + \frac{1}{2}\right) + 2 \, a \log\left(-\frac{1}{2} \, c^{2} + i \, {\left(c + 1\right)} d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - c - \frac{1}{2}\right) - 2 \, a \log\left(-\frac{1}{2} \, c^{2} + i \, {\left(c - 1\right)} d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + c - \frac{1}{2}\right) - 2 \, {\left(b x + a\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1}\right) - 2 \, {\left(b x + a\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1}\right) + 2 \, {\left(b x + a\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1}\right) + 2 \, {\left(b x + a\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1}\right) + i \, {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1} + 1\right) - i \, {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1} + 1\right) - i \, {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1} + 1\right) + i \, {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1} + 1\right)}{8 \, b}"," ",0,"1/8*(4*b*x*log(-(d*cos(2*b*x + 2*a) + (c + 1)*sin(2*b*x + 2*a) + d)/(d*cos(2*b*x + 2*a) + (c - 1)*sin(2*b*x + 2*a) + d)) + 2*a*log(1/2*c^2 + I*(c + 1)*d - 1/2*d^2 - 1/2*(c^2 + d^2 + 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + c + 1/2) - 2*a*log(1/2*c^2 + I*(c - 1)*d - 1/2*d^2 - 1/2*(c^2 + d^2 - 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - c + 1/2) + 2*a*log(-1/2*c^2 + I*(c + 1)*d + 1/2*d^2 + 1/2*(c^2 + d^2 + 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) - c - 1/2) - 2*a*log(-1/2*c^2 + I*(c - 1)*d + 1/2*d^2 + 1/2*(c^2 + d^2 - 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) + c - 1/2) - 2*(b*x + a)*log((c^2 + d^2 - (c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1)) - 2*(b*x + a)*log((c^2 + d^2 - (c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1)) + 2*(b*x + a)*log((c^2 + d^2 - (c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1)) + 2*(b*x + a)*log((c^2 + d^2 - (c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1)) + I*dilog(-(c^2 + d^2 - (c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1) + 1) - I*dilog(-(c^2 + d^2 - (c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1) + 1) - I*dilog(-(c^2 + d^2 - (c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1) + 1) + I*dilog(-(c^2 + d^2 - (c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1) + 1))/b","B",0
337,0,0,0,0.551520," ","integrate(arctanh(c+d*cot(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(d \cot\left(b x + a\right) + c\right)}{x}, x\right)"," ",0,"integral(arctanh(d*cot(b*x + a) + c)/x, x)","F",0
338,1,180,0,0.457241," ","integrate(x^2*arctanh(1+I*d+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{2 i \, b^{4} x^{4} + 4 \, b^{3} x^{3} \log\left(-\frac{{\left({\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{d}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-{\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) - 2 i \, a^{4} + 4 \, a^{3} \log\left(\frac{{\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i}{d - i}\right) - 6 \, b x {\rm polylog}\left(3, {\left(i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) - 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left({\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) - 3 i \, {\rm polylog}\left(4, {\left(i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{24 \, b^{3}}"," ",0,"1/24*(2*I*b^4*x^4 + 4*b^3*x^3*log(-((d - I)*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/d) + 6*I*b^2*x^2*dilog(-(-I*d - 1)*e^(2*I*b*x + 2*I*a)) - 2*I*a^4 + 4*a^3*log(((d - I)*e^(2*I*b*x + 2*I*a) + I)/(d - I)) - 6*b*x*polylog(3, (I*d + 1)*e^(2*I*b*x + 2*I*a)) - 4*(b^3*x^3 + a^3)*log((-I*d - 1)*e^(2*I*b*x + 2*I*a) + 1) - 3*I*polylog(4, (I*d + 1)*e^(2*I*b*x + 2*I*a)))/b^3","C",0
339,1,157,0,1.122277," ","integrate(x*arctanh(1+I*d+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{4 i \, b^{3} x^{3} + 6 \, b^{2} x^{2} \log\left(-\frac{{\left({\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{d}\right) + 4 i \, a^{3} + 6 i \, b x {\rm Li}_2\left(-{\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) - 6 \, a^{2} \log\left(\frac{{\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i}{d - i}\right) - 6 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left({\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) - 3 \, {\rm polylog}\left(3, {\left(i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{24 \, b^{2}}"," ",0,"1/24*(4*I*b^3*x^3 + 6*b^2*x^2*log(-((d - I)*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/d) + 4*I*a^3 + 6*I*b*x*dilog(-(-I*d - 1)*e^(2*I*b*x + 2*I*a)) - 6*a^2*log(((d - I)*e^(2*I*b*x + 2*I*a) + I)/(d - I)) - 6*(b^2*x^2 - a^2)*log((-I*d - 1)*e^(2*I*b*x + 2*I*a) + 1) - 3*polylog(3, (I*d + 1)*e^(2*I*b*x + 2*I*a)))/b^2","C",0
340,1,122,0,0.448756," ","integrate(arctanh(1+I*d+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{2 i \, b^{2} x^{2} + 2 \, b x \log\left(-\frac{{\left({\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{d}\right) - 2 i \, a^{2} - 2 \, {\left(b x + a\right)} \log\left({\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) + 2 \, a \log\left(\frac{{\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i}{d - i}\right) + i \, {\rm Li}_2\left(-{\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{4 \, b}"," ",0,"1/4*(2*I*b^2*x^2 + 2*b*x*log(-((d - I)*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/d) - 2*I*a^2 - 2*(b*x + a)*log((-I*d - 1)*e^(2*I*b*x + 2*I*a) + 1) + 2*a*log(((d - I)*e^(2*I*b*x + 2*I*a) + I)/(d - I)) + I*dilog(-(-I*d - 1)*e^(2*I*b*x + 2*I*a)))/b","A",0
341,0,0,0,0.550442," ","integrate(arctanh(1+I*d+d*cot(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(-\frac{{\left({\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{d}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*log(-((d - I)*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/d)/x, x)","F",0
342,1,180,0,0.603920," ","integrate(-x^2*arctanh(-1+I*d+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{2 i \, b^{4} x^{4} - 4 \, b^{3} x^{3} \log\left(-\frac{d e^{\left(2 i \, b x + 2 i \, a\right)}}{{\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-{\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) - 2 i \, a^{4} + 4 \, a^{3} \log\left(\frac{{\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}{d + i}\right) - 6 \, b x {\rm polylog}\left(3, {\left(-i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) - 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left({\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) - 3 i \, {\rm polylog}\left(4, {\left(-i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{24 \, b^{3}}"," ",0,"1/24*(2*I*b^4*x^4 - 4*b^3*x^3*log(-d*e^(2*I*b*x + 2*I*a)/((d + I)*e^(2*I*b*x + 2*I*a) - I)) + 6*I*b^2*x^2*dilog(-(I*d - 1)*e^(2*I*b*x + 2*I*a)) - 2*I*a^4 + 4*a^3*log(((d + I)*e^(2*I*b*x + 2*I*a) - I)/(d + I)) - 6*b*x*polylog(3, (-I*d + 1)*e^(2*I*b*x + 2*I*a)) - 4*(b^3*x^3 + a^3)*log((I*d - 1)*e^(2*I*b*x + 2*I*a) + 1) - 3*I*polylog(4, (-I*d + 1)*e^(2*I*b*x + 2*I*a)))/b^3","C",0
343,1,157,0,0.649269," ","integrate(-x*arctanh(-1+I*d+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{4 i \, b^{3} x^{3} - 6 \, b^{2} x^{2} \log\left(-\frac{d e^{\left(2 i \, b x + 2 i \, a\right)}}{{\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) + 4 i \, a^{3} + 6 i \, b x {\rm Li}_2\left(-{\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) - 6 \, a^{2} \log\left(\frac{{\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}{d + i}\right) - 6 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left({\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) - 3 \, {\rm polylog}\left(3, {\left(-i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{24 \, b^{2}}"," ",0,"1/24*(4*I*b^3*x^3 - 6*b^2*x^2*log(-d*e^(2*I*b*x + 2*I*a)/((d + I)*e^(2*I*b*x + 2*I*a) - I)) + 4*I*a^3 + 6*I*b*x*dilog(-(I*d - 1)*e^(2*I*b*x + 2*I*a)) - 6*a^2*log(((d + I)*e^(2*I*b*x + 2*I*a) - I)/(d + I)) - 6*(b^2*x^2 - a^2)*log((I*d - 1)*e^(2*I*b*x + 2*I*a) + 1) - 3*polylog(3, (-I*d + 1)*e^(2*I*b*x + 2*I*a)))/b^2","C",0
344,1,122,0,0.716749," ","integrate(-arctanh(-1+I*d+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{2 i \, b^{2} x^{2} - 2 \, b x \log\left(-\frac{d e^{\left(2 i \, b x + 2 i \, a\right)}}{{\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) - 2 i \, a^{2} - 2 \, {\left(b x + a\right)} \log\left({\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) + 2 \, a \log\left(\frac{{\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}{d + i}\right) + i \, {\rm Li}_2\left(-{\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{4 \, b}"," ",0,"1/4*(2*I*b^2*x^2 - 2*b*x*log(-d*e^(2*I*b*x + 2*I*a)/((d + I)*e^(2*I*b*x + 2*I*a) - I)) - 2*I*a^2 - 2*(b*x + a)*log((I*d - 1)*e^(2*I*b*x + 2*I*a) + 1) + 2*a*log(((d + I)*e^(2*I*b*x + 2*I*a) - I)/(d + I)) + I*dilog(-(I*d - 1)*e^(2*I*b*x + 2*I*a)))/b","A",0
345,0,0,0,0.418040," ","integrate(-arctanh(-1+I*d+d*cot(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\log\left(-\frac{d e^{\left(2 i \, b x + 2 i \, a\right)}}{{\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right)}{2 \, x}, x\right)"," ",0,"integral(-1/2*log(-d*e^(2*I*b*x + 2*I*a)/((d + I)*e^(2*I*b*x + 2*I*a) - I))/x, x)","F",0
346,1,65,0,0.842295," ","integrate(arctanh(exp(x)),x, algorithm=""fricas"")","\frac{1}{2} \, x \log\left(-\frac{\cosh\left(x\right) + \sinh\left(x\right) + 1}{\cosh\left(x\right) + \sinh\left(x\right) - 1}\right) - \frac{1}{2} \, x \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + \frac{1}{2} \, x \log\left(-\cosh\left(x\right) - \sinh\left(x\right) + 1\right) + \frac{1}{2} \, {\rm Li}_2\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - \frac{1}{2} \, {\rm Li}_2\left(-\cosh\left(x\right) - \sinh\left(x\right)\right)"," ",0,"1/2*x*log(-(cosh(x) + sinh(x) + 1)/(cosh(x) + sinh(x) - 1)) - 1/2*x*log(cosh(x) + sinh(x) + 1) + 1/2*x*log(-cosh(x) - sinh(x) + 1) + 1/2*dilog(cosh(x) + sinh(x)) - 1/2*dilog(-cosh(x) - sinh(x))","B",0
347,1,95,0,0.544334," ","integrate(x*arctanh(exp(x)),x, algorithm=""fricas"")","\frac{1}{4} \, x^{2} \log\left(-\frac{\cosh\left(x\right) + \sinh\left(x\right) + 1}{\cosh\left(x\right) + \sinh\left(x\right) - 1}\right) - \frac{1}{4} \, x^{2} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + \frac{1}{4} \, x^{2} \log\left(-\cosh\left(x\right) - \sinh\left(x\right) + 1\right) + \frac{1}{2} \, x {\rm Li}_2\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - \frac{1}{2} \, x {\rm Li}_2\left(-\cosh\left(x\right) - \sinh\left(x\right)\right) - \frac{1}{2} \, {\rm polylog}\left(3, \cosh\left(x\right) + \sinh\left(x\right)\right) + \frac{1}{2} \, {\rm polylog}\left(3, -\cosh\left(x\right) - \sinh\left(x\right)\right)"," ",0,"1/4*x^2*log(-(cosh(x) + sinh(x) + 1)/(cosh(x) + sinh(x) - 1)) - 1/4*x^2*log(cosh(x) + sinh(x) + 1) + 1/4*x^2*log(-cosh(x) - sinh(x) + 1) + 1/2*x*dilog(cosh(x) + sinh(x)) - 1/2*x*dilog(-cosh(x) - sinh(x)) - 1/2*polylog(3, cosh(x) + sinh(x)) + 1/2*polylog(3, -cosh(x) - sinh(x))","C",0
348,1,120,0,0.529706," ","integrate(x^2*arctanh(exp(x)),x, algorithm=""fricas"")","\frac{1}{6} \, x^{3} \log\left(-\frac{\cosh\left(x\right) + \sinh\left(x\right) + 1}{\cosh\left(x\right) + \sinh\left(x\right) - 1}\right) - \frac{1}{6} \, x^{3} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + \frac{1}{6} \, x^{3} \log\left(-\cosh\left(x\right) - \sinh\left(x\right) + 1\right) + \frac{1}{2} \, x^{2} {\rm Li}_2\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - \frac{1}{2} \, x^{2} {\rm Li}_2\left(-\cosh\left(x\right) - \sinh\left(x\right)\right) - x {\rm polylog}\left(3, \cosh\left(x\right) + \sinh\left(x\right)\right) + x {\rm polylog}\left(3, -\cosh\left(x\right) - \sinh\left(x\right)\right) + {\rm polylog}\left(4, \cosh\left(x\right) + \sinh\left(x\right)\right) - {\rm polylog}\left(4, -\cosh\left(x\right) - \sinh\left(x\right)\right)"," ",0,"1/6*x^3*log(-(cosh(x) + sinh(x) + 1)/(cosh(x) + sinh(x) - 1)) - 1/6*x^3*log(cosh(x) + sinh(x) + 1) + 1/6*x^3*log(-cosh(x) - sinh(x) + 1) + 1/2*x^2*dilog(cosh(x) + sinh(x)) - 1/2*x^2*dilog(-cosh(x) - sinh(x)) - x*polylog(3, cosh(x) + sinh(x)) + x*polylog(3, -cosh(x) - sinh(x)) + polylog(4, cosh(x) + sinh(x)) - polylog(4, -cosh(x) - sinh(x))","C",0
349,1,138,0,0.667746," ","integrate(arctanh(exp(b*x+a)),x, algorithm=""fricas"")","\frac{b x \log\left(-\frac{\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1}{\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1}\right) - b x \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) - a \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) + {\left(b x + a\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right) + {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right)}{2 \, b}"," ",0,"1/2*(b*x*log(-(cosh(b*x + a) + sinh(b*x + a) + 1)/(cosh(b*x + a) + sinh(b*x + a) - 1)) - b*x*log(cosh(b*x + a) + sinh(b*x + a) + 1) - a*log(cosh(b*x + a) + sinh(b*x + a) - 1) + (b*x + a)*log(-cosh(b*x + a) - sinh(b*x + a) + 1) + dilog(cosh(b*x + a) + sinh(b*x + a)) - dilog(-cosh(b*x + a) - sinh(b*x + a)))/b","B",0
350,1,199,0,0.896464," ","integrate(x*arctanh(exp(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} \log\left(-\frac{\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1}{\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1}\right) - b^{2} x^{2} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) + 2 \, b x {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 2 \, b x {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) + a^{2} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) + {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right) - 2 \, {\rm polylog}\left(3, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + 2 \, {\rm polylog}\left(3, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right)}{4 \, b^{2}}"," ",0,"1/4*(b^2*x^2*log(-(cosh(b*x + a) + sinh(b*x + a) + 1)/(cosh(b*x + a) + sinh(b*x + a) - 1)) - b^2*x^2*log(cosh(b*x + a) + sinh(b*x + a) + 1) + 2*b*x*dilog(cosh(b*x + a) + sinh(b*x + a)) - 2*b*x*dilog(-cosh(b*x + a) - sinh(b*x + a)) + a^2*log(cosh(b*x + a) + sinh(b*x + a) - 1) + (b^2*x^2 - a^2)*log(-cosh(b*x + a) - sinh(b*x + a) + 1) - 2*polylog(3, cosh(b*x + a) + sinh(b*x + a)) + 2*polylog(3, -cosh(b*x + a) - sinh(b*x + a)))/b^2","C",0
351,1,248,0,0.604651," ","integrate(x^2*arctanh(exp(b*x+a)),x, algorithm=""fricas"")","\frac{b^{3} x^{3} \log\left(-\frac{\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1}{\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1}\right) - b^{3} x^{3} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) + 3 \, b^{2} x^{2} {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 3 \, b^{2} x^{2} {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) - a^{3} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) - 6 \, b x {\rm polylog}\left(3, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + 6 \, b x {\rm polylog}\left(3, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) + {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right) + 6 \, {\rm polylog}\left(4, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 6 \, {\rm polylog}\left(4, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right)}{6 \, b^{3}}"," ",0,"1/6*(b^3*x^3*log(-(cosh(b*x + a) + sinh(b*x + a) + 1)/(cosh(b*x + a) + sinh(b*x + a) - 1)) - b^3*x^3*log(cosh(b*x + a) + sinh(b*x + a) + 1) + 3*b^2*x^2*dilog(cosh(b*x + a) + sinh(b*x + a)) - 3*b^2*x^2*dilog(-cosh(b*x + a) - sinh(b*x + a)) - a^3*log(cosh(b*x + a) + sinh(b*x + a) - 1) - 6*b*x*polylog(3, cosh(b*x + a) + sinh(b*x + a)) + 6*b*x*polylog(3, -cosh(b*x + a) - sinh(b*x + a)) + (b^3*x^3 + a^3)*log(-cosh(b*x + a) - sinh(b*x + a) + 1) + 6*polylog(4, cosh(b*x + a) + sinh(b*x + a)) - 6*polylog(4, -cosh(b*x + a) - sinh(b*x + a)))/b^3","C",0
352,1,284,0,0.488438," ","integrate(arctanh(a+b*f^(d*x+c)),x, algorithm=""fricas"")","\frac{d x \log\left(f\right) \log\left(-\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}\right) + c \log\left(b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1\right) \log\left(f\right) - c \log\left(b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1\right) \log\left(f\right) - {\left(d x + c\right)} \log\left(f\right) \log\left(\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{a + 1}\right) + {\left(d x + c\right)} \log\left(f\right) \log\left(\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}{a - 1}\right) - {\rm Li}_2\left(-\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{a + 1} + 1\right) + {\rm Li}_2\left(-\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}{a - 1} + 1\right)}{2 \, d \log\left(f\right)}"," ",0,"1/2*(d*x*log(f)*log(-(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)) + c*log(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)*log(f) - c*log(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)*log(f) - (d*x + c)*log(f)*log((b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(a + 1)) + (d*x + c)*log(f)*log((b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)/(a - 1)) - dilog(-(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(a + 1) + 1) + dilog(-(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)/(a - 1) + 1))/(d*log(f))","A",0
353,1,396,0,0.683867," ","integrate(x*arctanh(a+b*f^(d*x+c)),x, algorithm=""fricas"")","\frac{d^{2} x^{2} \log\left(f\right)^{2} \log\left(-\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}\right) - c^{2} \log\left(b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1\right) \log\left(f\right)^{2} + c^{2} \log\left(b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1\right) \log\left(f\right)^{2} - 2 \, d x {\rm Li}_2\left(-\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{a + 1} + 1\right) \log\left(f\right) + 2 \, d x {\rm Li}_2\left(-\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}{a - 1} + 1\right) \log\left(f\right) - {\left(d^{2} x^{2} - c^{2}\right)} \log\left(f\right)^{2} \log\left(\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{a + 1}\right) + {\left(d^{2} x^{2} - c^{2}\right)} \log\left(f\right)^{2} \log\left(\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}{a - 1}\right) + 2 \, {\rm polylog}\left(3, -\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right)}{a + 1}\right) - 2 \, {\rm polylog}\left(3, -\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right)}{a - 1}\right)}{4 \, d^{2} \log\left(f\right)^{2}}"," ",0,"1/4*(d^2*x^2*log(f)^2*log(-(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)) - c^2*log(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)*log(f)^2 + c^2*log(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)*log(f)^2 - 2*d*x*dilog(-(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(a + 1) + 1)*log(f) + 2*d*x*dilog(-(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)/(a - 1) + 1)*log(f) - (d^2*x^2 - c^2)*log(f)^2*log((b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(a + 1)) + (d^2*x^2 - c^2)*log(f)^2*log((b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)/(a - 1)) + 2*polylog(3, -(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)))/(a + 1)) - 2*polylog(3, -(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)))/(a - 1)))/(d^2*log(f)^2)","C",0
354,1,480,0,0.528481," ","integrate(x^2*arctanh(a+b*f^(d*x+c)),x, algorithm=""fricas"")","\frac{d^{3} x^{3} \log\left(f\right)^{3} \log\left(-\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}\right) - 3 \, d^{2} x^{2} {\rm Li}_2\left(-\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{a + 1} + 1\right) \log\left(f\right)^{2} + 3 \, d^{2} x^{2} {\rm Li}_2\left(-\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}{a - 1} + 1\right) \log\left(f\right)^{2} + c^{3} \log\left(b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1\right) \log\left(f\right)^{3} - c^{3} \log\left(b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1\right) \log\left(f\right)^{3} - {\left(d^{3} x^{3} + c^{3}\right)} \log\left(f\right)^{3} \log\left(\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{a + 1}\right) + {\left(d^{3} x^{3} + c^{3}\right)} \log\left(f\right)^{3} \log\left(\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}{a - 1}\right) + 6 \, d x \log\left(f\right) {\rm polylog}\left(3, -\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right)}{a + 1}\right) - 6 \, d x \log\left(f\right) {\rm polylog}\left(3, -\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right)}{a - 1}\right) - 6 \, {\rm polylog}\left(4, -\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right)}{a + 1}\right) + 6 \, {\rm polylog}\left(4, -\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right)}{a - 1}\right)}{6 \, d^{3} \log\left(f\right)^{3}}"," ",0,"1/6*(d^3*x^3*log(f)^3*log(-(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)) - 3*d^2*x^2*dilog(-(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(a + 1) + 1)*log(f)^2 + 3*d^2*x^2*dilog(-(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)/(a - 1) + 1)*log(f)^2 + c^3*log(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)*log(f)^3 - c^3*log(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)*log(f)^3 - (d^3*x^3 + c^3)*log(f)^3*log((b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(a + 1)) + (d^3*x^3 + c^3)*log(f)^3*log((b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)/(a - 1)) + 6*d*x*log(f)*polylog(3, -(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)))/(a + 1)) - 6*d*x*log(f)*polylog(3, -(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)))/(a - 1)) - 6*polylog(4, -(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)))/(a + 1)) + 6*polylog(4, -(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)))/(a - 1)))/(d^3*log(f)^3)","C",0
355,1,234,0,0.476255," ","integrate(exp(c*(b*x+a))*arctanh(sinh(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{{\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\right)} \log\left(-\frac{\sinh\left(b c x + a c\right) + 1}{\sinh\left(b c x + a c\right) - 1}\right) + \sqrt{2} \log\left(\frac{3 \, {\left(2 \, \sqrt{2} + 3\right)} \cosh\left(b c x + a c\right)^{2} - 4 \, {\left(3 \, \sqrt{2} + 4\right)} \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right) + 3 \, {\left(2 \, \sqrt{2} + 3\right)} \sinh\left(b c x + a c\right)^{2} - 2 \, \sqrt{2} - 3}{\cosh\left(b c x + a c\right)^{2} + \sinh\left(b c x + a c\right)^{2} - 3}\right) + \log\left(\frac{2 \, {\left(\cosh\left(b c x + a c\right)^{2} + \sinh\left(b c x + a c\right)^{2} - 3\right)}}{\cosh\left(b c x + a c\right)^{2} - 2 \, \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)^{2}}\right)}{2 \, b c}"," ",0,"1/2*((cosh(b*c*x + a*c) + sinh(b*c*x + a*c))*log(-(sinh(b*c*x + a*c) + 1)/(sinh(b*c*x + a*c) - 1)) + sqrt(2)*log((3*(2*sqrt(2) + 3)*cosh(b*c*x + a*c)^2 - 4*(3*sqrt(2) + 4)*cosh(b*c*x + a*c)*sinh(b*c*x + a*c) + 3*(2*sqrt(2) + 3)*sinh(b*c*x + a*c)^2 - 2*sqrt(2) - 3)/(cosh(b*c*x + a*c)^2 + sinh(b*c*x + a*c)^2 - 3)) + log(2*(cosh(b*c*x + a*c)^2 + sinh(b*c*x + a*c)^2 - 3)/(cosh(b*c*x + a*c)^2 - 2*cosh(b*c*x + a*c)*sinh(b*c*x + a*c) + sinh(b*c*x + a*c)^2)))/(b*c)","B",0
356,1,93,0,0.455137," ","integrate(exp(c*(b*x+a))*arctanh(cosh(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{{\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\right)} \log\left(-\frac{\cosh\left(b c x + a c\right) + 1}{\cosh\left(b c x + a c\right) - 1}\right) + 2 \, \log\left(\frac{2 \, \sinh\left(b c x + a c\right)}{\cosh\left(b c x + a c\right) - \sinh\left(b c x + a c\right)}\right)}{2 \, b c}"," ",0,"1/2*((cosh(b*c*x + a*c) + sinh(b*c*x + a*c))*log(-(cosh(b*c*x + a*c) + 1)/(cosh(b*c*x + a*c) - 1)) + 2*log(2*sinh(b*c*x + a*c)/(cosh(b*c*x + a*c) - sinh(b*c*x + a*c))))/(b*c)","A",0
357,1,46,0,0.472744," ","integrate(exp(c*(b*x+a))*arctanh(tanh(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{{\left(b c x + a c - 1\right)} \cosh\left(b c x + a c\right) + {\left(b c x + a c - 1\right)} \sinh\left(b c x + a c\right)}{b c}"," ",0,"((b*c*x + a*c - 1)*cosh(b*c*x + a*c) + (b*c*x + a*c - 1)*sinh(b*c*x + a*c))/(b*c)","A",0
358,1,25,0,0.596561," ","integrate(exp(c*(b*x+a))*arctanh(coth(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{{\left(b c x + a c - 1\right)} e^{\left(b c x + a c\right)}}{b c}"," ",0,"(b*c*x + a*c - 1)*e^(b*c*x + a*c)/(b*c)","A",0
359,1,92,0,0.478054," ","integrate(exp(c*(b*x+a))*arctanh(sech(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{{\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\right)} \log\left(\frac{\cosh\left(b c x + a c\right) + 1}{\cosh\left(b c x + a c\right) - 1}\right) + 2 \, \log\left(\frac{2 \, \sinh\left(b c x + a c\right)}{\cosh\left(b c x + a c\right) - \sinh\left(b c x + a c\right)}\right)}{2 \, b c}"," ",0,"1/2*((cosh(b*c*x + a*c) + sinh(b*c*x + a*c))*log((cosh(b*c*x + a*c) + 1)/(cosh(b*c*x + a*c) - 1)) + 2*log(2*sinh(b*c*x + a*c)/(cosh(b*c*x + a*c) - sinh(b*c*x + a*c))))/(b*c)","A",0
360,1,233,0,1.473379," ","integrate(exp(c*(b*x+a))*arctanh(csch(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{{\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\right)} \log\left(\frac{\sinh\left(b c x + a c\right) + 1}{\sinh\left(b c x + a c\right) - 1}\right) + \sqrt{2} \log\left(\frac{3 \, {\left(2 \, \sqrt{2} + 3\right)} \cosh\left(b c x + a c\right)^{2} - 4 \, {\left(3 \, \sqrt{2} + 4\right)} \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right) + 3 \, {\left(2 \, \sqrt{2} + 3\right)} \sinh\left(b c x + a c\right)^{2} - 2 \, \sqrt{2} - 3}{\cosh\left(b c x + a c\right)^{2} + \sinh\left(b c x + a c\right)^{2} - 3}\right) + \log\left(\frac{2 \, {\left(\cosh\left(b c x + a c\right)^{2} + \sinh\left(b c x + a c\right)^{2} - 3\right)}}{\cosh\left(b c x + a c\right)^{2} - 2 \, \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)^{2}}\right)}{2 \, b c}"," ",0,"1/2*((cosh(b*c*x + a*c) + sinh(b*c*x + a*c))*log((sinh(b*c*x + a*c) + 1)/(sinh(b*c*x + a*c) - 1)) + sqrt(2)*log((3*(2*sqrt(2) + 3)*cosh(b*c*x + a*c)^2 - 4*(3*sqrt(2) + 4)*cosh(b*c*x + a*c)*sinh(b*c*x + a*c) + 3*(2*sqrt(2) + 3)*sinh(b*c*x + a*c)^2 - 2*sqrt(2) - 3)/(cosh(b*c*x + a*c)^2 + sinh(b*c*x + a*c)^2 - 3)) + log(2*(cosh(b*c*x + a*c)^2 + sinh(b*c*x + a*c)^2 - 3)/(cosh(b*c*x + a*c)^2 - 2*cosh(b*c*x + a*c)*sinh(b*c*x + a*c) + sinh(b*c*x + a*c)^2)))/(b*c)","B",0
361,1,327,0,0.552468," ","integrate((a+b*arctanh(c*x^n))*(d+e*log(f*x^m))/x,x, algorithm=""fricas"")","\frac{2 \, a e m n^{2} \log\left(x\right)^{2} - 2 \, b e m {\rm polylog}\left(3, c \cosh\left(n \log\left(x\right)\right) + c \sinh\left(n \log\left(x\right)\right)\right) + 2 \, b e m {\rm polylog}\left(3, -c \cosh\left(n \log\left(x\right)\right) - c \sinh\left(n \log\left(x\right)\right)\right) + 2 \, {\left(b e m n \log\left(x\right) + b e n \log\left(f\right) + b d n\right)} {\rm Li}_2\left(c \cosh\left(n \log\left(x\right)\right) + c \sinh\left(n \log\left(x\right)\right)\right) - 2 \, {\left(b e m n \log\left(x\right) + b e n \log\left(f\right) + b d n\right)} {\rm Li}_2\left(-c \cosh\left(n \log\left(x\right)\right) - c \sinh\left(n \log\left(x\right)\right)\right) - {\left(b e m n^{2} \log\left(x\right)^{2} + 2 \, {\left(b e n^{2} \log\left(f\right) + b d n^{2}\right)} \log\left(x\right)\right)} \log\left(c \cosh\left(n \log\left(x\right)\right) + c \sinh\left(n \log\left(x\right)\right) + 1\right) + {\left(b e m n^{2} \log\left(x\right)^{2} + 2 \, {\left(b e n^{2} \log\left(f\right) + b d n^{2}\right)} \log\left(x\right)\right)} \log\left(-c \cosh\left(n \log\left(x\right)\right) - c \sinh\left(n \log\left(x\right)\right) + 1\right) + 4 \, {\left(a e n^{2} \log\left(f\right) + a d n^{2}\right)} \log\left(x\right) + {\left(b e m n^{2} \log\left(x\right)^{2} + 2 \, {\left(b e n^{2} \log\left(f\right) + b d n^{2}\right)} \log\left(x\right)\right)} \log\left(-\frac{c \cosh\left(n \log\left(x\right)\right) + c \sinh\left(n \log\left(x\right)\right) + 1}{c \cosh\left(n \log\left(x\right)\right) + c \sinh\left(n \log\left(x\right)\right) - 1}\right)}{4 \, n^{2}}"," ",0,"1/4*(2*a*e*m*n^2*log(x)^2 - 2*b*e*m*polylog(3, c*cosh(n*log(x)) + c*sinh(n*log(x))) + 2*b*e*m*polylog(3, -c*cosh(n*log(x)) - c*sinh(n*log(x))) + 2*(b*e*m*n*log(x) + b*e*n*log(f) + b*d*n)*dilog(c*cosh(n*log(x)) + c*sinh(n*log(x))) - 2*(b*e*m*n*log(x) + b*e*n*log(f) + b*d*n)*dilog(-c*cosh(n*log(x)) - c*sinh(n*log(x))) - (b*e*m*n^2*log(x)^2 + 2*(b*e*n^2*log(f) + b*d*n^2)*log(x))*log(c*cosh(n*log(x)) + c*sinh(n*log(x)) + 1) + (b*e*m*n^2*log(x)^2 + 2*(b*e*n^2*log(f) + b*d*n^2)*log(x))*log(-c*cosh(n*log(x)) - c*sinh(n*log(x)) + 1) + 4*(a*e*n^2*log(f) + a*d*n^2)*log(x) + (b*e*m*n^2*log(x)^2 + 2*(b*e*n^2*log(f) + b*d*n^2)*log(x))*log(-(c*cosh(n*log(x)) + c*sinh(n*log(x)) + 1)/(c*cosh(n*log(x)) + c*sinh(n*log(x)) - 1)))/n^2","C",0
