1,1,45,0,0.443810," ","integrate(x^3*arctan(b*x^4+a),x, algorithm=""fricas"")","\frac{2 \, {\left(b x^{4} + a\right)} \arctan\left(b x^{4} + a\right) - \log\left(b^{2} x^{8} + 2 \, a b x^{4} + a^{2} + 1\right)}{8 \, b}"," ",0,"1/8*(2*(b*x^4 + a)*arctan(b*x^4 + a) - log(b^2*x^8 + 2*a*b*x^4 + a^2 + 1))/b","A",0
2,1,58,0,0.483424," ","integrate(x^(-1+n)*arctan(a+b*x^n),x, algorithm=""fricas"")","\frac{2 \, b x^{n} \arctan\left(b x^{n} + a\right) + 2 \, a \arctan\left(b x^{n} + a\right) - \log\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2} + 1\right)}{2 \, b n}"," ",0,"1/2*(2*b*x^n*arctan(b*x^n + a) + 2*a*arctan(b*x^n + a) - log(b^2*x^(2*n) + 2*a*b*x^n + a^2 + 1))/(b*n)","A",0
3,1,76,0,0.457273," ","integrate(x^5*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","-\frac{{\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)} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{288 \, e^{3}}"," ",0,"-1/288*((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)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)))/e^3","A",0
4,1,65,0,0.450090," ","integrate(x^3*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","-\frac{{\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)} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{32 \, e^{2}}"," ",0,"-1/32*((2*e*x^3 - 3*d*x)*sqrt(e*x^2 + d)*sqrt(-e) - (8*e^2*x^4 - 3*d^2)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)))/e^2","A",0
5,1,49,0,0.689686," ","integrate(x*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","-\frac{\sqrt{e x^{2} + d} \sqrt{-e} x - {\left(2 \, e x^{2} + d\right)} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{4 \, e}"," ",0,"-1/4*(sqrt(e*x^2 + d)*sqrt(-e)*x - (2*e*x^2 + d)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)))/e","A",0
6,0,0,0,0.645246," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{x}, x\right)"," ",0,"integral(arctan(sqrt(-e)*x/sqrt(e*x^2 + d))/x, x)","F",0
7,1,44,0,0.616694," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^3,x, algorithm=""fricas"")","-\frac{\sqrt{e x^{2} + d} \sqrt{-e} x + d \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{2 \, d x^{2}}"," ",0,"-1/2*(sqrt(e*x^2 + d)*sqrt(-e)*x + d*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)))/(d*x^2)","A",0
8,1,58,0,0.628709," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^5,x, algorithm=""fricas"")","-\frac{3 \, d^{2} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - {\left(2 \, e x^{3} - d x\right)} \sqrt{e x^{2} + d} \sqrt{-e}}{12 \, d^{2} x^{4}}"," ",0,"-1/12*(3*d^2*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - (2*e*x^3 - d*x)*sqrt(e*x^2 + d)*sqrt(-e))/(d^2*x^4)","A",0
9,1,68,0,0.838976," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^7,x, algorithm=""fricas"")","-\frac{15 \, d^{3} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) + {\left(8 \, e^{2} x^{5} - 4 \, d e x^{3} + 3 \, d^{2} x\right)} \sqrt{e x^{2} + d} \sqrt{-e}}{90 \, d^{3} x^{6}}"," ",0,"-1/90*(15*d^3*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) + (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
10,1,80,0,0.794876," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^9,x, algorithm=""fricas"")","-\frac{35 \, d^{4} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - {\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}}{280 \, d^{4} x^{8}}"," ",0,"-1/280*(35*d^4*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - (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
11,1,79,0,0.475672," ","integrate(x^6*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","\frac{35 \, e^{4} x^{7} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - {\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}}{245 \, e^{4}}"," ",0,"1/245*(35*e^4*x^7*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - (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
12,1,68,0,0.491993," ","integrate(x^4*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","\frac{15 \, e^{3} x^{5} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - {\left(3 \, e^{2} x^{4} - 4 \, d e x^{2} + 8 \, d^{2}\right)} \sqrt{e x^{2} + d} \sqrt{-e}}{75 \, e^{3}}"," ",0,"1/75*(15*e^3*x^5*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - (3*e^2*x^4 - 4*d*e*x^2 + 8*d^2)*sqrt(e*x^2 + d)*sqrt(-e))/e^3","A",0
13,1,56,0,0.441877," ","integrate(x^2*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","\frac{3 \, e^{2} x^{3} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - \sqrt{e x^{2} + d} {\left(e x^{2} - 2 \, d\right)} \sqrt{-e}}{9 \, e^{2}}"," ",0,"1/9*(3*e^2*x^3*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - sqrt(e*x^2 + d)*(e*x^2 - 2*d)*sqrt(-e))/e^2","A",0
14,1,41,0,0.441855," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","\frac{e x \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - \sqrt{e x^{2} + d} \sqrt{-e}}{e}"," ",0,"(e*x*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - sqrt(e*x^2 + d)*sqrt(-e))/e","A",0
15,1,148,0,0.598812," ","integrate(arctan(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) - 2 \, \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{2 \, x}, -\frac{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) + \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{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) - 2*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)))/x, -(x*sqrt(e/d)*arctan(sqrt(e*x^2 + d)*d*sqrt(-e)*sqrt(e/d)/(e^2*x^2 + d*e)) + arctan(sqrt(-e)*x/sqrt(e*x^2 + d)))/x]","A",0
16,1,198,0,0.595935," ","integrate(arctan(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 \, \sqrt{e x^{2} + d} \sqrt{-e} x - 4 \, d \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + 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) - \sqrt{e x^{2} + d} \sqrt{-e} x - 2 \, d \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + 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*sqrt(e*x^2 + d)*sqrt(-e)*x - 4*d*arctan(sqrt(-e)*x/sqrt(e*x^2 + 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)) - sqrt(e*x^2 + d)*sqrt(-e)*x - 2*d*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)))/(d*x^3)]","A",0
17,1,228,0,0.633977," ","integrate(arctan(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) - 16 \, d^{2} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) + 2 \, {\left(3 \, e x^{3} - 2 \, d x\right)} \sqrt{e x^{2} + d} \sqrt{-e}}{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) + 8 \, d^{2} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - {\left(3 \, e x^{3} - 2 \, d x\right)} \sqrt{e x^{2} + d} \sqrt{-e}}{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) - 16*d^2*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) + 2*(3*e*x^3 - 2*d*x)*sqrt(e*x^2 + d)*sqrt(-e))/(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)) + 8*d^2*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - (3*e*x^3 - 2*d*x)*sqrt(e*x^2 + d)*sqrt(-e))/(d^2*x^5)]","A",0
18,0,0,0,0.530093," ","integrate(x^(9/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(x^{\frac{9}{2}} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right), x\right)"," ",0,"integral(x^(9/2)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)), x)","F",0
19,0,0,0,0.599061," ","integrate(x^(5/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(x^{\frac{5}{2}} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right), x\right)"," ",0,"integral(x^(5/2)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)), x)","F",0
20,0,0,0,0.481427," ","integrate(x^(1/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{x} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right), x\right)"," ",0,"integral(sqrt(x)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)), x)","F",0
21,0,0,0,0.476211," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{x^{\frac{3}{2}}}, x\right)"," ",0,"integral(arctan(sqrt(-e)*x/sqrt(e*x^2 + d))/x^(3/2), x)","F",0
22,0,0,0,0.478301," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{x^{\frac{7}{2}}}, x\right)"," ",0,"integral(arctan(sqrt(-e)*x/sqrt(e*x^2 + d))/x^(7/2), x)","F",0
23,0,0,0,0.548747," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{x^{\frac{11}{2}}}, x\right)"," ",0,"integral(arctan(sqrt(-e)*x/sqrt(e*x^2 + d))/x^(11/2), x)","F",0
24,0,0,0,0.437406," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(15/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{x^{\frac{15}{2}}}, x\right)"," ",0,"integral(arctan(sqrt(-e)*x/sqrt(e*x^2 + d))/x^(15/2), x)","F",0
25,0,0,0,0.548607," ","integrate(x^(7/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(x^{\frac{7}{2}} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right), x\right)"," ",0,"integral(x^(7/2)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)), x)","F",0
26,0,0,0,1.269610," ","integrate(x^(3/2)*arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(x^{\frac{3}{2}} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right), x\right)"," ",0,"integral(x^(3/2)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)), x)","F",0
27,0,0,0,0.516340," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{\sqrt{x}}, x\right)"," ",0,"integral(arctan(sqrt(-e)*x/sqrt(e*x^2 + d))/sqrt(x), x)","F",0
28,0,0,0,0.537253," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{x^{\frac{5}{2}}}, x\right)"," ",0,"integral(arctan(sqrt(-e)*x/sqrt(e*x^2 + d))/x^(5/2), x)","F",0
29,0,0,0,0.546613," ","integrate(arctan(x*(-e)^(1/2)/(e*x^2+d)^(1/2))/x^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{x^{\frac{9}{2}}}, x\right)"," ",0,"integral(arctan(sqrt(-e)*x/sqrt(e*x^2 + d))/x^(9/2), x)","F",0
30,1,47,0,0.530564," ","integrate(arctan(x^2+x+1)/x^2,x, algorithm=""fricas"")","\frac{2 \, x \arctan\left(x + 1\right) + x \log\left(x^{2} + 2 \, x + 2\right) - 2 \, x \log\left(x^{2} + 1\right) + 2 \, x \log\left(x\right) - 4 \, \arctan\left(x^{2} + x + 1\right)}{4 \, x}"," ",0,"1/4*(2*x*arctan(x + 1) + x*log(x^2 + 2*x + 2) - 2*x*log(x^2 + 1) + 2*x*log(x) - 4*arctan(x^2 + x + 1))/x","A",0
31,0,0,0,0.607932," ","integrate((a+b*arctan((-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 \arctan\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}^{n}}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(b*arctan(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)^n/(c^2*x^2 - 1), x)","F",0
32,0,0,0,0.607060," ","integrate((a+b*arctan((-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} \arctan\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)^{3} + 3 \, a b^{2} \arctan\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)^{2} + 3 \, a^{2} b \arctan\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a^{3}}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(b^3*arctan(sqrt(-c*x + 1)/sqrt(c*x + 1))^3 + 3*a*b^2*arctan(sqrt(-c*x + 1)/sqrt(c*x + 1))^2 + 3*a^2*b*arctan(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a^3)/(c^2*x^2 - 1), x)","F",0
33,0,0,0,0.457239," ","integrate((a+b*arctan((-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} \arctan\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)^{2} + 2 \, a b \arctan\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a^{2}}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(b^2*arctan(sqrt(-c*x + 1)/sqrt(c*x + 1))^2 + 2*a*b*arctan(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a^2)/(c^2*x^2 - 1), x)","F",0
34,0,0,0,0.565951," ","integrate((a+b*arctan((-c*x+1)^(1/2)/(c*x+1)^(1/2)))/(-c^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \arctan\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(b*arctan(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)/(c^2*x^2 - 1), x)","F",0
35,0,0,0,0.494847," ","integrate(1/(-c^2*x^2+1)/(a+b*arctan((-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)} \arctan\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)*arctan(sqrt(-c*x + 1)/sqrt(c*x + 1)) - a), x)","F",0
36,0,0,0,0.570549," ","integrate(1/(-c^2*x^2+1)/(a+b*arctan((-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)} \arctan\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)} \arctan\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)*arctan(sqrt(-c*x + 1)/sqrt(c*x + 1))^2 - a^2 + 2*(a*b*c^2*x^2 - a*b)*arctan(sqrt(-c*x + 1)/sqrt(c*x + 1))), x)","F",0
37,1,33,0,0.516718," ","integrate(x^m*arctan(tan(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
38,1,13,0,0.824597," ","integrate(x^2*arctan(tan(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
39,1,13,0,0.489182," ","integrate(x*arctan(tan(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
40,1,10,0,0.760088," ","integrate(arctan(tan(b*x+a)),x, algorithm=""fricas"")","\frac{1}{2} \, b x^{2} + a x"," ",0,"1/2*b*x^2 + a*x","A",0
41,1,8,0,0.794039," ","integrate(arctan(tan(b*x+a))/x,x, algorithm=""fricas"")","b x + a \log\left(x\right)"," ",0,"b*x + a*log(x)","A",0
42,1,42,0,0.551033," ","integrate(x^m*(1/2*pi-arccot(cot(b*x+a))),x, algorithm=""fricas"")","-\frac{{\left(2 \, {\left(b m + b\right)} x^{2} - {\left(\pi {\left(m + 2\right)} - 2 \, a m - 4 \, a\right)} x\right)} x^{m}}{2 \, {\left(m^{2} + 3 \, m + 2\right)}}"," ",0,"-1/2*(2*(b*m + b)*x^2 - (pi*(m + 2) - 2*a*m - 4*a)*x)*x^m/(m^2 + 3*m + 2)","A",0
43,1,17,0,0.443859," ","integrate(x^2*(1/2*pi-arccot(cot(b*x+a))),x, algorithm=""fricas"")","-\frac{1}{4} \, b x^{4} + \frac{1}{6} \, {\left(\pi - 2 \, a\right)} x^{3}"," ",0,"-1/4*b*x^4 + 1/6*(pi - 2*a)*x^3","A",0
44,1,17,0,0.394013," ","integrate(x*(1/2*pi-arccot(cot(b*x+a))),x, algorithm=""fricas"")","-\frac{1}{3} \, b x^{3} + \frac{1}{4} \, {\left(\pi - 2 \, a\right)} x^{2}"," ",0,"-1/3*b*x^3 + 1/4*(pi - 2*a)*x^2","A",0
45,1,15,0,0.674138," ","integrate(1/2*pi-arccot(cot(b*x+a)),x, algorithm=""fricas"")","-\frac{1}{2} \, b x^{2} + \frac{1}{2} \, {\left(\pi - 2 \, a\right)} x"," ",0,"-1/2*b*x^2 + 1/2*(pi - 2*a)*x","A",0
46,1,14,0,0.468944," ","integrate((1/2*pi-arccot(cot(b*x+a)))/x,x, algorithm=""fricas"")","-b x + \frac{1}{2} \, {\left(\pi - 2 \, a\right)} \log\left(x\right)"," ",0,"-b*x + 1/2*(pi - 2*a)*log(x)","A",0
47,1,10,0,0.588792," ","integrate(arctan(tan(b*x+a)),x, algorithm=""fricas"")","\frac{1}{2} \, b x^{2} + a x"," ",0,"1/2*b*x^2 + a*x","A",0
48,1,1973,0,0.755249," ","integrate(x^2*arctan(c+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{16 \, b^{3} x^{3} \arctan\left(d \tan\left(b x + a\right) + c\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{2 \, {\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1} + 1\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{2 \, {\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{2 \, {\left(-i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1} + 1\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{2 \, {\left(-i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1} + 1\right) + 4 i \, a^{3} \log\left(\frac{{\left(i \, c d + d^{2} + d\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \tan\left(b x + a\right) - d - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 i \, a^{3} \log\left(\frac{{\left(i \, c d + d^{2} - d\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \tan\left(b x + a\right) + d - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 i \, a^{3} \log\left(\frac{{\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \tan\left(b x + a\right) - d + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 i \, a^{3} \log\left(\frac{{\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \tan\left(b x + a\right) + d + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 6 i \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, c d + d^{2} + {\left(2 i \, c^{2} - 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) - 6 i \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, c d + d^{2} + {\left(-2 i \, c^{2} - 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) - 6 i \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, c d + d^{2} + {\left(2 i \, c^{2} - 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + 6 i \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, c d + d^{2} + {\left(-2 i \, c^{2} - 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(-4 i \, b^{3} x^{3} - 4 i \, a^{3}\right)} \log\left(-\frac{2 \, {\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(4 i \, b^{3} x^{3} + 4 i \, a^{3}\right)} \log\left(-\frac{2 \, {\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(4 i \, b^{3} x^{3} + 4 i \, a^{3}\right)} \log\left(-\frac{2 \, {\left(-i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(-4 i \, b^{3} x^{3} - 4 i \, a^{3}\right)} \log\left(-\frac{2 \, {\left(-i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) + 3 \, {\rm polylog}\left(4, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, c d + d^{2} + {\left(2 i \, c^{2} - 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) + 3 \, {\rm polylog}\left(4, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, c d + d^{2} + {\left(-2 i \, c^{2} - 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) - 3 \, {\rm polylog}\left(4, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, c d + d^{2} + {\left(2 i \, c^{2} - 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) - 3 \, {\rm polylog}\left(4, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, c d + d^{2} + {\left(-2 i \, c^{2} - 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right)}{48 \, b^{3}}"," ",0,"1/48*(16*b^3*x^3*arctan(d*tan(b*x + a) + c) + 6*b^2*x^2*dilog((2*(I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1) + 1) - 6*b^2*x^2*dilog((2*(I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1) + 1) + 6*b^2*x^2*dilog((2*(-I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1) + 1) - 6*b^2*x^2*dilog((2*(-I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1) + 1) + 4*I*a^3*log(((I*c*d + d^2 + d)*tan(b*x + a)^2 - c^2 + I*c*d + (I*c^2 + I*d^2 + 2*I*d + I)*tan(b*x + a) - d - 1)/(tan(b*x + a)^2 + 1)) - 4*I*a^3*log(((I*c*d + d^2 - d)*tan(b*x + a)^2 - c^2 + I*c*d + (I*c^2 + I*d^2 - 2*I*d + I)*tan(b*x + a) + d - 1)/(tan(b*x + a)^2 + 1)) + 4*I*a^3*log(((I*c*d - d^2 + d)*tan(b*x + a)^2 + c^2 + I*c*d + (I*c^2 + I*d^2 - 2*I*d + I)*tan(b*x + a) - d + 1)/(tan(b*x + a)^2 + 1)) - 4*I*a^3*log(((I*c*d - d^2 - d)*tan(b*x + a)^2 + c^2 + I*c*d + (I*c^2 + I*d^2 + 2*I*d + I)*tan(b*x + a) + d + 1)/(tan(b*x + a)^2 + 1)) + 6*I*b*x*polylog(3, ((c^2 + 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 - 2*I*c*d + d^2 + (2*I*c^2 - 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) - 6*I*b*x*polylog(3, ((c^2 - 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 + 2*I*c*d + d^2 + (-2*I*c^2 - 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) - 6*I*b*x*polylog(3, ((c^2 + 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 - 2*I*c*d + d^2 + (2*I*c^2 - 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + 6*I*b*x*polylog(3, ((c^2 - 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 + 2*I*c*d + d^2 + (-2*I*c^2 - 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + (-4*I*b^3*x^3 - 4*I*a^3)*log(-(2*(I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + (4*I*b^3*x^3 + 4*I*a^3)*log(-(2*(I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) + (4*I*b^3*x^3 + 4*I*a^3)*log(-(2*(-I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + (-4*I*b^3*x^3 - 4*I*a^3)*log(-(2*(-I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) + 3*polylog(4, ((c^2 + 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 - 2*I*c*d + d^2 + (2*I*c^2 - 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) + 3*polylog(4, ((c^2 - 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 + 2*I*c*d + d^2 + (-2*I*c^2 - 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) - 3*polylog(4, ((c^2 + 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 - 2*I*c*d + d^2 + (2*I*c^2 - 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) - 3*polylog(4, ((c^2 - 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 + 2*I*c*d + d^2 + (-2*I*c^2 - 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)))/b^3","C",0
49,1,1557,0,0.671855," ","integrate(x*arctan(c+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{8 \, b^{2} x^{2} \arctan\left(d \tan\left(b x + a\right) + c\right) + 2 \, b x {\rm Li}_2\left(\frac{2 \, {\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1} + 1\right) - 2 \, b x {\rm Li}_2\left(\frac{2 \, {\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1} + 1\right) + 2 \, b x {\rm Li}_2\left(\frac{2 \, {\left(-i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1} + 1\right) - 2 \, b x {\rm Li}_2\left(\frac{2 \, {\left(-i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1} + 1\right) - 2 i \, a^{2} \log\left(\frac{{\left(i \, c d + d^{2} + d\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \tan\left(b x + a\right) - d - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 i \, a^{2} \log\left(\frac{{\left(i \, c d + d^{2} - d\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \tan\left(b x + a\right) + d - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 i \, a^{2} \log\left(\frac{{\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \tan\left(b x + a\right) - d + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 i \, a^{2} \log\left(\frac{{\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \tan\left(b x + a\right) + d + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + {\left(-2 i \, b^{2} x^{2} + 2 i \, a^{2}\right)} \log\left(-\frac{2 \, {\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(2 i \, b^{2} x^{2} - 2 i \, a^{2}\right)} \log\left(-\frac{2 \, {\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(2 i \, b^{2} x^{2} - 2 i \, a^{2}\right)} \log\left(-\frac{2 \, {\left(-i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(-2 i \, b^{2} x^{2} + 2 i \, a^{2}\right)} \log\left(-\frac{2 \, {\left(-i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) + i \, {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, c d + d^{2} + {\left(2 i \, c^{2} - 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) - i \, {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, c d + d^{2} + {\left(-2 i \, c^{2} - 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) - i \, {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, c d + d^{2} + {\left(2 i \, c^{2} - 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + i \, {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, c d + d^{2} + {\left(-2 i \, c^{2} - 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right)}{16 \, b^{2}}"," ",0,"1/16*(8*b^2*x^2*arctan(d*tan(b*x + a) + c) + 2*b*x*dilog((2*(I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1) + 1) - 2*b*x*dilog((2*(I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1) + 1) + 2*b*x*dilog((2*(-I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1) + 1) - 2*b*x*dilog((2*(-I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1) + 1) - 2*I*a^2*log(((I*c*d + d^2 + d)*tan(b*x + a)^2 - c^2 + I*c*d + (I*c^2 + I*d^2 + 2*I*d + I)*tan(b*x + a) - d - 1)/(tan(b*x + a)^2 + 1)) + 2*I*a^2*log(((I*c*d + d^2 - d)*tan(b*x + a)^2 - c^2 + I*c*d + (I*c^2 + I*d^2 - 2*I*d + I)*tan(b*x + a) + d - 1)/(tan(b*x + a)^2 + 1)) - 2*I*a^2*log(((I*c*d - d^2 + d)*tan(b*x + a)^2 + c^2 + I*c*d + (I*c^2 + I*d^2 - 2*I*d + I)*tan(b*x + a) - d + 1)/(tan(b*x + a)^2 + 1)) + 2*I*a^2*log(((I*c*d - d^2 - d)*tan(b*x + a)^2 + c^2 + I*c*d + (I*c^2 + I*d^2 + 2*I*d + I)*tan(b*x + a) + d + 1)/(tan(b*x + a)^2 + 1)) + (-2*I*b^2*x^2 + 2*I*a^2)*log(-(2*(I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + (2*I*b^2*x^2 - 2*I*a^2)*log(-(2*(I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) + (2*I*b^2*x^2 - 2*I*a^2)*log(-(2*(-I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + (-2*I*b^2*x^2 + 2*I*a^2)*log(-(2*(-I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) + I*polylog(3, ((c^2 + 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 - 2*I*c*d + d^2 + (2*I*c^2 - 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) - I*polylog(3, ((c^2 - 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 + 2*I*c*d + d^2 + (-2*I*c^2 - 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) - I*polylog(3, ((c^2 + 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 - 2*I*c*d + d^2 + (2*I*c^2 - 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + I*polylog(3, ((c^2 - 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 + 2*I*c*d + d^2 + (-2*I*c^2 - 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)))/b^2","C",0
50,1,1117,0,0.695849," ","integrate(arctan(c+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{8 \, b x \arctan\left(d \tan\left(b x + a\right) + c\right) + {\left(-2 i \, b x - 2 i \, a\right)} \log\left(-\frac{2 \, {\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(2 i \, b x + 2 i \, a\right)} \log\left(-\frac{2 \, {\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(2 i \, b x + 2 i \, a\right)} \log\left(-\frac{2 \, {\left(-i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(-2 i \, b x - 2 i \, a\right)} \log\left(-\frac{2 \, {\left(-i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) + 2 i \, a \log\left(\frac{{\left(i \, c d + d^{2} + d\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \tan\left(b x + a\right) - d - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 i \, a \log\left(\frac{{\left(i \, c d + d^{2} - d\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \tan\left(b x + a\right) + d - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 i \, a \log\left(\frac{{\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \tan\left(b x + a\right) - d + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 i \, a \log\left(\frac{{\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \tan\left(b x + a\right) + d + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + {\rm Li}_2\left(\frac{2 \, {\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1} + 1\right) - {\rm Li}_2\left(\frac{2 \, {\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1} + 1\right) + {\rm Li}_2\left(\frac{2 \, {\left(-i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1} + 1\right) - {\rm Li}_2\left(\frac{2 \, {\left(-i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1} + 1\right)}{8 \, b}"," ",0,"1/8*(8*b*x*arctan(d*tan(b*x + a) + c) + (-2*I*b*x - 2*I*a)*log(-(2*(I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + (2*I*b*x + 2*I*a)*log(-(2*(I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) + (2*I*b*x + 2*I*a)*log(-(2*(-I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + (-2*I*b*x - 2*I*a)*log(-(2*(-I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) + 2*I*a*log(((I*c*d + d^2 + d)*tan(b*x + a)^2 - c^2 + I*c*d + (I*c^2 + I*d^2 + 2*I*d + I)*tan(b*x + a) - d - 1)/(tan(b*x + a)^2 + 1)) - 2*I*a*log(((I*c*d + d^2 - d)*tan(b*x + a)^2 - c^2 + I*c*d + (I*c^2 + I*d^2 - 2*I*d + I)*tan(b*x + a) + d - 1)/(tan(b*x + a)^2 + 1)) + 2*I*a*log(((I*c*d - d^2 + d)*tan(b*x + a)^2 + c^2 + I*c*d + (I*c^2 + I*d^2 - 2*I*d + I)*tan(b*x + a) - d + 1)/(tan(b*x + a)^2 + 1)) - 2*I*a*log(((I*c*d - d^2 - d)*tan(b*x + a)^2 + c^2 + I*c*d + (I*c^2 + I*d^2 + 2*I*d + I)*tan(b*x + a) + d + 1)/(tan(b*x + a)^2 + 1)) + dilog((2*(I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1) + 1) - dilog((2*(I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1) + 1) + dilog((2*(-I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1) + 1) - dilog((2*(-I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1) + 1))/b","B",0
51,0,0,0,0.428137," ","integrate(arctan(c+d*tan(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(d \tan\left(b x + a\right) + c\right)}{x}, x\right)"," ",0,"integral(arctan(d*tan(b*x + a) + c)/x, x)","F",0
52,1,322,0,0.571752," ","integrate(x^2*arctan(c+(1+I*c)*tan(b*x+a)),x, algorithm=""fricas"")","-\frac{b^{4} x^{4} - 2 i \, b^{3} x^{3} \log\left(-\frac{{\left(c e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{c - i}\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) - a^{4} - 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) - 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) + 12 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 12 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) - {\left(-2 i \, b^{3} x^{3} - 2 i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) - {\left(-2 i \, b^{3} x^{3} - 2 i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) - 12 \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) - 12 \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right)}{12 \, b^{3}}"," ",0,"-1/12*(b^4*x^4 - 2*I*b^3*x^3*log(-(c*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/(c - I)) + 6*b^2*x^2*dilog(1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) + 6*b^2*x^2*dilog(-1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) - a^4 - 2*I*a^3*log(1/2*(2*c*e^(I*b*x + I*a) + I*sqrt(4*I*c))/c) - 2*I*a^3*log(1/2*(2*c*e^(I*b*x + I*a) - I*sqrt(4*I*c))/c) + 12*I*b*x*polylog(3, 1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) + 12*I*b*x*polylog(3, -1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) - (-2*I*b^3*x^3 - 2*I*a^3)*log(1/2*sqrt(4*I*c)*e^(I*b*x + I*a) + 1) - (-2*I*b^3*x^3 - 2*I*a^3)*log(-1/2*sqrt(4*I*c)*e^(I*b*x + I*a) + 1) - 12*polylog(4, 1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) - 12*polylog(4, -1/2*sqrt(4*I*c)*e^(I*b*x + I*a)))/b^3","C",0
53,1,271,0,0.492263," ","integrate(x*arctan(c+(1+I*c)*tan(b*x+a)),x, algorithm=""fricas"")","-\frac{2 \, b^{3} x^{3} - 3 i \, b^{2} x^{2} \log\left(-\frac{{\left(c e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{c - i}\right) + 2 \, a^{3} + 6 \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 6 \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) + 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) - {\left(-3 i \, b^{2} x^{2} + 3 i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) - {\left(-3 i \, b^{2} x^{2} + 3 i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) + 6 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 6 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right)}{12 \, b^{2}}"," ",0,"-1/12*(2*b^3*x^3 - 3*I*b^2*x^2*log(-(c*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/(c - I)) + 2*a^3 + 6*b*x*dilog(1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) + 6*b*x*dilog(-1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) + 3*I*a^2*log(1/2*(2*c*e^(I*b*x + I*a) + I*sqrt(4*I*c))/c) + 3*I*a^2*log(1/2*(2*c*e^(I*b*x + I*a) - I*sqrt(4*I*c))/c) - (-3*I*b^2*x^2 + 3*I*a^2)*log(1/2*sqrt(4*I*c)*e^(I*b*x + I*a) + 1) - (-3*I*b^2*x^2 + 3*I*a^2)*log(-1/2*sqrt(4*I*c)*e^(I*b*x + I*a) + 1) + 6*I*polylog(3, 1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) + 6*I*polylog(3, -1/2*sqrt(4*I*c)*e^(I*b*x + I*a)))/b^2","C",0
54,1,202,0,0.630430," ","integrate(arctan(c+(1+I*c)*tan(b*x+a)),x, algorithm=""fricas"")","-\frac{b^{2} x^{2} - i \, b x \log\left(-\frac{{\left(c e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{c - i}\right) - a^{2} - {\left(-i \, b x - i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) - {\left(-i \, b x - i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) - i \, a \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) - i \, a \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) + {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right)}{2 \, b}"," ",0,"-1/2*(b^2*x^2 - I*b*x*log(-(c*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/(c - I)) - a^2 - (-I*b*x - I*a)*log(1/2*sqrt(4*I*c)*e^(I*b*x + I*a) + 1) - (-I*b*x - I*a)*log(-1/2*sqrt(4*I*c)*e^(I*b*x + I*a) + 1) - I*a*log(1/2*(2*c*e^(I*b*x + I*a) + I*sqrt(4*I*c))/c) - I*a*log(1/2*(2*c*e^(I*b*x + I*a) - I*sqrt(4*I*c))/c) + dilog(1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) + dilog(-1/2*sqrt(4*I*c)*e^(I*b*x + I*a)))/b","B",0
55,0,0,0,0.635069," ","integrate(arctan(c+(1+I*c)*tan(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, \log\left(-\frac{{\left(c e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{c - i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*I*log(-(c*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/(c - I))/x, x)","F",0
56,1,320,0,0.507531," ","integrate(x^2*arctan(c+(-1+I*c)*tan(b*x+a)),x, algorithm=""fricas"")","\frac{b^{4} x^{4} + 2 i \, b^{3} x^{3} \log\left(-\frac{{\left(c + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)}}{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) - a^{4} - 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) - 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) + 12 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 12 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + {\left(2 i \, b^{3} x^{3} + 2 i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) + {\left(2 i \, b^{3} x^{3} + 2 i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) - 12 \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) - 12 \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(b^4*x^4 + 2*I*b^3*x^3*log(-(c + I)*e^(2*I*b*x + 2*I*a)/(c*e^(2*I*b*x + 2*I*a) - I)) + 6*b^2*x^2*dilog(1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) + 6*b^2*x^2*dilog(-1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) - a^4 - 2*I*a^3*log(1/2*(2*c*e^(I*b*x + I*a) + I*sqrt(-4*I*c))/c) - 2*I*a^3*log(1/2*(2*c*e^(I*b*x + I*a) - I*sqrt(-4*I*c))/c) + 12*I*b*x*polylog(3, 1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) + 12*I*b*x*polylog(3, -1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) + (2*I*b^3*x^3 + 2*I*a^3)*log(1/2*sqrt(-4*I*c)*e^(I*b*x + I*a) + 1) + (2*I*b^3*x^3 + 2*I*a^3)*log(-1/2*sqrt(-4*I*c)*e^(I*b*x + I*a) + 1) - 12*polylog(4, 1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) - 12*polylog(4, -1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)))/b^3","C",0
57,1,269,0,0.710759," ","integrate(x*arctan(c+(-1+I*c)*tan(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} + 3 i \, b^{2} x^{2} \log\left(-\frac{{\left(c + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)}}{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) + 2 \, a^{3} + 6 \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 6 \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) + 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) + {\left(3 i \, b^{2} x^{2} - 3 i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) + {\left(3 i \, b^{2} x^{2} - 3 i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) + 6 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 6 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*b^3*x^3 + 3*I*b^2*x^2*log(-(c + I)*e^(2*I*b*x + 2*I*a)/(c*e^(2*I*b*x + 2*I*a) - I)) + 2*a^3 + 6*b*x*dilog(1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) + 6*b*x*dilog(-1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) + 3*I*a^2*log(1/2*(2*c*e^(I*b*x + I*a) + I*sqrt(-4*I*c))/c) + 3*I*a^2*log(1/2*(2*c*e^(I*b*x + I*a) - I*sqrt(-4*I*c))/c) + (3*I*b^2*x^2 - 3*I*a^2)*log(1/2*sqrt(-4*I*c)*e^(I*b*x + I*a) + 1) + (3*I*b^2*x^2 - 3*I*a^2)*log(-1/2*sqrt(-4*I*c)*e^(I*b*x + I*a) + 1) + 6*I*polylog(3, 1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) + 6*I*polylog(3, -1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)))/b^2","C",0
58,1,200,0,0.752154," ","integrate(arctan(c+(-1+I*c)*tan(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} + i \, b x \log\left(-\frac{{\left(c + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)}}{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) - a^{2} + {\left(i \, b x + i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) - i \, a \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) - i \, a \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) + {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right)}{2 \, b}"," ",0,"1/2*(b^2*x^2 + I*b*x*log(-(c + I)*e^(2*I*b*x + 2*I*a)/(c*e^(2*I*b*x + 2*I*a) - I)) - a^2 + (I*b*x + I*a)*log(1/2*sqrt(-4*I*c)*e^(I*b*x + I*a) + 1) + (I*b*x + I*a)*log(-1/2*sqrt(-4*I*c)*e^(I*b*x + I*a) + 1) - I*a*log(1/2*(2*c*e^(I*b*x + I*a) + I*sqrt(-4*I*c))/c) - I*a*log(1/2*(2*c*e^(I*b*x + I*a) - I*sqrt(-4*I*c))/c) + dilog(1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) + dilog(-1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)))/b","B",0
59,0,0,0,0.422749," ","integrate(arctan(c+(-1+I*c)*tan(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, \log\left(-\frac{{\left(c + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)}}{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*I*log(-(c + I)*e^(2*I*b*x + 2*I*a)/(c*e^(2*I*b*x + 2*I*a) - I))/x, x)","F",0
60,1,15,0,0.482526," ","integrate(1/2*pi-arccot(cot(b*x+a)),x, algorithm=""fricas"")","-\frac{1}{2} \, b x^{2} + \frac{1}{2} \, {\left(\pi - 2 \, a\right)} x"," ",0,"-1/2*b*x^2 + 1/2*(pi - 2*a)*x","A",0
61,1,1585,0,0.780065," ","integrate(x^2*arctan(c+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{16 \, b^{3} x^{3} \arctan\left(d \cot\left(b x + a\right) + c\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1} + 1\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1} + 1\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1} + 1\right) - 4 i \, a^{3} \log\left(\frac{1}{2} \, c^{2} + i \, c d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 4 i \, a^{3} \log\left(\frac{1}{2} \, c^{2} + i \, c d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 4 i \, a^{3} \log\left(-\frac{1}{2} \, c^{2} + i \, c d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) - \frac{1}{2}\right) - 4 i \, a^{3} \log\left(-\frac{1}{2} \, c^{2} + i \, c d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) - \frac{1}{2}\right) + 6 i \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, d + 1}\right) - 6 i \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, d + 1}\right) - 6 i \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, d + 1}\right) + 6 i \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(4 i \, b^{3} x^{3} + 4 i \, a^{3}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(-4 i \, b^{3} x^{3} - 4 i \, a^{3}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(-4 i \, b^{3} x^{3} - 4 i \, a^{3}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(4 i \, b^{3} x^{3} + 4 i \, a^{3}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1}\right) - 3 \, {\rm polylog}\left(4, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, d + 1}\right) + 3 \, {\rm polylog}\left(4, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, d + 1}\right) - 3 \, {\rm polylog}\left(4, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, d + 1}\right) + 3 \, {\rm polylog}\left(4, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, d + 1}\right)}{48 \, b^{3}}"," ",0,"1/48*(16*b^3*x^3*arctan(d*cot(b*x + a) + c) + 6*b^2*x^2*dilog(-(c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1) + 1) + 6*b^2*x^2*dilog(-(c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1) + 1) - 6*b^2*x^2*dilog(-(c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1) + 1) - 6*b^2*x^2*dilog(-(c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1) + 1) - 4*I*a^3*log(1/2*c^2 + I*c*d - 1/2*d^2 - 1/2*(c^2 + d^2 + 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*d + I)*sin(2*b*x + 2*a) + 1/2) + 4*I*a^3*log(1/2*c^2 + I*c*d - 1/2*d^2 - 1/2*(c^2 + d^2 - 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*d + I)*sin(2*b*x + 2*a) + 1/2) + 4*I*a^3*log(-1/2*c^2 + I*c*d + 1/2*d^2 + 1/2*(c^2 + d^2 + 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*d + I)*sin(2*b*x + 2*a) - 1/2) - 4*I*a^3*log(-1/2*c^2 + I*c*d + 1/2*d^2 + 1/2*(c^2 + d^2 - 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*d + I)*sin(2*b*x + 2*a) - 1/2) + 6*I*b*x*polylog(3, ((c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*d + 1)) - 6*I*b*x*polylog(3, ((c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*d + 1)) - 6*I*b*x*polylog(3, ((c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*d + 1)) + 6*I*b*x*polylog(3, ((c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*d + 1)) + (4*I*b^3*x^3 + 4*I*a^3)*log((c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1)) + (-4*I*b^3*x^3 - 4*I*a^3)*log((c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1)) + (-4*I*b^3*x^3 - 4*I*a^3)*log((c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1)) + (4*I*b^3*x^3 + 4*I*a^3)*log((c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1)) - 3*polylog(4, ((c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*d + 1)) + 3*polylog(4, ((c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*d + 1)) - 3*polylog(4, ((c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*d + 1)) + 3*polylog(4, ((c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*d + 1)))/b^3","C",0
62,1,1285,0,0.913368," ","integrate(x*arctan(c+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{8 \, b^{2} x^{2} \arctan\left(d \cot\left(b x + a\right) + c\right) + 2 \, b x {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1} + 1\right) + 2 \, b x {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1} + 1\right) - 2 \, b x {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1} + 1\right) - 2 \, b x {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1} + 1\right) + 2 i \, a^{2} \log\left(\frac{1}{2} \, c^{2} + i \, c d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) - 2 i \, a^{2} \log\left(\frac{1}{2} \, c^{2} + i \, c d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) - 2 i \, a^{2} \log\left(-\frac{1}{2} \, c^{2} + i \, c d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) - \frac{1}{2}\right) + 2 i \, a^{2} \log\left(-\frac{1}{2} \, c^{2} + i \, c d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) - \frac{1}{2}\right) + {\left(2 i \, b^{2} x^{2} - 2 i \, a^{2}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(-2 i \, b^{2} x^{2} + 2 i \, a^{2}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(-2 i \, b^{2} x^{2} + 2 i \, a^{2}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(2 i \, b^{2} x^{2} - 2 i \, a^{2}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1}\right) + i \, {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, d + 1}\right) - i \, {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, d + 1}\right) - i \, {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, d + 1}\right) + i \, {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, d + 1}\right)}{16 \, b^{2}}"," ",0,"1/16*(8*b^2*x^2*arctan(d*cot(b*x + a) + c) + 2*b*x*dilog(-(c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1) + 1) + 2*b*x*dilog(-(c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1) + 1) - 2*b*x*dilog(-(c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1) + 1) - 2*b*x*dilog(-(c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1) + 1) + 2*I*a^2*log(1/2*c^2 + I*c*d - 1/2*d^2 - 1/2*(c^2 + d^2 + 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*d + I)*sin(2*b*x + 2*a) + 1/2) - 2*I*a^2*log(1/2*c^2 + I*c*d - 1/2*d^2 - 1/2*(c^2 + d^2 - 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*d + I)*sin(2*b*x + 2*a) + 1/2) - 2*I*a^2*log(-1/2*c^2 + I*c*d + 1/2*d^2 + 1/2*(c^2 + d^2 + 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*d + I)*sin(2*b*x + 2*a) - 1/2) + 2*I*a^2*log(-1/2*c^2 + I*c*d + 1/2*d^2 + 1/2*(c^2 + d^2 - 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*d + I)*sin(2*b*x + 2*a) - 1/2) + (2*I*b^2*x^2 - 2*I*a^2)*log((c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1)) + (-2*I*b^2*x^2 + 2*I*a^2)*log((c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1)) + (-2*I*b^2*x^2 + 2*I*a^2)*log((c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1)) + (2*I*b^2*x^2 - 2*I*a^2)*log((c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1)) + I*polylog(3, ((c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*d + 1)) - I*polylog(3, ((c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*d + 1)) - I*polylog(3, ((c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*d + 1)) + I*polylog(3, ((c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*d + 1)))/b^2","C",0
63,1,961,0,0.714656," ","integrate(arctan(c+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{8 \, b x \arctan\left(d \cot\left(b x + a\right) + c\right) - 2 i \, a \log\left(\frac{1}{2} \, c^{2} + i \, c d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 i \, a \log\left(\frac{1}{2} \, c^{2} + i \, c d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 i \, a \log\left(-\frac{1}{2} \, c^{2} + i \, c d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) - \frac{1}{2}\right) - 2 i \, a \log\left(-\frac{1}{2} \, c^{2} + i \, c d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) - \frac{1}{2}\right) + {\left(2 i \, b x + 2 i \, a\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(-2 i \, b x - 2 i \, a\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(-2 i \, b x - 2 i \, a\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(2 i \, b x + 2 i \, a\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1}\right) + {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1} + 1\right) + {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1} + 1\right) - {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1} + 1\right) - {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1} + 1\right)}{8 \, b}"," ",0,"1/8*(8*b*x*arctan(d*cot(b*x + a) + c) - 2*I*a*log(1/2*c^2 + I*c*d - 1/2*d^2 - 1/2*(c^2 + d^2 + 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*d + I)*sin(2*b*x + 2*a) + 1/2) + 2*I*a*log(1/2*c^2 + I*c*d - 1/2*d^2 - 1/2*(c^2 + d^2 - 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*d + I)*sin(2*b*x + 2*a) + 1/2) + 2*I*a*log(-1/2*c^2 + I*c*d + 1/2*d^2 + 1/2*(c^2 + d^2 + 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*d + I)*sin(2*b*x + 2*a) - 1/2) - 2*I*a*log(-1/2*c^2 + I*c*d + 1/2*d^2 + 1/2*(c^2 + d^2 - 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*d + I)*sin(2*b*x + 2*a) - 1/2) + (2*I*b*x + 2*I*a)*log((c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1)) + (-2*I*b*x - 2*I*a)*log((c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1)) + (-2*I*b*x - 2*I*a)*log((c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1)) + (2*I*b*x + 2*I*a)*log((c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1)) + dilog(-(c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1) + 1) + dilog(-(c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1) + 1) - dilog(-(c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1) + 1) - dilog(-(c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1) + 1))/b","B",0
64,0,0,0,0.481982," ","integrate(arctan(c+d*cot(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(d \cot\left(b x + a\right) + c\right)}{x}, x\right)"," ",0,"integral(arctan(d*cot(b*x + a) + c)/x, x)","F",0
65,1,165,0,0.419424," ","integrate(-x^2*arctan(-c-(1-I*c)*cot(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{4} x^{4} + 4 i \, b^{3} x^{3} \log\left(-\frac{{\left(c + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)}}{c e^{\left(2 i \, b x + 2 i \, a\right)} + i}\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) - 2 \, a^{4} - 4 i \, a^{3} \log\left(\frac{c e^{\left(2 i \, b x + 2 i \, a\right)} + i}{c}\right) + 6 i \, b x {\rm polylog}\left(3, i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(4 i \, b^{3} x^{3} + 4 i \, a^{3}\right)} \log\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) - 3 \, {\rm polylog}\left(4, i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{24 \, b^{3}}"," ",0,"1/24*(2*b^4*x^4 + 4*I*b^3*x^3*log(-(c + I)*e^(2*I*b*x + 2*I*a)/(c*e^(2*I*b*x + 2*I*a) + I)) + 6*b^2*x^2*dilog(I*c*e^(2*I*b*x + 2*I*a)) - 2*a^4 - 4*I*a^3*log((c*e^(2*I*b*x + 2*I*a) + I)/c) + 6*I*b*x*polylog(3, I*c*e^(2*I*b*x + 2*I*a)) + (4*I*b^3*x^3 + 4*I*a^3)*log(-I*c*e^(2*I*b*x + 2*I*a) + 1) - 3*polylog(4, I*c*e^(2*I*b*x + 2*I*a)))/b^3","C",0
66,1,143,0,0.433643," ","integrate(-x*arctan(-c-(1-I*c)*cot(b*x+a)),x, algorithm=""fricas"")","\frac{4 \, b^{3} x^{3} + 6 i \, b^{2} x^{2} \log\left(-\frac{{\left(c + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)}}{c e^{\left(2 i \, b x + 2 i \, a\right)} + i}\right) + 4 \, a^{3} + 6 \, b x {\rm Li}_2\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + 6 i \, a^{2} \log\left(\frac{c e^{\left(2 i \, b x + 2 i \, a\right)} + i}{c}\right) + {\left(6 i \, b^{2} x^{2} - 6 i \, a^{2}\right)} \log\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) + 3 i \, {\rm polylog}\left(3, i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{24 \, b^{2}}"," ",0,"1/24*(4*b^3*x^3 + 6*I*b^2*x^2*log(-(c + I)*e^(2*I*b*x + 2*I*a)/(c*e^(2*I*b*x + 2*I*a) + I)) + 4*a^3 + 6*b*x*dilog(I*c*e^(2*I*b*x + 2*I*a)) + 6*I*a^2*log((c*e^(2*I*b*x + 2*I*a) + I)/c) + (6*I*b^2*x^2 - 6*I*a^2)*log(-I*c*e^(2*I*b*x + 2*I*a) + 1) + 3*I*polylog(3, I*c*e^(2*I*b*x + 2*I*a)))/b^2","C",0
67,1,111,0,0.627200," ","integrate(-arctan(-c-(1-I*c)*cot(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{2} x^{2} + 2 i \, b x \log\left(-\frac{{\left(c + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)}}{c e^{\left(2 i \, b x + 2 i \, a\right)} + i}\right) - 2 \, a^{2} + {\left(2 i \, b x + 2 i \, a\right)} \log\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) - 2 i \, a \log\left(\frac{c e^{\left(2 i \, b x + 2 i \, a\right)} + i}{c}\right) + {\rm Li}_2\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{4 \, b}"," ",0,"1/4*(2*b^2*x^2 + 2*I*b*x*log(-(c + I)*e^(2*I*b*x + 2*I*a)/(c*e^(2*I*b*x + 2*I*a) + I)) - 2*a^2 + (2*I*b*x + 2*I*a)*log(-I*c*e^(2*I*b*x + 2*I*a) + 1) - 2*I*a*log((c*e^(2*I*b*x + 2*I*a) + I)/c) + dilog(I*c*e^(2*I*b*x + 2*I*a)))/b","A",0
68,0,0,0,0.491090," ","integrate(-arctan(-c-(1-I*c)*cot(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, \log\left(-\frac{{\left(c + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)}}{c e^{\left(2 i \, b x + 2 i \, a\right)} + i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*I*log(-(c + I)*e^(2*I*b*x + 2*I*a)/(c*e^(2*I*b*x + 2*I*a) + I))/x, x)","F",0
69,1,166,0,0.765786," ","integrate(-x^2*arctan(-c-(-1-I*c)*cot(b*x+a)),x, algorithm=""fricas"")","-\frac{2 \, b^{4} x^{4} - 4 i \, b^{3} x^{3} \log\left(-\frac{{\left(c e^{\left(2 i \, b x + 2 i \, a\right)} - i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{c - i}\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) - 2 \, a^{4} - 4 i \, a^{3} \log\left(\frac{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}{c}\right) + 6 i \, b x {\rm polylog}\left(3, -i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) - {\left(-4 i \, b^{3} x^{3} - 4 i \, a^{3}\right)} \log\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) - 3 \, {\rm polylog}\left(4, -i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{24 \, b^{3}}"," ",0,"-1/24*(2*b^4*x^4 - 4*I*b^3*x^3*log(-(c*e^(2*I*b*x + 2*I*a) - I)*e^(-2*I*b*x - 2*I*a)/(c - I)) + 6*b^2*x^2*dilog(-I*c*e^(2*I*b*x + 2*I*a)) - 2*a^4 - 4*I*a^3*log((c*e^(2*I*b*x + 2*I*a) - I)/c) + 6*I*b*x*polylog(3, -I*c*e^(2*I*b*x + 2*I*a)) - (-4*I*b^3*x^3 - 4*I*a^3)*log(I*c*e^(2*I*b*x + 2*I*a) + 1) - 3*polylog(4, -I*c*e^(2*I*b*x + 2*I*a)))/b^3","C",0
70,1,144,0,0.680834," ","integrate(-x*arctan(-c-(-1-I*c)*cot(b*x+a)),x, algorithm=""fricas"")","-\frac{4 \, b^{3} x^{3} - 6 i \, b^{2} x^{2} \log\left(-\frac{{\left(c e^{\left(2 i \, b x + 2 i \, a\right)} - i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{c - i}\right) + 4 \, a^{3} + 6 \, b x {\rm Li}_2\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + 6 i \, a^{2} \log\left(\frac{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}{c}\right) - {\left(-6 i \, b^{2} x^{2} + 6 i \, a^{2}\right)} \log\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) + 3 i \, {\rm polylog}\left(3, -i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{24 \, b^{2}}"," ",0,"-1/24*(4*b^3*x^3 - 6*I*b^2*x^2*log(-(c*e^(2*I*b*x + 2*I*a) - I)*e^(-2*I*b*x - 2*I*a)/(c - I)) + 4*a^3 + 6*b*x*dilog(-I*c*e^(2*I*b*x + 2*I*a)) + 6*I*a^2*log((c*e^(2*I*b*x + 2*I*a) - I)/c) - (-6*I*b^2*x^2 + 6*I*a^2)*log(I*c*e^(2*I*b*x + 2*I*a) + 1) + 3*I*polylog(3, -I*c*e^(2*I*b*x + 2*I*a)))/b^2","C",0
71,1,112,0,0.547410," ","integrate(-arctan(-c-(-1-I*c)*cot(b*x+a)),x, algorithm=""fricas"")","-\frac{2 \, b^{2} x^{2} - 2 i \, b x \log\left(-\frac{{\left(c e^{\left(2 i \, b x + 2 i \, a\right)} - i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{c - i}\right) - 2 \, a^{2} - {\left(-2 i \, b x - 2 i \, a\right)} \log\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) - 2 i \, a \log\left(\frac{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}{c}\right) + {\rm Li}_2\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{4 \, b}"," ",0,"-1/4*(2*b^2*x^2 - 2*I*b*x*log(-(c*e^(2*I*b*x + 2*I*a) - I)*e^(-2*I*b*x - 2*I*a)/(c - I)) - 2*a^2 - (-2*I*b*x - 2*I*a)*log(I*c*e^(2*I*b*x + 2*I*a) + 1) - 2*I*a*log((c*e^(2*I*b*x + 2*I*a) - I)/c) + dilog(-I*c*e^(2*I*b*x + 2*I*a)))/b","A",0
72,0,0,0,0.829613," ","integrate(-arctan(-c-(-1-I*c)*cot(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, \log\left(-\frac{{\left(c e^{\left(2 i \, b x + 2 i \, a\right)} - i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{c - i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*I*log(-(c*e^(2*I*b*x + 2*I*a) - I)*e^(-2*I*b*x - 2*I*a)/(c - I))/x, x)","F",0
73,1,58,0,0.604436," ","integrate(arctan(sinh(x)),x, algorithm=""fricas"")","x \arctan\left(\sinh\left(x\right)\right) + i \, x \log\left(i \, \cosh\left(x\right) + i \, \sinh\left(x\right) + 1\right) - i \, x \log\left(-i \, \cosh\left(x\right) - i \, \sinh\left(x\right) + 1\right) - i \, {\rm Li}_2\left(i \, \cosh\left(x\right) + i \, \sinh\left(x\right)\right) + i \, {\rm Li}_2\left(-i \, \cosh\left(x\right) - i \, \sinh\left(x\right)\right)"," ",0,"x*arctan(sinh(x)) + I*x*log(I*cosh(x) + I*sinh(x) + 1) - I*x*log(-I*cosh(x) - I*sinh(x) + 1) - I*dilog(I*cosh(x) + I*sinh(x)) + I*dilog(-I*cosh(x) - I*sinh(x))","B",0
74,1,93,0,0.450706," ","integrate(x*arctan(sinh(x)),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} \arctan\left(\sinh\left(x\right)\right) + \frac{1}{2} i \, x^{2} \log\left(i \, \cosh\left(x\right) + i \, \sinh\left(x\right) + 1\right) - \frac{1}{2} i \, x^{2} \log\left(-i \, \cosh\left(x\right) - i \, \sinh\left(x\right) + 1\right) - i \, x {\rm Li}_2\left(i \, \cosh\left(x\right) + i \, \sinh\left(x\right)\right) + i \, x {\rm Li}_2\left(-i \, \cosh\left(x\right) - i \, \sinh\left(x\right)\right) + i \, {\rm polylog}\left(3, i \, \cosh\left(x\right) + i \, \sinh\left(x\right)\right) - i \, {\rm polylog}\left(3, -i \, \cosh\left(x\right) - i \, \sinh\left(x\right)\right)"," ",0,"1/2*x^2*arctan(sinh(x)) + 1/2*I*x^2*log(I*cosh(x) + I*sinh(x) + 1) - 1/2*I*x^2*log(-I*cosh(x) - I*sinh(x) + 1) - I*x*dilog(I*cosh(x) + I*sinh(x)) + I*x*dilog(-I*cosh(x) - I*sinh(x)) + I*polylog(3, I*cosh(x) + I*sinh(x)) - I*polylog(3, -I*cosh(x) - I*sinh(x))","C",0
75,1,125,0,0.584447," ","integrate(x^2*arctan(sinh(x)),x, algorithm=""fricas"")","\frac{1}{3} \, x^{3} \arctan\left(\sinh\left(x\right)\right) + \frac{1}{3} i \, x^{3} \log\left(i \, \cosh\left(x\right) + i \, \sinh\left(x\right) + 1\right) - \frac{1}{3} i \, x^{3} \log\left(-i \, \cosh\left(x\right) - i \, \sinh\left(x\right) + 1\right) - i \, x^{2} {\rm Li}_2\left(i \, \cosh\left(x\right) + i \, \sinh\left(x\right)\right) + i \, x^{2} {\rm Li}_2\left(-i \, \cosh\left(x\right) - i \, \sinh\left(x\right)\right) + 2 i \, x {\rm polylog}\left(3, i \, \cosh\left(x\right) + i \, \sinh\left(x\right)\right) - 2 i \, x {\rm polylog}\left(3, -i \, \cosh\left(x\right) - i \, \sinh\left(x\right)\right) - 2 i \, {\rm polylog}\left(4, i \, \cosh\left(x\right) + i \, \sinh\left(x\right)\right) + 2 i \, {\rm polylog}\left(4, -i \, \cosh\left(x\right) - i \, \sinh\left(x\right)\right)"," ",0,"1/3*x^3*arctan(sinh(x)) + 1/3*I*x^3*log(I*cosh(x) + I*sinh(x) + 1) - 1/3*I*x^3*log(-I*cosh(x) - I*sinh(x) + 1) - I*x^2*dilog(I*cosh(x) + I*sinh(x)) + I*x^2*dilog(-I*cosh(x) - I*sinh(x)) + 2*I*x*polylog(3, I*cosh(x) + I*sinh(x)) - 2*I*x*polylog(3, -I*cosh(x) - I*sinh(x)) - 2*I*polylog(4, I*cosh(x) + I*sinh(x)) + 2*I*polylog(4, -I*cosh(x) - I*sinh(x))","C",0
76,1,1448,0,0.596769," ","integrate((f*x+e)^3*arctan(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{24 i \, f^{3} {\rm polylog}\left(5, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 24 i \, f^{3} {\rm polylog}\left(5, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 24 i \, f^{3} {\rm polylog}\left(5, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 24 i \, f^{3} {\rm polylog}\left(5, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\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\right)} \arctan\left(\frac{\sinh\left(b x + a\right)}{\cosh\left(b x + 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(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\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(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\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(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\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(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-i \, b^{4} f^{3} x^{4} - 4 i \, b^{4} e f^{2} x^{3} - 6 i \, b^{4} e^{2} f x^{2} - 4 i \, b^{4} e^{3} x - 4 i \, a b^{3} e^{3} + 6 i \, a^{2} b^{2} e^{2} f - 4 i \, a^{3} b e f^{2} + i \, a^{4} f^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{4} f^{3} x^{4} - 4 i \, b^{4} e f^{2} x^{3} - 6 i \, b^{4} e^{2} f x^{2} - 4 i \, b^{4} e^{3} x - 4 i \, a b^{3} e^{3} + 6 i \, a^{2} b^{2} e^{2} f - 4 i \, a^{3} b e f^{2} + i \, a^{4} f^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{4} f^{3} x^{4} + 4 i \, b^{4} e f^{2} x^{3} + 6 i \, b^{4} e^{2} f x^{2} + 4 i \, b^{4} e^{3} x + 4 i \, a b^{3} e^{3} - 6 i \, a^{2} b^{2} e^{2} f + 4 i \, a^{3} b e f^{2} - i \, a^{4} f^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{4} f^{3} x^{4} + 4 i \, b^{4} e f^{2} x^{3} + 6 i \, b^{4} e^{2} f x^{2} + 4 i \, b^{4} e^{3} x + 4 i \, a b^{3} e^{3} - 6 i \, a^{2} b^{2} e^{2} f + 4 i \, a^{3} b e f^{2} - i \, a^{4} f^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(4 i \, a b^{3} e^{3} - 6 i \, a^{2} b^{2} e^{2} f + 4 i \, a^{3} b e f^{2} - i \, a^{4} f^{3}\right)} \log\left(i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(4 i \, a b^{3} e^{3} - 6 i \, a^{2} b^{2} e^{2} f + 4 i \, a^{3} b e f^{2} - i \, a^{4} f^{3}\right)} \log\left(-i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-4 i \, a b^{3} e^{3} + 6 i \, a^{2} b^{2} e^{2} f - 4 i \, a^{3} b e f^{2} + i \, a^{4} f^{3}\right)} \log\left(i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-4 i \, a b^{3} e^{3} + 6 i \, a^{2} b^{2} e^{2} f - 4 i \, a^{3} b e f^{2} + i \, a^{4} f^{3}\right)} \log\left(-i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-24 i \, b f^{3} x - 24 i \, b e f^{2}\right)} {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-24 i \, b f^{3} x - 24 i \, b e f^{2}\right)} {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(24 i \, b f^{3} x + 24 i \, b e f^{2}\right)} {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(24 i \, b f^{3} x + 24 i \, b e f^{2}\right)} {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(12 i \, b^{2} f^{3} x^{2} + 24 i \, b^{2} e f^{2} x + 12 i \, b^{2} e^{2} f\right)} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(12 i \, b^{2} f^{3} x^{2} + 24 i \, b^{2} e f^{2} x + 12 i \, b^{2} e^{2} f\right)} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-12 i \, b^{2} f^{3} x^{2} - 24 i \, b^{2} e f^{2} x - 12 i \, b^{2} e^{2} f\right)} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-12 i \, b^{2} f^{3} x^{2} - 24 i \, b^{2} e f^{2} x - 12 i \, b^{2} e^{2} f\right)} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{8 \, b^{4}}"," ",0,"1/8*(24*I*f^3*polylog(5, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 24*I*f^3*polylog(5, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 24*I*f^3*polylog(5, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 24*I*f^3*polylog(5, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 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)*arctan(sinh(b*x + a)/cosh(b*x + 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(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + 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(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + 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(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + 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(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-I*b^4*f^3*x^4 - 4*I*b^4*e*f^2*x^3 - 6*I*b^4*e^2*f*x^2 - 4*I*b^4*e^3*x - 4*I*a*b^3*e^3 + 6*I*a^2*b^2*e^2*f - 4*I*a^3*b*e*f^2 + I*a^4*f^3)*log(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^4*f^3*x^4 - 4*I*b^4*e*f^2*x^3 - 6*I*b^4*e^2*f*x^2 - 4*I*b^4*e^3*x - 4*I*a*b^3*e^3 + 6*I*a^2*b^2*e^2*f - 4*I*a^3*b*e*f^2 + I*a^4*f^3)*log(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^4*f^3*x^4 + 4*I*b^4*e*f^2*x^3 + 6*I*b^4*e^2*f*x^2 + 4*I*b^4*e^3*x + 4*I*a*b^3*e^3 - 6*I*a^2*b^2*e^2*f + 4*I*a^3*b*e*f^2 - I*a^4*f^3)*log(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^4*f^3*x^4 + 4*I*b^4*e*f^2*x^3 + 6*I*b^4*e^2*f*x^2 + 4*I*b^4*e^3*x + 4*I*a*b^3*e^3 - 6*I*a^2*b^2*e^2*f + 4*I*a^3*b*e*f^2 - I*a^4*f^3)*log(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (4*I*a*b^3*e^3 - 6*I*a^2*b^2*e^2*f + 4*I*a^3*b*e*f^2 - I*a^4*f^3)*log(I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (4*I*a*b^3*e^3 - 6*I*a^2*b^2*e^2*f + 4*I*a^3*b*e*f^2 - I*a^4*f^3)*log(-I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-4*I*a*b^3*e^3 + 6*I*a^2*b^2*e^2*f - 4*I*a^3*b*e*f^2 + I*a^4*f^3)*log(I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-4*I*a*b^3*e^3 + 6*I*a^2*b^2*e^2*f - 4*I*a^3*b*e*f^2 + I*a^4*f^3)*log(-I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-24*I*b*f^3*x - 24*I*b*e*f^2)*polylog(4, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-24*I*b*f^3*x - 24*I*b*e*f^2)*polylog(4, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (24*I*b*f^3*x + 24*I*b*e*f^2)*polylog(4, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (24*I*b*f^3*x + 24*I*b*e*f^2)*polylog(4, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (12*I*b^2*f^3*x^2 + 24*I*b^2*e*f^2*x + 12*I*b^2*e^2*f)*polylog(3, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (12*I*b^2*f^3*x^2 + 24*I*b^2*e*f^2*x + 12*I*b^2*e^2*f)*polylog(3, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-12*I*b^2*f^3*x^2 - 24*I*b^2*e*f^2*x - 12*I*b^2*e^2*f)*polylog(3, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-12*I*b^2*f^3*x^2 - 24*I*b^2*e*f^2*x - 12*I*b^2*e^2*f)*polylog(3, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))))/b^4","C",0
77,1,994,0,0.607995," ","integrate((f*x+e)^2*arctan(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{-6 i \, f^{2} {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, f^{2} {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, f^{2} {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, f^{2} {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x\right)} \arctan\left(\frac{\sinh\left(b x + a\right)}{\cosh\left(b x + a\right)}\right) + {\left(-3 i \, b^{2} f^{2} x^{2} - 6 i \, b^{2} e f x - 3 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-3 i \, b^{2} f^{2} x^{2} - 6 i \, b^{2} e f x - 3 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(3 i \, b^{2} f^{2} x^{2} + 6 i \, b^{2} e f x + 3 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(3 i \, b^{2} f^{2} x^{2} + 6 i \, b^{2} e f x + 3 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-i \, b^{3} f^{2} x^{3} - 3 i \, b^{3} e f x^{2} - 3 i \, b^{3} e^{2} x - 3 i \, a b^{2} e^{2} + 3 i \, a^{2} b e f - i \, a^{3} f^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{3} f^{2} x^{3} - 3 i \, b^{3} e f x^{2} - 3 i \, b^{3} e^{2} x - 3 i \, a b^{2} e^{2} + 3 i \, a^{2} b e f - i \, a^{3} f^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{3} f^{2} x^{3} + 3 i \, b^{3} e f x^{2} + 3 i \, b^{3} e^{2} x + 3 i \, a b^{2} e^{2} - 3 i \, a^{2} b e f + i \, a^{3} f^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{3} f^{2} x^{3} + 3 i \, b^{3} e f x^{2} + 3 i \, b^{3} e^{2} x + 3 i \, a b^{2} e^{2} - 3 i \, a^{2} b e f + i \, a^{3} f^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(3 i \, a b^{2} e^{2} - 3 i \, a^{2} b e f + i \, a^{3} f^{2}\right)} \log\left(i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(3 i \, a b^{2} e^{2} - 3 i \, a^{2} b e f + i \, a^{3} f^{2}\right)} \log\left(-i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-3 i \, a b^{2} e^{2} + 3 i \, a^{2} b e f - i \, a^{3} f^{2}\right)} \log\left(i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-3 i \, a b^{2} e^{2} + 3 i \, a^{2} b e f - i \, a^{3} f^{2}\right)} \log\left(-i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(6 i \, b f^{2} x + 6 i \, b e f\right)} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(6 i \, b f^{2} x + 6 i \, b e f\right)} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-6 i \, b f^{2} x - 6 i \, b e f\right)} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-6 i \, b f^{2} x - 6 i \, b e f\right)} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{6 \, b^{3}}"," ",0,"1/6*(-6*I*f^2*polylog(4, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*f^2*polylog(4, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*f^2*polylog(4, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*f^2*polylog(4, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 2*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x)*arctan(sinh(b*x + a)/cosh(b*x + a)) + (-3*I*b^2*f^2*x^2 - 6*I*b^2*e*f*x - 3*I*b^2*e^2)*dilog(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-3*I*b^2*f^2*x^2 - 6*I*b^2*e*f*x - 3*I*b^2*e^2)*dilog(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (3*I*b^2*f^2*x^2 + 6*I*b^2*e*f*x + 3*I*b^2*e^2)*dilog(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (3*I*b^2*f^2*x^2 + 6*I*b^2*e*f*x + 3*I*b^2*e^2)*dilog(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-I*b^3*f^2*x^3 - 3*I*b^3*e*f*x^2 - 3*I*b^3*e^2*x - 3*I*a*b^2*e^2 + 3*I*a^2*b*e*f - I*a^3*f^2)*log(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^3*f^2*x^3 - 3*I*b^3*e*f*x^2 - 3*I*b^3*e^2*x - 3*I*a*b^2*e^2 + 3*I*a^2*b*e*f - I*a^3*f^2)*log(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^3*f^2*x^3 + 3*I*b^3*e*f*x^2 + 3*I*b^3*e^2*x + 3*I*a*b^2*e^2 - 3*I*a^2*b*e*f + I*a^3*f^2)*log(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^3*f^2*x^3 + 3*I*b^3*e*f*x^2 + 3*I*b^3*e^2*x + 3*I*a*b^2*e^2 - 3*I*a^2*b*e*f + I*a^3*f^2)*log(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (3*I*a*b^2*e^2 - 3*I*a^2*b*e*f + I*a^3*f^2)*log(I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (3*I*a*b^2*e^2 - 3*I*a^2*b*e*f + I*a^3*f^2)*log(-I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-3*I*a*b^2*e^2 + 3*I*a^2*b*e*f - I*a^3*f^2)*log(I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-3*I*a*b^2*e^2 + 3*I*a^2*b*e*f - I*a^3*f^2)*log(-I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (6*I*b*f^2*x + 6*I*b*e*f)*polylog(3, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (6*I*b*f^2*x + 6*I*b*e*f)*polylog(3, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-6*I*b*f^2*x - 6*I*b*e*f)*polylog(3, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-6*I*b*f^2*x - 6*I*b*e*f)*polylog(3, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
78,1,596,0,0.639942," ","integrate((f*x+e)*arctan(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x\right)} \arctan\left(\frac{\sinh\left(b x + a\right)}{\cosh\left(b x + a\right)}\right) + {\left(-2 i \, b f x - 2 i \, b e\right)} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-2 i \, b f x - 2 i \, b e\right)} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(2 i \, b f x + 2 i \, b e\right)} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(2 i \, b f x + 2 i \, b e\right)} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-i \, b^{2} f x^{2} - 2 i \, b^{2} e x - 2 i \, a b e + i \, a^{2} f\right)} \log\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{2} f x^{2} - 2 i \, b^{2} e x - 2 i \, a b e + i \, a^{2} f\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{2} f x^{2} + 2 i \, b^{2} e x + 2 i \, a b e - i \, a^{2} f\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{2} f x^{2} + 2 i \, b^{2} e x + 2 i \, a b e - i \, a^{2} f\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(2 i \, a b e - i \, a^{2} f\right)} \log\left(i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(2 i \, a b e - i \, a^{2} f\right)} \log\left(-i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-2 i \, a b e + i \, a^{2} f\right)} \log\left(i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-2 i \, a b e + i \, a^{2} f\right)} \log\left(-i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + 2 i \, f {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, f {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, f {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, f {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{4 \, b^{2}}"," ",0,"1/4*(2*(b^2*f*x^2 + 2*b^2*e*x)*arctan(sinh(b*x + a)/cosh(b*x + a)) + (-2*I*b*f*x - 2*I*b*e)*dilog(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-2*I*b*f*x - 2*I*b*e)*dilog(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (2*I*b*f*x + 2*I*b*e)*dilog(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (2*I*b*f*x + 2*I*b*e)*dilog(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-I*b^2*f*x^2 - 2*I*b^2*e*x - 2*I*a*b*e + I*a^2*f)*log(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^2*f*x^2 - 2*I*b^2*e*x - 2*I*a*b*e + I*a^2*f)*log(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^2*f*x^2 + 2*I*b^2*e*x + 2*I*a*b*e - I*a^2*f)*log(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^2*f*x^2 + 2*I*b^2*e*x + 2*I*a*b*e - I*a^2*f)*log(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (2*I*a*b*e - I*a^2*f)*log(I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (2*I*a*b*e - I*a^2*f)*log(-I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-2*I*a*b*e + I*a^2*f)*log(I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-2*I*a*b*e + I*a^2*f)*log(-I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + 2*I*f*polylog(3, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*f*polylog(3, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*f*polylog(3, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*f*polylog(3, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
79,1,334,0,0.934643," ","integrate(arctan(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b x \arctan\left(\frac{\sinh\left(b x + a\right)}{\cosh\left(b x + a\right)}\right) + {\left(-i \, b x - i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + i \, a \log\left(i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + i \, a \log\left(-i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) - i \, a \log\left(i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) - i \, a \log\left(-i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) - i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(2*b*x*arctan(sinh(b*x + a)/cosh(b*x + a)) + (-I*b*x - I*a)*log(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b*x - I*a)*log(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b*x + I*a)*log(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b*x + I*a)*log(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + I*a*log(I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + I*a*log(-I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) - I*a*log(I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) - I*a*log(-I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) - I*dilog(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) - I*dilog(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + I*dilog(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + I*dilog(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
80,0,0,0,0.580336," ","integrate(arctan(tanh(b*x+a))/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(\tanh\left(b x + a\right)\right)}{f x + e}, x\right)"," ",0,"integral(arctan(tanh(b*x + a))/(f*x + e), x)","F",0
81,1,1335,0,0.626256," ","integrate(x^2*arctan(c+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} \arctan\left(\frac{c \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{\cosh\left(b x + a\right)}\right) + 3 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 3 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - i \, a^{3} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a^{3} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a^{3} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a^{3} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - 6 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(i \, b^{3} x^{3} + i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{3} x^{3} + i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{3} x^{3} - i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{3} x^{3} - i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 6 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{6 \, b^{3}}"," ",0,"1/6*(2*b^3*x^3*arctan((c*cosh(b*x + a) + d*sinh(b*x + a))/cosh(b*x + a)) + 3*I*b^2*x^2*dilog(1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 3*I*b^2*x^2*dilog(-1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 3*I*b^2*x^2*dilog(1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 3*I*b^2*x^2*dilog(-1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - I*a^3*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 - 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a^3*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 - 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a^3*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 + 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a^3*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 + 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - 6*I*b*x*polylog(3, 1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*b*x*polylog(3, -1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*b*x*polylog(3, 1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*b*x*polylog(3, -1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + (I*b^3*x^3 + I*a^3)*log(1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^3*x^3 + I*a^3)*log(-1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^3*x^3 - I*a^3)*log(1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^3*x^3 - I*a^3)*log(-1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 6*I*polylog(4, 1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*polylog(4, -1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*polylog(4, 1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*polylog(4, -1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
82,1,1103,0,0.930172," ","integrate(x*arctan(c+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{2} x^{2} \arctan\left(\frac{c \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{\cosh\left(b x + a\right)}\right) + 2 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + i \, a^{2} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a^{2} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a^{2} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a^{2} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + {\left(i \, b^{2} x^{2} - i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{2} x^{2} - i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{2} x^{2} + i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{2} x^{2} + i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 2 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{4 \, b^{2}}"," ",0,"1/4*(2*b^2*x^2*arctan((c*cosh(b*x + a) + d*sinh(b*x + a))/cosh(b*x + a)) + 2*I*b*x*dilog(1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*b*x*dilog(-1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*b*x*dilog(1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*b*x*dilog(-1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + I*a^2*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 - 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a^2*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 - 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a^2*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 + 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a^2*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 + 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + (I*b^2*x^2 - I*a^2)*log(1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^2*x^2 - I*a^2)*log(-1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^2*x^2 + I*a^2)*log(1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^2*x^2 + I*a^2)*log(-1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 2*I*polylog(3, 1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*polylog(3, -1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*polylog(3, 1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*polylog(3, -1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
83,1,851,0,1.138051," ","integrate(arctan(c+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b x \arctan\left(\frac{c \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{\cosh\left(b x + a\right)}\right) - i \, a \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + {\left(i \, b x + i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(2*b*x*arctan((c*cosh(b*x + a) + d*sinh(b*x + a))/cosh(b*x + a)) - I*a*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 - 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 - 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 + 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 + 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + (I*b*x + I*a)*log(1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b*x + I*a)*log(-1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b*x - I*a)*log(1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b*x - I*a)*log(-1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + I*dilog(1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + I*dilog(-1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - I*dilog(1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - I*dilog(-1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
84,0,0,0,0.512836," ","integrate(arctan(c+d*tanh(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(d \tanh\left(b x + a\right) + c\right)}{x}, x\right)"," ",0,"integral(arctan(d*tanh(b*x + a) + c)/x, x)","F",0
85,1,291,0,0.725850," ","integrate(x^2*arctan(c+(I+c)*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{-i \, b^{4} x^{4} + 2 i \, b^{3} x^{3} \log\left(-\frac{{\left(c + i\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c e^{\left(2 \, b x + 2 \, a\right)} - i}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + i \, a^{4} - 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) - 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) - 12 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) - 12 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + {\left(2 i \, b^{3} x^{3} + 2 i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(2 i \, b^{3} x^{3} + 2 i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + 12 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + 12 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(-I*b^4*x^4 + 2*I*b^3*x^3*log(-(c + I)*e^(2*b*x + 2*a)/(c*e^(2*b*x + 2*a) - I)) + 6*I*b^2*x^2*dilog(1/2*sqrt(-4*I*c)*e^(b*x + a)) + 6*I*b^2*x^2*dilog(-1/2*sqrt(-4*I*c)*e^(b*x + a)) + I*a^4 - 2*I*a^3*log(1/2*(2*c*e^(b*x + a) + I*sqrt(-4*I*c))/c) - 2*I*a^3*log(1/2*(2*c*e^(b*x + a) - I*sqrt(-4*I*c))/c) - 12*I*b*x*polylog(3, 1/2*sqrt(-4*I*c)*e^(b*x + a)) - 12*I*b*x*polylog(3, -1/2*sqrt(-4*I*c)*e^(b*x + a)) + (2*I*b^3*x^3 + 2*I*a^3)*log(1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + (2*I*b^3*x^3 + 2*I*a^3)*log(-1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + 12*I*polylog(4, 1/2*sqrt(-4*I*c)*e^(b*x + a)) + 12*I*polylog(4, -1/2*sqrt(-4*I*c)*e^(b*x + a)))/b^3","C",0
86,1,245,0,0.616150," ","integrate(x*arctan(c+(I+c)*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{-2 i \, b^{3} x^{3} + 3 i \, b^{2} x^{2} \log\left(-\frac{{\left(c + i\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c e^{\left(2 \, b x + 2 \, a\right)} - i}\right) - 2 i \, a^{3} + 6 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + 6 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) + 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) + {\left(3 i \, b^{2} x^{2} - 3 i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(3 i \, b^{2} x^{2} - 3 i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) - 6 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) - 6 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(-2*I*b^3*x^3 + 3*I*b^2*x^2*log(-(c + I)*e^(2*b*x + 2*a)/(c*e^(2*b*x + 2*a) - I)) - 2*I*a^3 + 6*I*b*x*dilog(1/2*sqrt(-4*I*c)*e^(b*x + a)) + 6*I*b*x*dilog(-1/2*sqrt(-4*I*c)*e^(b*x + a)) + 3*I*a^2*log(1/2*(2*c*e^(b*x + a) + I*sqrt(-4*I*c))/c) + 3*I*a^2*log(1/2*(2*c*e^(b*x + a) - I*sqrt(-4*I*c))/c) + (3*I*b^2*x^2 - 3*I*a^2)*log(1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + (3*I*b^2*x^2 - 3*I*a^2)*log(-1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) - 6*I*polylog(3, 1/2*sqrt(-4*I*c)*e^(b*x + a)) - 6*I*polylog(3, -1/2*sqrt(-4*I*c)*e^(b*x + a)))/b^2","C",0
87,1,187,0,0.674552," ","integrate(arctan(c+(I+c)*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{-i \, b^{2} x^{2} + i \, b x \log\left(-\frac{{\left(c + i\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c e^{\left(2 \, b x + 2 \, a\right)} - i}\right) + i \, a^{2} + {\left(i \, b x + i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) - i \, a \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) - i \, a \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) + i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right)}{2 \, b}"," ",0,"1/2*(-I*b^2*x^2 + I*b*x*log(-(c + I)*e^(2*b*x + 2*a)/(c*e^(2*b*x + 2*a) - I)) + I*a^2 + (I*b*x + I*a)*log(1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + (I*b*x + I*a)*log(-1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) - I*a*log(1/2*(2*c*e^(b*x + a) + I*sqrt(-4*I*c))/c) - I*a*log(1/2*(2*c*e^(b*x + a) - I*sqrt(-4*I*c))/c) + I*dilog(1/2*sqrt(-4*I*c)*e^(b*x + a)) + I*dilog(-1/2*sqrt(-4*I*c)*e^(b*x + a)))/b","B",0
88,0,0,0,1.003049," ","integrate(arctan(c+(I+c)*tanh(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, \log\left(-\frac{{\left(c + i\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c e^{\left(2 \, b x + 2 \, a\right)} - i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*I*log(-(c + I)*e^(2*b*x + 2*a)/(c*e^(2*b*x + 2*a) - I))/x, x)","F",0
89,1,291,0,0.614606," ","integrate(x^2*arctan(c-(I-c)*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{i \, b^{4} x^{4} + 2 i \, b^{3} x^{3} \log\left(-\frac{{\left(c e^{\left(2 \, b x + 2 \, a\right)} + i\right)} e^{\left(-2 \, b x - 2 \, a\right)}}{c - i}\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) - i \, a^{4} + 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) + 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) + 12 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + 12 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + {\left(-2 i \, b^{3} x^{3} - 2 i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(-2 i \, b^{3} x^{3} - 2 i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) - 12 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) - 12 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(I*b^4*x^4 + 2*I*b^3*x^3*log(-(c*e^(2*b*x + 2*a) + I)*e^(-2*b*x - 2*a)/(c - I)) - 6*I*b^2*x^2*dilog(1/2*sqrt(4*I*c)*e^(b*x + a)) - 6*I*b^2*x^2*dilog(-1/2*sqrt(4*I*c)*e^(b*x + a)) - I*a^4 + 2*I*a^3*log(1/2*(2*c*e^(b*x + a) + I*sqrt(4*I*c))/c) + 2*I*a^3*log(1/2*(2*c*e^(b*x + a) - I*sqrt(4*I*c))/c) + 12*I*b*x*polylog(3, 1/2*sqrt(4*I*c)*e^(b*x + a)) + 12*I*b*x*polylog(3, -1/2*sqrt(4*I*c)*e^(b*x + a)) + (-2*I*b^3*x^3 - 2*I*a^3)*log(1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + (-2*I*b^3*x^3 - 2*I*a^3)*log(-1/2*sqrt(4*I*c)*e^(b*x + a) + 1) - 12*I*polylog(4, 1/2*sqrt(4*I*c)*e^(b*x + a)) - 12*I*polylog(4, -1/2*sqrt(4*I*c)*e^(b*x + a)))/b^3","C",0
90,1,245,0,0.520645," ","integrate(x*arctan(c-(I-c)*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 i \, b^{3} x^{3} + 3 i \, b^{2} x^{2} \log\left(-\frac{{\left(c e^{\left(2 \, b x + 2 \, a\right)} + i\right)} e^{\left(-2 \, b x - 2 \, a\right)}}{c - i}\right) + 2 i \, a^{3} - 6 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) - 6 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) - 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) - 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) + {\left(-3 i \, b^{2} x^{2} + 3 i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(-3 i \, b^{2} x^{2} + 3 i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + 6 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + 6 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*I*b^3*x^3 + 3*I*b^2*x^2*log(-(c*e^(2*b*x + 2*a) + I)*e^(-2*b*x - 2*a)/(c - I)) + 2*I*a^3 - 6*I*b*x*dilog(1/2*sqrt(4*I*c)*e^(b*x + a)) - 6*I*b*x*dilog(-1/2*sqrt(4*I*c)*e^(b*x + a)) - 3*I*a^2*log(1/2*(2*c*e^(b*x + a) + I*sqrt(4*I*c))/c) - 3*I*a^2*log(1/2*(2*c*e^(b*x + a) - I*sqrt(4*I*c))/c) + (-3*I*b^2*x^2 + 3*I*a^2)*log(1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + (-3*I*b^2*x^2 + 3*I*a^2)*log(-1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + 6*I*polylog(3, 1/2*sqrt(4*I*c)*e^(b*x + a)) + 6*I*polylog(3, -1/2*sqrt(4*I*c)*e^(b*x + a)))/b^2","C",0
91,1,187,0,0.551405," ","integrate(arctan(c-(I-c)*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{i \, b^{2} x^{2} + i \, b x \log\left(-\frac{{\left(c e^{\left(2 \, b x + 2 \, a\right)} + i\right)} e^{\left(-2 \, b x - 2 \, a\right)}}{c - i}\right) - i \, a^{2} + {\left(-i \, b x - i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + i \, a \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) + i \, a \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) - i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) - i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right)}{2 \, b}"," ",0,"1/2*(I*b^2*x^2 + I*b*x*log(-(c*e^(2*b*x + 2*a) + I)*e^(-2*b*x - 2*a)/(c - I)) - I*a^2 + (-I*b*x - I*a)*log(1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + (-I*b*x - I*a)*log(-1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + I*a*log(1/2*(2*c*e^(b*x + a) + I*sqrt(4*I*c))/c) + I*a*log(1/2*(2*c*e^(b*x + a) - I*sqrt(4*I*c))/c) - I*dilog(1/2*sqrt(4*I*c)*e^(b*x + a)) - I*dilog(-1/2*sqrt(4*I*c)*e^(b*x + a)))/b","B",0
92,0,0,0,0.640923," ","integrate(arctan(c-(I-c)*tanh(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, \log\left(-\frac{{\left(c e^{\left(2 \, b x + 2 \, a\right)} + i\right)} e^{\left(-2 \, b x - 2 \, a\right)}}{c - i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*I*log(-(c*e^(2*b*x + 2*a) + I)*e^(-2*b*x - 2*a)/(c - I))/x, x)","F",0
93,1,1448,0,1.066619," ","integrate((f*x+e)^3*arctan(coth(b*x+a)),x, algorithm=""fricas"")","\frac{-24 i \, f^{3} {\rm polylog}\left(5, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 24 i \, f^{3} {\rm polylog}\left(5, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 24 i \, f^{3} {\rm polylog}\left(5, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 24 i \, f^{3} {\rm polylog}\left(5, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\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\right)} \arctan\left(\frac{\cosh\left(b x + a\right)}{\sinh\left(b x + 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(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\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(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\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(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\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(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(i \, b^{4} f^{3} x^{4} + 4 i \, b^{4} e f^{2} x^{3} + 6 i \, b^{4} e^{2} f x^{2} + 4 i \, b^{4} e^{3} x + 4 i \, a b^{3} e^{3} - 6 i \, a^{2} b^{2} e^{2} f + 4 i \, a^{3} b e f^{2} - i \, a^{4} f^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{4} f^{3} x^{4} + 4 i \, b^{4} e f^{2} x^{3} + 6 i \, b^{4} e^{2} f x^{2} + 4 i \, b^{4} e^{3} x + 4 i \, a b^{3} e^{3} - 6 i \, a^{2} b^{2} e^{2} f + 4 i \, a^{3} b e f^{2} - i \, a^{4} f^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{4} f^{3} x^{4} - 4 i \, b^{4} e f^{2} x^{3} - 6 i \, b^{4} e^{2} f x^{2} - 4 i \, b^{4} e^{3} x - 4 i \, a b^{3} e^{3} + 6 i \, a^{2} b^{2} e^{2} f - 4 i \, a^{3} b e f^{2} + i \, a^{4} f^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{4} f^{3} x^{4} - 4 i \, b^{4} e f^{2} x^{3} - 6 i \, b^{4} e^{2} f x^{2} - 4 i \, b^{4} e^{3} x - 4 i \, a b^{3} e^{3} + 6 i \, a^{2} b^{2} e^{2} f - 4 i \, a^{3} b e f^{2} + i \, a^{4} f^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-4 i \, a b^{3} e^{3} + 6 i \, a^{2} b^{2} e^{2} f - 4 i \, a^{3} b e f^{2} + i \, a^{4} f^{3}\right)} \log\left(i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-4 i \, a b^{3} e^{3} + 6 i \, a^{2} b^{2} e^{2} f - 4 i \, a^{3} b e f^{2} + i \, a^{4} f^{3}\right)} \log\left(-i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(4 i \, a b^{3} e^{3} - 6 i \, a^{2} b^{2} e^{2} f + 4 i \, a^{3} b e f^{2} - i \, a^{4} f^{3}\right)} \log\left(i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(4 i \, a b^{3} e^{3} - 6 i \, a^{2} b^{2} e^{2} f + 4 i \, a^{3} b e f^{2} - i \, a^{4} f^{3}\right)} \log\left(-i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(24 i \, b f^{3} x + 24 i \, b e f^{2}\right)} {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(24 i \, b f^{3} x + 24 i \, b e f^{2}\right)} {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-24 i \, b f^{3} x - 24 i \, b e f^{2}\right)} {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-24 i \, b f^{3} x - 24 i \, b e f^{2}\right)} {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-12 i \, b^{2} f^{3} x^{2} - 24 i \, b^{2} e f^{2} x - 12 i \, b^{2} e^{2} f\right)} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-12 i \, b^{2} f^{3} x^{2} - 24 i \, b^{2} e f^{2} x - 12 i \, b^{2} e^{2} f\right)} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(12 i \, b^{2} f^{3} x^{2} + 24 i \, b^{2} e f^{2} x + 12 i \, b^{2} e^{2} f\right)} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(12 i \, b^{2} f^{3} x^{2} + 24 i \, b^{2} e f^{2} x + 12 i \, b^{2} e^{2} f\right)} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{8 \, b^{4}}"," ",0,"1/8*(-24*I*f^3*polylog(5, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 24*I*f^3*polylog(5, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 24*I*f^3*polylog(5, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 24*I*f^3*polylog(5, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 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)*arctan(cosh(b*x + a)/sinh(b*x + 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(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + 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(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + 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(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + 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(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (I*b^4*f^3*x^4 + 4*I*b^4*e*f^2*x^3 + 6*I*b^4*e^2*f*x^2 + 4*I*b^4*e^3*x + 4*I*a*b^3*e^3 - 6*I*a^2*b^2*e^2*f + 4*I*a^3*b*e*f^2 - I*a^4*f^3)*log(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^4*f^3*x^4 + 4*I*b^4*e*f^2*x^3 + 6*I*b^4*e^2*f*x^2 + 4*I*b^4*e^3*x + 4*I*a*b^3*e^3 - 6*I*a^2*b^2*e^2*f + 4*I*a^3*b*e*f^2 - I*a^4*f^3)*log(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^4*f^3*x^4 - 4*I*b^4*e*f^2*x^3 - 6*I*b^4*e^2*f*x^2 - 4*I*b^4*e^3*x - 4*I*a*b^3*e^3 + 6*I*a^2*b^2*e^2*f - 4*I*a^3*b*e*f^2 + I*a^4*f^3)*log(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^4*f^3*x^4 - 4*I*b^4*e*f^2*x^3 - 6*I*b^4*e^2*f*x^2 - 4*I*b^4*e^3*x - 4*I*a*b^3*e^3 + 6*I*a^2*b^2*e^2*f - 4*I*a^3*b*e*f^2 + I*a^4*f^3)*log(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-4*I*a*b^3*e^3 + 6*I*a^2*b^2*e^2*f - 4*I*a^3*b*e*f^2 + I*a^4*f^3)*log(I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-4*I*a*b^3*e^3 + 6*I*a^2*b^2*e^2*f - 4*I*a^3*b*e*f^2 + I*a^4*f^3)*log(-I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (4*I*a*b^3*e^3 - 6*I*a^2*b^2*e^2*f + 4*I*a^3*b*e*f^2 - I*a^4*f^3)*log(I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (4*I*a*b^3*e^3 - 6*I*a^2*b^2*e^2*f + 4*I*a^3*b*e*f^2 - I*a^4*f^3)*log(-I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (24*I*b*f^3*x + 24*I*b*e*f^2)*polylog(4, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (24*I*b*f^3*x + 24*I*b*e*f^2)*polylog(4, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-24*I*b*f^3*x - 24*I*b*e*f^2)*polylog(4, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-24*I*b*f^3*x - 24*I*b*e*f^2)*polylog(4, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-12*I*b^2*f^3*x^2 - 24*I*b^2*e*f^2*x - 12*I*b^2*e^2*f)*polylog(3, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-12*I*b^2*f^3*x^2 - 24*I*b^2*e*f^2*x - 12*I*b^2*e^2*f)*polylog(3, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (12*I*b^2*f^3*x^2 + 24*I*b^2*e*f^2*x + 12*I*b^2*e^2*f)*polylog(3, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (12*I*b^2*f^3*x^2 + 24*I*b^2*e*f^2*x + 12*I*b^2*e^2*f)*polylog(3, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))))/b^4","C",0
94,1,994,0,0.573192," ","integrate((f*x+e)^2*arctan(coth(b*x+a)),x, algorithm=""fricas"")","\frac{6 i \, f^{2} {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, f^{2} {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, f^{2} {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, f^{2} {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x\right)} \arctan\left(\frac{\cosh\left(b x + a\right)}{\sinh\left(b x + a\right)}\right) + {\left(3 i \, b^{2} f^{2} x^{2} + 6 i \, b^{2} e f x + 3 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(3 i \, b^{2} f^{2} x^{2} + 6 i \, b^{2} e f x + 3 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-3 i \, b^{2} f^{2} x^{2} - 6 i \, b^{2} e f x - 3 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-3 i \, b^{2} f^{2} x^{2} - 6 i \, b^{2} e f x - 3 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(i \, b^{3} f^{2} x^{3} + 3 i \, b^{3} e f x^{2} + 3 i \, b^{3} e^{2} x + 3 i \, a b^{2} e^{2} - 3 i \, a^{2} b e f + i \, a^{3} f^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{3} f^{2} x^{3} + 3 i \, b^{3} e f x^{2} + 3 i \, b^{3} e^{2} x + 3 i \, a b^{2} e^{2} - 3 i \, a^{2} b e f + i \, a^{3} f^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{3} f^{2} x^{3} - 3 i \, b^{3} e f x^{2} - 3 i \, b^{3} e^{2} x - 3 i \, a b^{2} e^{2} + 3 i \, a^{2} b e f - i \, a^{3} f^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{3} f^{2} x^{3} - 3 i \, b^{3} e f x^{2} - 3 i \, b^{3} e^{2} x - 3 i \, a b^{2} e^{2} + 3 i \, a^{2} b e f - i \, a^{3} f^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-3 i \, a b^{2} e^{2} + 3 i \, a^{2} b e f - i \, a^{3} f^{2}\right)} \log\left(i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-3 i \, a b^{2} e^{2} + 3 i \, a^{2} b e f - i \, a^{3} f^{2}\right)} \log\left(-i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(3 i \, a b^{2} e^{2} - 3 i \, a^{2} b e f + i \, a^{3} f^{2}\right)} \log\left(i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(3 i \, a b^{2} e^{2} - 3 i \, a^{2} b e f + i \, a^{3} f^{2}\right)} \log\left(-i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-6 i \, b f^{2} x - 6 i \, b e f\right)} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-6 i \, b f^{2} x - 6 i \, b e f\right)} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(6 i \, b f^{2} x + 6 i \, b e f\right)} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(6 i \, b f^{2} x + 6 i \, b e f\right)} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{6 \, b^{3}}"," ",0,"1/6*(6*I*f^2*polylog(4, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*f^2*polylog(4, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*f^2*polylog(4, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*f^2*polylog(4, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 2*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x)*arctan(cosh(b*x + a)/sinh(b*x + a)) + (3*I*b^2*f^2*x^2 + 6*I*b^2*e*f*x + 3*I*b^2*e^2)*dilog(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (3*I*b^2*f^2*x^2 + 6*I*b^2*e*f*x + 3*I*b^2*e^2)*dilog(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-3*I*b^2*f^2*x^2 - 6*I*b^2*e*f*x - 3*I*b^2*e^2)*dilog(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-3*I*b^2*f^2*x^2 - 6*I*b^2*e*f*x - 3*I*b^2*e^2)*dilog(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (I*b^3*f^2*x^3 + 3*I*b^3*e*f*x^2 + 3*I*b^3*e^2*x + 3*I*a*b^2*e^2 - 3*I*a^2*b*e*f + I*a^3*f^2)*log(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^3*f^2*x^3 + 3*I*b^3*e*f*x^2 + 3*I*b^3*e^2*x + 3*I*a*b^2*e^2 - 3*I*a^2*b*e*f + I*a^3*f^2)*log(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^3*f^2*x^3 - 3*I*b^3*e*f*x^2 - 3*I*b^3*e^2*x - 3*I*a*b^2*e^2 + 3*I*a^2*b*e*f - I*a^3*f^2)*log(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^3*f^2*x^3 - 3*I*b^3*e*f*x^2 - 3*I*b^3*e^2*x - 3*I*a*b^2*e^2 + 3*I*a^2*b*e*f - I*a^3*f^2)*log(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-3*I*a*b^2*e^2 + 3*I*a^2*b*e*f - I*a^3*f^2)*log(I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-3*I*a*b^2*e^2 + 3*I*a^2*b*e*f - I*a^3*f^2)*log(-I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (3*I*a*b^2*e^2 - 3*I*a^2*b*e*f + I*a^3*f^2)*log(I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (3*I*a*b^2*e^2 - 3*I*a^2*b*e*f + I*a^3*f^2)*log(-I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-6*I*b*f^2*x - 6*I*b*e*f)*polylog(3, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-6*I*b*f^2*x - 6*I*b*e*f)*polylog(3, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (6*I*b*f^2*x + 6*I*b*e*f)*polylog(3, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (6*I*b*f^2*x + 6*I*b*e*f)*polylog(3, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
95,1,596,0,0.521421," ","integrate((f*x+e)*arctan(coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x\right)} \arctan\left(\frac{\cosh\left(b x + a\right)}{\sinh\left(b x + a\right)}\right) + {\left(2 i \, b f x + 2 i \, b e\right)} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(2 i \, b f x + 2 i \, b e\right)} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-2 i \, b f x - 2 i \, b e\right)} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-2 i \, b f x - 2 i \, b e\right)} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(i \, b^{2} f x^{2} + 2 i \, b^{2} e x + 2 i \, a b e - i \, a^{2} f\right)} \log\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{2} f x^{2} + 2 i \, b^{2} e x + 2 i \, a b e - i \, a^{2} f\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{2} f x^{2} - 2 i \, b^{2} e x - 2 i \, a b e + i \, a^{2} f\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{2} f x^{2} - 2 i \, b^{2} e x - 2 i \, a b e + i \, a^{2} f\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-2 i \, a b e + i \, a^{2} f\right)} \log\left(i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-2 i \, a b e + i \, a^{2} f\right)} \log\left(-i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(2 i \, a b e - i \, a^{2} f\right)} \log\left(i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(2 i \, a b e - i \, a^{2} f\right)} \log\left(-i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) - 2 i \, f {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, f {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, f {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, f {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{4 \, b^{2}}"," ",0,"1/4*(2*(b^2*f*x^2 + 2*b^2*e*x)*arctan(cosh(b*x + a)/sinh(b*x + a)) + (2*I*b*f*x + 2*I*b*e)*dilog(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (2*I*b*f*x + 2*I*b*e)*dilog(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-2*I*b*f*x - 2*I*b*e)*dilog(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-2*I*b*f*x - 2*I*b*e)*dilog(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (I*b^2*f*x^2 + 2*I*b^2*e*x + 2*I*a*b*e - I*a^2*f)*log(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^2*f*x^2 + 2*I*b^2*e*x + 2*I*a*b*e - I*a^2*f)*log(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^2*f*x^2 - 2*I*b^2*e*x - 2*I*a*b*e + I*a^2*f)*log(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^2*f*x^2 - 2*I*b^2*e*x - 2*I*a*b*e + I*a^2*f)*log(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-2*I*a*b*e + I*a^2*f)*log(I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-2*I*a*b*e + I*a^2*f)*log(-I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (2*I*a*b*e - I*a^2*f)*log(I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (2*I*a*b*e - I*a^2*f)*log(-I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) - 2*I*f*polylog(3, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*f*polylog(3, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*f*polylog(3, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*f*polylog(3, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
96,1,334,0,0.474781," ","integrate(arctan(coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b x \arctan\left(\frac{\cosh\left(b x + a\right)}{\sinh\left(b x + a\right)}\right) + {\left(i \, b x + i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - i \, a \log\left(i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) - i \, a \log\left(-i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + i \, a \log\left(i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + i \, a \log\left(-i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(2*b*x*arctan(cosh(b*x + a)/sinh(b*x + a)) + (I*b*x + I*a)*log(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b*x + I*a)*log(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b*x - I*a)*log(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b*x - I*a)*log(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - I*a*log(I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) - I*a*log(-I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + I*a*log(I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + I*a*log(-I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + I*dilog(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + I*dilog(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) - I*dilog(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) - I*dilog(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
97,0,0,0,0.456088," ","integrate(arctan(coth(b*x+a))/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(\coth\left(b x + a\right)\right)}{f x + e}, x\right)"," ",0,"integral(arctan(coth(b*x + a))/(f*x + e), x)","F",0
98,1,1315,0,0.589622," ","integrate(x^2*arctan(c+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} \arctan\left(\frac{d \cosh\left(b x + a\right) + c \sinh\left(b x + a\right)}{\sinh\left(b x + a\right)}\right) + 3 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 3 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - i \, a^{3} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a^{3} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a^{3} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a^{3} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - 6 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(i \, b^{3} x^{3} + i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{3} x^{3} + i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{3} x^{3} - i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{3} x^{3} - i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 6 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{6 \, b^{3}}"," ",0,"1/6*(2*b^3*x^3*arctan((d*cosh(b*x + a) + c*sinh(b*x + a))/sinh(b*x + a)) + 3*I*b^2*x^2*dilog(1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 3*I*b^2*x^2*dilog(-1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 3*I*b^2*x^2*dilog(1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 3*I*b^2*x^2*dilog(-1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - I*a^3*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 - 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a^3*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 - 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a^3*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 + 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a^3*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 + 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - 6*I*b*x*polylog(3, 1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*b*x*polylog(3, -1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*b*x*polylog(3, 1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*b*x*polylog(3, -1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + (I*b^3*x^3 + I*a^3)*log(1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^3*x^3 + I*a^3)*log(-1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^3*x^3 - I*a^3)*log(1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^3*x^3 - I*a^3)*log(-1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 6*I*polylog(4, 1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*polylog(4, -1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*polylog(4, 1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*polylog(4, -1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
99,1,1087,0,0.645365," ","integrate(x*arctan(c+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{2} x^{2} \arctan\left(\frac{d \cosh\left(b x + a\right) + c \sinh\left(b x + a\right)}{\sinh\left(b x + a\right)}\right) + 2 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + i \, a^{2} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a^{2} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a^{2} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a^{2} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + {\left(i \, b^{2} x^{2} - i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{2} x^{2} - i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{2} x^{2} + i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{2} x^{2} + i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 2 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{4 \, b^{2}}"," ",0,"1/4*(2*b^2*x^2*arctan((d*cosh(b*x + a) + c*sinh(b*x + a))/sinh(b*x + a)) + 2*I*b*x*dilog(1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*b*x*dilog(-1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*b*x*dilog(1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*b*x*dilog(-1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + I*a^2*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 - 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a^2*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 - 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a^2*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 + 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a^2*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 + 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + (I*b^2*x^2 - I*a^2)*log(1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^2*x^2 - I*a^2)*log(-1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^2*x^2 + I*a^2)*log(1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^2*x^2 + I*a^2)*log(-1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 2*I*polylog(3, 1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*polylog(3, -1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*polylog(3, 1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*polylog(3, -1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
100,1,839,0,0.965269," ","integrate(arctan(c+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b x \arctan\left(\frac{d \cosh\left(b x + a\right) + c \sinh\left(b x + a\right)}{\sinh\left(b x + a\right)}\right) - i \, a \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + {\left(i \, b x + i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(2*b*x*arctan((d*cosh(b*x + a) + c*sinh(b*x + a))/sinh(b*x + a)) - I*a*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 - 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 - 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 + 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 + 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + (I*b*x + I*a)*log(1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b*x + I*a)*log(-1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b*x - I*a)*log(1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b*x - I*a)*log(-1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + I*dilog(1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + I*dilog(-1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - I*dilog(1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - I*dilog(-1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
101,0,0,0,0.470226," ","integrate(arctan(c+d*coth(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(d \coth\left(b x + a\right) + c\right)}{x}, x\right)"," ",0,"integral(arctan(d*coth(b*x + a) + c)/x, x)","F",0
102,1,291,0,0.513186," ","integrate(x^2*arctan(c+(I+c)*coth(b*x+a)),x, algorithm=""fricas"")","\frac{-i \, b^{4} x^{4} + 2 i \, b^{3} x^{3} \log\left(-\frac{{\left(c + i\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c e^{\left(2 \, b x + 2 \, a\right)} + i}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + i \, a^{4} - 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) - 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) - 12 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) - 12 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + {\left(2 i \, b^{3} x^{3} + 2 i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(2 i \, b^{3} x^{3} + 2 i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + 12 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + 12 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(-I*b^4*x^4 + 2*I*b^3*x^3*log(-(c + I)*e^(2*b*x + 2*a)/(c*e^(2*b*x + 2*a) + I)) + 6*I*b^2*x^2*dilog(1/2*sqrt(4*I*c)*e^(b*x + a)) + 6*I*b^2*x^2*dilog(-1/2*sqrt(4*I*c)*e^(b*x + a)) + I*a^4 - 2*I*a^3*log(1/2*(2*c*e^(b*x + a) + I*sqrt(4*I*c))/c) - 2*I*a^3*log(1/2*(2*c*e^(b*x + a) - I*sqrt(4*I*c))/c) - 12*I*b*x*polylog(3, 1/2*sqrt(4*I*c)*e^(b*x + a)) - 12*I*b*x*polylog(3, -1/2*sqrt(4*I*c)*e^(b*x + a)) + (2*I*b^3*x^3 + 2*I*a^3)*log(1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + (2*I*b^3*x^3 + 2*I*a^3)*log(-1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + 12*I*polylog(4, 1/2*sqrt(4*I*c)*e^(b*x + a)) + 12*I*polylog(4, -1/2*sqrt(4*I*c)*e^(b*x + a)))/b^3","C",0
103,1,245,0,0.556487," ","integrate(x*arctan(c+(I+c)*coth(b*x+a)),x, algorithm=""fricas"")","\frac{-2 i \, b^{3} x^{3} + 3 i \, b^{2} x^{2} \log\left(-\frac{{\left(c + i\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c e^{\left(2 \, b x + 2 \, a\right)} + i}\right) - 2 i \, a^{3} + 6 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + 6 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) + 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) + {\left(3 i \, b^{2} x^{2} - 3 i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(3 i \, b^{2} x^{2} - 3 i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) - 6 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) - 6 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(-2*I*b^3*x^3 + 3*I*b^2*x^2*log(-(c + I)*e^(2*b*x + 2*a)/(c*e^(2*b*x + 2*a) + I)) - 2*I*a^3 + 6*I*b*x*dilog(1/2*sqrt(4*I*c)*e^(b*x + a)) + 6*I*b*x*dilog(-1/2*sqrt(4*I*c)*e^(b*x + a)) + 3*I*a^2*log(1/2*(2*c*e^(b*x + a) + I*sqrt(4*I*c))/c) + 3*I*a^2*log(1/2*(2*c*e^(b*x + a) - I*sqrt(4*I*c))/c) + (3*I*b^2*x^2 - 3*I*a^2)*log(1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + (3*I*b^2*x^2 - 3*I*a^2)*log(-1/2*sqrt(4*I*c)*e^(b*x + a) + 1) - 6*I*polylog(3, 1/2*sqrt(4*I*c)*e^(b*x + a)) - 6*I*polylog(3, -1/2*sqrt(4*I*c)*e^(b*x + a)))/b^2","C",0
104,1,187,0,0.529212," ","integrate(arctan(c+(I+c)*coth(b*x+a)),x, algorithm=""fricas"")","\frac{-i \, b^{2} x^{2} + i \, b x \log\left(-\frac{{\left(c + i\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c e^{\left(2 \, b x + 2 \, a\right)} + i}\right) + i \, a^{2} + {\left(i \, b x + i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) - i \, a \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) - i \, a \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) + i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right)}{2 \, b}"," ",0,"1/2*(-I*b^2*x^2 + I*b*x*log(-(c + I)*e^(2*b*x + 2*a)/(c*e^(2*b*x + 2*a) + I)) + I*a^2 + (I*b*x + I*a)*log(1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + (I*b*x + I*a)*log(-1/2*sqrt(4*I*c)*e^(b*x + a) + 1) - I*a*log(1/2*(2*c*e^(b*x + a) + I*sqrt(4*I*c))/c) - I*a*log(1/2*(2*c*e^(b*x + a) - I*sqrt(4*I*c))/c) + I*dilog(1/2*sqrt(4*I*c)*e^(b*x + a)) + I*dilog(-1/2*sqrt(4*I*c)*e^(b*x + a)))/b","B",0
105,0,0,0,0.455846," ","integrate(arctan(c+(I+c)*coth(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, \log\left(-\frac{{\left(c + i\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c e^{\left(2 \, b x + 2 \, a\right)} + i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*I*log(-(c + I)*e^(2*b*x + 2*a)/(c*e^(2*b*x + 2*a) + I))/x, x)","F",0
106,1,291,0,0.476975," ","integrate(x^2*arctan(c-(I-c)*coth(b*x+a)),x, algorithm=""fricas"")","\frac{i \, b^{4} x^{4} + 2 i \, b^{3} x^{3} \log\left(-\frac{{\left(c e^{\left(2 \, b x + 2 \, a\right)} - i\right)} e^{\left(-2 \, b x - 2 \, a\right)}}{c - i}\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) - i \, a^{4} + 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) + 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) + 12 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + 12 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + {\left(-2 i \, b^{3} x^{3} - 2 i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(-2 i \, b^{3} x^{3} - 2 i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) - 12 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) - 12 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(I*b^4*x^4 + 2*I*b^3*x^3*log(-(c*e^(2*b*x + 2*a) - I)*e^(-2*b*x - 2*a)/(c - I)) - 6*I*b^2*x^2*dilog(1/2*sqrt(-4*I*c)*e^(b*x + a)) - 6*I*b^2*x^2*dilog(-1/2*sqrt(-4*I*c)*e^(b*x + a)) - I*a^4 + 2*I*a^3*log(1/2*(2*c*e^(b*x + a) + I*sqrt(-4*I*c))/c) + 2*I*a^3*log(1/2*(2*c*e^(b*x + a) - I*sqrt(-4*I*c))/c) + 12*I*b*x*polylog(3, 1/2*sqrt(-4*I*c)*e^(b*x + a)) + 12*I*b*x*polylog(3, -1/2*sqrt(-4*I*c)*e^(b*x + a)) + (-2*I*b^3*x^3 - 2*I*a^3)*log(1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + (-2*I*b^3*x^3 - 2*I*a^3)*log(-1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) - 12*I*polylog(4, 1/2*sqrt(-4*I*c)*e^(b*x + a)) - 12*I*polylog(4, -1/2*sqrt(-4*I*c)*e^(b*x + a)))/b^3","C",0
107,1,245,0,0.489691," ","integrate(x*arctan(c-(I-c)*coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 i \, b^{3} x^{3} + 3 i \, b^{2} x^{2} \log\left(-\frac{{\left(c e^{\left(2 \, b x + 2 \, a\right)} - i\right)} e^{\left(-2 \, b x - 2 \, a\right)}}{c - i}\right) + 2 i \, a^{3} - 6 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) - 6 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) - 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) - 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) + {\left(-3 i \, b^{2} x^{2} + 3 i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(-3 i \, b^{2} x^{2} + 3 i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + 6 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + 6 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*I*b^3*x^3 + 3*I*b^2*x^2*log(-(c*e^(2*b*x + 2*a) - I)*e^(-2*b*x - 2*a)/(c - I)) + 2*I*a^3 - 6*I*b*x*dilog(1/2*sqrt(-4*I*c)*e^(b*x + a)) - 6*I*b*x*dilog(-1/2*sqrt(-4*I*c)*e^(b*x + a)) - 3*I*a^2*log(1/2*(2*c*e^(b*x + a) + I*sqrt(-4*I*c))/c) - 3*I*a^2*log(1/2*(2*c*e^(b*x + a) - I*sqrt(-4*I*c))/c) + (-3*I*b^2*x^2 + 3*I*a^2)*log(1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + (-3*I*b^2*x^2 + 3*I*a^2)*log(-1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + 6*I*polylog(3, 1/2*sqrt(-4*I*c)*e^(b*x + a)) + 6*I*polylog(3, -1/2*sqrt(-4*I*c)*e^(b*x + a)))/b^2","C",0
108,1,187,0,0.512708," ","integrate(arctan(c-(I-c)*coth(b*x+a)),x, algorithm=""fricas"")","\frac{i \, b^{2} x^{2} + i \, b x \log\left(-\frac{{\left(c e^{\left(2 \, b x + 2 \, a\right)} - i\right)} e^{\left(-2 \, b x - 2 \, a\right)}}{c - i}\right) - i \, a^{2} + {\left(-i \, b x - i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + i \, a \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) + i \, a \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) - i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) - i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right)}{2 \, b}"," ",0,"1/2*(I*b^2*x^2 + I*b*x*log(-(c*e^(2*b*x + 2*a) - I)*e^(-2*b*x - 2*a)/(c - I)) - I*a^2 + (-I*b*x - I*a)*log(1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + (-I*b*x - I*a)*log(-1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + I*a*log(1/2*(2*c*e^(b*x + a) + I*sqrt(-4*I*c))/c) + I*a*log(1/2*(2*c*e^(b*x + a) - I*sqrt(-4*I*c))/c) - I*dilog(1/2*sqrt(-4*I*c)*e^(b*x + a)) - I*dilog(-1/2*sqrt(-4*I*c)*e^(b*x + a)))/b","B",0
109,0,0,0,0.506268," ","integrate(arctan(c-(I-c)*coth(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, \log\left(-\frac{{\left(c e^{\left(2 \, b x + 2 \, a\right)} - i\right)} e^{\left(-2 \, b x - 2 \, a\right)}}{c - i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*I*log(-(c*e^(2*b*x + 2*a) - I)*e^(-2*b*x - 2*a)/(c - I))/x, x)","F",0
110,1,40,0,0.464742," ","integrate(arctan(exp(x)),x, algorithm=""fricas"")","x \arctan\left(e^{x}\right) + \frac{1}{2} i \, x \log\left(i \, e^{x} + 1\right) - \frac{1}{2} i \, x \log\left(-i \, e^{x} + 1\right) - \frac{1}{2} i \, {\rm Li}_2\left(i \, e^{x}\right) + \frac{1}{2} i \, {\rm Li}_2\left(-i \, e^{x}\right)"," ",0,"x*arctan(e^x) + 1/2*I*x*log(I*e^x + 1) - 1/2*I*x*log(-I*e^x + 1) - 1/2*I*dilog(I*e^x) + 1/2*I*dilog(-I*e^x)","B",0
111,1,65,0,0.450863," ","integrate(x*arctan(exp(x)),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} \arctan\left(e^{x}\right) + \frac{1}{4} i \, x^{2} \log\left(i \, e^{x} + 1\right) - \frac{1}{4} i \, x^{2} \log\left(-i \, e^{x} + 1\right) - \frac{1}{2} i \, x {\rm Li}_2\left(i \, e^{x}\right) + \frac{1}{2} i \, x {\rm Li}_2\left(-i \, e^{x}\right) + \frac{1}{2} i \, {\rm polylog}\left(3, i \, e^{x}\right) - \frac{1}{2} i \, {\rm polylog}\left(3, -i \, e^{x}\right)"," ",0,"1/2*x^2*arctan(e^x) + 1/4*I*x^2*log(I*e^x + 1) - 1/4*I*x^2*log(-I*e^x + 1) - 1/2*I*x*dilog(I*e^x) + 1/2*I*x*dilog(-I*e^x) + 1/2*I*polylog(3, I*e^x) - 1/2*I*polylog(3, -I*e^x)","C",0
112,1,87,0,0.480650," ","integrate(x^2*arctan(exp(x)),x, algorithm=""fricas"")","\frac{1}{3} \, x^{3} \arctan\left(e^{x}\right) + \frac{1}{6} i \, x^{3} \log\left(i \, e^{x} + 1\right) - \frac{1}{6} i \, x^{3} \log\left(-i \, e^{x} + 1\right) - \frac{1}{2} i \, x^{2} {\rm Li}_2\left(i \, e^{x}\right) + \frac{1}{2} i \, x^{2} {\rm Li}_2\left(-i \, e^{x}\right) + i \, x {\rm polylog}\left(3, i \, e^{x}\right) - i \, x {\rm polylog}\left(3, -i \, e^{x}\right) - i \, {\rm polylog}\left(4, i \, e^{x}\right) + i \, {\rm polylog}\left(4, -i \, e^{x}\right)"," ",0,"1/3*x^3*arctan(e^x) + 1/6*I*x^3*log(I*e^x + 1) - 1/6*I*x^3*log(-I*e^x + 1) - 1/2*I*x^2*dilog(I*e^x) + 1/2*I*x^2*dilog(-I*e^x) + I*x*polylog(3, I*e^x) - I*x*polylog(3, -I*e^x) - I*polylog(4, I*e^x) + I*polylog(4, -I*e^x)","C",0
113,1,103,0,0.499840," ","integrate(arctan(exp(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b x \arctan\left(e^{\left(b x + a\right)}\right) + i \, a \log\left(e^{\left(b x + a\right)} + i\right) - i \, a \log\left(e^{\left(b x + a\right)} - i\right) + {\left(i \, b x + i \, a\right)} \log\left(i \, e^{\left(b x + a\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(-i \, e^{\left(b x + a\right)} + 1\right) - i \, {\rm Li}_2\left(i \, e^{\left(b x + a\right)}\right) + i \, {\rm Li}_2\left(-i \, e^{\left(b x + a\right)}\right)}{2 \, b}"," ",0,"1/2*(2*b*x*arctan(e^(b*x + a)) + I*a*log(e^(b*x + a) + I) - I*a*log(e^(b*x + a) - I) + (I*b*x + I*a)*log(I*e^(b*x + a) + 1) + (-I*b*x - I*a)*log(-I*e^(b*x + a) + 1) - I*dilog(I*e^(b*x + a)) + I*dilog(-I*e^(b*x + a)))/b","B",0
114,1,151,0,0.804723," ","integrate(x*arctan(exp(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{2} x^{2} \arctan\left(e^{\left(b x + a\right)}\right) - 2 i \, b x {\rm Li}_2\left(i \, e^{\left(b x + a\right)}\right) + 2 i \, b x {\rm Li}_2\left(-i \, e^{\left(b x + a\right)}\right) - i \, a^{2} \log\left(e^{\left(b x + a\right)} + i\right) + i \, a^{2} \log\left(e^{\left(b x + a\right)} - i\right) + {\left(i \, b^{2} x^{2} - i \, a^{2}\right)} \log\left(i \, e^{\left(b x + a\right)} + 1\right) + {\left(-i \, b^{2} x^{2} + i \, a^{2}\right)} \log\left(-i \, e^{\left(b x + a\right)} + 1\right) + 2 i \, {\rm polylog}\left(3, i \, e^{\left(b x + a\right)}\right) - 2 i \, {\rm polylog}\left(3, -i \, e^{\left(b x + a\right)}\right)}{4 \, b^{2}}"," ",0,"1/4*(2*b^2*x^2*arctan(e^(b*x + a)) - 2*I*b*x*dilog(I*e^(b*x + a)) + 2*I*b*x*dilog(-I*e^(b*x + a)) - I*a^2*log(e^(b*x + a) + I) + I*a^2*log(e^(b*x + a) - I) + (I*b^2*x^2 - I*a^2)*log(I*e^(b*x + a) + 1) + (-I*b^2*x^2 + I*a^2)*log(-I*e^(b*x + a) + 1) + 2*I*polylog(3, I*e^(b*x + a)) - 2*I*polylog(3, -I*e^(b*x + a)))/b^2","C",0
115,1,187,0,0.520826," ","integrate(x^2*arctan(exp(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} \arctan\left(e^{\left(b x + a\right)}\right) - 3 i \, b^{2} x^{2} {\rm Li}_2\left(i \, e^{\left(b x + a\right)}\right) + 3 i \, b^{2} x^{2} {\rm Li}_2\left(-i \, e^{\left(b x + a\right)}\right) + i \, a^{3} \log\left(e^{\left(b x + a\right)} + i\right) - i \, a^{3} \log\left(e^{\left(b x + a\right)} - i\right) + 6 i \, b x {\rm polylog}\left(3, i \, e^{\left(b x + a\right)}\right) - 6 i \, b x {\rm polylog}\left(3, -i \, e^{\left(b x + a\right)}\right) + {\left(i \, b^{3} x^{3} + i \, a^{3}\right)} \log\left(i \, e^{\left(b x + a\right)} + 1\right) + {\left(-i \, b^{3} x^{3} - i \, a^{3}\right)} \log\left(-i \, e^{\left(b x + a\right)} + 1\right) - 6 i \, {\rm polylog}\left(4, i \, e^{\left(b x + a\right)}\right) + 6 i \, {\rm polylog}\left(4, -i \, e^{\left(b x + a\right)}\right)}{6 \, b^{3}}"," ",0,"1/6*(2*b^3*x^3*arctan(e^(b*x + a)) - 3*I*b^2*x^2*dilog(I*e^(b*x + a)) + 3*I*b^2*x^2*dilog(-I*e^(b*x + a)) + I*a^3*log(e^(b*x + a) + I) - I*a^3*log(e^(b*x + a) - I) + 6*I*b*x*polylog(3, I*e^(b*x + a)) - 6*I*b*x*polylog(3, -I*e^(b*x + a)) + (I*b^3*x^3 + I*a^3)*log(I*e^(b*x + a) + 1) + (-I*b^3*x^3 - I*a^3)*log(-I*e^(b*x + a) + 1) - 6*I*polylog(4, I*e^(b*x + a)) + 6*I*polylog(4, -I*e^(b*x + a)))/b^3","C",0
116,1,212,0,1.031943," ","integrate(arctan(a+b*f^(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d x \arctan\left(b f^{d x + c} + a\right) \log\left(f\right) + i \, c \log\left(b f^{d x + c} + a + i\right) \log\left(f\right) - i \, c \log\left(b f^{d x + c} + a - i\right) \log\left(f\right) + {\left(i \, d x + i \, c\right)} \log\left(f\right) \log\left(\frac{a^{2} + {\left(a b + i \, b\right)} f^{d x + c} + 1}{a^{2} + 1}\right) + {\left(-i \, d x - i \, c\right)} \log\left(f\right) \log\left(\frac{a^{2} + {\left(a b - i \, b\right)} f^{d x + c} + 1}{a^{2} + 1}\right) + i \, {\rm Li}_2\left(-\frac{a^{2} + {\left(a b + i \, b\right)} f^{d x + c} + 1}{a^{2} + 1} + 1\right) - i \, {\rm Li}_2\left(-\frac{a^{2} + {\left(a b - i \, b\right)} f^{d x + c} + 1}{a^{2} + 1} + 1\right)}{2 \, d \log\left(f\right)}"," ",0,"1/2*(2*d*x*arctan(b*f^(d*x + c) + a)*log(f) + I*c*log(b*f^(d*x + c) + a + I)*log(f) - I*c*log(b*f^(d*x + c) + a - I)*log(f) + (I*d*x + I*c)*log(f)*log((a^2 + (a*b + I*b)*f^(d*x + c) + 1)/(a^2 + 1)) + (-I*d*x - I*c)*log(f)*log((a^2 + (a*b - I*b)*f^(d*x + c) + 1)/(a^2 + 1)) + I*dilog(-(a^2 + (a*b + I*b)*f^(d*x + c) + 1)/(a^2 + 1) + 1) - I*dilog(-(a^2 + (a*b - I*b)*f^(d*x + c) + 1)/(a^2 + 1) + 1))/(d*log(f))","A",0
117,1,304,0,0.454807," ","integrate(x*arctan(a+b*f^(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d^{2} x^{2} \arctan\left(b f^{d x + c} + a\right) \log\left(f\right)^{2} - i \, c^{2} \log\left(b f^{d x + c} + a + i\right) \log\left(f\right)^{2} + i \, c^{2} \log\left(b f^{d x + c} + a - i\right) \log\left(f\right)^{2} + 2 i \, d x {\rm Li}_2\left(-\frac{a^{2} + {\left(a b + i \, b\right)} f^{d x + c} + 1}{a^{2} + 1} + 1\right) \log\left(f\right) - 2 i \, d x {\rm Li}_2\left(-\frac{a^{2} + {\left(a b - i \, b\right)} f^{d x + c} + 1}{a^{2} + 1} + 1\right) \log\left(f\right) + {\left(i \, d^{2} x^{2} - i \, c^{2}\right)} \log\left(f\right)^{2} \log\left(\frac{a^{2} + {\left(a b + i \, b\right)} f^{d x + c} + 1}{a^{2} + 1}\right) + {\left(-i \, d^{2} x^{2} + i \, c^{2}\right)} \log\left(f\right)^{2} \log\left(\frac{a^{2} + {\left(a b - i \, b\right)} f^{d x + c} + 1}{a^{2} + 1}\right) - 2 i \, {\rm polylog}\left(3, -\frac{{\left(a b + i \, b\right)} f^{d x + c}}{a^{2} + 1}\right) + 2 i \, {\rm polylog}\left(3, -\frac{{\left(a b - i \, b\right)} f^{d x + c}}{a^{2} + 1}\right)}{4 \, d^{2} \log\left(f\right)^{2}}"," ",0,"1/4*(2*d^2*x^2*arctan(b*f^(d*x + c) + a)*log(f)^2 - I*c^2*log(b*f^(d*x + c) + a + I)*log(f)^2 + I*c^2*log(b*f^(d*x + c) + a - I)*log(f)^2 + 2*I*d*x*dilog(-(a^2 + (a*b + I*b)*f^(d*x + c) + 1)/(a^2 + 1) + 1)*log(f) - 2*I*d*x*dilog(-(a^2 + (a*b - I*b)*f^(d*x + c) + 1)/(a^2 + 1) + 1)*log(f) + (I*d^2*x^2 - I*c^2)*log(f)^2*log((a^2 + (a*b + I*b)*f^(d*x + c) + 1)/(a^2 + 1)) + (-I*d^2*x^2 + I*c^2)*log(f)^2*log((a^2 + (a*b - I*b)*f^(d*x + c) + 1)/(a^2 + 1)) - 2*I*polylog(3, -(a*b + I*b)*f^(d*x + c)/(a^2 + 1)) + 2*I*polylog(3, -(a*b - I*b)*f^(d*x + c)/(a^2 + 1)))/(d^2*log(f)^2)","C",0
118,1,378,0,0.811764," ","integrate(x^2*arctan(a+b*f^(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d^{3} x^{3} \arctan\left(b f^{d x + c} + a\right) \log\left(f\right)^{3} + 3 i \, d^{2} x^{2} {\rm Li}_2\left(-\frac{a^{2} + {\left(a b + i \, b\right)} f^{d x + c} + 1}{a^{2} + 1} + 1\right) \log\left(f\right)^{2} - 3 i \, d^{2} x^{2} {\rm Li}_2\left(-\frac{a^{2} + {\left(a b - i \, b\right)} f^{d x + c} + 1}{a^{2} + 1} + 1\right) \log\left(f\right)^{2} + i \, c^{3} \log\left(b f^{d x + c} + a + i\right) \log\left(f\right)^{3} - i \, c^{3} \log\left(b f^{d x + c} + a - i\right) \log\left(f\right)^{3} + {\left(i \, d^{3} x^{3} + i \, c^{3}\right)} \log\left(f\right)^{3} \log\left(\frac{a^{2} + {\left(a b + i \, b\right)} f^{d x + c} + 1}{a^{2} + 1}\right) + {\left(-i \, d^{3} x^{3} - i \, c^{3}\right)} \log\left(f\right)^{3} \log\left(\frac{a^{2} + {\left(a b - i \, b\right)} f^{d x + c} + 1}{a^{2} + 1}\right) - 6 i \, d x \log\left(f\right) {\rm polylog}\left(3, -\frac{{\left(a b + i \, b\right)} f^{d x + c}}{a^{2} + 1}\right) + 6 i \, d x \log\left(f\right) {\rm polylog}\left(3, -\frac{{\left(a b - i \, b\right)} f^{d x + c}}{a^{2} + 1}\right) + 6 i \, {\rm polylog}\left(4, -\frac{{\left(a b + i \, b\right)} f^{d x + c}}{a^{2} + 1}\right) - 6 i \, {\rm polylog}\left(4, -\frac{{\left(a b - i \, b\right)} f^{d x + c}}{a^{2} + 1}\right)}{6 \, d^{3} \log\left(f\right)^{3}}"," ",0,"1/6*(2*d^3*x^3*arctan(b*f^(d*x + c) + a)*log(f)^3 + 3*I*d^2*x^2*dilog(-(a^2 + (a*b + I*b)*f^(d*x + c) + 1)/(a^2 + 1) + 1)*log(f)^2 - 3*I*d^2*x^2*dilog(-(a^2 + (a*b - I*b)*f^(d*x + c) + 1)/(a^2 + 1) + 1)*log(f)^2 + I*c^3*log(b*f^(d*x + c) + a + I)*log(f)^3 - I*c^3*log(b*f^(d*x + c) + a - I)*log(f)^3 + (I*d^3*x^3 + I*c^3)*log(f)^3*log((a^2 + (a*b + I*b)*f^(d*x + c) + 1)/(a^2 + 1)) + (-I*d^3*x^3 - I*c^3)*log(f)^3*log((a^2 + (a*b - I*b)*f^(d*x + c) + 1)/(a^2 + 1)) - 6*I*d*x*log(f)*polylog(3, -(a*b + I*b)*f^(d*x + c)/(a^2 + 1)) + 6*I*d*x*log(f)*polylog(3, -(a*b - I*b)*f^(d*x + c)/(a^2 + 1)) + 6*I*polylog(4, -(a*b + I*b)*f^(d*x + c)/(a^2 + 1)) - 6*I*polylog(4, -(a*b - I*b)*f^(d*x + c)/(a^2 + 1)))/(d^3*log(f)^3)","C",0
119,1,28,0,0.554005," ","integrate(arctan(exp(x))/exp(x),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(2 \, x e^{x} - e^{x} \log\left(e^{\left(2 \, x\right)} + 1\right) - 2 \, \arctan\left(e^{x}\right)\right)} e^{\left(-x\right)}"," ",0,"1/2*(2*x*e^x - e^x*log(e^(2*x) + 1) - 2*arctan(e^x))*e^(-x)","A",0
120,1,50,0,0.674983," ","integrate(arctan(x)/(-1+x)^3,x, algorithm=""fricas"")","\frac{{\left(x^{2} - 2 \, x + 1\right)} \log\left(x^{2} + 1\right) - 2 \, {\left(x^{2} - 2 \, x + 1\right)} \log\left(x - 1\right) - 2 \, x - 4 \, \arctan\left(x\right) + 2}{8 \, {\left(x^{2} - 2 \, x + 1\right)}}"," ",0,"1/8*((x^2 - 2*x + 1)*log(x^2 + 1) - 2*(x^2 - 2*x + 1)*log(x - 1) - 2*x - 4*arctan(x) + 2)/(x^2 - 2*x + 1)","A",0
121,1,77,0,1.129912," ","integrate(arctan(1+2*x)/(4+3*x)^3,x, algorithm=""fricas"")","\frac{{\left(48 \, x^{2} + 128 \, x - 11\right)} \arctan\left(2 \, x + 1\right) - 5 \, {\left(9 \, x^{2} + 24 \, x + 16\right)} \log\left(2 \, x^{2} + 2 \, x + 1\right) + 10 \, {\left(9 \, x^{2} + 24 \, x + 16\right)} \log\left(3 \, x + 4\right) - 51 \, x - 68}{578 \, {\left(9 \, x^{2} + 24 \, x + 16\right)}}"," ",0,"1/578*((48*x^2 + 128*x - 11)*arctan(2*x + 1) - 5*(9*x^2 + 24*x + 16)*log(2*x^2 + 2*x + 1) + 10*(9*x^2 + 24*x + 16)*log(3*x + 4) - 51*x - 68)/(9*x^2 + 24*x + 16)","A",0
122,1,18,0,0.652542," ","integrate(arctan((1+x)^(1/2)),x, algorithm=""fricas"")","{\left(x + 2\right)} \arctan\left(\sqrt{x + 1}\right) - \sqrt{x + 1}"," ",0,"(x + 2)*arctan(sqrt(x + 1)) - sqrt(x + 1)","A",0
123,1,5,0,0.501304," ","integrate(1/(x^2+1)/(2+arctan(x)),x, algorithm=""fricas"")","\log\left(\arctan\left(x\right) + 2\right)"," ",0,"log(arctan(x) + 2)","A",0
124,1,15,0,0.576959," ","integrate(1/(a*x^2+a)/(b-2*b*arctan(x)),x, algorithm=""fricas"")","-\frac{\log\left(2 \, \arctan\left(x\right) - 1\right)}{2 \, a b}"," ",0,"-1/2*log(2*arctan(x) - 1)/(a*b)","A",0
125,1,26,0,0.538868," ","integrate((x+x^3+(1+x)^2*arctan(x))/(1+x)^2/(x^2+1),x, algorithm=""fricas"")","\frac{{\left(x + 1\right)} \arctan\left(x\right)^{2} + 2 \, {\left(x + 1\right)} \log\left(x + 1\right) + 2}{2 \, {\left(x + 1\right)}}"," ",0,"1/2*((x + 1)*arctan(x)^2 + 2*(x + 1)*log(x + 1) + 2)/(x + 1)","A",0
126,1,40,0,0.566900," ","integrate(-x^3*arctan(x^(1/2)-(1+x)^(1/2)),x, algorithm=""fricas"")","\frac{1}{4} \, {\left(x^{4} - 1\right)} \arctan\left(\sqrt{x + 1} - \sqrt{x}\right) + \frac{1}{840} \, {\left(15 \, x^{3} - 21 \, x^{2} + 35 \, x - 105\right)} \sqrt{x}"," ",0,"1/4*(x^4 - 1)*arctan(sqrt(x + 1) - sqrt(x)) + 1/840*(15*x^3 - 21*x^2 + 35*x - 105)*sqrt(x)","A",0
127,1,35,0,0.580214," ","integrate(-x^2*arctan(x^(1/2)-(1+x)^(1/2)),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(x^{3} + 1\right)} \arctan\left(\sqrt{x + 1} - \sqrt{x}\right) + \frac{1}{90} \, {\left(3 \, x^{2} - 5 \, x + 15\right)} \sqrt{x}"," ",0,"1/3*(x^3 + 1)*arctan(sqrt(x + 1) - sqrt(x)) + 1/90*(3*x^2 - 5*x + 15)*sqrt(x)","A",0
128,1,28,0,0.992129," ","integrate(-x*arctan(x^(1/2)-(1+x)^(1/2)),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(x^{2} - 1\right)} \arctan\left(\sqrt{x + 1} - \sqrt{x}\right) + \frac{1}{12} \, {\left(x - 3\right)} \sqrt{x}"," ",0,"1/2*(x^2 - 1)*arctan(sqrt(x + 1) - sqrt(x)) + 1/12*(x - 3)*sqrt(x)","A",0
129,1,22,0,0.428403," ","integrate(-arctan(x^(1/2)-(1+x)^(1/2)),x, algorithm=""fricas"")","{\left(x + 1\right)} \arctan\left(\sqrt{x + 1} - \sqrt{x}\right) + \frac{1}{2} \, \sqrt{x}"," ",0,"(x + 1)*arctan(sqrt(x + 1) - sqrt(x)) + 1/2*sqrt(x)","A",0
130,0,0,0,0.750128," ","integrate(-arctan(x^(1/2)-(1+x)^(1/2))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(\sqrt{x + 1} - \sqrt{x}\right)}{x}, x\right)"," ",0,"integral(arctan(sqrt(x + 1) - sqrt(x))/x, x)","F",0
131,1,28,0,0.613555," ","integrate(-arctan(x^(1/2)-(1+x)^(1/2))/x^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(x + 1\right)} \arctan\left(\sqrt{x + 1} - \sqrt{x}\right) - \sqrt{x}}{2 \, x}"," ",0,"-1/2*(2*(x + 1)*arctan(sqrt(x + 1) - sqrt(x)) - sqrt(x))/x","A",0
132,1,35,0,0.566515," ","integrate(-arctan(x^(1/2)-(1+x)^(1/2))/x^3,x, algorithm=""fricas"")","\frac{6 \, {\left(x^{2} - 1\right)} \arctan\left(\sqrt{x + 1} - \sqrt{x}\right) - {\left(3 \, x - 1\right)} \sqrt{x}}{12 \, x^{2}}"," ",0,"1/12*(6*(x^2 - 1)*arctan(sqrt(x + 1) - sqrt(x)) - (3*x - 1)*sqrt(x))/x^2","A",0
133,1,40,0,0.500825," ","integrate(-arctan(x^(1/2)-(1+x)^(1/2))/x^4,x, algorithm=""fricas"")","-\frac{30 \, {\left(x^{3} + 1\right)} \arctan\left(\sqrt{x + 1} - \sqrt{x}\right) - {\left(15 \, x^{2} - 5 \, x + 3\right)} \sqrt{x}}{90 \, x^{3}}"," ",0,"-1/90*(30*(x^3 + 1)*arctan(sqrt(x + 1) - sqrt(x)) - (15*x^2 - 5*x + 3)*sqrt(x))/x^3","A",0
134,1,126,0,0.785045," ","integrate(arctan(c*x/(-c^2*x^2+a)^(1/2))^m/(d-c^2*d*x^2/a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-c^{2} x^{2} + a} a \left(-\arctan\left(\frac{\sqrt{-c^{2} x^{2} + a} c x}{c^{2} x^{2} - a}\right)\right)^{m} \sqrt{-\frac{c^{2} d x^{2} - a d}{a}} \arctan\left(\frac{\sqrt{-c^{2} x^{2} + a} c x}{c^{2} x^{2} - a}\right)}{a c d m + a c d - {\left(c^{3} d m + c^{3} d\right)} x^{2}}"," ",0,"-sqrt(-c^2*x^2 + a)*a*(-arctan(sqrt(-c^2*x^2 + a)*c*x/(c^2*x^2 - a)))^m*sqrt(-(c^2*d*x^2 - a*d)/a)*arctan(sqrt(-c^2*x^2 + a)*c*x/(c^2*x^2 - a))/(a*c*d*m + a*c*d - (c^3*d*m + c^3*d)*x^2)","B",0
135,0,0,0,0.527231," ","integrate(arctan(c*x/(-c^2*x^2+a)^(1/2))^2/(d-c^2*d*x^2/a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a \sqrt{-\frac{c^{2} d x^{2} - a d}{a}} \arctan\left(\frac{\sqrt{-c^{2} x^{2} + a} c x}{c^{2} x^{2} - a}\right)^{2}}{c^{2} d x^{2} - a d}, x\right)"," ",0,"integral(-a*sqrt(-(c^2*d*x^2 - a*d)/a)*arctan(sqrt(-c^2*x^2 + a)*c*x/(c^2*x^2 - a))^2/(c^2*d*x^2 - a*d), x)","F",0
136,0,0,0,0.954092," ","integrate(arctan(c*x/(-c^2*x^2+a)^(1/2))/(d-c^2*d*x^2/a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a \sqrt{-\frac{c^{2} d x^{2} - a d}{a}} \arctan\left(\frac{\sqrt{-c^{2} x^{2} + a} c x}{c^{2} x^{2} - a}\right)}{c^{2} d x^{2} - a d}, x\right)"," ",0,"integral(a*sqrt(-(c^2*d*x^2 - a*d)/a)*arctan(sqrt(-c^2*x^2 + a)*c*x/(c^2*x^2 - a))/(c^2*d*x^2 - a*d), x)","F",0
137,1,83,0,0.551196," ","integrate(1/arctan(c*x/(-c^2*x^2+a)^(1/2))/(d-c^2*d*x^2/a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-c^{2} x^{2} + a} a \sqrt{-\frac{c^{2} d x^{2} - a d}{a}} \log\left(2 \, \arctan\left(\frac{\sqrt{-c^{2} x^{2} + a} c x}{c^{2} x^{2} - a}\right)\right)}{c^{3} d x^{2} - a c d}"," ",0,"-sqrt(-c^2*x^2 + a)*a*sqrt(-(c^2*d*x^2 - a*d)/a)*log(2*arctan(sqrt(-c^2*x^2 + a)*c*x/(c^2*x^2 - a)))/(c^3*d*x^2 - a*c*d)","A",0
138,1,82,0,0.444133," ","integrate(1/arctan(c*x/(-c^2*x^2+a)^(1/2))^2/(d-c^2*d*x^2/a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-c^{2} x^{2} + a} a \sqrt{-\frac{c^{2} d x^{2} - a d}{a}}}{{\left(c^{3} d x^{2} - a c d\right)} \arctan\left(\frac{\sqrt{-c^{2} x^{2} + a} c x}{c^{2} x^{2} - a}\right)}"," ",0,"-sqrt(-c^2*x^2 + a)*a*sqrt(-(c^2*d*x^2 - a*d)/a)/((c^3*d*x^2 - a*c*d)*arctan(sqrt(-c^2*x^2 + a)*c*x/(c^2*x^2 - a)))","A",0
139,1,82,0,0.542987," ","integrate(1/arctan(c*x/(-c^2*x^2+a)^(1/2))^3/(d-c^2*d*x^2/a)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{-c^{2} x^{2} + a} a \sqrt{-\frac{c^{2} d x^{2} - a d}{a}}}{2 \, {\left(c^{3} d x^{2} - a c d\right)} \arctan\left(\frac{\sqrt{-c^{2} x^{2} + a} c x}{c^{2} x^{2} - a}\right)^{2}}"," ",0,"1/2*sqrt(-c^2*x^2 + a)*a*sqrt(-(c^2*d*x^2 - a*d)/a)/((c^3*d*x^2 - a*c*d)*arctan(sqrt(-c^2*x^2 + a)*c*x/(c^2*x^2 - a))^2)","A",0
140,1,132,0,0.679774," ","integrate(arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))^m/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2} + a} \left(-\arctan\left(\frac{b x \sqrt{-\frac{b e^{2} x^{2} + a e^{2}}{b}}}{b e x^{2} + a e}\right)\right)^{m} \sqrt{-\frac{b e^{2} x^{2} + a e^{2}}{b}} \arctan\left(\frac{b x \sqrt{-\frac{b e^{2} x^{2} + a e^{2}}{b}}}{b e x^{2} + a e}\right)}{a e m + {\left(b e m + b e\right)} x^{2} + a e}"," ",0,"-sqrt(b*x^2 + a)*(-arctan(b*x*sqrt(-(b*e^2*x^2 + a*e^2)/b)/(b*e*x^2 + a*e)))^m*sqrt(-(b*e^2*x^2 + a*e^2)/b)*arctan(b*x*sqrt(-(b*e^2*x^2 + a*e^2)/b)/(b*e*x^2 + a*e))/(a*e*m + (b*e*m + b*e)*x^2 + a*e)","A",0
141,0,0,0,0.840416," ","integrate(arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))^2/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(\frac{b x \sqrt{-\frac{b e^{2} x^{2} + a e^{2}}{b}}}{b e x^{2} + a e}\right)^{2}}{\sqrt{b x^{2} + a}}, x\right)"," ",0,"integral(arctan(b*x*sqrt(-(b*e^2*x^2 + a*e^2)/b)/(b*e*x^2 + a*e))^2/sqrt(b*x^2 + a), x)","F",0
142,0,0,0,0.716898," ","integrate(arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\arctan\left(\frac{b x \sqrt{-\frac{b e^{2} x^{2} + a e^{2}}{b}}}{b e x^{2} + a e}\right)}{\sqrt{b x^{2} + a}}, x\right)"," ",0,"integral(-arctan(b*x*sqrt(-(b*e^2*x^2 + a*e^2)/b)/(b*e*x^2 + a*e))/sqrt(b*x^2 + a), x)","F",0
143,1,83,0,0.666805," ","integrate(1/arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2} + a} \sqrt{-\frac{b e^{2} x^{2} + a e^{2}}{b}} \log\left(2 \, \arctan\left(\frac{b x \sqrt{-\frac{b e^{2} x^{2} + a e^{2}}{b}}}{b e x^{2} + a e}\right)\right)}{b e x^{2} + a e}"," ",0,"sqrt(b*x^2 + a)*sqrt(-(b*e^2*x^2 + a*e^2)/b)*log(2*arctan(b*x*sqrt(-(b*e^2*x^2 + a*e^2)/b)/(b*e*x^2 + a*e)))/(b*e*x^2 + a*e)","A",0
144,1,82,0,0.819052," ","integrate(1/arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))^2/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{b x^{2} + a} \sqrt{-\frac{b e^{2} x^{2} + a e^{2}}{b}}}{{\left(b e x^{2} + a e\right)} \arctan\left(\frac{b x \sqrt{-\frac{b e^{2} x^{2} + a e^{2}}{b}}}{b e x^{2} + a e}\right)}"," ",0,"sqrt(b*x^2 + a)*sqrt(-(b*e^2*x^2 + a*e^2)/b)/((b*e*x^2 + a*e)*arctan(b*x*sqrt(-(b*e^2*x^2 + a*e^2)/b)/(b*e*x^2 + a*e)))","A",0
145,1,83,0,0.613653," ","integrate(1/arctan(e*x/(-a*e^2/b-e^2*x^2)^(1/2))^3/(b*x^2+a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{b x^{2} + a} \sqrt{-\frac{b e^{2} x^{2} + a e^{2}}{b}}}{2 \, {\left(b e x^{2} + a e\right)} \arctan\left(\frac{b x \sqrt{-\frac{b e^{2} x^{2} + a e^{2}}{b}}}{b e x^{2} + a e}\right)^{2}}"," ",0,"-1/2*sqrt(b*x^2 + a)*sqrt(-(b*e^2*x^2 + a*e^2)/b)/((b*e*x^2 + a*e)*arctan(b*x*sqrt(-(b*e^2*x^2 + a*e^2)/b)/(b*e*x^2 + a*e))^2)","A",0
146,0,0,0,0.544383," ","integrate(arctan(c*(b*x+a))*log(d*(b*x+a))/(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\arctan\left(b c x + a c\right) \log\left(b d x + a d\right)}{b x + a}, x\right)"," ",0,"integral(arctan(b*c*x + a*c)*log(b*d*x + a*d)/(b*x + a), x)","F",0
147,1,75,0,0.701242," ","integrate(exp(c*(b*x+a))*arctan(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)} \arctan\left(\sinh\left(b c x + a c\right)\right) - \log\left(\frac{2 \, \cosh\left(b c x + a c\right)}{\cosh\left(b c x + a c\right) - \sinh\left(b c x + a c\right)}\right)}{b c}"," ",0,"((cosh(b*c*x + a*c) + sinh(b*c*x + a*c))*arctan(sinh(b*c*x + a*c)) - log(2*cosh(b*c*x + a*c)/(cosh(b*c*x + a*c) - sinh(b*c*x + a*c))))/(b*c)","A",0
148,1,221,0,0.881141," ","integrate(exp(c*(b*x+a))*arctan(cosh(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{2 \, {\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\right)} \arctan\left(\cosh\left(b c x + a c\right)\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*(2*(cosh(b*c*x + a*c) + sinh(b*c*x + a*c))*arctan(cosh(b*c*x + a*c)) + 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
149,1,431,0,0.506144," ","integrate(exp(c*(b*x+a))*arctan(tanh(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} e^{\left(b c x + a c\right)} + \sqrt{2} \sqrt{\sqrt{2} b^{3} c^{3} \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{3}{4}} e^{\left(b c x + a c\right)} + b^{2} c^{2} \sqrt{\frac{1}{b^{4} c^{4}}} + e^{\left(2 \, b c x + 2 \, a c\right)}} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} - 1\right) + 4 \, \sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} e^{\left(b c x + a c\right)} + \sqrt{2} \sqrt{-\sqrt{2} b^{3} c^{3} \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{3}{4}} e^{\left(b c x + a c\right)} + b^{2} c^{2} \sqrt{\frac{1}{b^{4} c^{4}}} + e^{\left(2 \, b c x + 2 \, a c\right)}} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} + 1\right) + \sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} \log\left(\sqrt{2} b^{3} c^{3} \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{3}{4}} e^{\left(b c x + a c\right)} + b^{2} c^{2} \sqrt{\frac{1}{b^{4} c^{4}}} + e^{\left(2 \, b c x + 2 \, a c\right)}\right) - \sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} b^{3} c^{3} \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{3}{4}} e^{\left(b c x + a c\right)} + b^{2} c^{2} \sqrt{\frac{1}{b^{4} c^{4}}} + e^{\left(2 \, b c x + 2 \, a c\right)}\right) + 4 \, \arctan\left(\frac{e^{\left(2 \, b c x + 2 \, a c\right)} - 1}{e^{\left(2 \, b c x + 2 \, a c\right)} + 1}\right) e^{\left(b c x + a c\right)}}{4 \, b c}"," ",0,"1/4*(4*sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*arctan(-sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*e^(b*c*x + a*c) + sqrt(2)*sqrt(sqrt(2)*b^3*c^3*(1/(b^4*c^4))^(3/4)*e^(b*c*x + a*c) + b^2*c^2*sqrt(1/(b^4*c^4)) + e^(2*b*c*x + 2*a*c))*b*c*(1/(b^4*c^4))^(1/4) - 1) + 4*sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*arctan(-sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*e^(b*c*x + a*c) + sqrt(2)*sqrt(-sqrt(2)*b^3*c^3*(1/(b^4*c^4))^(3/4)*e^(b*c*x + a*c) + b^2*c^2*sqrt(1/(b^4*c^4)) + e^(2*b*c*x + 2*a*c))*b*c*(1/(b^4*c^4))^(1/4) + 1) + sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*log(sqrt(2)*b^3*c^3*(1/(b^4*c^4))^(3/4)*e^(b*c*x + a*c) + b^2*c^2*sqrt(1/(b^4*c^4)) + e^(2*b*c*x + 2*a*c)) - sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*log(-sqrt(2)*b^3*c^3*(1/(b^4*c^4))^(3/4)*e^(b*c*x + a*c) + b^2*c^2*sqrt(1/(b^4*c^4)) + e^(2*b*c*x + 2*a*c)) + 4*arctan((e^(2*b*c*x + 2*a*c) - 1)/(e^(2*b*c*x + 2*a*c) + 1))*e^(b*c*x + a*c))/(b*c)","B",0
150,1,431,0,0.682665," ","integrate(exp(c*(b*x+a))*arctan(coth(b*c*x+a*c)),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} e^{\left(b c x + a c\right)} + \sqrt{2} \sqrt{\sqrt{2} b^{3} c^{3} \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{3}{4}} e^{\left(b c x + a c\right)} + b^{2} c^{2} \sqrt{\frac{1}{b^{4} c^{4}}} + e^{\left(2 \, b c x + 2 \, a c\right)}} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} - 1\right) + 4 \, \sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} e^{\left(b c x + a c\right)} + \sqrt{2} \sqrt{-\sqrt{2} b^{3} c^{3} \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{3}{4}} e^{\left(b c x + a c\right)} + b^{2} c^{2} \sqrt{\frac{1}{b^{4} c^{4}}} + e^{\left(2 \, b c x + 2 \, a c\right)}} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} + 1\right) + \sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} \log\left(\sqrt{2} b^{3} c^{3} \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{3}{4}} e^{\left(b c x + a c\right)} + b^{2} c^{2} \sqrt{\frac{1}{b^{4} c^{4}}} + e^{\left(2 \, b c x + 2 \, a c\right)}\right) - \sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} b^{3} c^{3} \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{3}{4}} e^{\left(b c x + a c\right)} + b^{2} c^{2} \sqrt{\frac{1}{b^{4} c^{4}}} + e^{\left(2 \, b c x + 2 \, a c\right)}\right) - 4 \, \arctan\left(\frac{e^{\left(2 \, b c x + 2 \, a c\right)} + 1}{e^{\left(2 \, b c x + 2 \, a c\right)} - 1}\right) e^{\left(b c x + a c\right)}}{4 \, b c}"," ",0,"-1/4*(4*sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*arctan(-sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*e^(b*c*x + a*c) + sqrt(2)*sqrt(sqrt(2)*b^3*c^3*(1/(b^4*c^4))^(3/4)*e^(b*c*x + a*c) + b^2*c^2*sqrt(1/(b^4*c^4)) + e^(2*b*c*x + 2*a*c))*b*c*(1/(b^4*c^4))^(1/4) - 1) + 4*sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*arctan(-sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*e^(b*c*x + a*c) + sqrt(2)*sqrt(-sqrt(2)*b^3*c^3*(1/(b^4*c^4))^(3/4)*e^(b*c*x + a*c) + b^2*c^2*sqrt(1/(b^4*c^4)) + e^(2*b*c*x + 2*a*c))*b*c*(1/(b^4*c^4))^(1/4) + 1) + sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*log(sqrt(2)*b^3*c^3*(1/(b^4*c^4))^(3/4)*e^(b*c*x + a*c) + b^2*c^2*sqrt(1/(b^4*c^4)) + e^(2*b*c*x + 2*a*c)) - sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*log(-sqrt(2)*b^3*c^3*(1/(b^4*c^4))^(3/4)*e^(b*c*x + a*c) + b^2*c^2*sqrt(1/(b^4*c^4)) + e^(2*b*c*x + 2*a*c)) - 4*arctan((e^(2*b*c*x + 2*a*c) + 1)/(e^(2*b*c*x + 2*a*c) - 1))*e^(b*c*x + a*c))/(b*c)","B",0
151,1,276,0,0.647432," ","integrate(exp(c*(b*x+a))*arctan(sech(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{2 \, {\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\right)} \arctan\left(\frac{2 \, {\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\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} + 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*(2*(cosh(b*c*x + a*c) + sinh(b*c*x + a*c))*arctan(2*(cosh(b*c*x + a*c) + sinh(b*c*x + a*c))/(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 + 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
152,1,131,0,0.606704," ","integrate(exp(c*(b*x+a))*arctan(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)} \arctan\left(\frac{2 \, {\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\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} - 1}\right) + \log\left(\frac{2 \, \cosh\left(b c x + a c\right)}{\cosh\left(b c x + a c\right) - \sinh\left(b c x + a c\right)}\right)}{b c}"," ",0,"((cosh(b*c*x + a*c) + sinh(b*c*x + a*c))*arctan(2*(cosh(b*c*x + a*c) + sinh(b*c*x + a*c))/(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 - 1)) + log(2*cosh(b*c*x + a*c)/(cosh(b*c*x + a*c) - sinh(b*c*x + a*c))))/(b*c)","B",0
153,1,246,0,0.615799," ","integrate((a+b*arctan(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 i \, b e m {\rm polylog}\left(3, i \, c x^{n}\right) - 2 i \, b e m {\rm polylog}\left(3, -i \, c x^{n}\right) + 2 \, {\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)} \arctan\left(c x^{n}\right) + {\left(-2 i \, b e m n \log\left(x\right) - 2 i \, b e n \log\left(f\right) - 2 i \, b d n\right)} {\rm Li}_2\left(i \, c x^{n}\right) + {\left(2 i \, b e m n \log\left(x\right) + 2 i \, b e n \log\left(f\right) + 2 i \, b d n\right)} {\rm Li}_2\left(-i \, c x^{n}\right) + {\left(i \, b e m n^{2} \log\left(x\right)^{2} + {\left(2 i \, b e n^{2} \log\left(f\right) + 2 i \, b d n^{2}\right)} \log\left(x\right)\right)} \log\left(i \, c x^{n} + 1\right) + {\left(-i \, b e m n^{2} \log\left(x\right)^{2} + {\left(-2 i \, b e n^{2} \log\left(f\right) - 2 i \, b d n^{2}\right)} \log\left(x\right)\right)} \log\left(-i \, c x^{n} + 1\right) + 4 \, {\left(a e n^{2} \log\left(f\right) + a d n^{2}\right)} \log\left(x\right)}{4 \, n^{2}}"," ",0,"1/4*(2*a*e*m*n^2*log(x)^2 + 2*I*b*e*m*polylog(3, I*c*x^n) - 2*I*b*e*m*polylog(3, -I*c*x^n) + 2*(b*e*m*n^2*log(x)^2 + 2*(b*e*n^2*log(f) + b*d*n^2)*log(x))*arctan(c*x^n) + (-2*I*b*e*m*n*log(x) - 2*I*b*e*n*log(f) - 2*I*b*d*n)*dilog(I*c*x^n) + (2*I*b*e*m*n*log(x) + 2*I*b*e*n*log(f) + 2*I*b*d*n)*dilog(-I*c*x^n) + (I*b*e*m*n^2*log(x)^2 + (2*I*b*e*n^2*log(f) + 2*I*b*d*n^2)*log(x))*log(I*c*x^n + 1) + (-I*b*e*m*n^2*log(x)^2 + (-2*I*b*e*n^2*log(f) - 2*I*b*d*n^2)*log(x))*log(-I*c*x^n + 1) + 4*(a*e*n^2*log(f) + a*d*n^2)*log(x))/n^2","C",0
