1,1,110,0,0.0608451,"\int x^6 \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^6*(a + b*ArcCsch[c*x]),x]","\frac{1}{7} x^7 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x^6 \sqrt{\frac{1}{c^2 x^2}+1}}{42 c}-\frac{5 b x^4 \sqrt{\frac{1}{c^2 x^2}+1}}{168 c^3}+\frac{5 b x^2 \sqrt{\frac{1}{c^2 x^2}+1}}{112 c^5}-\frac{5 b \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{112 c^7}","\frac{1}{7} x^7 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x^6 \sqrt{\frac{1}{c^2 x^2}+1}}{42 c}-\frac{5 b x^4 \sqrt{\frac{1}{c^2 x^2}+1}}{168 c^3}+\frac{5 b x^2 \sqrt{\frac{1}{c^2 x^2}+1}}{112 c^5}-\frac{5 b \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{112 c^7}",1,"(5*b*Sqrt[1 + 1/(c^2*x^2)]*x^2)/(112*c^5) - (5*b*Sqrt[1 + 1/(c^2*x^2)]*x^4)/(168*c^3) + (b*Sqrt[1 + 1/(c^2*x^2)]*x^6)/(42*c) + (x^7*(a + b*ArcCsch[c*x]))/7 - (5*b*ArcTanh[Sqrt[1 + 1/(c^2*x^2)]])/(112*c^7)","A",7,5,12,0.4167,1,"{6284, 266, 51, 63, 208}"
2,1,86,0,0.0441296,"\int x^5 \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^5*(a + b*ArcCsch[c*x]),x]","\frac{1}{6} x^6 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x^5 \sqrt{\frac{1}{c^2 x^2}+1}}{30 c}-\frac{2 b x^3 \sqrt{\frac{1}{c^2 x^2}+1}}{45 c^3}+\frac{4 b x \sqrt{\frac{1}{c^2 x^2}+1}}{45 c^5}","\frac{1}{6} x^6 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x^5 \sqrt{\frac{1}{c^2 x^2}+1}}{30 c}-\frac{2 b x^3 \sqrt{\frac{1}{c^2 x^2}+1}}{45 c^3}+\frac{4 b x \sqrt{\frac{1}{c^2 x^2}+1}}{45 c^5}",1,"(4*b*Sqrt[1 + 1/(c^2*x^2)]*x)/(45*c^5) - (2*b*Sqrt[1 + 1/(c^2*x^2)]*x^3)/(45*c^3) + (b*Sqrt[1 + 1/(c^2*x^2)]*x^5)/(30*c) + (x^6*(a + b*ArcCsch[c*x]))/6","A",4,3,12,0.2500,1,"{6284, 271, 191}"
3,1,86,0,0.047877,"\int x^4 \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^4*(a + b*ArcCsch[c*x]),x]","\frac{1}{5} x^5 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x^4 \sqrt{\frac{1}{c^2 x^2}+1}}{20 c}-\frac{3 b x^2 \sqrt{\frac{1}{c^2 x^2}+1}}{40 c^3}+\frac{3 b \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{40 c^5}","\frac{1}{5} x^5 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x^4 \sqrt{\frac{1}{c^2 x^2}+1}}{20 c}-\frac{3 b x^2 \sqrt{\frac{1}{c^2 x^2}+1}}{40 c^3}+\frac{3 b \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{40 c^5}",1,"(-3*b*Sqrt[1 + 1/(c^2*x^2)]*x^2)/(40*c^3) + (b*Sqrt[1 + 1/(c^2*x^2)]*x^4)/(20*c) + (x^5*(a + b*ArcCsch[c*x]))/5 + (3*b*ArcTanh[Sqrt[1 + 1/(c^2*x^2)]])/(40*c^5)","A",6,5,12,0.4167,1,"{6284, 266, 51, 63, 208}"
4,1,62,0,0.0274502,"\int x^3 \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^3*(a + b*ArcCsch[c*x]),x]","\frac{1}{4} x^4 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x^3 \sqrt{\frac{1}{c^2 x^2}+1}}{12 c}-\frac{b x \sqrt{\frac{1}{c^2 x^2}+1}}{6 c^3}","\frac{1}{4} x^4 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x^3 \sqrt{\frac{1}{c^2 x^2}+1}}{12 c}-\frac{b x \sqrt{\frac{1}{c^2 x^2}+1}}{6 c^3}",1,"-(b*Sqrt[1 + 1/(c^2*x^2)]*x)/(6*c^3) + (b*Sqrt[1 + 1/(c^2*x^2)]*x^3)/(12*c) + (x^4*(a + b*ArcCsch[c*x]))/4","A",3,3,12,0.2500,1,"{6284, 271, 191}"
5,1,62,0,0.0350997,"\int x^2 \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^2*(a + b*ArcCsch[c*x]),x]","\frac{1}{3} x^3 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x^2 \sqrt{\frac{1}{c^2 x^2}+1}}{6 c}-\frac{b \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{6 c^3}","\frac{1}{3} x^3 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x^2 \sqrt{\frac{1}{c^2 x^2}+1}}{6 c}-\frac{b \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{6 c^3}",1,"(b*Sqrt[1 + 1/(c^2*x^2)]*x^2)/(6*c) + (x^3*(a + b*ArcCsch[c*x]))/3 - (b*ArcTanh[Sqrt[1 + 1/(c^2*x^2)]])/(6*c^3)","A",5,5,12,0.4167,1,"{6284, 266, 51, 63, 208}"
6,1,38,0,0.0128323,"\int x \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x*(a + b*ArcCsch[c*x]),x]","\frac{1}{2} x^2 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x \sqrt{\frac{1}{c^2 x^2}+1}}{2 c}","\frac{1}{2} x^2 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x \sqrt{\frac{1}{c^2 x^2}+1}}{2 c}",1,"(b*Sqrt[1 + 1/(c^2*x^2)]*x)/(2*c) + (x^2*(a + b*ArcCsch[c*x]))/2","A",2,2,10,0.2000,1,"{6284, 191}"
7,1,30,0,0.0209549,"\int \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[a + b*ArcCsch[c*x],x]","a x+\frac{b \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{c}+b x \text{csch}^{-1}(c x)","a x+\frac{b \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{c}+b x \text{csch}^{-1}(c x)",1,"a*x + b*x*ArcCsch[c*x] + (b*ArcTanh[Sqrt[1 + 1/(c^2*x^2)]])/c","A",5,4,8,0.5000,1,"{6278, 266, 63, 208}"
8,1,56,0,0.0898566,"\int \frac{a+b \text{csch}^{-1}(c x)}{x} \, dx","Int[(a + b*ArcCsch[c*x])/x,x]","-\frac{1}{2} b \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)+\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{2 b}-\log \left(1-e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)","\frac{1}{2} b \text{PolyLog}\left(2,e^{-2 \text{csch}^{-1}(c x)}\right)-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{2 b}-\log \left(1-e^{-2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)",1,"(a + b*ArcCsch[c*x])^2/(2*b) - (a + b*ArcCsch[c*x])*Log[1 - E^(2*ArcCsch[c*x])] - (b*PolyLog[2, E^(2*ArcCsch[c*x])])/2","A",6,6,12,0.5000,0,"{6282, 5659, 3716, 2190, 2279, 2391}"
9,1,30,0,0.0238494,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^2} \, dx","Int[(a + b*ArcCsch[c*x])/x^2,x]","b c \sqrt{\frac{1}{c^2 x^2}+1}-\frac{a+b \text{csch}^{-1}(c x)}{x}","b c \sqrt{\frac{1}{c^2 x^2}+1}-\frac{a+b \text{csch}^{-1}(c x)}{x}",1,"b*c*Sqrt[1 + 1/(c^2*x^2)] - (a + b*ArcCsch[c*x])/x","A",2,2,12,0.1667,1,"{6284, 261}"
10,1,50,0,0.0372564,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^3} \, dx","Int[(a + b*ArcCsch[c*x])/x^3,x]","-\frac{a+b \text{csch}^{-1}(c x)}{2 x^2}+\frac{b c \sqrt{\frac{1}{c^2 x^2}+1}}{4 x}-\frac{1}{4} b c^2 \text{csch}^{-1}(c x)","-\frac{a+b \text{csch}^{-1}(c x)}{2 x^2}+\frac{b c \sqrt{\frac{1}{c^2 x^2}+1}}{4 x}-\frac{1}{4} b c^2 \text{csch}^{-1}(c x)",1,"(b*c*Sqrt[1 + 1/(c^2*x^2)])/(4*x) - (b*c^2*ArcCsch[c*x])/4 - (a + b*ArcCsch[c*x])/(2*x^2)","A",4,4,12,0.3333,1,"{6284, 335, 321, 215}"
11,1,58,0,0.0428057,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^4} \, dx","Int[(a + b*ArcCsch[c*x])/x^4,x]","-\frac{a+b \text{csch}^{-1}(c x)}{3 x^3}+\frac{1}{9} b c^3 \left(\frac{1}{c^2 x^2}+1\right)^{3/2}-\frac{1}{3} b c^3 \sqrt{\frac{1}{c^2 x^2}+1}","-\frac{a+b \text{csch}^{-1}(c x)}{3 x^3}+\frac{1}{9} b c^3 \left(\frac{1}{c^2 x^2}+1\right)^{3/2}-\frac{1}{3} b c^3 \sqrt{\frac{1}{c^2 x^2}+1}",1,"-(b*c^3*Sqrt[1 + 1/(c^2*x^2)])/3 + (b*c^3*(1 + 1/(c^2*x^2))^(3/2))/9 - (a + b*ArcCsch[c*x])/(3*x^3)","A",4,3,12,0.2500,1,"{6284, 266, 43}"
12,1,74,0,0.0480371,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^5} \, dx","Int[(a + b*ArcCsch[c*x])/x^5,x]","-\frac{a+b \text{csch}^{-1}(c x)}{4 x^4}-\frac{3 b c^3 \sqrt{\frac{1}{c^2 x^2}+1}}{32 x}+\frac{b c \sqrt{\frac{1}{c^2 x^2}+1}}{16 x^3}+\frac{3}{32} b c^4 \text{csch}^{-1}(c x)","-\frac{a+b \text{csch}^{-1}(c x)}{4 x^4}-\frac{3 b c^3 \sqrt{\frac{1}{c^2 x^2}+1}}{32 x}+\frac{b c \sqrt{\frac{1}{c^2 x^2}+1}}{16 x^3}+\frac{3}{32} b c^4 \text{csch}^{-1}(c x)",1,"(b*c*Sqrt[1 + 1/(c^2*x^2)])/(16*x^3) - (3*b*c^3*Sqrt[1 + 1/(c^2*x^2)])/(32*x) + (3*b*c^4*ArcCsch[c*x])/32 - (a + b*ArcCsch[c*x])/(4*x^4)","A",5,4,12,0.3333,1,"{6284, 335, 321, 215}"
13,1,79,0,0.051031,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^6} \, dx","Int[(a + b*ArcCsch[c*x])/x^6,x]","-\frac{a+b \text{csch}^{-1}(c x)}{5 x^5}+\frac{1}{25} b c^5 \left(\frac{1}{c^2 x^2}+1\right)^{5/2}-\frac{2}{15} b c^5 \left(\frac{1}{c^2 x^2}+1\right)^{3/2}+\frac{1}{5} b c^5 \sqrt{\frac{1}{c^2 x^2}+1}","-\frac{a+b \text{csch}^{-1}(c x)}{5 x^5}+\frac{1}{25} b c^5 \left(\frac{1}{c^2 x^2}+1\right)^{5/2}-\frac{2}{15} b c^5 \left(\frac{1}{c^2 x^2}+1\right)^{3/2}+\frac{1}{5} b c^5 \sqrt{\frac{1}{c^2 x^2}+1}",1,"(b*c^5*Sqrt[1 + 1/(c^2*x^2)])/5 - (2*b*c^5*(1 + 1/(c^2*x^2))^(3/2))/15 + (b*c^5*(1 + 1/(c^2*x^2))^(5/2))/25 - (a + b*ArcCsch[c*x])/(5*x^5)","A",4,3,12,0.2500,1,"{6284, 266, 43}"
14,1,98,0,0.0636193,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^7} \, dx","Int[(a + b*ArcCsch[c*x])/x^7,x]","-\frac{a+b \text{csch}^{-1}(c x)}{6 x^6}+\frac{5 b c^5 \sqrt{\frac{1}{c^2 x^2}+1}}{96 x}-\frac{5 b c^3 \sqrt{\frac{1}{c^2 x^2}+1}}{144 x^3}+\frac{b c \sqrt{\frac{1}{c^2 x^2}+1}}{36 x^5}-\frac{5}{96} b c^6 \text{csch}^{-1}(c x)","-\frac{a+b \text{csch}^{-1}(c x)}{6 x^6}+\frac{5 b c^5 \sqrt{\frac{1}{c^2 x^2}+1}}{96 x}-\frac{5 b c^3 \sqrt{\frac{1}{c^2 x^2}+1}}{144 x^3}+\frac{b c \sqrt{\frac{1}{c^2 x^2}+1}}{36 x^5}-\frac{5}{96} b c^6 \text{csch}^{-1}(c x)",1,"(b*c*Sqrt[1 + 1/(c^2*x^2)])/(36*x^5) - (5*b*c^3*Sqrt[1 + 1/(c^2*x^2)])/(144*x^3) + (5*b*c^5*Sqrt[1 + 1/(c^2*x^2)])/(96*x) - (5*b*c^6*ArcCsch[c*x])/96 - (a + b*ArcCsch[c*x])/(6*x^6)","A",6,4,12,0.3333,1,"{6284, 335, 321, 215}"
15,1,105,0,0.118674,"\int x^3 \left(a+b \text{csch}^{-1}(c x)\right)^2 \, dx","Int[x^3*(a + b*ArcCsch[c*x])^2,x]","\frac{b x^3 \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)}{6 c}-\frac{b x \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)}{3 c^3}+\frac{1}{4} x^4 \left(a+b \text{csch}^{-1}(c x)\right)^2+\frac{b^2 x^2}{12 c^2}-\frac{b^2 \log (x)}{3 c^4}","\frac{b x^3 \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)}{6 c}-\frac{b x \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)}{3 c^3}+\frac{1}{4} x^4 \left(a+b \text{csch}^{-1}(c x)\right)^2+\frac{b^2 x^2}{12 c^2}-\frac{b^2 \log (x)}{3 c^4}",1,"(b^2*x^2)/(12*c^2) - (b*Sqrt[1 + 1/(c^2*x^2)]*x*(a + b*ArcCsch[c*x]))/(3*c^3) + (b*Sqrt[1 + 1/(c^2*x^2)]*x^3*(a + b*ArcCsch[c*x]))/(6*c) + (x^4*(a + b*ArcCsch[c*x])^2)/4 - (b^2*Log[x])/(3*c^4)","A",5,5,14,0.3571,1,"{6286, 5452, 4185, 4184, 3475}"
16,1,122,0,0.1323214,"\int x^2 \left(a+b \text{csch}^{-1}(c x)\right)^2 \, dx","Int[x^2*(a + b*ArcCsch[c*x])^2,x]","-\frac{b^2 \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c x)}\right)}{3 c^3}+\frac{b^2 \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c x)}\right)}{3 c^3}+\frac{b x^2 \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)}{3 c}-\frac{2 b \tanh ^{-1}\left(e^{\text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{3 c^3}+\frac{1}{3} x^3 \left(a+b \text{csch}^{-1}(c x)\right)^2+\frac{b^2 x}{3 c^2}","-\frac{b^2 \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c x)}\right)}{3 c^3}+\frac{b^2 \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c x)}\right)}{3 c^3}+\frac{b x^2 \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)}{3 c}-\frac{2 b \tanh ^{-1}\left(e^{\text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{3 c^3}+\frac{1}{3} x^3 \left(a+b \text{csch}^{-1}(c x)\right)^2+\frac{b^2 x}{3 c^2}",1,"(b^2*x)/(3*c^2) + (b*Sqrt[1 + 1/(c^2*x^2)]*x^2*(a + b*ArcCsch[c*x]))/(3*c) + (x^3*(a + b*ArcCsch[c*x])^2)/3 - (2*b*(a + b*ArcCsch[c*x])*ArcTanh[E^ArcCsch[c*x]])/(3*c^3) - (b^2*PolyLog[2, -E^ArcCsch[c*x]])/(3*c^3) + (b^2*PolyLog[2, E^ArcCsch[c*x]])/(3*c^3)","A",8,6,14,0.4286,1,"{6286, 5452, 4185, 4182, 2279, 2391}"
17,1,54,0,0.0760874,"\int x \left(a+b \text{csch}^{-1}(c x)\right)^2 \, dx","Int[x*(a + b*ArcCsch[c*x])^2,x]","\frac{b x \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)}{c}+\frac{1}{2} x^2 \left(a+b \text{csch}^{-1}(c x)\right)^2+\frac{b^2 \log (x)}{c^2}","\frac{b x \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)}{c}+\frac{1}{2} x^2 \left(a+b \text{csch}^{-1}(c x)\right)^2+\frac{b^2 \log (x)}{c^2}",1,"(b*Sqrt[1 + 1/(c^2*x^2)]*x*(a + b*ArcCsch[c*x]))/c + (x^2*(a + b*ArcCsch[c*x])^2)/2 + (b^2*Log[x])/c^2","A",4,4,12,0.3333,1,"{6286, 5452, 4184, 3475}"
18,1,68,0,0.0676694,"\int \left(a+b \text{csch}^{-1}(c x)\right)^2 \, dx","Int[(a + b*ArcCsch[c*x])^2,x]","\frac{2 b^2 \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c x)}\right)}{c}-\frac{2 b^2 \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c x)}\right)}{c}+x \left(a+b \text{csch}^{-1}(c x)\right)^2+\frac{4 b \tanh ^{-1}\left(e^{\text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{c}","\frac{2 b^2 \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c x)}\right)}{c}-\frac{2 b^2 \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c x)}\right)}{c}+x \left(a+b \text{csch}^{-1}(c x)\right)^2+\frac{4 b \tanh ^{-1}\left(e^{\text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{c}",1,"x*(a + b*ArcCsch[c*x])^2 + (4*b*(a + b*ArcCsch[c*x])*ArcTanh[E^ArcCsch[c*x]])/c + (2*b^2*PolyLog[2, -E^ArcCsch[c*x]])/c - (2*b^2*PolyLog[2, E^ArcCsch[c*x]])/c","A",7,5,10,0.5000,1,"{6280, 5452, 4182, 2279, 2391}"
19,1,81,0,0.1377822,"\int \frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{x} \, dx","Int[(a + b*ArcCsch[c*x])^2/x,x]","-b \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,e^{2 \text{csch}^{-1}(c x)}\right)+\frac{\left(a+b \text{csch}^{-1}(c x)\right)^3}{3 b}-\log \left(1-e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)^2","-b \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{2} b^2 \text{PolyLog}\left(3,e^{2 \text{csch}^{-1}(c x)}\right)+\frac{\left(a+b \text{csch}^{-1}(c x)\right)^3}{3 b}-\log \left(1-e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)^2",1,"(a + b*ArcCsch[c*x])^3/(3*b) - (a + b*ArcCsch[c*x])^2*Log[1 - E^(2*ArcCsch[c*x])] - b*(a + b*ArcCsch[c*x])*PolyLog[2, E^(2*ArcCsch[c*x])] + (b^2*PolyLog[3, E^(2*ArcCsch[c*x])])/2","A",6,6,14,0.4286,1,"{6286, 3716, 2190, 2531, 2282, 6589}"
20,1,49,0,0.069934,"\int \frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{x^2} \, dx","Int[(a + b*ArcCsch[c*x])^2/x^2,x]","2 b c \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{x}-\frac{2 b^2}{x}","2 b c \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{x}-\frac{2 b^2}{x}",1,"(-2*b^2)/x + 2*b*c*Sqrt[1 + 1/(c^2*x^2)]*(a + b*ArcCsch[c*x]) - (a + b*ArcCsch[c*x])^2/x","A",4,3,14,0.2143,1,"{6286, 3296, 2637}"
21,1,87,0,0.0824147,"\int \frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{x^3} \, dx","Int[(a + b*ArcCsch[c*x])^2/x^3,x]","\frac{b c \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)}{2 x}-\frac{1}{2} a b c^2 \text{csch}^{-1}(c x)-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{2 x^2}-\frac{1}{4} b^2 c^2 \text{csch}^{-1}(c x)^2-\frac{b^2}{4 x^2}","\frac{b c \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)}{2 x}-\frac{1}{2} a b c^2 \text{csch}^{-1}(c x)-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{2 x^2}-\frac{1}{4} b^2 c^2 \text{csch}^{-1}(c x)^2-\frac{b^2}{4 x^2}",1,"-b^2/(4*x^2) - (a*b*c^2*ArcCsch[c*x])/2 - (b^2*c^2*ArcCsch[c*x]^2)/4 + (b*c*Sqrt[1 + 1/(c^2*x^2)]*(a + b*ArcCsch[c*x]))/(2*x) - (a + b*ArcCsch[c*x])^2/(2*x^2)","A",4,3,14,0.2143,1,"{6286, 5446, 3310}"
22,1,100,0,0.1082595,"\int \frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{x^4} \, dx","Int[(a + b*ArcCsch[c*x])^2/x^4,x]","-\frac{4}{9} b c^3 \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)+\frac{2 b c \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)}{9 x^2}-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{3 x^3}+\frac{4 b^2 c^2}{9 x}-\frac{2 b^2}{27 x^3}","-\frac{4}{9} b c^3 \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)+\frac{2 b c \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)}{9 x^2}-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{3 x^3}+\frac{4 b^2 c^2}{9 x}-\frac{2 b^2}{27 x^3}",1,"(-2*b^2)/(27*x^3) + (4*b^2*c^2)/(9*x) - (4*b*c^3*Sqrt[1 + 1/(c^2*x^2)]*(a + b*ArcCsch[c*x]))/9 + (2*b*c*Sqrt[1 + 1/(c^2*x^2)]*(a + b*ArcCsch[c*x]))/(9*x^2) - (a + b*ArcCsch[c*x])^2/(3*x^3)","A",5,5,14,0.3571,1,"{6286, 5446, 3310, 3296, 2637}"
23,1,132,0,0.1169343,"\int \frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{x^5} \, dx","Int[(a + b*ArcCsch[c*x])^2/x^5,x]","-\frac{3 b c^3 \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)}{16 x}+\frac{b c \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)}{8 x^3}+\frac{3}{16} a b c^4 \text{csch}^{-1}(c x)-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{4 x^4}+\frac{3 b^2 c^2}{32 x^2}+\frac{3}{32} b^2 c^4 \text{csch}^{-1}(c x)^2-\frac{b^2}{32 x^4}","-\frac{3 b c^3 \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)}{16 x}+\frac{b c \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)}{8 x^3}+\frac{3}{16} a b c^4 \text{csch}^{-1}(c x)-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{4 x^4}+\frac{3 b^2 c^2}{32 x^2}+\frac{3}{32} b^2 c^4 \text{csch}^{-1}(c x)^2-\frac{b^2}{32 x^4}",1,"-b^2/(32*x^4) + (3*b^2*c^2)/(32*x^2) + (3*a*b*c^4*ArcCsch[c*x])/16 + (3*b^2*c^4*ArcCsch[c*x]^2)/32 + (b*c*Sqrt[1 + 1/(c^2*x^2)]*(a + b*ArcCsch[c*x]))/(8*x^3) - (3*b*c^3*Sqrt[1 + 1/(c^2*x^2)]*(a + b*ArcCsch[c*x]))/(16*x) - (a + b*ArcCsch[c*x])^2/(4*x^4)","A",5,3,14,0.2143,1,"{6286, 5446, 3310}"
24,1,195,0,0.2323958,"\int x^3 \left(a+b \text{csch}^{-1}(c x)\right)^3 \, dx","Int[x^3*(a + b*ArcCsch[c*x])^3,x]","\frac{b^3 \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)}{2 c^4}+\frac{b^2 x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{4 c^2}+\frac{b^2 \log \left(1-e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{c^4}+\frac{b x^3 \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2}{4 c}-\frac{b x \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2}{2 c^3}-\frac{b \left(a+b \text{csch}^{-1}(c x)\right)^2}{2 c^4}+\frac{1}{4} x^4 \left(a+b \text{csch}^{-1}(c x)\right)^3+\frac{b^3 x \sqrt{\frac{1}{c^2 x^2}+1}}{4 c^3}","\frac{b^3 \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)}{2 c^4}+\frac{b^2 x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{4 c^2}+\frac{b^2 \log \left(1-e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{c^4}+\frac{b x^3 \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2}{4 c}-\frac{b x \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2}{2 c^3}-\frac{b \left(a+b \text{csch}^{-1}(c x)\right)^2}{2 c^4}+\frac{1}{4} x^4 \left(a+b \text{csch}^{-1}(c x)\right)^3+\frac{b^3 x \sqrt{\frac{1}{c^2 x^2}+1}}{4 c^3}",1,"(b^3*Sqrt[1 + 1/(c^2*x^2)]*x)/(4*c^3) + (b^2*x^2*(a + b*ArcCsch[c*x]))/(4*c^2) - (b*(a + b*ArcCsch[c*x])^2)/(2*c^4) - (b*Sqrt[1 + 1/(c^2*x^2)]*x*(a + b*ArcCsch[c*x])^2)/(2*c^3) + (b*Sqrt[1 + 1/(c^2*x^2)]*x^3*(a + b*ArcCsch[c*x])^2)/(4*c) + (x^4*(a + b*ArcCsch[c*x])^3)/4 + (b^2*(a + b*ArcCsch[c*x])*Log[1 - E^(2*ArcCsch[c*x])])/c^4 + (b^3*PolyLog[2, E^(2*ArcCsch[c*x])])/(2*c^4)","A",10,10,14,0.7143,1,"{6286, 5452, 4186, 3767, 8, 4184, 3716, 2190, 2279, 2391}"
25,1,194,0,0.2080911,"\int x^2 \left(a+b \text{csch}^{-1}(c x)\right)^3 \, dx","Int[x^2*(a + b*ArcCsch[c*x])^3,x]","-\frac{b^2 \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{c^3}+\frac{b^2 \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{c^3}+\frac{b^3 \text{PolyLog}\left(3,-e^{\text{csch}^{-1}(c x)}\right)}{c^3}-\frac{b^3 \text{PolyLog}\left(3,e^{\text{csch}^{-1}(c x)}\right)}{c^3}+\frac{b^2 x \left(a+b \text{csch}^{-1}(c x)\right)}{c^2}+\frac{b x^2 \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2}{2 c}-\frac{b \tanh ^{-1}\left(e^{\text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)^2}{c^3}+\frac{1}{3} x^3 \left(a+b \text{csch}^{-1}(c x)\right)^3+\frac{b^3 \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{c^3}","-\frac{b^2 \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{c^3}+\frac{b^2 \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{c^3}+\frac{b^3 \text{PolyLog}\left(3,-e^{\text{csch}^{-1}(c x)}\right)}{c^3}-\frac{b^3 \text{PolyLog}\left(3,e^{\text{csch}^{-1}(c x)}\right)}{c^3}+\frac{b^2 x \left(a+b \text{csch}^{-1}(c x)\right)}{c^2}+\frac{b x^2 \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2}{2 c}-\frac{b \tanh ^{-1}\left(e^{\text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)^2}{c^3}+\frac{1}{3} x^3 \left(a+b \text{csch}^{-1}(c x)\right)^3+\frac{b^3 \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{c^3}",1,"(b^2*x*(a + b*ArcCsch[c*x]))/c^2 + (b*Sqrt[1 + 1/(c^2*x^2)]*x^2*(a + b*ArcCsch[c*x])^2)/(2*c) + (x^3*(a + b*ArcCsch[c*x])^3)/3 - (b*(a + b*ArcCsch[c*x])^2*ArcTanh[E^ArcCsch[c*x]])/c^3 + (b^3*ArcTanh[Sqrt[1 + 1/(c^2*x^2)]])/c^3 - (b^2*(a + b*ArcCsch[c*x])*PolyLog[2, -E^ArcCsch[c*x]])/c^3 + (b^2*(a + b*ArcCsch[c*x])*PolyLog[2, E^ArcCsch[c*x]])/c^3 + (b^3*PolyLog[3, -E^ArcCsch[c*x]])/c^3 - (b^3*PolyLog[3, E^ArcCsch[c*x]])/c^3","A",11,8,14,0.5714,1,"{6286, 5452, 4186, 3770, 4182, 2531, 2282, 6589}"
26,1,117,0,0.1598445,"\int x \left(a+b \text{csch}^{-1}(c x)\right)^3 \, dx","Int[x*(a + b*ArcCsch[c*x])^3,x]","-\frac{3 b^3 \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)}{2 c^2}-\frac{3 b^2 \log \left(1-e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{c^2}+\frac{3 b x \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2}{2 c}+\frac{3 b \left(a+b \text{csch}^{-1}(c x)\right)^2}{2 c^2}+\frac{1}{2} x^2 \left(a+b \text{csch}^{-1}(c x)\right)^3","-\frac{3 b^3 \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)}{2 c^2}-\frac{3 b^2 \log \left(1-e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{c^2}+\frac{3 b x \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2}{2 c}+\frac{3 b \left(a+b \text{csch}^{-1}(c x)\right)^2}{2 c^2}+\frac{1}{2} x^2 \left(a+b \text{csch}^{-1}(c x)\right)^3",1,"(3*b*(a + b*ArcCsch[c*x])^2)/(2*c^2) + (3*b*Sqrt[1 + 1/(c^2*x^2)]*x*(a + b*ArcCsch[c*x])^2)/(2*c) + (x^2*(a + b*ArcCsch[c*x])^3)/2 - (3*b^2*(a + b*ArcCsch[c*x])*Log[1 - E^(2*ArcCsch[c*x])])/c^2 - (3*b^3*PolyLog[2, E^(2*ArcCsch[c*x])])/(2*c^2)","A",7,7,12,0.5833,1,"{6286, 5452, 4184, 3716, 2190, 2279, 2391}"
27,1,120,0,0.1174913,"\int \left(a+b \text{csch}^{-1}(c x)\right)^3 \, dx","Int[(a + b*ArcCsch[c*x])^3,x]","\frac{6 b^2 \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{c}-\frac{6 b^2 \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{c}-\frac{6 b^3 \text{PolyLog}\left(3,-e^{\text{csch}^{-1}(c x)}\right)}{c}+\frac{6 b^3 \text{PolyLog}\left(3,e^{\text{csch}^{-1}(c x)}\right)}{c}+x \left(a+b \text{csch}^{-1}(c x)\right)^3+\frac{6 b \tanh ^{-1}\left(e^{\text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)^2}{c}","\frac{6 b^2 \text{PolyLog}\left(2,-e^{\text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{c}-\frac{6 b^2 \text{PolyLog}\left(2,e^{\text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{c}-\frac{6 b^3 \text{PolyLog}\left(3,-e^{\text{csch}^{-1}(c x)}\right)}{c}+\frac{6 b^3 \text{PolyLog}\left(3,e^{\text{csch}^{-1}(c x)}\right)}{c}+x \left(a+b \text{csch}^{-1}(c x)\right)^3+\frac{6 b \tanh ^{-1}\left(e^{\text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)^2}{c}",1,"x*(a + b*ArcCsch[c*x])^3 + (6*b*(a + b*ArcCsch[c*x])^2*ArcTanh[E^ArcCsch[c*x]])/c + (6*b^2*(a + b*ArcCsch[c*x])*PolyLog[2, -E^ArcCsch[c*x]])/c - (6*b^2*(a + b*ArcCsch[c*x])*PolyLog[2, E^ArcCsch[c*x]])/c - (6*b^3*PolyLog[3, -E^ArcCsch[c*x]])/c + (6*b^3*PolyLog[3, E^ArcCsch[c*x]])/c","A",9,6,10,0.6000,1,"{6280, 5452, 4182, 2531, 2282, 6589}"
28,1,110,0,0.153647,"\int \frac{\left(a+b \text{csch}^{-1}(c x)\right)^3}{x} \, dx","Int[(a + b*ArcCsch[c*x])^3/x,x]","\frac{3}{2} b^2 \text{PolyLog}\left(3,e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)-\frac{3}{2} b \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)^2-\frac{3}{4} b^3 \text{PolyLog}\left(4,e^{2 \text{csch}^{-1}(c x)}\right)+\frac{\left(a+b \text{csch}^{-1}(c x)\right)^4}{4 b}-\log \left(1-e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)^3","\frac{3}{2} b^2 \text{PolyLog}\left(3,e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)-\frac{3}{2} b \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)^2-\frac{3}{4} b^3 \text{PolyLog}\left(4,e^{2 \text{csch}^{-1}(c x)}\right)+\frac{\left(a+b \text{csch}^{-1}(c x)\right)^4}{4 b}-\log \left(1-e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)^3",1,"(a + b*ArcCsch[c*x])^4/(4*b) - (a + b*ArcCsch[c*x])^3*Log[1 - E^(2*ArcCsch[c*x])] - (3*b*(a + b*ArcCsch[c*x])^2*PolyLog[2, E^(2*ArcCsch[c*x])])/2 + (3*b^2*(a + b*ArcCsch[c*x])*PolyLog[3, E^(2*ArcCsch[c*x])])/2 - (3*b^3*PolyLog[4, E^(2*ArcCsch[c*x])])/4","A",7,7,14,0.5000,1,"{6286, 3716, 2190, 2531, 6609, 2282, 6589}"
29,1,78,0,0.0989242,"\int \frac{\left(a+b \text{csch}^{-1}(c x)\right)^3}{x^2} \, dx","Int[(a + b*ArcCsch[c*x])^3/x^2,x]","-\frac{6 b^2 \left(a+b \text{csch}^{-1}(c x)\right)}{x}+3 b c \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^3}{x}+6 b^3 c \sqrt{\frac{1}{c^2 x^2}+1}","-\frac{6 b^2 \left(a+b \text{csch}^{-1}(c x)\right)}{x}+3 b c \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^3}{x}+6 b^3 c \sqrt{\frac{1}{c^2 x^2}+1}",1,"6*b^3*c*Sqrt[1 + 1/(c^2*x^2)] - (6*b^2*(a + b*ArcCsch[c*x]))/x + 3*b*c*Sqrt[1 + 1/(c^2*x^2)]*(a + b*ArcCsch[c*x])^2 - (a + b*ArcCsch[c*x])^3/x","A",5,3,14,0.2143,1,"{6286, 3296, 2638}"
30,1,123,0,0.1063236,"\int \frac{\left(a+b \text{csch}^{-1}(c x)\right)^3}{x^3} \, dx","Int[(a + b*ArcCsch[c*x])^3/x^3,x]","-\frac{3 b^2 \left(a+b \text{csch}^{-1}(c x)\right)}{4 x^2}+\frac{3 b c \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2}{4 x}-\frac{1}{4} c^2 \left(a+b \text{csch}^{-1}(c x)\right)^3-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^3}{2 x^2}+\frac{3 b^3 c \sqrt{\frac{1}{c^2 x^2}+1}}{8 x}-\frac{3}{8} b^3 c^2 \text{csch}^{-1}(c x)","-\frac{3 b^2 \left(a+b \text{csch}^{-1}(c x)\right)}{4 x^2}+\frac{3 b c \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2}{4 x}-\frac{1}{4} c^2 \left(a+b \text{csch}^{-1}(c x)\right)^3-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^3}{2 x^2}+\frac{3 b^3 c \sqrt{\frac{1}{c^2 x^2}+1}}{8 x}-\frac{3}{8} b^3 c^2 \text{csch}^{-1}(c x)",1,"(3*b^3*c*Sqrt[1 + 1/(c^2*x^2)])/(8*x) - (3*b^3*c^2*ArcCsch[c*x])/8 - (3*b^2*(a + b*ArcCsch[c*x]))/(4*x^2) + (3*b*c*Sqrt[1 + 1/(c^2*x^2)]*(a + b*ArcCsch[c*x])^2)/(4*x) - (c^2*(a + b*ArcCsch[c*x])^3)/4 - (a + b*ArcCsch[c*x])^3/(2*x^2)","A",6,6,14,0.4286,1,"{6286, 5446, 3311, 32, 2635, 8}"
31,1,166,0,0.1705048,"\int \frac{\left(a+b \text{csch}^{-1}(c x)\right)^3}{x^4} \, dx","Int[(a + b*ArcCsch[c*x])^3/x^4,x]","\frac{4 b^2 c^2 \left(a+b \text{csch}^{-1}(c x)\right)}{3 x}-\frac{2 b^2 \left(a+b \text{csch}^{-1}(c x)\right)}{9 x^3}-\frac{2}{3} b c^3 \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2+\frac{b c \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2}{3 x^2}-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^3}{3 x^3}+\frac{2}{27} b^3 c^3 \left(\frac{1}{c^2 x^2}+1\right)^{3/2}-\frac{14}{9} b^3 c^3 \sqrt{\frac{1}{c^2 x^2}+1}","\frac{4 b^2 c^2 \left(a+b \text{csch}^{-1}(c x)\right)}{3 x}-\frac{2 b^2 \left(a+b \text{csch}^{-1}(c x)\right)}{9 x^3}-\frac{2}{3} b c^3 \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2+\frac{b c \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2}{3 x^2}-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^3}{3 x^3}+\frac{2}{27} b^3 c^3 \left(\frac{1}{c^2 x^2}+1\right)^{3/2}-\frac{14}{9} b^3 c^3 \sqrt{\frac{1}{c^2 x^2}+1}",1,"(-14*b^3*c^3*Sqrt[1 + 1/(c^2*x^2)])/9 + (2*b^3*c^3*(1 + 1/(c^2*x^2))^(3/2))/27 - (2*b^2*(a + b*ArcCsch[c*x]))/(9*x^3) + (4*b^2*c^2*(a + b*ArcCsch[c*x]))/(3*x) - (2*b*c^3*Sqrt[1 + 1/(c^2*x^2)]*(a + b*ArcCsch[c*x])^2)/3 + (b*c*Sqrt[1 + 1/(c^2*x^2)]*(a + b*ArcCsch[c*x])^2)/(3*x^2) - (a + b*ArcCsch[c*x])^3/(3*x^3)","A",8,6,14,0.4286,1,"{6286, 5446, 3311, 3296, 2638, 2633}"
32,1,204,0,0.1813613,"\int \frac{\left(a+b \text{csch}^{-1}(c x)\right)^3}{x^5} \, dx","Int[(a + b*ArcCsch[c*x])^3/x^5,x]","\frac{9 b^2 c^2 \left(a+b \text{csch}^{-1}(c x)\right)}{32 x^2}-\frac{3 b^2 \left(a+b \text{csch}^{-1}(c x)\right)}{32 x^4}-\frac{9 b c^3 \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2}{32 x}+\frac{3 b c \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2}{16 x^3}+\frac{3}{32} c^4 \left(a+b \text{csch}^{-1}(c x)\right)^3-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^3}{4 x^4}-\frac{45 b^3 c^3 \sqrt{\frac{1}{c^2 x^2}+1}}{256 x}+\frac{3 b^3 c \sqrt{\frac{1}{c^2 x^2}+1}}{128 x^3}+\frac{45}{256} b^3 c^4 \text{csch}^{-1}(c x)","\frac{9 b^2 c^2 \left(a+b \text{csch}^{-1}(c x)\right)}{32 x^2}-\frac{3 b^2 \left(a+b \text{csch}^{-1}(c x)\right)}{32 x^4}-\frac{9 b c^3 \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2}{32 x}+\frac{3 b c \sqrt{\frac{1}{c^2 x^2}+1} \left(a+b \text{csch}^{-1}(c x)\right)^2}{16 x^3}+\frac{3}{32} c^4 \left(a+b \text{csch}^{-1}(c x)\right)^3-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^3}{4 x^4}-\frac{45 b^3 c^3 \sqrt{\frac{1}{c^2 x^2}+1}}{256 x}+\frac{3 b^3 c \sqrt{\frac{1}{c^2 x^2}+1}}{128 x^3}+\frac{45}{256} b^3 c^4 \text{csch}^{-1}(c x)",1,"(3*b^3*c*Sqrt[1 + 1/(c^2*x^2)])/(128*x^3) - (45*b^3*c^3*Sqrt[1 + 1/(c^2*x^2)])/(256*x) + (45*b^3*c^4*ArcCsch[c*x])/256 - (3*b^2*(a + b*ArcCsch[c*x]))/(32*x^4) + (9*b^2*c^2*(a + b*ArcCsch[c*x]))/(32*x^2) + (3*b*c*Sqrt[1 + 1/(c^2*x^2)]*(a + b*ArcCsch[c*x])^2)/(16*x^3) - (9*b*c^3*Sqrt[1 + 1/(c^2*x^2)]*(a + b*ArcCsch[c*x])^2)/(32*x) + (3*c^4*(a + b*ArcCsch[c*x])^3)/32 - (a + b*ArcCsch[c*x])^3/(4*x^4)","A",10,6,14,0.4286,1,"{6286, 5446, 3311, 32, 2635, 8}"
33,0,0,0,0.0151715,"\int \frac{x}{a+b \text{csch}^{-1}(c x)} \, dx","Int[x/(a + b*ArcCsch[c*x]),x]","\int \frac{x}{a+b \text{csch}^{-1}(c x)} \, dx","\text{Int}\left(\frac{x}{a+b \text{csch}^{-1}(c x)},x\right)",0,"Defer[Int][x/(a + b*ArcCsch[c*x]), x]","A",0,0,0,0,-1,"{}"
34,0,0,0,0.0058766,"\int \frac{1}{a+b \text{csch}^{-1}(c x)} \, dx","Int[(a + b*ArcCsch[c*x])^(-1),x]","\int \frac{1}{a+b \text{csch}^{-1}(c x)} \, dx","\text{Int}\left(\frac{1}{a+b \text{csch}^{-1}(c x)},x\right)",0,"Defer[Int][(a + b*ArcCsch[c*x])^(-1), x]","A",0,0,0,0,-1,"{}"
35,0,0,0,0.0261483,"\int \frac{1}{x \left(a+b \text{csch}^{-1}(c x)\right)} \, dx","Int[1/(x*(a + b*ArcCsch[c*x])),x]","\int \frac{1}{x \left(a+b \text{csch}^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \text{csch}^{-1}(c x)\right)},x\right)",0,"Defer[Int][1/(x*(a + b*ArcCsch[c*x])), x]","A",0,0,0,0,-1,"{}"
36,1,46,0,0.104262,"\int \frac{1}{x^2 \left(a+b \text{csch}^{-1}(c x)\right)} \, dx","Int[1/(x^2*(a + b*ArcCsch[c*x])),x]","\frac{c \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\text{csch}^{-1}(c x)\right)}{b}-\frac{c \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\text{csch}^{-1}(c x)\right)}{b}","\frac{c \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\text{csch}^{-1}(c x)\right)}{b}-\frac{c \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\text{csch}^{-1}(c x)\right)}{b}",1,"-((c*Cosh[a/b]*CoshIntegral[a/b + ArcCsch[c*x]])/b) + (c*Sinh[a/b]*SinhIntegral[a/b + ArcCsch[c*x]])/b","A",4,4,14,0.2857,1,"{6286, 3303, 3298, 3301}"
37,1,63,0,0.1405648,"\int \frac{1}{x^3 \left(a+b \text{csch}^{-1}(c x)\right)} \, dx","Int[1/(x^3*(a + b*ArcCsch[c*x])),x]","\frac{c^2 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \text{csch}^{-1}(c x)\right)}{2 b}-\frac{c^2 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \text{csch}^{-1}(c x)\right)}{2 b}","\frac{c^2 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \text{csch}^{-1}(c x)\right)}{2 b}-\frac{c^2 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \text{csch}^{-1}(c x)\right)}{2 b}",1,"(c^2*CoshIntegral[(2*a)/b + 2*ArcCsch[c*x]]*Sinh[(2*a)/b])/(2*b) - (c^2*Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCsch[c*x]])/(2*b)","A",6,6,14,0.4286,1,"{6286, 5448, 12, 3303, 3298, 3301}"
38,1,117,0,0.2402906,"\int \frac{1}{x^4 \left(a+b \text{csch}^{-1}(c x)\right)} \, dx","Int[1/(x^4*(a + b*ArcCsch[c*x])),x]","\frac{c^3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\text{csch}^{-1}(c x)\right)}{4 b}-\frac{c^3 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \text{csch}^{-1}(c x)\right)}{4 b}-\frac{c^3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\text{csch}^{-1}(c x)\right)}{4 b}+\frac{c^3 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \text{csch}^{-1}(c x)\right)}{4 b}","\frac{c^3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\text{csch}^{-1}(c x)\right)}{4 b}-\frac{c^3 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \text{csch}^{-1}(c x)\right)}{4 b}-\frac{c^3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\text{csch}^{-1}(c x)\right)}{4 b}+\frac{c^3 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \text{csch}^{-1}(c x)\right)}{4 b}",1,"(c^3*Cosh[a/b]*CoshIntegral[a/b + ArcCsch[c*x]])/(4*b) - (c^3*Cosh[(3*a)/b]*CoshIntegral[(3*a)/b + 3*ArcCsch[c*x]])/(4*b) - (c^3*Sinh[a/b]*SinhIntegral[a/b + ArcCsch[c*x]])/(4*b) + (c^3*Sinh[(3*a)/b]*SinhIntegral[(3*a)/b + 3*ArcCsch[c*x]])/(4*b)","A",9,5,14,0.3571,1,"{6286, 5448, 3303, 3298, 3301}"
39,0,0,0,0.0242095,"\int (d x)^m \left(a+b \text{csch}^{-1}(c x)\right)^3 \, dx","Int[(d*x)^m*(a + b*ArcCsch[c*x])^3,x]","\int (d x)^m \left(a+b \text{csch}^{-1}(c x)\right)^3 \, dx","\text{Int}\left((d x)^m \left(a+b \text{csch}^{-1}(c x)\right)^3,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcCsch[c*x])^3, x]","A",0,0,0,0,-1,"{}"
40,0,0,0,0.0251134,"\int (d x)^m \left(a+b \text{csch}^{-1}(c x)\right)^2 \, dx","Int[(d*x)^m*(a + b*ArcCsch[c*x])^2,x]","\int (d x)^m \left(a+b \text{csch}^{-1}(c x)\right)^2 \, dx","\text{Int}\left((d x)^m \left(a+b \text{csch}^{-1}(c x)\right)^2,x\right)",0,"Defer[Int][(d*x)^m*(a + b*ArcCsch[c*x])^2, x]","A",0,0,0,0,-1,"{}"
41,1,67,0,0.0451583,"\int (d x)^m \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[(d*x)^m*(a + b*ArcCsch[c*x]),x]","\frac{(d x)^{m+1} \left(a+b \text{csch}^{-1}(c x)\right)}{d (m+1)}+\frac{b (d x)^m \, _2F_1\left(\frac{1}{2},-\frac{m}{2};1-\frac{m}{2};-\frac{1}{c^2 x^2}\right)}{c m (m+1)}","\frac{(d x)^{m+1} \left(a+b \text{csch}^{-1}(c x)\right)}{d (m+1)}+\frac{b (d x)^m \, _2F_1\left(\frac{1}{2},-\frac{m}{2};1-\frac{m}{2};-\frac{1}{c^2 x^2}\right)}{c m (m+1)}",1,"((d*x)^(1 + m)*(a + b*ArcCsch[c*x]))/(d*(1 + m)) + (b*(d*x)^m*Hypergeometric2F1[1/2, -m/2, 1 - m/2, -(1/(c^2*x^2))])/(c*m*(1 + m))","A",3,3,14,0.2143,1,"{6284, 339, 364}"
42,0,0,0,0.027665,"\int \frac{(d x)^m}{a+b \text{csch}^{-1}(c x)} \, dx","Int[(d*x)^m/(a + b*ArcCsch[c*x]),x]","\int \frac{(d x)^m}{a+b \text{csch}^{-1}(c x)} \, dx","\text{Int}\left(\frac{(d x)^m}{a+b \text{csch}^{-1}(c x)},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcCsch[c*x]), x]","A",0,0,0,0,-1,"{}"
43,0,0,0,0.0271329,"\int \frac{(d x)^m}{\left(a+b \text{csch}^{-1}(c x)\right)^2} \, dx","Int[(d*x)^m/(a + b*ArcCsch[c*x])^2,x]","\int \frac{(d x)^m}{\left(a+b \text{csch}^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{(d x)^m}{\left(a+b \text{csch}^{-1}(c x)\right)^2},x\right)",0,"Defer[Int][(d*x)^m/(a + b*ArcCsch[c*x])^2, x]","A",0,0,0,0,-1,"{}"
44,1,167,0,0.3836297,"\int (d+e x)^3 \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[(d + e*x)^3*(a + b*ArcCsch[c*x]),x]","\frac{(d+e x)^4 \left(a+b \text{csch}^{-1}(c x)\right)}{4 e}+\frac{b e x \sqrt{\frac{1}{c^2 x^2}+1} \left(9 c^2 d^2-e^2\right)}{6 c^3}+\frac{b d \left(2 c^2 d^2-e^2\right) \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{2 c^3}+\frac{b d e^2 x^2 \sqrt{\frac{1}{c^2 x^2}+1}}{2 c}+\frac{b e^3 x^3 \sqrt{\frac{1}{c^2 x^2}+1}}{12 c}-\frac{b d^4 \text{csch}^{-1}(c x)}{4 e}","\frac{(d+e x)^4 \left(a+b \text{csch}^{-1}(c x)\right)}{4 e}+\frac{b e x \sqrt{\frac{1}{c^2 x^2}+1} \left(9 c^2 d^2-e^2\right)}{6 c^3}+\frac{b d \left(2 c^2 d^2-e^2\right) \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{2 c^3}+\frac{b d e^2 x^2 \sqrt{\frac{1}{c^2 x^2}+1}}{2 c}+\frac{b e^3 x^3 \sqrt{\frac{1}{c^2 x^2}+1}}{12 c}-\frac{b d^4 \text{csch}^{-1}(c x)}{4 e}",1,"(b*e*(9*c^2*d^2 - e^2)*Sqrt[1 + 1/(c^2*x^2)]*x)/(6*c^3) + (b*d*e^2*Sqrt[1 + 1/(c^2*x^2)]*x^2)/(2*c) + (b*e^3*Sqrt[1 + 1/(c^2*x^2)]*x^3)/(12*c) - (b*d^4*ArcCsch[c*x])/(4*e) + ((d + e*x)^4*(a + b*ArcCsch[c*x]))/(4*e) + (b*d*(2*c^2*d^2 - e^2)*ArcTanh[Sqrt[1 + 1/(c^2*x^2)]])/(2*c^3)","A",11,9,16,0.5625,1,"{6290, 1568, 1475, 1807, 844, 215, 266, 63, 208}"
45,1,122,0,0.2593895,"\int (d+e x)^2 \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[(d + e*x)^2*(a + b*ArcCsch[c*x]),x]","\frac{(d+e x)^3 \left(a+b \text{csch}^{-1}(c x)\right)}{3 e}+\frac{b \left(6 c^2 d^2-e^2\right) \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{6 c^3}+\frac{b d e x \sqrt{\frac{1}{c^2 x^2}+1}}{c}+\frac{b e^2 x^2 \sqrt{\frac{1}{c^2 x^2}+1}}{6 c}-\frac{b d^3 \text{csch}^{-1}(c x)}{3 e}","\frac{(d+e x)^3 \left(a+b \text{csch}^{-1}(c x)\right)}{3 e}+\frac{b \left(6 c^2 d^2-e^2\right) \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{6 c^3}+\frac{b d e x \sqrt{\frac{1}{c^2 x^2}+1}}{c}+\frac{b e^2 x^2 \sqrt{\frac{1}{c^2 x^2}+1}}{6 c}-\frac{b d^3 \text{csch}^{-1}(c x)}{3 e}",1,"(b*d*e*Sqrt[1 + 1/(c^2*x^2)]*x)/c + (b*e^2*Sqrt[1 + 1/(c^2*x^2)]*x^2)/(6*c) - (b*d^3*ArcCsch[c*x])/(3*e) + ((d + e*x)^3*(a + b*ArcCsch[c*x]))/(3*e) + (b*(6*c^2*d^2 - e^2)*ArcTanh[Sqrt[1 + 1/(c^2*x^2)]])/(6*c^3)","A",10,9,16,0.5625,1,"{6290, 1568, 1475, 1807, 844, 215, 266, 63, 208}"
46,1,81,0,0.160567,"\int (d+e x) \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[(d + e*x)*(a + b*ArcCsch[c*x]),x]","\frac{(d+e x)^2 \left(a+b \text{csch}^{-1}(c x)\right)}{2 e}+\frac{b d \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{c}+\frac{b e x \sqrt{\frac{1}{c^2 x^2}+1}}{2 c}-\frac{b d^2 \text{csch}^{-1}(c x)}{2 e}","\frac{(d+e x)^2 \left(a+b \text{csch}^{-1}(c x)\right)}{2 e}+\frac{b d \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{c}+\frac{b e x \sqrt{\frac{1}{c^2 x^2}+1}}{2 c}-\frac{b d^2 \text{csch}^{-1}(c x)}{2 e}",1,"(b*e*Sqrt[1 + 1/(c^2*x^2)]*x)/(2*c) - (b*d^2*ArcCsch[c*x])/(2*e) + ((d + e*x)^2*(a + b*ArcCsch[c*x]))/(2*e) + (b*d*ArcTanh[Sqrt[1 + 1/(c^2*x^2)]])/c","A",9,9,14,0.6429,1,"{6290, 1568, 1396, 1807, 844, 215, 266, 63, 208}"
47,1,30,0,0.0220054,"\int \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[a + b*ArcCsch[c*x],x]","a x+\frac{b \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{c}+b x \text{csch}^{-1}(c x)","a x+\frac{b \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{c}+b x \text{csch}^{-1}(c x)",1,"a*x + b*x*ArcCsch[c*x] + (b*ArcTanh[Sqrt[1 + 1/(c^2*x^2)]])/c","A",5,4,8,0.5000,1,"{6278, 266, 63, 208}"
48,1,215,0,0.3897294,"\int \frac{a+b \text{csch}^{-1}(c x)}{d+e x} \, dx","Int[(a + b*ArcCsch[c*x])/(d + e*x),x]","\frac{b \text{PolyLog}\left(2,\frac{\left(e-\sqrt{c^2 d^2+e^2}\right) e^{\text{csch}^{-1}(c x)}}{c d}\right)}{e}+\frac{b \text{PolyLog}\left(2,\frac{\left(\sqrt{c^2 d^2+e^2}+e\right) e^{\text{csch}^{-1}(c x)}}{c d}\right)}{e}-\frac{b \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)}{2 e}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{\left(e-\sqrt{c^2 d^2+e^2}\right) e^{\text{csch}^{-1}(c x)}}{c d}\right)}{e}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{\left(\sqrt{c^2 d^2+e^2}+e\right) e^{\text{csch}^{-1}(c x)}}{c d}\right)}{e}-\frac{\log \left(1-e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{e}","\frac{b \text{PolyLog}\left(2,\frac{\left(e-\sqrt{c^2 d^2+e^2}\right) e^{\text{csch}^{-1}(c x)}}{c d}\right)}{e}+\frac{b \text{PolyLog}\left(2,\frac{\left(\sqrt{c^2 d^2+e^2}+e\right) e^{\text{csch}^{-1}(c x)}}{c d}\right)}{e}-\frac{b \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)}{2 e}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{\left(e-\sqrt{c^2 d^2+e^2}\right) e^{\text{csch}^{-1}(c x)}}{c d}\right)}{e}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{\left(\sqrt{c^2 d^2+e^2}+e\right) e^{\text{csch}^{-1}(c x)}}{c d}\right)}{e}-\frac{\log \left(1-e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{e}",1,"((a + b*ArcCsch[c*x])*Log[1 - ((e - Sqrt[c^2*d^2 + e^2])*E^ArcCsch[c*x])/(c*d)])/e + ((a + b*ArcCsch[c*x])*Log[1 - ((e + Sqrt[c^2*d^2 + e^2])*E^ArcCsch[c*x])/(c*d)])/e - ((a + b*ArcCsch[c*x])*Log[1 - E^(2*ArcCsch[c*x])])/e + (b*PolyLog[2, ((e - Sqrt[c^2*d^2 + e^2])*E^ArcCsch[c*x])/(c*d)])/e + (b*PolyLog[2, ((e + Sqrt[c^2*d^2 + e^2])*E^ArcCsch[c*x])/(c*d)])/e - (b*PolyLog[2, E^(2*ArcCsch[c*x])])/(2*e)","A",4,2,16,0.1250,1,"{6289, 2518}"
49,1,98,0,0.1537098,"\int \frac{a+b \text{csch}^{-1}(c x)}{(d+e x)^2} \, dx","Int[(a + b*ArcCsch[c*x])/(d + e*x)^2,x]","-\frac{a+b \text{csch}^{-1}(c x)}{e (d+e x)}+\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{e}{x}}{c \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d^2+e^2}}\right)}{d \sqrt{c^2 d^2+e^2}}+\frac{b \text{csch}^{-1}(c x)}{d e}","-\frac{a+b \text{csch}^{-1}(c x)}{e (d+e x)}+\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{e}{x}}{c \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d^2+e^2}}\right)}{d \sqrt{c^2 d^2+e^2}}+\frac{b \text{csch}^{-1}(c x)}{d e}",1,"(b*ArcCsch[c*x])/(d*e) - (a + b*ArcCsch[c*x])/(e*(d + e*x)) + (b*ArcTanh[(c^2*d - e/x)/(c*Sqrt[c^2*d^2 + e^2]*Sqrt[1 + 1/(c^2*x^2)])])/(d*Sqrt[c^2*d^2 + e^2])","A",7,7,16,0.4375,1,"{6290, 1568, 1475, 844, 215, 725, 206}"
50,1,163,0,0.2918401,"\int \frac{a+b \text{csch}^{-1}(c x)}{(d+e x)^3} \, dx","Int[(a + b*ArcCsch[c*x])/(d + e*x)^3,x]","-\frac{a+b \text{csch}^{-1}(c x)}{2 e (d+e x)^2}-\frac{b c e \sqrt{\frac{1}{c^2 x^2}+1}}{2 d \left(c^2 d^2+e^2\right) \left(\frac{d}{x}+e\right)}+\frac{b \left(2 c^2 d^2+e^2\right) \tanh ^{-1}\left(\frac{c^2 d-\frac{e}{x}}{c \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d^2+e^2}}\right)}{2 d^2 \left(c^2 d^2+e^2\right)^{3/2}}+\frac{b \text{csch}^{-1}(c x)}{2 d^2 e}","-\frac{a+b \text{csch}^{-1}(c x)}{2 e (d+e x)^2}-\frac{b c e \sqrt{\frac{1}{c^2 x^2}+1}}{2 d \left(c^2 d^2+e^2\right) \left(\frac{d}{x}+e\right)}+\frac{b \left(2 c^2 d^2+e^2\right) \tanh ^{-1}\left(\frac{c^2 d-\frac{e}{x}}{c \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d^2+e^2}}\right)}{2 d^2 \left(c^2 d^2+e^2\right)^{3/2}}+\frac{b \text{csch}^{-1}(c x)}{2 d^2 e}",1,"-(b*c*e*Sqrt[1 + 1/(c^2*x^2)])/(2*d*(c^2*d^2 + e^2)*(e + d/x)) + (b*ArcCsch[c*x])/(2*d^2*e) - (a + b*ArcCsch[c*x])/(2*e*(d + e*x)^2) + (b*(2*c^2*d^2 + e^2)*ArcTanh[(c^2*d - e/x)/(c*Sqrt[c^2*d^2 + e^2]*Sqrt[1 + 1/(c^2*x^2)])])/(2*d^2*(c^2*d^2 + e^2)^(3/2))","A",8,8,16,0.5000,1,"{6290, 1568, 1475, 1651, 844, 215, 725, 206}"
51,1,918,0,3.2527987,"\int x^2 \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^2*Sqrt[d + e*x]*(a + b*ArcCsch[c*x]),x]","-\frac{32 b \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \sqrt{c^2 x^2+1} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right) d^4}{105 c e^3 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{d+e x}}+\frac{32 b c \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} \sqrt{c^2 x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right) d^3}{105 \left(-c^2\right)^{3/2} e^2 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{d+e x}}+\frac{2 (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right) d^2}{3 e^3}-\frac{32 b c \sqrt{d+e x} \sqrt{c^2 x^2+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right) d^2}{105 \left(-c^2\right)^{3/2} e^2 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}-\frac{4 b \sqrt{d+e x} \left(c^2 x^2+1\right) d}{105 c^3 e \sqrt{1+\frac{1}{c^2 x^2}} x}-\frac{4 (d+e x)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right) d}{5 e^3}-\frac{4 b c \left(c^2 d^2+e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} \sqrt{c^2 x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right) d}{105 \left(-c^2\right)^{5/2} e^2 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{d+e x}}+\frac{4 b (d+e x)^{3/2} \left(c^2 x^2+1\right)}{35 c^3 e \sqrt{1+\frac{1}{c^2 x^2}} x}+\frac{2 (d+e x)^{7/2} \left(a+b \text{csch}^{-1}(c x)\right)}{7 e^3}-\frac{4 b c \left(c^2 d^2-3 e^2\right) \sqrt{d+e x} \sqrt{c^2 x^2+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{35 \left(-c^2\right)^{5/2} e^2 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}","-\frac{32 b \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \sqrt{c^2 x^2+1} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right) d^4}{105 c e^3 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{d+e x}}+\frac{32 b c \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} \sqrt{c^2 x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right) d^3}{105 \left(-c^2\right)^{3/2} e^2 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{d+e x}}+\frac{2 (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right) d^2}{3 e^3}-\frac{32 b c \sqrt{d+e x} \sqrt{c^2 x^2+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right) d^2}{105 \left(-c^2\right)^{3/2} e^2 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}-\frac{4 b \sqrt{d+e x} \left(c^2 x^2+1\right) d}{105 c^3 e \sqrt{1+\frac{1}{c^2 x^2}} x}-\frac{4 (d+e x)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right) d}{5 e^3}-\frac{4 b c \left(c^2 d^2+e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} \sqrt{c^2 x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right) d}{105 \left(-c^2\right)^{5/2} e^2 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{d+e x}}+\frac{4 b (d+e x)^{3/2} \left(c^2 x^2+1\right)}{35 c^3 e \sqrt{1+\frac{1}{c^2 x^2}} x}+\frac{2 (d+e x)^{7/2} \left(a+b \text{csch}^{-1}(c x)\right)}{7 e^3}-\frac{4 b c \left(c^2 d^2-3 e^2\right) \sqrt{d+e x} \sqrt{c^2 x^2+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{35 \left(-c^2\right)^{5/2} e^2 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}",1,"(-4*b*d*Sqrt[d + e*x]*(1 + c^2*x^2))/(105*c^3*e*Sqrt[1 + 1/(c^2*x^2)]*x) + (4*b*(d + e*x)^(3/2)*(1 + c^2*x^2))/(35*c^3*e*Sqrt[1 + 1/(c^2*x^2)]*x) + (2*d^2*(d + e*x)^(3/2)*(a + b*ArcCsch[c*x]))/(3*e^3) - (4*d*(d + e*x)^(5/2)*(a + b*ArcCsch[c*x]))/(5*e^3) + (2*(d + e*x)^(7/2)*(a + b*ArcCsch[c*x]))/(7*e^3) - (32*b*c*d^2*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(105*(-c^2)^(3/2)*e^2*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]) - (4*b*c*(c^2*d^2 - 3*e^2)*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(35*(-c^2)^(5/2)*e^2*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]) + (32*b*c*d^3*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(105*(-c^2)^(3/2)*e^2*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (4*b*c*d*(c^2*d^2 + e^2)*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(105*(-c^2)^(5/2)*e^2*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (32*b*d^4*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(105*c*e^3*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",31,16,21,0.7619,1,"{43, 6310, 12, 6721, 6742, 743, 844, 719, 424, 419, 958, 932, 168, 538, 537, 833}"
52,1,679,0,2.5191422,"\int x \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x*Sqrt[d + e*x]*(a + b*ArcCsch[c*x]),x]","-\frac{2 d (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^2}+\frac{2 (d+e x)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e^2}+\frac{4 b c \sqrt{c^2 x^2+1} \left(c^2 d^2+e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{5/2} e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{8 b d^3 \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{15 c e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{8 b c d^2 \sqrt{c^2 x^2+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{3/2} e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b \left(c^2 x^2+1\right) \sqrt{d+e x}}{15 c^3 x \sqrt{\frac{1}{c^2 x^2}+1}}+\frac{8 b c d \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{3/2} e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}","-\frac{2 d (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^2}+\frac{2 (d+e x)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e^2}+\frac{4 b c \sqrt{c^2 x^2+1} \left(c^2 d^2+e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{5/2} e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{8 b d^3 \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{15 c e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{8 b c d^2 \sqrt{c^2 x^2+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{3/2} e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b \left(c^2 x^2+1\right) \sqrt{d+e x}}{15 c^3 x \sqrt{\frac{1}{c^2 x^2}+1}}+\frac{8 b c d \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{3/2} e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}",1,"(4*b*Sqrt[d + e*x]*(1 + c^2*x^2))/(15*c^3*Sqrt[1 + 1/(c^2*x^2)]*x) - (2*d*(d + e*x)^(3/2)*(a + b*ArcCsch[c*x]))/(3*e^2) + (2*(d + e*x)^(5/2)*(a + b*ArcCsch[c*x]))/(5*e^2) + (8*b*c*d*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(15*(-c^2)^(3/2)*e*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]) - (8*b*c*d^2*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(15*(-c^2)^(3/2)*e*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (4*b*c*(c^2*d^2 + e^2)*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(15*(-c^2)^(5/2)*e*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (8*b*d^3*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(15*c*e^2*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",24,15,19,0.7895,1,"{43, 6310, 12, 6721, 6742, 743, 844, 719, 424, 419, 958, 932, 168, 538, 537}"
53,1,429,0,0.7083675,"\int \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[Sqrt[d + e*x]*(a + b*ArcCsch[c*x]),x]","\frac{2 (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e}-\frac{4 b d^2 \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{3 c e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b c d \sqrt{c^2 x^2+1} \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 \left(-c^2\right)^{3/2} x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b c \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 \left(-c^2\right)^{3/2} x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}}}","\frac{2 (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e}-\frac{4 b d^2 \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{3 c e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b c d \sqrt{c^2 x^2+1} \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 \left(-c^2\right)^{3/2} x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b c \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 \left(-c^2\right)^{3/2} x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}}}",1,"(2*(d + e*x)^(3/2)*(a + b*ArcCsch[c*x]))/(3*e) + (4*b*c*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(3*(-c^2)^(3/2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(d + e*x)/(d + e/Sqrt[-c^2])]) + (4*b*c*d*Sqrt[(d + e*x)/(d + e/Sqrt[-c^2])]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(3*(-c^2)^(3/2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (4*b*d^2*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(3*c*e*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",15,11,18,0.6111,1,"{6290, 1574, 958, 719, 419, 933, 168, 538, 537, 844, 424}"
54,0,0,0,0.0760624,"\int \frac{\sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{x} \, dx","Int[(Sqrt[d + e*x]*(a + b*ArcCsch[c*x]))/x,x]","\int \frac{\sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{x} \, dx","\text{Int}\left(\frac{\sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{x},x\right)",0,"Defer[Int][(Sqrt[d + e*x]*(a + b*ArcCsch[c*x]))/x, x]","A",0,0,0,0,-1,"{}"
55,0,0,0,0.0789321,"\int \frac{\sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{x^2} \, dx","Int[(Sqrt[d + e*x]*(a + b*ArcCsch[c*x]))/x^2,x]","\int \frac{\sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{x^2} \, dx","\text{Int}\left(\frac{\sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{x^2},x\right)",0,"Defer[Int][(Sqrt[d + e*x]*(a + b*ArcCsch[c*x]))/x^2, x]","A",0,0,0,0,-1,"{}"
56,1,486,0,1.0226342,"\int (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[(d + e*x)^(3/2)*(a + b*ArcCsch[c*x]),x]","\frac{2 (d+e x)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e}-\frac{4 b c \sqrt{c^2 x^2+1} \left(2 c^2 d^2-e^2\right) \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{5/2} x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{4 b d^3 \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{5 c e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b e \left(c^2 x^2+1\right) \sqrt{d+e x}}{15 c^3 x \sqrt{\frac{1}{c^2 x^2}+1}}+\frac{28 b c d \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{3/2} x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}}}","\frac{2 (d+e x)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e}-\frac{4 b c \sqrt{c^2 x^2+1} \left(2 c^2 d^2-e^2\right) \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{5/2} x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{4 b d^3 \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{5 c e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b e \left(c^2 x^2+1\right) \sqrt{d+e x}}{15 c^3 x \sqrt{\frac{1}{c^2 x^2}+1}}+\frac{28 b c d \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{3/2} x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}}}",1,"(4*b*e*Sqrt[d + e*x]*(1 + c^2*x^2))/(15*c^3*Sqrt[1 + 1/(c^2*x^2)]*x) + (2*(d + e*x)^(5/2)*(a + b*ArcCsch[c*x]))/(5*e) + (28*b*c*d*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(15*(-c^2)^(3/2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(d + e*x)/(d + e/Sqrt[-c^2])]) - (4*b*c*(2*c^2*d^2 - e^2)*Sqrt[(d + e*x)/(d + e/Sqrt[-c^2])]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(15*(-c^2)^(5/2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (4*b*d^3*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(5*c*e*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",22,13,18,0.7222,1,"{6290, 1574, 958, 719, 419, 933, 168, 538, 537, 844, 424, 931, 1584}"
57,1,939,0,2.8713284,"\int \frac{x^3 \left(a+b \text{csch}^{-1}(c x)\right)}{\sqrt{d+e x}} \, dx","Int[(x^3*(a + b*ArcCsch[c*x]))/Sqrt[d + e*x],x]","\frac{64 b \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \sqrt{c^2 x^2+1} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right) d^4}{35 c e^4 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right) d^3}{e^4}-\frac{64 b c \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} \sqrt{c^2 x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right) d^3}{35 \left(-c^2\right)^{3/2} e^3 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{d+e x}}+\frac{2 (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right) d^2}{e^4}+\frac{24 b c \sqrt{d+e x} \sqrt{c^2 x^2+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right) d^2}{35 \left(-c^2\right)^{3/2} e^3 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}-\frac{4 b \sqrt{d+e x} \left(c^2 x^2+1\right) d}{21 c^3 e^2 \sqrt{1+\frac{1}{c^2 x^2}} x}-\frac{6 (d+e x)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right) d}{5 e^4}-\frac{32 b c \left(c^2 d^2+e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} \sqrt{c^2 x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right) d}{105 \left(-c^2\right)^{5/2} e^3 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{d+e x}}+\frac{4 b \sqrt{d+e x} \left(c^2 x^2+1\right)}{35 c^3 e \sqrt{1+\frac{1}{c^2 x^2}}}+\frac{2 (d+e x)^{7/2} \left(a+b \text{csch}^{-1}(c x)\right)}{7 e^4}+\frac{4 b c \left(2 c^2 d^2+9 e^2\right) \sqrt{d+e x} \sqrt{c^2 x^2+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{105 \left(-c^2\right)^{5/2} e^3 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}","\frac{64 b \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \sqrt{c^2 x^2+1} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right) d^4}{35 c e^4 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right) d^3}{e^4}-\frac{64 b c \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} \sqrt{c^2 x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right) d^3}{35 \left(-c^2\right)^{3/2} e^3 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{d+e x}}+\frac{2 (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right) d^2}{e^4}+\frac{24 b c \sqrt{d+e x} \sqrt{c^2 x^2+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right) d^2}{35 \left(-c^2\right)^{3/2} e^3 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}-\frac{4 b \sqrt{d+e x} \left(c^2 x^2+1\right) d}{21 c^3 e^2 \sqrt{1+\frac{1}{c^2 x^2}} x}-\frac{6 (d+e x)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right) d}{5 e^4}-\frac{32 b c \left(c^2 d^2+e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} \sqrt{c^2 x^2+1} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right) d}{105 \left(-c^2\right)^{5/2} e^3 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{d+e x}}+\frac{4 b \sqrt{d+e x} \left(c^2 x^2+1\right)}{35 c^3 e \sqrt{1+\frac{1}{c^2 x^2}}}+\frac{2 (d+e x)^{7/2} \left(a+b \text{csch}^{-1}(c x)\right)}{7 e^4}+\frac{4 b c \left(2 c^2 d^2+9 e^2\right) \sqrt{d+e x} \sqrt{c^2 x^2+1} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{105 \left(-c^2\right)^{5/2} e^3 \sqrt{1+\frac{1}{c^2 x^2}} x \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}",1,"(4*b*Sqrt[d + e*x]*(1 + c^2*x^2))/(35*c^3*e*Sqrt[1 + 1/(c^2*x^2)]) - (4*b*d*Sqrt[d + e*x]*(1 + c^2*x^2))/(21*c^3*e^2*Sqrt[1 + 1/(c^2*x^2)]*x) - (2*d^3*Sqrt[d + e*x]*(a + b*ArcCsch[c*x]))/e^4 + (2*d^2*(d + e*x)^(3/2)*(a + b*ArcCsch[c*x]))/e^4 - (6*d*(d + e*x)^(5/2)*(a + b*ArcCsch[c*x]))/(5*e^4) + (2*(d + e*x)^(7/2)*(a + b*ArcCsch[c*x]))/(7*e^4) + (24*b*c*d^2*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(35*(-c^2)^(3/2)*e^3*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]) + (4*b*c*(2*c^2*d^2 + 9*e^2)*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(105*(-c^2)^(5/2)*e^3*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]) - (64*b*c*d^3*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(35*(-c^2)^(3/2)*e^3*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (32*b*c*d*(c^2*d^2 + e^2)*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(105*(-c^2)^(5/2)*e^3*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (64*b*d^4*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(35*c*e^4*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",27,17,21,0.8095,1,"{43, 6310, 12, 6721, 6742, 719, 424, 944, 419, 932, 168, 538, 537, 833, 844, 942, 1654}"
58,1,707,0,2.1416825,"\int \frac{x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{\sqrt{d+e x}} \, dx","Int[(x^2*(a + b*ArcCsch[c*x]))/Sqrt[d + e*x],x]","\frac{2 d^2 \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{e^3}-\frac{4 d (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^3}+\frac{2 (d+e x)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e^3}+\frac{32 b c d^2 \sqrt{c^2 x^2+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{3/2} e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b c \sqrt{c^2 x^2+1} \left(c^2 d^2+e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{5/2} e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{32 b d^3 \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{15 c e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{4 b c d \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{5 \left(-c^2\right)^{3/2} e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}+\frac{4 b \left(c^2 x^2+1\right) \sqrt{d+e x}}{15 c^3 e x \sqrt{\frac{1}{c^2 x^2}+1}}","\frac{2 d^2 \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{e^3}-\frac{4 d (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^3}+\frac{2 (d+e x)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e^3}+\frac{32 b c d^2 \sqrt{c^2 x^2+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{3/2} e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b c \sqrt{c^2 x^2+1} \left(c^2 d^2+e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{5/2} e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{32 b d^3 \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{15 c e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{4 b c d \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{5 \left(-c^2\right)^{3/2} e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}+\frac{4 b \left(c^2 x^2+1\right) \sqrt{d+e x}}{15 c^3 e x \sqrt{\frac{1}{c^2 x^2}+1}}",1,"(4*b*Sqrt[d + e*x]*(1 + c^2*x^2))/(15*c^3*e*Sqrt[1 + 1/(c^2*x^2)]*x) + (2*d^2*Sqrt[d + e*x]*(a + b*ArcCsch[c*x]))/e^3 - (4*d*(d + e*x)^(3/2)*(a + b*ArcCsch[c*x]))/(3*e^3) + (2*(d + e*x)^(5/2)*(a + b*ArcCsch[c*x]))/(5*e^3) - (4*b*c*d*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(5*(-c^2)^(3/2)*e^2*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]) + (32*b*c*d^2*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(15*(-c^2)^(3/2)*e^2*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (4*b*c*(c^2*d^2 + e^2)*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(15*(-c^2)^(5/2)*e^2*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (32*b*d^3*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(15*c*e^3*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",20,15,21,0.7143,1,"{43, 6310, 12, 6721, 6742, 719, 424, 944, 419, 932, 168, 538, 537, 833, 844}"
59,1,474,0,1.7506303,"\int \frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{\sqrt{d+e x}} \, dx","Int[(x*(a + b*ArcCsch[c*x]))/Sqrt[d + e*x],x]","-\frac{2 d \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{e^2}+\frac{2 (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^2}+\frac{8 b d^2 \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{3 c e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{8 b c d \sqrt{c^2 x^2+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 \left(-c^2\right)^{3/2} e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b c \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 \left(-c^2\right)^{3/2} e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}","-\frac{2 d \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{e^2}+\frac{2 (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^2}+\frac{8 b d^2 \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{3 c e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{8 b c d \sqrt{c^2 x^2+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 \left(-c^2\right)^{3/2} e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b c \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 \left(-c^2\right)^{3/2} e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}",1,"(-2*d*Sqrt[d + e*x]*(a + b*ArcCsch[c*x]))/e^2 + (2*(d + e*x)^(3/2)*(a + b*ArcCsch[c*x]))/(3*e^2) + (4*b*c*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(3*(-c^2)^(3/2)*e*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]) - (8*b*c*d*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(3*(-c^2)^(3/2)*e*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (8*b*d^2*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(3*c*e^2*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",14,13,19,0.6842,1,"{43, 6310, 12, 6721, 6742, 719, 424, 944, 419, 932, 168, 538, 537}"
60,1,284,0,0.4137141,"\int \frac{a+b \text{csch}^{-1}(c x)}{\sqrt{d+e x}} \, dx","Int[(a + b*ArcCsch[c*x])/Sqrt[d + e*x],x]","\frac{2 \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{e}+\frac{4 b c \sqrt{c^2 x^2+1} \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{\left(-c^2\right)^{3/2} x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{4 b d \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{c e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}","\frac{2 \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{e}+\frac{4 b c \sqrt{c^2 x^2+1} \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{\left(-c^2\right)^{3/2} x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{4 b d \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{c e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}",1,"(2*Sqrt[d + e*x]*(a + b*ArcCsch[c*x]))/e + (4*b*c*Sqrt[(d + e*x)/(d + e/Sqrt[-c^2])]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/((-c^2)^(3/2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (4*b*d*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(c*e*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",9,9,18,0.5000,1,"{6290, 1574, 944, 719, 419, 933, 168, 538, 537}"
61,0,0,0,0.0767769,"\int \frac{a+b \text{csch}^{-1}(c x)}{x \sqrt{d+e x}} \, dx","Int[(a + b*ArcCsch[c*x])/(x*Sqrt[d + e*x]),x]","\int \frac{a+b \text{csch}^{-1}(c x)}{x \sqrt{d+e x}} \, dx","\text{Int}\left(\frac{a+b \text{csch}^{-1}(c x)}{x \sqrt{d+e x}},x\right)",0,"Defer[Int][(a + b*ArcCsch[c*x])/(x*Sqrt[d + e*x]), x]","A",0,0,0,0,-1,"{}"
62,0,0,0,0.0821906,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^2 \sqrt{d+e x}} \, dx","Int[(a + b*ArcCsch[c*x])/(x^2*Sqrt[d + e*x]),x]","\int \frac{a+b \text{csch}^{-1}(c x)}{x^2 \sqrt{d+e x}} \, dx","\text{Int}\left(\frac{a+b \text{csch}^{-1}(c x)}{x^2 \sqrt{d+e x}},x\right)",0,"Defer[Int][(a + b*ArcCsch[c*x])/(x^2*Sqrt[d + e*x]), x]","A",0,0,0,0,-1,"{}"
63,1,731,0,2.6359509,"\int \frac{x^3 \left(a+b \text{csch}^{-1}(c x)\right)}{(d+e x)^{3/2}} \, dx","Int[(x^3*(a + b*ArcCsch[c*x]))/(d + e*x)^(3/2),x]","\frac{2 d^3 \left(a+b \text{csch}^{-1}(c x)\right)}{e^4 \sqrt{d+e x}}+\frac{6 d^2 \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{e^4}-\frac{2 d (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{e^4}+\frac{2 (d+e x)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e^4}+\frac{8 b c d^2 \sqrt{c^2 x^2+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{\left(-c^2\right)^{3/2} e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{4 b c \sqrt{c^2 x^2+1} \left(2 c^2 d^2-e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{5/2} e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{64 b d^3 \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{5 c e^4 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b \left(c^2 x^2+1\right) \sqrt{d+e x}}{15 c^3 e^2 x \sqrt{\frac{1}{c^2 x^2}+1}}-\frac{32 b c d \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{3/2} e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}","\frac{2 d^3 \left(a+b \text{csch}^{-1}(c x)\right)}{e^4 \sqrt{d+e x}}+\frac{6 d^2 \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{e^4}-\frac{2 d (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{e^4}+\frac{2 (d+e x)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e^4}+\frac{8 b c d^2 \sqrt{c^2 x^2+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{\left(-c^2\right)^{3/2} e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{4 b c \sqrt{c^2 x^2+1} \left(2 c^2 d^2-e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{5/2} e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{64 b d^3 \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{5 c e^4 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b \left(c^2 x^2+1\right) \sqrt{d+e x}}{15 c^3 e^2 x \sqrt{\frac{1}{c^2 x^2}+1}}-\frac{32 b c d \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 \left(-c^2\right)^{3/2} e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}",1,"(4*b*Sqrt[d + e*x]*(1 + c^2*x^2))/(15*c^3*e^2*Sqrt[1 + 1/(c^2*x^2)]*x) + (2*d^3*(a + b*ArcCsch[c*x]))/(e^4*Sqrt[d + e*x]) + (6*d^2*Sqrt[d + e*x]*(a + b*ArcCsch[c*x]))/e^4 - (2*d*(d + e*x)^(3/2)*(a + b*ArcCsch[c*x]))/e^4 + (2*(d + e*x)^(5/2)*(a + b*ArcCsch[c*x]))/(5*e^4) - (32*b*c*d*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(15*(-c^2)^(3/2)*e^3*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]) + (8*b*c*d^2*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/((-c^2)^(3/2)*e^3*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (4*b*c*(2*c^2*d^2 - e^2)*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(15*(-c^2)^(5/2)*e^3*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (64*b*d^3*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(5*c*e^4*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",23,15,21,0.7143,1,"{43, 6310, 12, 6721, 6742, 719, 419, 932, 168, 538, 537, 844, 424, 931, 1584}"
64,1,499,0,2.0095805,"\int \frac{x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{(d+e x)^{3/2}} \, dx","Int[(x^2*(a + b*ArcCsch[c*x]))/(d + e*x)^(3/2),x]","-\frac{2 d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{e^3 \sqrt{d+e x}}-\frac{4 d \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{e^3}+\frac{2 (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^3}+\frac{32 b d^2 \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{3 c e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{20 b c d \sqrt{c^2 x^2+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 \left(-c^2\right)^{3/2} e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b c \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 \left(-c^2\right)^{3/2} e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}","-\frac{2 d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{e^3 \sqrt{d+e x}}-\frac{4 d \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{e^3}+\frac{2 (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^3}+\frac{32 b d^2 \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{3 c e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{20 b c d \sqrt{c^2 x^2+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 \left(-c^2\right)^{3/2} e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b c \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 \left(-c^2\right)^{3/2} e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}",1,"(-2*d^2*(a + b*ArcCsch[c*x]))/(e^3*Sqrt[d + e*x]) - (4*d*Sqrt[d + e*x]*(a + b*ArcCsch[c*x]))/e^3 + (2*(d + e*x)^(3/2)*(a + b*ArcCsch[c*x]))/(3*e^3) + (4*b*c*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(3*(-c^2)^(3/2)*e^2*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]) - (20*b*c*d*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(3*(-c^2)^(3/2)*e^2*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (32*b*d^2*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(3*c*e^3*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",16,13,21,0.6190,1,"{43, 6310, 12, 6721, 6742, 719, 419, 932, 168, 538, 537, 844, 424}"
65,1,318,0,1.6913115,"\int \frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{(d+e x)^{3/2}} \, dx","Int[(x*(a + b*ArcCsch[c*x]))/(d + e*x)^(3/2),x]","\frac{2 \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{e^2}+\frac{2 d \left(a+b \text{csch}^{-1}(c x)\right)}{e^2 \sqrt{d+e x}}-\frac{8 b d \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{c e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b c \sqrt{c^2 x^2+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{\left(-c^2\right)^{3/2} e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}","\frac{2 \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{e^2}+\frac{2 d \left(a+b \text{csch}^{-1}(c x)\right)}{e^2 \sqrt{d+e x}}-\frac{8 b d \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{c e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}+\frac{4 b c \sqrt{c^2 x^2+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{\left(-c^2\right)^{3/2} e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}",1,"(2*d*(a + b*ArcCsch[c*x]))/(e^2*Sqrt[d + e*x]) + (2*Sqrt[d + e*x]*(a + b*ArcCsch[c*x]))/e^2 + (4*b*c*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/((-c^2)^(3/2)*e*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (8*b*d*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(c*e^2*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",11,11,19,0.5789,1,"{43, 6310, 12, 6721, 6742, 719, 419, 932, 168, 538, 537}"
66,1,149,0,0.2840506,"\int \frac{a+b \text{csch}^{-1}(c x)}{(d+e x)^{3/2}} \, dx","Int[(a + b*ArcCsch[c*x])/(d + e*x)^(3/2),x]","\frac{4 b \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{c e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{2 \left(a+b \text{csch}^{-1}(c x)\right)}{e \sqrt{d+e x}}","\frac{4 b \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{c e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{2 \left(a+b \text{csch}^{-1}(c x)\right)}{e \sqrt{d+e x}}",1,"(-2*(a + b*ArcCsch[c*x]))/(e*Sqrt[d + e*x]) + (4*b*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(c*e*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",6,6,18,0.3333,1,"{6290, 1574, 933, 168, 538, 537}"
67,0,0,0,0.0901345,"\int \frac{a+b \text{csch}^{-1}(c x)}{x (d+e x)^{3/2}} \, dx","Int[(a + b*ArcCsch[c*x])/(x*(d + e*x)^(3/2)),x]","\int \frac{a+b \text{csch}^{-1}(c x)}{x (d+e x)^{3/2}} \, dx","\text{Int}\left(\frac{a+b \text{csch}^{-1}(c x)}{x (d+e x)^{3/2}},x\right)",0,"Defer[Int][(a + b*ArcCsch[c*x])/(x*(d + e*x)^(3/2)), x]","A",0,0,0,0,-1,"{}"
68,0,0,0,0.0989249,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^2 (d+e x)^{3/2}} \, dx","Int[(a + b*ArcCsch[c*x])/(x^2*(d + e*x)^(3/2)),x]","\int \frac{a+b \text{csch}^{-1}(c x)}{x^2 (d+e x)^{3/2}} \, dx","\text{Int}\left(\frac{a+b \text{csch}^{-1}(c x)}{x^2 (d+e x)^{3/2}},x\right)",0,"Defer[Int][(a + b*ArcCsch[c*x])/(x^2*(d + e*x)^(3/2)), x]","A",0,0,0,0,-1,"{}"
69,1,777,0,3.1855405,"\int \frac{x^3 \left(a+b \text{csch}^{-1}(c x)\right)}{(d+e x)^{5/2}} \, dx","Int[(x^3*(a + b*ArcCsch[c*x]))/(d + e*x)^(5/2),x]","\frac{2 d^3 \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^4 (d+e x)^{3/2}}-\frac{6 d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{e^4 \sqrt{d+e x}}-\frac{6 d \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{e^4}+\frac{2 (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^4}+\frac{4 b d^2 \left(c^2 x^2+1\right)}{3 c e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{d+e x}}-\frac{8 b \sqrt{-c^2} d^2 \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 c e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}+\frac{4 b c \sqrt{c^2 x^2+1} \left(2 c^2 d^2+e^2\right) \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 \left(-c^2\right)^{3/2} e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}+\frac{64 b d^2 \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{3 c e^4 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{32 b c d \sqrt{c^2 x^2+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 \left(-c^2\right)^{3/2} e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}","\frac{2 d^3 \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^4 (d+e x)^{3/2}}-\frac{6 d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{e^4 \sqrt{d+e x}}-\frac{6 d \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{e^4}+\frac{2 (d+e x)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^4}+\frac{4 b d^2 \left(c^2 x^2+1\right)}{3 c e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{d+e x}}-\frac{8 b \sqrt{-c^2} d^2 \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 c e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}+\frac{4 b c \sqrt{c^2 x^2+1} \left(2 c^2 d^2+e^2\right) \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 \left(-c^2\right)^{3/2} e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}+\frac{64 b d^2 \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{3 c e^4 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{32 b c d \sqrt{c^2 x^2+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 \left(-c^2\right)^{3/2} e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}",1,"(4*b*d^2*(1 + c^2*x^2))/(3*c*e^2*(c^2*d^2 + e^2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (2*d^3*(a + b*ArcCsch[c*x]))/(3*e^4*(d + e*x)^(3/2)) - (6*d^2*(a + b*ArcCsch[c*x]))/(e^4*Sqrt[d + e*x]) - (6*d*Sqrt[d + e*x]*(a + b*ArcCsch[c*x]))/e^4 + (2*(d + e*x)^(3/2)*(a + b*ArcCsch[c*x]))/(3*e^4) - (8*b*Sqrt[-c^2]*d^2*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(3*c*e^3*(c^2*d^2 + e^2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]) + (4*b*c*(2*c^2*d^2 + e^2)*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(3*(-c^2)^(3/2)*e^3*(c^2*d^2 + e^2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]) - (32*b*c*d*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(3*(-c^2)^(3/2)*e^3*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (64*b*d^2*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(3*c*e^4*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",31,18,21,0.8571,1,"{43, 6310, 12, 6721, 6742, 745, 21, 719, 424, 958, 932, 168, 538, 537, 835, 844, 419, 1651}"
70,1,569,0,2.4970492,"\int \frac{x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{(d+e x)^{5/2}} \, dx","Int[(x^2*(a + b*ArcCsch[c*x]))/(d + e*x)^(5/2),x]","-\frac{2 d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^3 (d+e x)^{3/2}}+\frac{4 d \left(a+b \text{csch}^{-1}(c x)\right)}{e^3 \sqrt{d+e x}}+\frac{2 \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{e^3}-\frac{4 b d \left(c^2 x^2+1\right)}{3 c e x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{d+e x}}+\frac{4 b \sqrt{-c^2} d \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 c e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}+\frac{4 b c \sqrt{c^2 x^2+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{\left(-c^2\right)^{3/2} e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{32 b d \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{3 c e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}","-\frac{2 d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^3 (d+e x)^{3/2}}+\frac{4 d \left(a+b \text{csch}^{-1}(c x)\right)}{e^3 \sqrt{d+e x}}+\frac{2 \sqrt{d+e x} \left(a+b \text{csch}^{-1}(c x)\right)}{e^3}-\frac{4 b d \left(c^2 x^2+1\right)}{3 c e x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{d+e x}}+\frac{4 b \sqrt{-c^2} d \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 c e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}+\frac{4 b c \sqrt{c^2 x^2+1} \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{\left(-c^2\right)^{3/2} e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}-\frac{32 b d \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{3 c e^3 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}",1,"(-4*b*d*(1 + c^2*x^2))/(3*c*e*(c^2*d^2 + e^2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (2*d^2*(a + b*ArcCsch[c*x]))/(3*e^3*(d + e*x)^(3/2)) + (4*d*(a + b*ArcCsch[c*x]))/(e^3*Sqrt[d + e*x]) + (2*Sqrt[d + e*x]*(a + b*ArcCsch[c*x]))/e^3 + (4*b*Sqrt[-c^2]*d*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(3*c*e^2*(c^2*d^2 + e^2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]) + (4*b*c*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/((-c^2)^(3/2)*e^2*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (32*b*d*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(3*c*e^3*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",25,17,21,0.8095,1,"{43, 6310, 12, 6721, 6742, 745, 21, 719, 424, 958, 932, 168, 538, 537, 835, 844, 419}"
71,1,393,0,2.1911855,"\int \frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{(d+e x)^{5/2}} \, dx","Int[(x*(a + b*ArcCsch[c*x]))/(d + e*x)^(5/2),x]","-\frac{2 \left(a+b \text{csch}^{-1}(c x)\right)}{e^2 \sqrt{d+e x}}+\frac{2 d \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^2 (d+e x)^{3/2}}+\frac{4 b \left(c^2 x^2+1\right)}{3 c x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{d+e x}}-\frac{4 b \sqrt{-c^2} \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 c e x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}+\frac{8 b \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{3 c e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}","-\frac{2 \left(a+b \text{csch}^{-1}(c x)\right)}{e^2 \sqrt{d+e x}}+\frac{2 d \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^2 (d+e x)^{3/2}}+\frac{4 b \left(c^2 x^2+1\right)}{3 c x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{d+e x}}-\frac{4 b \sqrt{-c^2} \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 c e x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{\frac{c^2 (d+e x)}{c^2 d-\sqrt{-c^2} e}}}+\frac{8 b \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{3 c e^2 x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}",1,"(4*b*(1 + c^2*x^2))/(3*c*(c^2*d^2 + e^2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (2*d*(a + b*ArcCsch[c*x]))/(3*e^2*(d + e*x)^(3/2)) - (2*(a + b*ArcCsch[c*x]))/(e^2*Sqrt[d + e*x]) - (4*b*Sqrt[-c^2]*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(3*c*e*(c^2*d^2 + e^2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(c^2*(d + e*x))/(c^2*d - Sqrt[-c^2]*e)]) + (8*b*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(3*c*e^2*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",19,14,19,0.7368,1,"{43, 6310, 12, 6721, 6742, 745, 21, 719, 424, 958, 932, 168, 538, 537}"
72,1,369,0,0.5666421,"\int \frac{a+b \text{csch}^{-1}(c x)}{(d+e x)^{5/2}} \, dx","Int[(a + b*ArcCsch[c*x])/(d + e*x)^(5/2),x]","-\frac{2 \left(a+b \text{csch}^{-1}(c x)\right)}{3 e (d+e x)^{3/2}}-\frac{4 b e \left(c^2 x^2+1\right)}{3 c d x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{d+e x}}+\frac{4 b \sqrt{-c^2} \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 c d x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}}}+\frac{4 b \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{3 c d e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}","-\frac{2 \left(a+b \text{csch}^{-1}(c x)\right)}{3 e (d+e x)^{3/2}}-\frac{4 b e \left(c^2 x^2+1\right)}{3 c d x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{d+e x}}+\frac{4 b \sqrt{-c^2} \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{3 c d x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}}}+\frac{4 b \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{3 c d e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}",1,"(-4*b*e*(1 + c^2*x^2))/(3*c*d*(c^2*d^2 + e^2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (2*(a + b*ArcCsch[c*x]))/(3*e*(d + e*x)^(3/2)) + (4*b*Sqrt[-c^2]*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(3*c*d*(c^2*d^2 + e^2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(d + e*x)/(d + e/Sqrt[-c^2])]) + (4*b*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(3*c*d*e*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",12,11,18,0.6111,1,"{6290, 1574, 958, 745, 21, 719, 424, 933, 168, 538, 537}"
73,0,0,0,0.0938044,"\int \frac{a+b \text{csch}^{-1}(c x)}{x (d+e x)^{5/2}} \, dx","Int[(a + b*ArcCsch[c*x])/(x*(d + e*x)^(5/2)),x]","\int \frac{a+b \text{csch}^{-1}(c x)}{x (d+e x)^{5/2}} \, dx","\text{Int}\left(\frac{a+b \text{csch}^{-1}(c x)}{x (d+e x)^{5/2}},x\right)",0,"Defer[Int][(a + b*ArcCsch[c*x])/(x*(d + e*x)^(5/2)), x]","A",0,0,0,0,-1,"{}"
74,0,0,0,0.1060081,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^2 (d+e x)^{5/2}} \, dx","Int[(a + b*ArcCsch[c*x])/(x^2*(d + e*x)^(5/2)),x]","\int \frac{a+b \text{csch}^{-1}(c x)}{x^2 (d+e x)^{5/2}} \, dx","\text{Int}\left(\frac{a+b \text{csch}^{-1}(c x)}{x^2 (d+e x)^{5/2}},x\right)",0,"Defer[Int][(a + b*ArcCsch[c*x])/(x^2*(d + e*x)^(5/2)), x]","A",0,0,0,0,-1,"{}"
75,1,785,0,1.0354385,"\int \frac{a+b \text{csch}^{-1}(c x)}{(d+e x)^{7/2}} \, dx","Int[(a + b*ArcCsch[c*x])/(d + e*x)^(7/2),x]","-\frac{2 \left(a+b \text{csch}^{-1}(c x)\right)}{5 e (d+e x)^{5/2}}-\frac{4 b e \left(c^2 x^2+1\right)}{5 c d^2 x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{d+e x}}-\frac{16 b c e \left(c^2 x^2+1\right)}{15 x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right)^2 \sqrt{d+e x}}-\frac{4 b e \left(c^2 x^2+1\right)}{15 c d x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) (d+e x)^{3/2}}-\frac{4 b \sqrt{-c^2} \sqrt{c^2 x^2+1} \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 c d x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{d+e x}}+\frac{4 b \sqrt{-c^2} \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{5 c d^2 x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}}}+\frac{16 b c \sqrt{-c^2} \sqrt{c^2 x^2+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right)^2 \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}}}+\frac{4 b \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{5 c d^2 e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}","-\frac{2 \left(a+b \text{csch}^{-1}(c x)\right)}{5 e (d+e x)^{5/2}}-\frac{4 b e \left(c^2 x^2+1\right)}{5 c d^2 x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{d+e x}}-\frac{16 b c e \left(c^2 x^2+1\right)}{15 x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right)^2 \sqrt{d+e x}}-\frac{4 b e \left(c^2 x^2+1\right)}{15 c d x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) (d+e x)^{3/2}}-\frac{4 b \sqrt{-c^2} \sqrt{c^2 x^2+1} \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-c^2} e}{c^2 d-\sqrt{-c^2} e}\right)}{15 c d x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right) \sqrt{d+e x}}-\frac{4 b c \sqrt{c^2 x^2+1} \left(7 c^2 d^2+3 e^2\right) \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 \sqrt{-c^2} e}{\sqrt{-c^2} e-c^2 d}\right)}{15 \sqrt{-c^2} d^2 x \sqrt{\frac{1}{c^2 x^2}+1} \left(c^2 d^2+e^2\right)^2 \sqrt{\frac{d+e x}{\frac{e}{\sqrt{-c^2}}+d}}}+\frac{4 b \sqrt{c^2 x^2+1} \sqrt{\frac{\sqrt{-c^2} (d+e x)}{\sqrt{-c^2} d+e}} \Pi \left(2;\sin ^{-1}\left(\frac{\sqrt{1-\sqrt{-c^2} x}}{\sqrt{2}}\right)|\frac{2 e}{\sqrt{-c^2} d+e}\right)}{5 c d^2 e x \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{d+e x}}",1,"(-4*b*e*(1 + c^2*x^2))/(15*c*d*(c^2*d^2 + e^2)*Sqrt[1 + 1/(c^2*x^2)]*x*(d + e*x)^(3/2)) - (16*b*c*e*(1 + c^2*x^2))/(15*(c^2*d^2 + e^2)^2*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (4*b*e*(1 + c^2*x^2))/(5*c*d^2*(c^2*d^2 + e^2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) - (2*(a + b*ArcCsch[c*x]))/(5*e*(d + e*x)^(5/2)) + (16*b*c*Sqrt[-c^2]*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(15*(c^2*d^2 + e^2)^2*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(d + e*x)/(d + e/Sqrt[-c^2])]) + (4*b*Sqrt[-c^2]*Sqrt[d + e*x]*Sqrt[1 + c^2*x^2]*EllipticE[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(5*c*d^2*(c^2*d^2 + e^2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[(d + e*x)/(d + e/Sqrt[-c^2])]) - (4*b*Sqrt[-c^2]*Sqrt[(d + e*x)/(d + e/Sqrt[-c^2])]*Sqrt[1 + c^2*x^2]*EllipticF[ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (-2*Sqrt[-c^2]*e)/(c^2*d - Sqrt[-c^2]*e)])/(15*c*d*(c^2*d^2 + e^2)*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x]) + (4*b*Sqrt[(Sqrt[-c^2]*(d + e*x))/(Sqrt[-c^2]*d + e)]*Sqrt[1 + c^2*x^2]*EllipticPi[2, ArcSin[Sqrt[1 - Sqrt[-c^2]*x]/Sqrt[2]], (2*e)/(Sqrt[-c^2]*d + e)])/(5*c*d^2*e*Sqrt[1 + 1/(c^2*x^2)]*x*Sqrt[d + e*x])","A",19,14,18,0.7778,1,"{6290, 1574, 958, 745, 835, 844, 719, 424, 419, 21, 933, 168, 538, 537}"
76,1,214,0,0.1320001,"\int x^4 \left(d+e x^2\right) \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^4*(d + e*x^2)*(a + b*ArcCsch[c*x]),x]","\frac{1}{5} d x^5 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{7} e x^7 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x^4 \sqrt{-c^2 x^2-1} \left(42 c^2 d-25 e\right)}{840 c^3 \sqrt{-c^2 x^2}}-\frac{b x^2 \sqrt{-c^2 x^2-1} \left(42 c^2 d-25 e\right)}{560 c^5 \sqrt{-c^2 x^2}}-\frac{b x \left(42 c^2 d-25 e\right) \tan ^{-1}\left(\frac{c x}{\sqrt{-c^2 x^2-1}}\right)}{560 c^6 \sqrt{-c^2 x^2}}+\frac{b e x^6 \sqrt{-c^2 x^2-1}}{42 c \sqrt{-c^2 x^2}}","\frac{1}{5} d x^5 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{7} e x^7 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x^4 \sqrt{-c^2 x^2-1} \left(42 c^2 d-25 e\right)}{840 c^3 \sqrt{-c^2 x^2}}-\frac{b x^2 \sqrt{-c^2 x^2-1} \left(42 c^2 d-25 e\right)}{560 c^5 \sqrt{-c^2 x^2}}-\frac{b x \left(42 c^2 d-25 e\right) \tan ^{-1}\left(\frac{c x}{\sqrt{-c^2 x^2-1}}\right)}{560 c^6 \sqrt{-c^2 x^2}}+\frac{b e x^6 \sqrt{-c^2 x^2-1}}{42 c \sqrt{-c^2 x^2}}",1,"-(b*(42*c^2*d - 25*e)*x^2*Sqrt[-1 - c^2*x^2])/(560*c^5*Sqrt[-(c^2*x^2)]) + (b*(42*c^2*d - 25*e)*x^4*Sqrt[-1 - c^2*x^2])/(840*c^3*Sqrt[-(c^2*x^2)]) + (b*e*x^6*Sqrt[-1 - c^2*x^2])/(42*c*Sqrt[-(c^2*x^2)]) + (d*x^5*(a + b*ArcCsch[c*x]))/5 + (e*x^7*(a + b*ArcCsch[c*x]))/7 - (b*(42*c^2*d - 25*e)*x*ArcTan[(c*x)/Sqrt[-1 - c^2*x^2]])/(560*c^6*Sqrt[-(c^2*x^2)])","A",7,7,19,0.3684,1,"{14, 6302, 12, 459, 321, 217, 203}"
77,1,167,0,0.1086772,"\int x^2 \left(d+e x^2\right) \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)*(a + b*ArcCsch[c*x]),x]","\frac{1}{3} d x^3 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{5} e x^5 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x^2 \sqrt{-c^2 x^2-1} \left(20 c^2 d-9 e\right)}{120 c^3 \sqrt{-c^2 x^2}}+\frac{b x \left(20 c^2 d-9 e\right) \tan ^{-1}\left(\frac{c x}{\sqrt{-c^2 x^2-1}}\right)}{120 c^4 \sqrt{-c^2 x^2}}+\frac{b e x^4 \sqrt{-c^2 x^2-1}}{20 c \sqrt{-c^2 x^2}}","\frac{1}{3} d x^3 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{5} e x^5 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x^2 \sqrt{-c^2 x^2-1} \left(20 c^2 d-9 e\right)}{120 c^3 \sqrt{-c^2 x^2}}+\frac{b x \left(20 c^2 d-9 e\right) \tan ^{-1}\left(\frac{c x}{\sqrt{-c^2 x^2-1}}\right)}{120 c^4 \sqrt{-c^2 x^2}}+\frac{b e x^4 \sqrt{-c^2 x^2-1}}{20 c \sqrt{-c^2 x^2}}",1,"(b*(20*c^2*d - 9*e)*x^2*Sqrt[-1 - c^2*x^2])/(120*c^3*Sqrt[-(c^2*x^2)]) + (b*e*x^4*Sqrt[-1 - c^2*x^2])/(20*c*Sqrt[-(c^2*x^2)]) + (d*x^3*(a + b*ArcCsch[c*x]))/3 + (e*x^5*(a + b*ArcCsch[c*x]))/5 + (b*(20*c^2*d - 9*e)*x*ArcTan[(c*x)/Sqrt[-1 - c^2*x^2]])/(120*c^4*Sqrt[-(c^2*x^2)])","A",6,7,19,0.3684,1,"{14, 6302, 12, 459, 321, 217, 203}"
78,1,115,0,0.0556023,"\int \left(d+e x^2\right) \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[(d + e*x^2)*(a + b*ArcCsch[c*x]),x]","d x \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{3} e x^3 \left(a+b \text{csch}^{-1}(c x)\right)-\frac{b x \left(6 c^2 d-e\right) \tan ^{-1}\left(\frac{c x}{\sqrt{-c^2 x^2-1}}\right)}{6 c^2 \sqrt{-c^2 x^2}}+\frac{b e x^2 \sqrt{-c^2 x^2-1}}{6 c \sqrt{-c^2 x^2}}","d x \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{3} e x^3 \left(a+b \text{csch}^{-1}(c x)\right)-\frac{b x \left(6 c^2 d-e\right) \tan ^{-1}\left(\frac{c x}{\sqrt{-c^2 x^2-1}}\right)}{6 c^2 \sqrt{-c^2 x^2}}+\frac{b e x^2 \sqrt{-c^2 x^2-1}}{6 c \sqrt{-c^2 x^2}}",1,"(b*e*x^2*Sqrt[-1 - c^2*x^2])/(6*c*Sqrt[-(c^2*x^2)]) + d*x*(a + b*ArcCsch[c*x]) + (e*x^3*(a + b*ArcCsch[c*x]))/3 - (b*(6*c^2*d - e)*x*ArcTan[(c*x)/Sqrt[-1 - c^2*x^2]])/(6*c^2*Sqrt[-(c^2*x^2)])","A",5,5,16,0.3125,1,"{6292, 12, 388, 217, 203}"
79,1,91,0,0.0676791,"\int \frac{\left(d+e x^2\right) \left(a+b \text{csch}^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)*(a + b*ArcCsch[c*x]))/x^2,x]","-\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{x}+e x \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b c d \sqrt{-c^2 x^2-1}}{\sqrt{-c^2 x^2}}-\frac{b e x \tan ^{-1}\left(\frac{c x}{\sqrt{-c^2 x^2-1}}\right)}{\sqrt{-c^2 x^2}}","-\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{x}+e x \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b c d \sqrt{-c^2 x^2-1}}{\sqrt{-c^2 x^2}}-\frac{b e x \tan ^{-1}\left(\frac{c x}{\sqrt{-c^2 x^2-1}}\right)}{\sqrt{-c^2 x^2}}",1,"(b*c*d*Sqrt[-1 - c^2*x^2])/Sqrt[-(c^2*x^2)] - (d*(a + b*ArcCsch[c*x]))/x + e*x*(a + b*ArcCsch[c*x]) - (b*e*x*ArcTan[(c*x)/Sqrt[-1 - c^2*x^2]])/Sqrt[-(c^2*x^2)]","A",4,5,19,0.2632,1,"{14, 6302, 451, 217, 203}"
80,1,109,0,0.079277,"\int \frac{\left(d+e x^2\right) \left(a+b \text{csch}^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)*(a + b*ArcCsch[c*x]))/x^4,x]","-\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{3 x^3}-\frac{e \left(a+b \text{csch}^{-1}(c x)\right)}{x}-\frac{b c \sqrt{-c^2 x^2-1} \left(2 c^2 d-9 e\right)}{9 \sqrt{-c^2 x^2}}+\frac{b c d \sqrt{-c^2 x^2-1}}{9 x^2 \sqrt{-c^2 x^2}}","-\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{3 x^3}-\frac{e \left(a+b \text{csch}^{-1}(c x)\right)}{x}-\frac{b c \sqrt{-c^2 x^2-1} \left(2 c^2 d-9 e\right)}{9 \sqrt{-c^2 x^2}}+\frac{b c d \sqrt{-c^2 x^2-1}}{9 x^2 \sqrt{-c^2 x^2}}",1,"-(b*c*(2*c^2*d - 9*e)*Sqrt[-1 - c^2*x^2])/(9*Sqrt[-(c^2*x^2)]) + (b*c*d*Sqrt[-1 - c^2*x^2])/(9*x^2*Sqrt[-(c^2*x^2)]) - (d*(a + b*ArcCsch[c*x]))/(3*x^3) - (e*(a + b*ArcCsch[c*x]))/x","A",4,5,19,0.2632,1,"{14, 6302, 12, 453, 264}"
81,1,158,0,0.1025678,"\int \frac{\left(d+e x^2\right) \left(a+b \text{csch}^{-1}(c x)\right)}{x^6} \, dx","Int[((d + e*x^2)*(a + b*ArcCsch[c*x]))/x^6,x]","-\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{5 x^5}-\frac{e \left(a+b \text{csch}^{-1}(c x)\right)}{3 x^3}+\frac{2 b c^3 \sqrt{-c^2 x^2-1} \left(12 c^2 d-25 e\right)}{225 \sqrt{-c^2 x^2}}-\frac{b c \sqrt{-c^2 x^2-1} \left(12 c^2 d-25 e\right)}{225 x^2 \sqrt{-c^2 x^2}}+\frac{b c d \sqrt{-c^2 x^2-1}}{25 x^4 \sqrt{-c^2 x^2}}","-\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{5 x^5}-\frac{e \left(a+b \text{csch}^{-1}(c x)\right)}{3 x^3}+\frac{2 b c^3 \sqrt{-c^2 x^2-1} \left(12 c^2 d-25 e\right)}{225 \sqrt{-c^2 x^2}}-\frac{b c \sqrt{-c^2 x^2-1} \left(12 c^2 d-25 e\right)}{225 x^2 \sqrt{-c^2 x^2}}+\frac{b c d \sqrt{-c^2 x^2-1}}{25 x^4 \sqrt{-c^2 x^2}}",1,"(2*b*c^3*(12*c^2*d - 25*e)*Sqrt[-1 - c^2*x^2])/(225*Sqrt[-(c^2*x^2)]) + (b*c*d*Sqrt[-1 - c^2*x^2])/(25*x^4*Sqrt[-(c^2*x^2)]) - (b*c*(12*c^2*d - 25*e)*Sqrt[-1 - c^2*x^2])/(225*x^2*Sqrt[-(c^2*x^2)]) - (d*(a + b*ArcCsch[c*x]))/(5*x^5) - (e*(a + b*ArcCsch[c*x]))/(3*x^3)","A",5,6,19,0.3158,1,"{14, 6302, 12, 453, 271, 264}"
82,1,205,0,0.1219165,"\int \frac{\left(d+e x^2\right) \left(a+b \text{csch}^{-1}(c x)\right)}{x^8} \, dx","Int[((d + e*x^2)*(a + b*ArcCsch[c*x]))/x^8,x]","-\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{7 x^7}-\frac{e \left(a+b \text{csch}^{-1}(c x)\right)}{5 x^5}-\frac{8 b c^5 \sqrt{-c^2 x^2-1} \left(30 c^2 d-49 e\right)}{3675 \sqrt{-c^2 x^2}}+\frac{4 b c^3 \sqrt{-c^2 x^2-1} \left(30 c^2 d-49 e\right)}{3675 x^2 \sqrt{-c^2 x^2}}-\frac{b c \sqrt{-c^2 x^2-1} \left(30 c^2 d-49 e\right)}{1225 x^4 \sqrt{-c^2 x^2}}+\frac{b c d \sqrt{-c^2 x^2-1}}{49 x^6 \sqrt{-c^2 x^2}}","-\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{7 x^7}-\frac{e \left(a+b \text{csch}^{-1}(c x)\right)}{5 x^5}-\frac{8 b c^5 \sqrt{-c^2 x^2-1} \left(30 c^2 d-49 e\right)}{3675 \sqrt{-c^2 x^2}}+\frac{4 b c^3 \sqrt{-c^2 x^2-1} \left(30 c^2 d-49 e\right)}{3675 x^2 \sqrt{-c^2 x^2}}-\frac{b c \sqrt{-c^2 x^2-1} \left(30 c^2 d-49 e\right)}{1225 x^4 \sqrt{-c^2 x^2}}+\frac{b c d \sqrt{-c^2 x^2-1}}{49 x^6 \sqrt{-c^2 x^2}}",1,"(-8*b*c^5*(30*c^2*d - 49*e)*Sqrt[-1 - c^2*x^2])/(3675*Sqrt[-(c^2*x^2)]) + (b*c*d*Sqrt[-1 - c^2*x^2])/(49*x^6*Sqrt[-(c^2*x^2)]) - (b*c*(30*c^2*d - 49*e)*Sqrt[-1 - c^2*x^2])/(1225*x^4*Sqrt[-(c^2*x^2)]) + (4*b*c^3*(30*c^2*d - 49*e)*Sqrt[-1 - c^2*x^2])/(3675*x^2*Sqrt[-(c^2*x^2)]) - (d*(a + b*ArcCsch[c*x]))/(7*x^7) - (e*(a + b*ArcCsch[c*x]))/(5*x^5)","A",6,6,19,0.3158,1,"{14, 6302, 12, 453, 271, 264}"
83,1,204,0,0.1612999,"\int x^5 \left(d+e x^2\right) \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^5*(d + e*x^2)*(a + b*ArcCsch[c*x]),x]","\frac{1}{6} d x^6 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{8} e x^8 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x \left(-c^2 x^2-1\right)^{5/2} \left(4 c^2 d-9 e\right)}{120 c^7 \sqrt{-c^2 x^2}}+\frac{b x \left(-c^2 x^2-1\right)^{3/2} \left(8 c^2 d-9 e\right)}{72 c^7 \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(4 c^2 d-3 e\right)}{24 c^7 \sqrt{-c^2 x^2}}-\frac{b e x \left(-c^2 x^2-1\right)^{7/2}}{56 c^7 \sqrt{-c^2 x^2}}","\frac{1}{6} d x^6 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{8} e x^8 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x \left(-c^2 x^2-1\right)^{5/2} \left(4 c^2 d-9 e\right)}{120 c^7 \sqrt{-c^2 x^2}}+\frac{b x \left(-c^2 x^2-1\right)^{3/2} \left(8 c^2 d-9 e\right)}{72 c^7 \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(4 c^2 d-3 e\right)}{24 c^7 \sqrt{-c^2 x^2}}-\frac{b e x \left(-c^2 x^2-1\right)^{7/2}}{56 c^7 \sqrt{-c^2 x^2}}",1,"(b*(4*c^2*d - 3*e)*x*Sqrt[-1 - c^2*x^2])/(24*c^7*Sqrt[-(c^2*x^2)]) + (b*(8*c^2*d - 9*e)*x*(-1 - c^2*x^2)^(3/2))/(72*c^7*Sqrt[-(c^2*x^2)]) + (b*(4*c^2*d - 9*e)*x*(-1 - c^2*x^2)^(5/2))/(120*c^7*Sqrt[-(c^2*x^2)]) - (b*e*x*(-1 - c^2*x^2)^(7/2))/(56*c^7*Sqrt[-(c^2*x^2)]) + (d*x^6*(a + b*ArcCsch[c*x]))/6 + (e*x^8*(a + b*ArcCsch[c*x]))/8","A",5,5,19,0.2632,1,"{14, 6302, 12, 446, 77}"
84,1,159,0,0.1339104,"\int x^3 \left(d+e x^2\right) \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)*(a + b*ArcCsch[c*x]),x]","\frac{1}{4} d x^4 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{6} e x^6 \left(a+b \text{csch}^{-1}(c x)\right)-\frac{b x \left(-c^2 x^2-1\right)^{3/2} \left(3 c^2 d-4 e\right)}{36 c^5 \sqrt{-c^2 x^2}}-\frac{b x \sqrt{-c^2 x^2-1} \left(3 c^2 d-2 e\right)}{12 c^5 \sqrt{-c^2 x^2}}+\frac{b e x \left(-c^2 x^2-1\right)^{5/2}}{30 c^5 \sqrt{-c^2 x^2}}","\frac{1}{4} d x^4 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{6} e x^6 \left(a+b \text{csch}^{-1}(c x)\right)-\frac{b x \left(-c^2 x^2-1\right)^{3/2} \left(3 c^2 d-4 e\right)}{36 c^5 \sqrt{-c^2 x^2}}-\frac{b x \sqrt{-c^2 x^2-1} \left(3 c^2 d-2 e\right)}{12 c^5 \sqrt{-c^2 x^2}}+\frac{b e x \left(-c^2 x^2-1\right)^{5/2}}{30 c^5 \sqrt{-c^2 x^2}}",1,"-(b*(3*c^2*d - 2*e)*x*Sqrt[-1 - c^2*x^2])/(12*c^5*Sqrt[-(c^2*x^2)]) - (b*(3*c^2*d - 4*e)*x*(-1 - c^2*x^2)^(3/2))/(36*c^5*Sqrt[-(c^2*x^2)]) + (b*e*x*(-1 - c^2*x^2)^(5/2))/(30*c^5*Sqrt[-(c^2*x^2)]) + (d*x^4*(a + b*ArcCsch[c*x]))/4 + (e*x^6*(a + b*ArcCsch[c*x]))/6","A",5,5,19,0.2632,1,"{14, 6302, 12, 446, 77}"
85,1,146,0,0.1057491,"\int x \left(d+e x^2\right) \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)*(a + b*ArcCsch[c*x]),x]","\frac{\left(d+e x^2\right)^2 \left(a+b \text{csch}^{-1}(c x)\right)}{4 e}-\frac{b c d^2 x \tan ^{-1}\left(\sqrt{-c^2 x^2-1}\right)}{4 e \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(2 c^2 d-e\right)}{4 c^3 \sqrt{-c^2 x^2}}-\frac{b e x \left(-c^2 x^2-1\right)^{3/2}}{12 c^3 \sqrt{-c^2 x^2}}","\frac{\left(d+e x^2\right)^2 \left(a+b \text{csch}^{-1}(c x)\right)}{4 e}-\frac{b c d^2 x \tan ^{-1}\left(\sqrt{-c^2 x^2-1}\right)}{4 e \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(2 c^2 d-e\right)}{4 c^3 \sqrt{-c^2 x^2}}-\frac{b e x \left(-c^2 x^2-1\right)^{3/2}}{12 c^3 \sqrt{-c^2 x^2}}",1,"(b*(2*c^2*d - e)*x*Sqrt[-1 - c^2*x^2])/(4*c^3*Sqrt[-(c^2*x^2)]) - (b*e*x*(-1 - c^2*x^2)^(3/2))/(12*c^3*Sqrt[-(c^2*x^2)]) + ((d + e*x^2)^2*(a + b*ArcCsch[c*x]))/(4*e) - (b*c*d^2*x*ArcTan[Sqrt[-1 - c^2*x^2]])/(4*e*Sqrt[-(c^2*x^2)])","A",6,5,17,0.2941,1,"{6300, 446, 88, 63, 205}"
86,1,115,0,0.2909175,"\int \frac{\left(d+e x^2\right) \left(a+b \text{csch}^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)*(a + b*ArcCsch[c*x]))/x,x]","-\frac{1}{2} b d \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)-d \log \left(\frac{1}{x}\right) \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{2} e x^2 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b e x \sqrt{\frac{1}{c^2 x^2}+1}}{2 c}+\frac{1}{2} b d \text{csch}^{-1}(c x)^2-b d \text{csch}^{-1}(c x) \log \left(1-e^{2 \text{csch}^{-1}(c x)}\right)+b d \log \left(\frac{1}{x}\right) \text{csch}^{-1}(c x)","-\frac{1}{2} b d \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)-d \log \left(\frac{1}{x}\right) \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{2} e x^2 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b e x \sqrt{\frac{1}{c^2 x^2}+1}}{2 c}+\frac{1}{2} b d \text{csch}^{-1}(c x)^2-b d \text{csch}^{-1}(c x) \log \left(1-e^{2 \text{csch}^{-1}(c x)}\right)+b d \log \left(\frac{1}{x}\right) \text{csch}^{-1}(c x)",1,"(b*e*Sqrt[1 + 1/(c^2*x^2)]*x)/(2*c) + (b*d*ArcCsch[c*x]^2)/2 + (e*x^2*(a + b*ArcCsch[c*x]))/2 - b*d*ArcCsch[c*x]*Log[1 - E^(2*ArcCsch[c*x])] + b*d*ArcCsch[c*x]*Log[x^(-1)] - d*(a + b*ArcCsch[c*x])*Log[x^(-1)] - (b*d*PolyLog[2, E^(2*ArcCsch[c*x])])/2","A",11,11,19,0.5789,1,"{6304, 14, 5789, 6742, 264, 2325, 5659, 3716, 2190, 2279, 2391}"
87,1,128,0,0.299569,"\int \frac{\left(d+e x^2\right) \left(a+b \text{csch}^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)*(a + b*ArcCsch[c*x]))/x^3,x]","-\frac{1}{2} b e \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)-\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{2 x^2}-e \log \left(\frac{1}{x}\right) \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b c d \sqrt{\frac{1}{c^2 x^2}+1}}{4 x}-\frac{1}{4} b c^2 d \text{csch}^{-1}(c x)+\frac{1}{2} b e \text{csch}^{-1}(c x)^2-b e \text{csch}^{-1}(c x) \log \left(1-e^{2 \text{csch}^{-1}(c x)}\right)+b e \log \left(\frac{1}{x}\right) \text{csch}^{-1}(c x)","-\frac{1}{2} b e \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)-\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{2 x^2}-e \log \left(\frac{1}{x}\right) \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b c d \sqrt{\frac{1}{c^2 x^2}+1}}{4 x}-\frac{1}{4} b c^2 d \text{csch}^{-1}(c x)+\frac{1}{2} b e \text{csch}^{-1}(c x)^2-b e \text{csch}^{-1}(c x) \log \left(1-e^{2 \text{csch}^{-1}(c x)}\right)+b e \log \left(\frac{1}{x}\right) \text{csch}^{-1}(c x)",1,"(b*c*d*Sqrt[1 + 1/(c^2*x^2)])/(4*x) - (b*c^2*d*ArcCsch[c*x])/4 + (b*e*ArcCsch[c*x]^2)/2 - (d*(a + b*ArcCsch[c*x]))/(2*x^2) - b*e*ArcCsch[c*x]*Log[1 - E^(2*ArcCsch[c*x])] + b*e*ArcCsch[c*x]*Log[x^(-1)] - e*(a + b*ArcCsch[c*x])*Log[x^(-1)] - (b*e*PolyLog[2, E^(2*ArcCsch[c*x])])/2","A",13,13,19,0.6842,1,"{6304, 14, 5789, 12, 6742, 321, 215, 2325, 5659, 3716, 2190, 2279, 2391}"
88,1,260,0,0.2581295,"\int x^2 \left(d+e x^2\right)^2 \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)^2*(a + b*ArcCsch[c*x]),x]","\frac{1}{3} d^2 x^3 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{2}{5} d e x^5 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{7} e^2 x^7 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x^2 \sqrt{-c^2 x^2-1} \left(280 c^4 d^2-252 c^2 d e+75 e^2\right)}{1680 c^5 \sqrt{-c^2 x^2}}+\frac{b x \left(280 c^4 d^2-252 c^2 d e+75 e^2\right) \tan ^{-1}\left(\frac{c x}{\sqrt{-c^2 x^2-1}}\right)}{1680 c^6 \sqrt{-c^2 x^2}}+\frac{b e x^4 \sqrt{-c^2 x^2-1} \left(84 c^2 d-25 e\right)}{840 c^3 \sqrt{-c^2 x^2}}+\frac{b e^2 x^6 \sqrt{-c^2 x^2-1}}{42 c \sqrt{-c^2 x^2}}","\frac{1}{3} d^2 x^3 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{2}{5} d e x^5 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{7} e^2 x^7 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b x^2 \sqrt{-c^2 x^2-1} \left(280 c^4 d^2-252 c^2 d e+75 e^2\right)}{1680 c^5 \sqrt{-c^2 x^2}}+\frac{b x \left(280 c^4 d^2-252 c^2 d e+75 e^2\right) \tan ^{-1}\left(\frac{c x}{\sqrt{-c^2 x^2-1}}\right)}{1680 c^6 \sqrt{-c^2 x^2}}+\frac{b e x^4 \sqrt{-c^2 x^2-1} \left(84 c^2 d-25 e\right)}{840 c^3 \sqrt{-c^2 x^2}}+\frac{b e^2 x^6 \sqrt{-c^2 x^2-1}}{42 c \sqrt{-c^2 x^2}}",1,"(b*(280*c^4*d^2 - 252*c^2*d*e + 75*e^2)*x^2*Sqrt[-1 - c^2*x^2])/(1680*c^5*Sqrt[-(c^2*x^2)]) + (b*(84*c^2*d - 25*e)*e*x^4*Sqrt[-1 - c^2*x^2])/(840*c^3*Sqrt[-(c^2*x^2)]) + (b*e^2*x^6*Sqrt[-1 - c^2*x^2])/(42*c*Sqrt[-(c^2*x^2)]) + (d^2*x^3*(a + b*ArcCsch[c*x]))/3 + (2*d*e*x^5*(a + b*ArcCsch[c*x]))/5 + (e^2*x^7*(a + b*ArcCsch[c*x]))/7 + (b*(280*c^4*d^2 - 252*c^2*d*e + 75*e^2)*x*ArcTan[(c*x)/Sqrt[-1 - c^2*x^2]])/(1680*c^6*Sqrt[-(c^2*x^2)])","A",7,8,21,0.3810,1,"{270, 6302, 12, 1267, 459, 321, 217, 203}"
89,1,197,0,0.1284024,"\int \left(d+e x^2\right)^2 \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^2*(a + b*ArcCsch[c*x]),x]","d^2 x \left(a+b \text{csch}^{-1}(c x)\right)+\frac{2}{3} d e x^3 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{5} e^2 x^5 \left(a+b \text{csch}^{-1}(c x)\right)-\frac{b x \left(120 c^4 d^2-40 c^2 d e+9 e^2\right) \tan ^{-1}\left(\frac{c x}{\sqrt{-c^2 x^2-1}}\right)}{120 c^4 \sqrt{-c^2 x^2}}+\frac{b e x^2 \sqrt{-c^2 x^2-1} \left(40 c^2 d-9 e\right)}{120 c^3 \sqrt{-c^2 x^2}}+\frac{b e^2 x^4 \sqrt{-c^2 x^2-1}}{20 c \sqrt{-c^2 x^2}}","d^2 x \left(a+b \text{csch}^{-1}(c x)\right)+\frac{2}{3} d e x^3 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{5} e^2 x^5 \left(a+b \text{csch}^{-1}(c x)\right)-\frac{b x \left(120 c^4 d^2-40 c^2 d e+9 e^2\right) \tan ^{-1}\left(\frac{c x}{\sqrt{-c^2 x^2-1}}\right)}{120 c^4 \sqrt{-c^2 x^2}}+\frac{b e x^2 \sqrt{-c^2 x^2-1} \left(40 c^2 d-9 e\right)}{120 c^3 \sqrt{-c^2 x^2}}+\frac{b e^2 x^4 \sqrt{-c^2 x^2-1}}{20 c \sqrt{-c^2 x^2}}",1,"(b*(40*c^2*d - 9*e)*e*x^2*Sqrt[-1 - c^2*x^2])/(120*c^3*Sqrt[-(c^2*x^2)]) + (b*e^2*x^4*Sqrt[-1 - c^2*x^2])/(20*c*Sqrt[-(c^2*x^2)]) + d^2*x*(a + b*ArcCsch[c*x]) + (2*d*e*x^3*(a + b*ArcCsch[c*x]))/3 + (e^2*x^5*(a + b*ArcCsch[c*x]))/5 - (b*(120*c^4*d^2 - 40*c^2*d*e + 9*e^2)*x*ArcTan[(c*x)/Sqrt[-1 - c^2*x^2]])/(120*c^4*Sqrt[-(c^2*x^2)])","A",6,7,18,0.3889,1,"{194, 6292, 12, 1159, 388, 217, 203}"
90,1,170,0,0.1387686,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \text{csch}^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)^2*(a + b*ArcCsch[c*x]))/x^2,x]","-\frac{d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{x}+2 d e x \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{3} e^2 x^3 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b c d^2 \sqrt{-c^2 x^2-1}}{\sqrt{-c^2 x^2}}-\frac{b e x \left(12 c^2 d-e\right) \tan ^{-1}\left(\frac{c x}{\sqrt{-c^2 x^2-1}}\right)}{6 c^2 \sqrt{-c^2 x^2}}+\frac{b e^2 x^2 \sqrt{-c^2 x^2-1}}{6 c \sqrt{-c^2 x^2}}","-\frac{d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{x}+2 d e x \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{3} e^2 x^3 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b c d^2 \sqrt{-c^2 x^2-1}}{\sqrt{-c^2 x^2}}-\frac{b e x \left(12 c^2 d-e\right) \tan ^{-1}\left(\frac{c x}{\sqrt{-c^2 x^2-1}}\right)}{6 c^2 \sqrt{-c^2 x^2}}+\frac{b e^2 x^2 \sqrt{-c^2 x^2-1}}{6 c \sqrt{-c^2 x^2}}",1,"(b*c*d^2*Sqrt[-1 - c^2*x^2])/Sqrt[-(c^2*x^2)] + (b*e^2*x^2*Sqrt[-1 - c^2*x^2])/(6*c*Sqrt[-(c^2*x^2)]) - (d^2*(a + b*ArcCsch[c*x]))/x + 2*d*e*x*(a + b*ArcCsch[c*x]) + (e^2*x^3*(a + b*ArcCsch[c*x]))/3 - (b*(12*c^2*d - e)*e*x*ArcTan[(c*x)/Sqrt[-1 - c^2*x^2]])/(6*c^2*Sqrt[-(c^2*x^2)])","A",6,7,21,0.3333,1,"{270, 6302, 12, 1265, 388, 217, 203}"
91,1,164,0,0.142695,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \text{csch}^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)^2*(a + b*ArcCsch[c*x]))/x^4,x]","-\frac{d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{3 x^3}-\frac{2 d e \left(a+b \text{csch}^{-1}(c x)\right)}{x}+e^2 x \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b c d^2 \sqrt{-c^2 x^2-1}}{9 x^2 \sqrt{-c^2 x^2}}-\frac{2 b c d \sqrt{-c^2 x^2-1} \left(c^2 d-9 e\right)}{9 \sqrt{-c^2 x^2}}-\frac{b e^2 x \tan ^{-1}\left(\frac{c x}{\sqrt{-c^2 x^2-1}}\right)}{\sqrt{-c^2 x^2}}","-\frac{d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{3 x^3}-\frac{2 d e \left(a+b \text{csch}^{-1}(c x)\right)}{x}+e^2 x \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b c d^2 \sqrt{-c^2 x^2-1}}{9 x^2 \sqrt{-c^2 x^2}}-\frac{2 b c d \sqrt{-c^2 x^2-1} \left(c^2 d-9 e\right)}{9 \sqrt{-c^2 x^2}}-\frac{b e^2 x \tan ^{-1}\left(\frac{c x}{\sqrt{-c^2 x^2-1}}\right)}{\sqrt{-c^2 x^2}}",1,"(-2*b*c*d*(c^2*d - 9*e)*Sqrt[-1 - c^2*x^2])/(9*Sqrt[-(c^2*x^2)]) + (b*c*d^2*Sqrt[-1 - c^2*x^2])/(9*x^2*Sqrt[-(c^2*x^2)]) - (d^2*(a + b*ArcCsch[c*x]))/(3*x^3) - (2*d*e*(a + b*ArcCsch[c*x]))/x + e^2*x*(a + b*ArcCsch[c*x]) - (b*e^2*x*ArcTan[(c*x)/Sqrt[-1 - c^2*x^2]])/Sqrt[-(c^2*x^2)]","A",6,7,21,0.3333,1,"{270, 6302, 12, 1265, 451, 217, 203}"
92,1,189,0,0.1597923,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \text{csch}^{-1}(c x)\right)}{x^6} \, dx","Int[((d + e*x^2)^2*(a + b*ArcCsch[c*x]))/x^6,x]","-\frac{d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{5 x^5}-\frac{2 d e \left(a+b \text{csch}^{-1}(c x)\right)}{3 x^3}-\frac{e^2 \left(a+b \text{csch}^{-1}(c x)\right)}{x}+\frac{b c \sqrt{-c^2 x^2-1} \left(24 c^4 d^2-100 c^2 d e+225 e^2\right)}{225 \sqrt{-c^2 x^2}}+\frac{b c d^2 \sqrt{-c^2 x^2-1}}{25 x^4 \sqrt{-c^2 x^2}}-\frac{2 b c d \sqrt{-c^2 x^2-1} \left(6 c^2 d-25 e\right)}{225 x^2 \sqrt{-c^2 x^2}}","-\frac{d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{5 x^5}-\frac{2 d e \left(a+b \text{csch}^{-1}(c x)\right)}{3 x^3}-\frac{e^2 \left(a+b \text{csch}^{-1}(c x)\right)}{x}+\frac{b c \sqrt{-c^2 x^2-1} \left(24 c^4 d^2-100 c^2 d e+225 e^2\right)}{225 \sqrt{-c^2 x^2}}+\frac{b c d^2 \sqrt{-c^2 x^2-1}}{25 x^4 \sqrt{-c^2 x^2}}-\frac{2 b c d \sqrt{-c^2 x^2-1} \left(6 c^2 d-25 e\right)}{225 x^2 \sqrt{-c^2 x^2}}",1,"(b*c*(24*c^4*d^2 - 100*c^2*d*e + 225*e^2)*Sqrt[-1 - c^2*x^2])/(225*Sqrt[-(c^2*x^2)]) + (b*c*d^2*Sqrt[-1 - c^2*x^2])/(25*x^4*Sqrt[-(c^2*x^2)]) - (2*b*c*d*(6*c^2*d - 25*e)*Sqrt[-1 - c^2*x^2])/(225*x^2*Sqrt[-(c^2*x^2)]) - (d^2*(a + b*ArcCsch[c*x]))/(5*x^5) - (2*d*e*(a + b*ArcCsch[c*x]))/(3*x^3) - (e^2*(a + b*ArcCsch[c*x]))/x","A",5,6,21,0.2857,1,"{270, 6302, 12, 1265, 453, 264}"
93,1,249,0,0.1966138,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \text{csch}^{-1}(c x)\right)}{x^8} \, dx","Int[((d + e*x^2)^2*(a + b*ArcCsch[c*x]))/x^8,x]","-\frac{d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{7 x^7}-\frac{2 d e \left(a+b \text{csch}^{-1}(c x)\right)}{5 x^5}-\frac{e^2 \left(a+b \text{csch}^{-1}(c x)\right)}{3 x^3}-\frac{2 b c^3 \sqrt{-c^2 x^2-1} \left(360 c^4 d^2-1176 c^2 d e+1225 e^2\right)}{11025 \sqrt{-c^2 x^2}}+\frac{b c \sqrt{-c^2 x^2-1} \left(360 c^4 d^2-1176 c^2 d e+1225 e^2\right)}{11025 x^2 \sqrt{-c^2 x^2}}+\frac{b c d^2 \sqrt{-c^2 x^2-1}}{49 x^6 \sqrt{-c^2 x^2}}-\frac{2 b c d \sqrt{-c^2 x^2-1} \left(15 c^2 d-49 e\right)}{1225 x^4 \sqrt{-c^2 x^2}}","-\frac{d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{7 x^7}-\frac{2 d e \left(a+b \text{csch}^{-1}(c x)\right)}{5 x^5}-\frac{e^2 \left(a+b \text{csch}^{-1}(c x)\right)}{3 x^3}-\frac{2 b c^3 \sqrt{-c^2 x^2-1} \left(360 c^4 d^2-1176 c^2 d e+1225 e^2\right)}{11025 \sqrt{-c^2 x^2}}+\frac{b c \sqrt{-c^2 x^2-1} \left(360 c^4 d^2-1176 c^2 d e+1225 e^2\right)}{11025 x^2 \sqrt{-c^2 x^2}}+\frac{b c d^2 \sqrt{-c^2 x^2-1}}{49 x^6 \sqrt{-c^2 x^2}}-\frac{2 b c d \sqrt{-c^2 x^2-1} \left(15 c^2 d-49 e\right)}{1225 x^4 \sqrt{-c^2 x^2}}",1,"(-2*b*c^3*(360*c^4*d^2 - 1176*c^2*d*e + 1225*e^2)*Sqrt[-1 - c^2*x^2])/(11025*Sqrt[-(c^2*x^2)]) + (b*c*d^2*Sqrt[-1 - c^2*x^2])/(49*x^6*Sqrt[-(c^2*x^2)]) - (2*b*c*d*(15*c^2*d - 49*e)*Sqrt[-1 - c^2*x^2])/(1225*x^4*Sqrt[-(c^2*x^2)]) + (b*c*(360*c^4*d^2 - 1176*c^2*d*e + 1225*e^2)*Sqrt[-1 - c^2*x^2])/(11025*x^2*Sqrt[-(c^2*x^2)]) - (d^2*(a + b*ArcCsch[c*x]))/(7*x^7) - (2*d*e*(a + b*ArcCsch[c*x]))/(5*x^5) - (e^2*(a + b*ArcCsch[c*x]))/(3*x^3)","A",6,7,21,0.3333,1,"{270, 6302, 12, 1265, 453, 271, 264}"
94,1,250,0,0.2346567,"\int x^3 \left(d+e x^2\right)^2 \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)^2*(a + b*ArcCsch[c*x]),x]","\frac{1}{4} d^2 x^4 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{3} d e x^6 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{8} e^2 x^8 \left(a+b \text{csch}^{-1}(c x)\right)-\frac{b x \left(-c^2 x^2-1\right)^{3/2} \left(6 c^4 d^2-16 c^2 d e+9 e^2\right)}{72 c^7 \sqrt{-c^2 x^2}}-\frac{b x \sqrt{-c^2 x^2-1} \left(6 c^4 d^2-8 c^2 d e+3 e^2\right)}{24 c^7 \sqrt{-c^2 x^2}}+\frac{b e x \left(-c^2 x^2-1\right)^{5/2} \left(8 c^2 d-9 e\right)}{120 c^7 \sqrt{-c^2 x^2}}-\frac{b e^2 x \left(-c^2 x^2-1\right)^{7/2}}{56 c^7 \sqrt{-c^2 x^2}}","\frac{1}{4} d^2 x^4 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{3} d e x^6 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{8} e^2 x^8 \left(a+b \text{csch}^{-1}(c x)\right)-\frac{b x \left(-c^2 x^2-1\right)^{3/2} \left(6 c^4 d^2-16 c^2 d e+9 e^2\right)}{72 c^7 \sqrt{-c^2 x^2}}-\frac{b x \sqrt{-c^2 x^2-1} \left(6 c^4 d^2-8 c^2 d e+3 e^2\right)}{24 c^7 \sqrt{-c^2 x^2}}+\frac{b e x \left(-c^2 x^2-1\right)^{5/2} \left(8 c^2 d-9 e\right)}{120 c^7 \sqrt{-c^2 x^2}}-\frac{b e^2 x \left(-c^2 x^2-1\right)^{7/2}}{56 c^7 \sqrt{-c^2 x^2}}",1,"-(b*(6*c^4*d^2 - 8*c^2*d*e + 3*e^2)*x*Sqrt[-1 - c^2*x^2])/(24*c^7*Sqrt[-(c^2*x^2)]) - (b*(6*c^4*d^2 - 16*c^2*d*e + 9*e^2)*x*(-1 - c^2*x^2)^(3/2))/(72*c^7*Sqrt[-(c^2*x^2)]) + (b*(8*c^2*d - 9*e)*e*x*(-1 - c^2*x^2)^(5/2))/(120*c^7*Sqrt[-(c^2*x^2)]) - (b*e^2*x*(-1 - c^2*x^2)^(7/2))/(56*c^7*Sqrt[-(c^2*x^2)]) + (d^2*x^4*(a + b*ArcCsch[c*x]))/4 + (d*e*x^6*(a + b*ArcCsch[c*x]))/3 + (e^2*x^8*(a + b*ArcCsch[c*x]))/8","A",5,6,21,0.2857,1,"{266, 43, 6302, 12, 1251, 771}"
95,1,203,0,0.1559749,"\int x \left(d+e x^2\right)^2 \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)^2*(a + b*ArcCsch[c*x]),x]","\frac{\left(d+e x^2\right)^3 \left(a+b \text{csch}^{-1}(c x)\right)}{6 e}+\frac{b x \sqrt{-c^2 x^2-1} \left(3 c^4 d^2-3 c^2 d e+e^2\right)}{6 c^5 \sqrt{-c^2 x^2}}-\frac{b c d^3 x \tan ^{-1}\left(\sqrt{-c^2 x^2-1}\right)}{6 e \sqrt{-c^2 x^2}}-\frac{b e x \left(-c^2 x^2-1\right)^{3/2} \left(3 c^2 d-2 e\right)}{18 c^5 \sqrt{-c^2 x^2}}+\frac{b e^2 x \left(-c^2 x^2-1\right)^{5/2}}{30 c^5 \sqrt{-c^2 x^2}}","\frac{\left(d+e x^2\right)^3 \left(a+b \text{csch}^{-1}(c x)\right)}{6 e}+\frac{b x \sqrt{-c^2 x^2-1} \left(3 c^4 d^2-3 c^2 d e+e^2\right)}{6 c^5 \sqrt{-c^2 x^2}}-\frac{b c d^3 x \tan ^{-1}\left(\sqrt{-c^2 x^2-1}\right)}{6 e \sqrt{-c^2 x^2}}-\frac{b e x \left(-c^2 x^2-1\right)^{3/2} \left(3 c^2 d-2 e\right)}{18 c^5 \sqrt{-c^2 x^2}}+\frac{b e^2 x \left(-c^2 x^2-1\right)^{5/2}}{30 c^5 \sqrt{-c^2 x^2}}",1,"(b*(3*c^4*d^2 - 3*c^2*d*e + e^2)*x*Sqrt[-1 - c^2*x^2])/(6*c^5*Sqrt[-(c^2*x^2)]) - (b*(3*c^2*d - 2*e)*e*x*(-1 - c^2*x^2)^(3/2))/(18*c^5*Sqrt[-(c^2*x^2)]) + (b*e^2*x*(-1 - c^2*x^2)^(5/2))/(30*c^5*Sqrt[-(c^2*x^2)]) + ((d + e*x^2)^3*(a + b*ArcCsch[c*x]))/(6*e) - (b*c*d^3*x*ArcTan[Sqrt[-1 - c^2*x^2]])/(6*e*Sqrt[-(c^2*x^2)])","A",6,5,19,0.2632,1,"{6300, 446, 88, 63, 205}"
96,1,178,0,0.4214487,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \text{csch}^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)^2*(a + b*ArcCsch[c*x]))/x,x]","-\frac{1}{2} b d^2 \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)-d^2 \log \left(\frac{1}{x}\right) \left(a+b \text{csch}^{-1}(c x)\right)+d e x^2 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{4} e^2 x^4 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b e x \sqrt{\frac{1}{c^2 x^2}+1} \left(6 c^2 d-e\right)}{6 c^3}+\frac{b e^2 x^3 \sqrt{\frac{1}{c^2 x^2}+1}}{12 c}+\frac{1}{2} b d^2 \text{csch}^{-1}(c x)^2-b d^2 \text{csch}^{-1}(c x) \log \left(1-e^{2 \text{csch}^{-1}(c x)}\right)+b d^2 \log \left(\frac{1}{x}\right) \text{csch}^{-1}(c x)","-\frac{1}{2} b d^2 \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)-d^2 \log \left(\frac{1}{x}\right) \left(a+b \text{csch}^{-1}(c x)\right)+d e x^2 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{4} e^2 x^4 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b e x \sqrt{\frac{1}{c^2 x^2}+1} \left(6 c^2 d-e\right)}{6 c^3}+\frac{b e^2 x^3 \sqrt{\frac{1}{c^2 x^2}+1}}{12 c}+\frac{1}{2} b d^2 \text{csch}^{-1}(c x)^2-b d^2 \text{csch}^{-1}(c x) \log \left(1-e^{2 \text{csch}^{-1}(c x)}\right)+b d^2 \log \left(\frac{1}{x}\right) \text{csch}^{-1}(c x)",1,"(b*(6*c^2*d - e)*e*Sqrt[1 + 1/(c^2*x^2)]*x)/(6*c^3) + (b*e^2*Sqrt[1 + 1/(c^2*x^2)]*x^3)/(12*c) + (b*d^2*ArcCsch[c*x]^2)/2 + d*e*x^2*(a + b*ArcCsch[c*x]) + (e^2*x^4*(a + b*ArcCsch[c*x]))/4 - b*d^2*ArcCsch[c*x]*Log[1 - E^(2*ArcCsch[c*x])] + b*d^2*ArcCsch[c*x]*Log[x^(-1)] - d^2*(a + b*ArcCsch[c*x])*Log[x^(-1)] - (b*d^2*PolyLog[2, E^(2*ArcCsch[c*x])])/2","A",12,13,21,0.6190,1,"{6304, 266, 43, 5789, 6742, 453, 264, 2325, 5659, 3716, 2190, 2279, 2391}"
97,1,178,0,0.4244223,"\int \frac{\left(d+e x^2\right)^2 \left(a+b \text{csch}^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)^2*(a + b*ArcCsch[c*x]))/x^3,x]","-b d e \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)-\frac{d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{2 x^2}-2 d e \log \left(\frac{1}{x}\right) \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{2} e^2 x^2 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b c d^2 \sqrt{\frac{1}{c^2 x^2}+1}}{4 x}-\frac{1}{4} b c^2 d^2 \text{csch}^{-1}(c x)+\frac{b e^2 x \sqrt{\frac{1}{c^2 x^2}+1}}{2 c}+b d e \text{csch}^{-1}(c x)^2-2 b d e \text{csch}^{-1}(c x) \log \left(1-e^{2 \text{csch}^{-1}(c x)}\right)+2 b d e \log \left(\frac{1}{x}\right) \text{csch}^{-1}(c x)","-b d e \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)-\frac{d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{2 x^2}-2 d e \log \left(\frac{1}{x}\right) \left(a+b \text{csch}^{-1}(c x)\right)+\frac{1}{2} e^2 x^2 \left(a+b \text{csch}^{-1}(c x)\right)+\frac{b c d^2 \sqrt{\frac{1}{c^2 x^2}+1}}{4 x}-\frac{1}{4} b c^2 d^2 \text{csch}^{-1}(c x)+\frac{b e^2 x \sqrt{\frac{1}{c^2 x^2}+1}}{2 c}+b d e \text{csch}^{-1}(c x)^2-2 b d e \text{csch}^{-1}(c x) \log \left(1-e^{2 \text{csch}^{-1}(c x)}\right)+2 b d e \log \left(\frac{1}{x}\right) \text{csch}^{-1}(c x)",1,"(b*c*d^2*Sqrt[1 + 1/(c^2*x^2)])/(4*x) + (b*e^2*Sqrt[1 + 1/(c^2*x^2)]*x)/(2*c) - (b*c^2*d^2*ArcCsch[c*x])/4 + b*d*e*ArcCsch[c*x]^2 - (d^2*(a + b*ArcCsch[c*x]))/(2*x^2) + (e^2*x^2*(a + b*ArcCsch[c*x]))/2 - 2*b*d*e*ArcCsch[c*x]*Log[1 - E^(2*ArcCsch[c*x])] + 2*b*d*e*ArcCsch[c*x]*Log[x^(-1)] - 2*d*e*(a + b*ArcCsch[c*x])*Log[x^(-1)] - b*d*e*PolyLog[2, E^(2*ArcCsch[c*x])]","A",14,15,21,0.7143,1,"{6304, 266, 43, 5789, 12, 6742, 264, 321, 215, 2325, 5659, 3716, 2190, 2279, 2391}"
98,1,512,0,1.1977938,"\int \frac{x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{d+e x^2} \, dx","Int[(x^2*(a + b*ArcCsch[c*x]))/(d + e*x^2),x]","-\frac{b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^{3/2}}+\frac{b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^{3/2}}-\frac{b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 e^{3/2}}+\frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{e}+\frac{b \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{c e}","-\frac{b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^{3/2}}+\frac{b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^{3/2}}-\frac{b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 e^{3/2}}+\frac{\sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^{3/2}}-\frac{\sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 e^{3/2}}+\frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{e}+\frac{b \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{c e}",1,"(x*(a + b*ArcCsch[c*x]))/e + (b*ArcTanh[Sqrt[1 + 1/(c^2*x^2)]])/(c*e) + (Sqrt[-d]*(a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*e^(3/2)) - (Sqrt[-d]*(a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*e^(3/2)) + (Sqrt[-d]*(a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*e^(3/2)) - (Sqrt[-d]*(a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*e^(3/2)) - (b*Sqrt[-d]*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/(2*e^(3/2)) + (b*Sqrt[-d]*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*e^(3/2)) - (b*Sqrt[-d]*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/(2*e^(3/2)) + (b*Sqrt[-d]*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*e^(3/2))","A",25,12,21,0.5714,1,"{6304, 5791, 5661, 266, 63, 208, 5706, 5799, 5561, 2190, 2279, 2391}"
99,1,449,0,1.1058249,"\int \frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{d+e x^2} \, dx","Int[(x*(a + b*ArcCsch[c*x]))/(d + e*x^2),x]","\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e}-\frac{b \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)}{2 e}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 e}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 e}-\frac{\log \left(1-e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{e}","\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e}+\frac{b \text{PolyLog}\left(2,e^{-2 \text{csch}^{-1}(c x)}\right)}{2 e}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 e}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 e}-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{b e}-\frac{\log \left(1-e^{-2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{e}",1,"((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*e) + ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*e) + ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*e) + ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*e) - ((a + b*ArcCsch[c*x])*Log[1 - E^(2*ArcCsch[c*x])])/e + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/(2*e) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*e) + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/(2*e) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*e) - (b*PolyLog[2, E^(2*ArcCsch[c*x])])/(2*e)","A",26,9,19,0.4737,0,"{6304, 5791, 5659, 3716, 2190, 2279, 2391, 5799, 5561}"
100,1,477,0,0.8491007,"\int \frac{a+b \text{csch}^{-1}(c x)}{d+e x^2} \, dx","Int[(a + b*ArcCsch[c*x])/(d + e*x^2),x]","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 \sqrt{-d} \sqrt{e}}","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 \sqrt{-d} \sqrt{e}}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 \sqrt{-d} \sqrt{e}}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 \sqrt{-d} \sqrt{e}}",1,"((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*Sqrt[-d]*Sqrt[e]) + ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*Sqrt[-d]*Sqrt[e]) - ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*Sqrt[-d]*Sqrt[e]) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/(2*Sqrt[-d]*Sqrt[e]) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*Sqrt[-d]*Sqrt[e]) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/(2*Sqrt[-d]*Sqrt[e]) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*Sqrt[-d]*Sqrt[e])","A",19,7,18,0.3889,1,"{6294, 5706, 5799, 5561, 2190, 2279, 2391}"
101,1,425,0,0.8624677,"\int \frac{a+b \text{csch}^{-1}(c x)}{x \left(d+e x^2\right)} \, dx","Int[(a + b*ArcCsch[c*x])/(x*(d + e*x^2)),x]","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 d}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 d}+\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{2 b d}","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 d}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 d}+\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{2 b d}",1,"(a + b*ArcCsch[c*x])^2/(2*b*d) - ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*d) - ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*d) - ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*d) - ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*d) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/(2*d) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*d) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/(2*d) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*d)","A",19,7,21,0.3333,1,"{6304, 5791, 5799, 5561, 2190, 2279, 2391}"
102,1,518,0,1.0598392,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^2 \left(d+e x^2\right)} \, dx","Int[(a + b*ArcCsch[c*x])/(x^2*(d + e*x^2)),x]","-\frac{b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 (-d)^{3/2}}+\frac{b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 (-d)^{3/2}}-\frac{b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 (-d)^{3/2}}+\frac{b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 (-d)^{3/2}}-\frac{a}{d x}+\frac{b c \sqrt{\frac{1}{c^2 x^2}+1}}{d}-\frac{b \text{csch}^{-1}(c x)}{d x}","-\frac{b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 (-d)^{3/2}}+\frac{b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 (-d)^{3/2}}-\frac{b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 (-d)^{3/2}}+\frac{b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 (-d)^{3/2}}+\frac{\sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 (-d)^{3/2}}-\frac{\sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 (-d)^{3/2}}-\frac{a}{d x}+\frac{b c \sqrt{\frac{1}{c^2 x^2}+1}}{d}-\frac{b \text{csch}^{-1}(c x)}{d x}",1,"(b*c*Sqrt[1 + 1/(c^2*x^2)])/d - a/(d*x) - (b*ArcCsch[c*x])/(d*x) + (Sqrt[e]*(a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*(-d)^(3/2)) - (Sqrt[e]*(a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*(-d)^(3/2)) + (Sqrt[e]*(a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*(-d)^(3/2)) - (Sqrt[e]*(a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*(-d)^(3/2)) - (b*Sqrt[e]*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/(2*(-d)^(3/2)) + (b*Sqrt[e]*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*(-d)^(3/2)) - (b*Sqrt[e]*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/(2*(-d)^(3/2)) + (b*Sqrt[e]*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*(-d)^(3/2))","A",24,10,21,0.4762,1,"{6304, 5791, 5653, 261, 5706, 5799, 5561, 2190, 2279, 2391}"
103,1,571,0,1.2815482,"\int \frac{x^5 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^5*(a + b*ArcCsch[c*x]))/(d + e*x^2)^2,x]","-\frac{b d \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{e^3}-\frac{b d \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{e^3}-\frac{b d \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{e^3}-\frac{b d \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{e^3}+\frac{b d \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)}{e^3}-\frac{d \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{e^3}-\frac{d \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{e^3}-\frac{d \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{e^3}-\frac{d \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{e^3}+\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{2 e^2 \left(\frac{d}{x^2}+e\right)}+\frac{2 d \log \left(1-e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{e^3}+\frac{x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{2 e^2}-\frac{b d \tan ^{-1}\left(\frac{\sqrt{c^2 d-e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}+1}}\right)}{2 e^{5/2} \sqrt{c^2 d-e}}+\frac{b x \sqrt{\frac{1}{c^2 x^2}+1}}{2 c e^2}","-\frac{b d \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{e^3}-\frac{b d \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{e^3}-\frac{b d \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{e^3}-\frac{b d \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{e^3}-\frac{b d \text{PolyLog}\left(2,e^{-2 \text{csch}^{-1}(c x)}\right)}{e^3}-\frac{d \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{e^3}-\frac{d \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{e^3}-\frac{d \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{e^3}-\frac{d \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{e^3}+\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{2 e^2 \left(\frac{d}{x^2}+e\right)}+\frac{2 d \left(a+b \text{csch}^{-1}(c x)\right)^2}{b e^3}+\frac{2 d \log \left(1-e^{-2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{e^3}+\frac{x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{2 e^2}-\frac{b d \tan ^{-1}\left(\frac{\sqrt{c^2 d-e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}+1}}\right)}{2 e^{5/2} \sqrt{c^2 d-e}}+\frac{b x \sqrt{\frac{1}{c^2 x^2}+1}}{2 c e^2}",1,"(b*Sqrt[1 + 1/(c^2*x^2)]*x)/(2*c*e^2) + (d*(a + b*ArcCsch[c*x]))/(2*e^2*(e + d/x^2)) + (x^2*(a + b*ArcCsch[c*x]))/(2*e^2) - (b*d*ArcTan[Sqrt[c^2*d - e]/(c*Sqrt[e]*Sqrt[1 + 1/(c^2*x^2)]*x)])/(2*Sqrt[c^2*d - e]*e^(5/2)) - (d*(a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/e^3 - (d*(a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/e^3 - (d*(a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/e^3 - (d*(a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/e^3 + (2*d*(a + b*ArcCsch[c*x])*Log[1 - E^(2*ArcCsch[c*x])])/e^3 - (b*d*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/e^3 - (b*d*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/e^3 - (b*d*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/e^3 - (b*d*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/e^3 + (b*d*PolyLog[2, E^(2*ArcCsch[c*x])])/e^3","A",31,14,21,0.6667,0,"{6304, 5791, 5661, 264, 5659, 3716, 2190, 2279, 2391, 5787, 377, 205, 5799, 5561}"
104,1,535,0,1.2485392,"\int \frac{x^3 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^3*(a + b*ArcCsch[c*x]))/(d + e*x^2)^2,x]","\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^2}-\frac{b \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)}{2 e^2}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^2}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 e^2}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^2}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 e^2}-\frac{a+b \text{csch}^{-1}(c x)}{2 e \left(\frac{d}{x^2}+e\right)}-\frac{\log \left(1-e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{e^2}+\frac{b \tan ^{-1}\left(\frac{\sqrt{c^2 d-e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}+1}}\right)}{2 e^{3/2} \sqrt{c^2 d-e}}","\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^2}+\frac{b \text{PolyLog}\left(2,e^{-2 \text{csch}^{-1}(c x)}\right)}{2 e^2}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^2}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 e^2}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^2}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 e^2}-\frac{a+b \text{csch}^{-1}(c x)}{2 e \left(\frac{d}{x^2}+e\right)}-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{b e^2}-\frac{\log \left(1-e^{-2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{e^2}+\frac{b \tan ^{-1}\left(\frac{\sqrt{c^2 d-e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}+1}}\right)}{2 e^{3/2} \sqrt{c^2 d-e}}",1,"-(a + b*ArcCsch[c*x])/(2*e*(e + d/x^2)) + (b*ArcTan[Sqrt[c^2*d - e]/(c*Sqrt[e]*Sqrt[1 + 1/(c^2*x^2)]*x)])/(2*Sqrt[c^2*d - e]*e^(3/2)) + ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*e^2) + ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*e^2) + ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*e^2) + ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*e^2) - ((a + b*ArcCsch[c*x])*Log[1 - E^(2*ArcCsch[c*x])])/e^2 + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/(2*e^2) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*e^2) + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/(2*e^2) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*e^2) - (b*PolyLog[2, E^(2*ArcCsch[c*x])])/(2*e^2)","A",29,12,21,0.5714,0,"{6304, 5791, 5659, 3716, 2190, 2279, 2391, 5787, 377, 205, 5799, 5561}"
105,1,139,0,0.1502641,"\int \frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x*(a + b*ArcCsch[c*x]))/(d + e*x^2)^2,x]","-\frac{a+b \text{csch}^{-1}(c x)}{2 e \left(d+e x^2\right)}+\frac{b c x \tan ^{-1}\left(\sqrt{-c^2 x^2-1}\right)}{2 d e \sqrt{-c^2 x^2}}+\frac{b c x \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{\sqrt{c^2 d-e}}\right)}{2 d \sqrt{e} \sqrt{-c^2 x^2} \sqrt{c^2 d-e}}","-\frac{a+b \text{csch}^{-1}(c x)}{2 e \left(d+e x^2\right)}+\frac{b c x \tan ^{-1}\left(\sqrt{-c^2 x^2-1}\right)}{2 d e \sqrt{-c^2 x^2}}+\frac{b c x \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{\sqrt{c^2 d-e}}\right)}{2 d \sqrt{e} \sqrt{-c^2 x^2} \sqrt{c^2 d-e}}",1,"-(a + b*ArcCsch[c*x])/(2*e*(d + e*x^2)) + (b*c*x*ArcTan[Sqrt[-1 - c^2*x^2]])/(2*d*e*Sqrt[-(c^2*x^2)]) + (b*c*x*ArcTanh[(Sqrt[e]*Sqrt[-1 - c^2*x^2])/Sqrt[c^2*d - e]])/(2*d*Sqrt[c^2*d - e]*Sqrt[e]*Sqrt[-(c^2*x^2)])","A",7,6,19,0.3158,1,"{6300, 446, 86, 63, 205, 208}"
106,1,515,0,1.1530659,"\int \frac{a+b \text{csch}^{-1}(c x)}{x \left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcCsch[c*x])/(x*(d + e*x^2)^2),x]","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d^2}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d^2}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 d^2}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d^2}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 d^2}-\frac{e \left(a+b \text{csch}^{-1}(c x)\right)}{2 d^2 \left(\frac{d}{x^2}+e\right)}+\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{2 b d^2}+\frac{b \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{c^2 d-e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}+1}}\right)}{2 d^2 \sqrt{c^2 d-e}}","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d^2}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d^2}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d^2}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 d^2}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d^2}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 d^2}-\frac{e \left(a+b \text{csch}^{-1}(c x)\right)}{2 d^2 \left(\frac{d}{x^2}+e\right)}+\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{2 b d^2}+\frac{b \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{c^2 d-e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}+1}}\right)}{2 d^2 \sqrt{c^2 d-e}}",1,"-(e*(a + b*ArcCsch[c*x]))/(2*d^2*(e + d/x^2)) + (a + b*ArcCsch[c*x])^2/(2*b*d^2) + (b*Sqrt[e]*ArcTan[Sqrt[c^2*d - e]/(c*Sqrt[e]*Sqrt[1 + 1/(c^2*x^2)]*x)])/(2*d^2*Sqrt[c^2*d - e]) - ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*d^2) - ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*d^2) - ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*d^2) - ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*d^2) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/(2*d^2) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*d^2) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/(2*d^2) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*d^2)","A",24,10,21,0.4762,1,"{6304, 5791, 5787, 377, 205, 5799, 5561, 2190, 2279, 2391}"
107,1,756,0,2.4683718,"\int \frac{x^4 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^4*(a + b*ArcCsch[c*x]))/(d + e*x^2)^2,x]","-\frac{3 b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 e^{5/2}}+\frac{3 b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 e^{5/2}}-\frac{3 b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 e^{5/2}}+\frac{3 b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{4 e^{5/2}}-\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{4 e^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{4 e^2 \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}+\frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{e^2}+\frac{b \sqrt{d} \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d-e}}\right)}{4 e^2 \sqrt{c^2 d-e}}+\frac{b \sqrt{d} \tanh ^{-1}\left(\frac{c^2 d+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d-e}}\right)}{4 e^2 \sqrt{c^2 d-e}}+\frac{b \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{c e^2}","-\frac{3 b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 e^{5/2}}+\frac{3 b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 e^{5/2}}-\frac{3 b \sqrt{-d} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 e^{5/2}}+\frac{3 b \sqrt{-d} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{4 e^{5/2}}+\frac{3 \sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 e^{5/2}}-\frac{3 \sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{4 e^{5/2}}-\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{4 e^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{4 e^2 \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}+\frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{e^2}+\frac{b \sqrt{d} \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d-e}}\right)}{4 e^2 \sqrt{c^2 d-e}}+\frac{b \sqrt{d} \tanh ^{-1}\left(\frac{c^2 d+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d-e}}\right)}{4 e^2 \sqrt{c^2 d-e}}+\frac{b \tanh ^{-1}\left(\sqrt{\frac{1}{c^2 x^2}+1}\right)}{c e^2}",1,"-(d*(a + b*ArcCsch[c*x]))/(4*e^2*(Sqrt[-d]*Sqrt[e] - d/x)) + (d*(a + b*ArcCsch[c*x]))/(4*e^2*(Sqrt[-d]*Sqrt[e] + d/x)) + (x*(a + b*ArcCsch[c*x]))/e^2 + (b*ArcTanh[Sqrt[1 + 1/(c^2*x^2)]])/(c*e^2) + (b*Sqrt[d]*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(4*Sqrt[c^2*d - e]*e^2) + (b*Sqrt[d]*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(4*Sqrt[c^2*d - e]*e^2) + (3*Sqrt[-d]*(a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(4*e^(5/2)) - (3*Sqrt[-d]*(a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(4*e^(5/2)) + (3*Sqrt[-d]*(a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(4*e^(5/2)) - (3*Sqrt[-d]*(a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(4*e^(5/2)) - (3*b*Sqrt[-d]*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/(4*e^(5/2)) + (3*b*Sqrt[-d]*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(4*e^(5/2)) - (3*b*Sqrt[-d]*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/(4*e^(5/2)) + (3*b*Sqrt[-d]*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(4*e^(5/2))","A",51,15,21,0.7143,1,"{6304, 5791, 5661, 266, 63, 208, 5706, 5801, 725, 206, 5799, 5561, 2190, 2279, 2391}"
108,1,719,0,1.2417629,"\int \frac{x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[(x^2*(a + b*ArcCsch[c*x]))/(d + e*x^2)^2,x]","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{4 \sqrt{-d} e^{3/2}}+\frac{a+b \text{csch}^{-1}(c x)}{4 e \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{a+b \text{csch}^{-1}(c x)}{4 e \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}-\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d-e}}\right)}{4 \sqrt{d} e \sqrt{c^2 d-e}}-\frac{b \tanh ^{-1}\left(\frac{c^2 d+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d-e}}\right)}{4 \sqrt{d} e \sqrt{c^2 d-e}}","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{4 \sqrt{-d} e^{3/2}}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 \sqrt{-d} e^{3/2}}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{4 \sqrt{-d} e^{3/2}}+\frac{a+b \text{csch}^{-1}(c x)}{4 e \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{a+b \text{csch}^{-1}(c x)}{4 e \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}-\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d-e}}\right)}{4 \sqrt{d} e \sqrt{c^2 d-e}}-\frac{b \tanh ^{-1}\left(\frac{c^2 d+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d-e}}\right)}{4 \sqrt{d} e \sqrt{c^2 d-e}}",1,"(a + b*ArcCsch[c*x])/(4*e*(Sqrt[-d]*Sqrt[e] - d/x)) - (a + b*ArcCsch[c*x])/(4*e*(Sqrt[-d]*Sqrt[e] + d/x)) - (b*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(4*Sqrt[d]*Sqrt[c^2*d - e]*e) - (b*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(4*Sqrt[d]*Sqrt[c^2*d - e]*e) + ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(4*Sqrt[-d]*e^(3/2)) - ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(4*Sqrt[-d]*e^(3/2)) + ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(4*Sqrt[-d]*e^(3/2)) - ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(4*Sqrt[-d]*e^(3/2)) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/(4*Sqrt[-d]*e^(3/2)) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(4*Sqrt[-d]*e^(3/2)) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/(4*Sqrt[-d]*e^(3/2)) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(4*Sqrt[-d]*e^(3/2))","A",27,10,21,0.4762,1,"{6304, 5706, 5801, 725, 206, 5799, 5561, 2190, 2279, 2391}"
109,1,713,0,2.1873599,"\int \frac{a+b \text{csch}^{-1}(c x)}{\left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcCsch[c*x])/(d + e*x^2)^2,x]","\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{a+b \text{csch}^{-1}(c x)}{4 d \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{a+b \text{csch}^{-1}(c x)}{4 d \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}+\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d-e}}\right)}{4 d^{3/2} \sqrt{c^2 d-e}}+\frac{b \tanh ^{-1}\left(\frac{c^2 d+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d-e}}\right)}{4 d^{3/2} \sqrt{c^2 d-e}}","\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 (-d)^{3/2} \sqrt{e}}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{4 (-d)^{3/2} \sqrt{e}}-\frac{a+b \text{csch}^{-1}(c x)}{4 d \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{a+b \text{csch}^{-1}(c x)}{4 d \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}+\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d-e}}\right)}{4 d^{3/2} \sqrt{c^2 d-e}}+\frac{b \tanh ^{-1}\left(\frac{c^2 d+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d-e}}\right)}{4 d^{3/2} \sqrt{c^2 d-e}}",1,"-(a + b*ArcCsch[c*x])/(4*d*(Sqrt[-d]*Sqrt[e] - d/x)) + (a + b*ArcCsch[c*x])/(4*d*(Sqrt[-d]*Sqrt[e] + d/x)) + (b*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(4*d^(3/2)*Sqrt[c^2*d - e]) + (b*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(4*d^(3/2)*Sqrt[c^2*d - e]) - ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(4*(-d)^(3/2)*Sqrt[e]) + ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(4*(-d)^(3/2)*Sqrt[e]) - ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(4*(-d)^(3/2)*Sqrt[e]) + ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(4*(-d)^(3/2)*Sqrt[e]) + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/(4*(-d)^(3/2)*Sqrt[e]) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(4*(-d)^(3/2)*Sqrt[e]) + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/(4*(-d)^(3/2)*Sqrt[e]) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(4*(-d)^(3/2)*Sqrt[e])","A",47,11,18,0.6111,1,"{6294, 5791, 5706, 5801, 725, 206, 5799, 5561, 2190, 2279, 2391}"
110,1,758,0,2.2464205,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^2 \left(d+e x^2\right)^2} \, dx","Int[(a + b*ArcCsch[c*x])/(x^2*(d + e*x^2)^2),x]","\frac{3 b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{5/2}}-\frac{3 b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{5/2}}+\frac{3 b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 (-d)^{5/2}}-\frac{3 b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{4 (-d)^{5/2}}+\frac{e \left(a+b \text{csch}^{-1}(c x)\right)}{4 d^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{e \left(a+b \text{csch}^{-1}(c x)\right)}{4 d^2 \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}-\frac{a}{d^2 x}-\frac{b e \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d-e}}\right)}{4 d^{5/2} \sqrt{c^2 d-e}}-\frac{b e \tanh ^{-1}\left(\frac{c^2 d+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d-e}}\right)}{4 d^{5/2} \sqrt{c^2 d-e}}+\frac{b c \sqrt{\frac{1}{c^2 x^2}+1}}{d^2}-\frac{b \text{csch}^{-1}(c x)}{d^2 x}","\frac{3 b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{5/2}}-\frac{3 b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{5/2}}+\frac{3 b \sqrt{e} \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 (-d)^{5/2}}-\frac{3 b \sqrt{e} \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{4 (-d)^{5/2}}-\frac{3 \sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{4 (-d)^{5/2}}+\frac{3 \sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{4 (-d)^{5/2}}+\frac{e \left(a+b \text{csch}^{-1}(c x)\right)}{4 d^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{e \left(a+b \text{csch}^{-1}(c x)\right)}{4 d^2 \left(\sqrt{-d} \sqrt{e}+\frac{d}{x}\right)}-\frac{a}{d^2 x}-\frac{b e \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d-e}}\right)}{4 d^{5/2} \sqrt{c^2 d-e}}-\frac{b e \tanh ^{-1}\left(\frac{c^2 d+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{\frac{1}{c^2 x^2}+1} \sqrt{c^2 d-e}}\right)}{4 d^{5/2} \sqrt{c^2 d-e}}+\frac{b c \sqrt{\frac{1}{c^2 x^2}+1}}{d^2}-\frac{b \text{csch}^{-1}(c x)}{d^2 x}",1,"(b*c*Sqrt[1 + 1/(c^2*x^2)])/d^2 - a/(d^2*x) - (b*ArcCsch[c*x])/(d^2*x) + (e*(a + b*ArcCsch[c*x]))/(4*d^2*(Sqrt[-d]*Sqrt[e] - d/x)) - (e*(a + b*ArcCsch[c*x]))/(4*d^2*(Sqrt[-d]*Sqrt[e] + d/x)) - (b*e*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(4*d^(5/2)*Sqrt[c^2*d - e]) - (b*e*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(4*d^(5/2)*Sqrt[c^2*d - e]) - (3*Sqrt[e]*(a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(4*(-d)^(5/2)) + (3*Sqrt[e]*(a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(4*(-d)^(5/2)) - (3*Sqrt[e]*(a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(4*(-d)^(5/2)) + (3*Sqrt[e]*(a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(4*(-d)^(5/2)) + (3*b*Sqrt[e]*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/(4*(-d)^(5/2)) - (3*b*Sqrt[e]*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(4*(-d)^(5/2)) + (3*b*Sqrt[e]*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/(4*(-d)^(5/2)) - (3*b*Sqrt[e]*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(4*(-d)^(5/2))","A",50,13,21,0.6190,1,"{6304, 5791, 5653, 261, 5706, 5801, 725, 206, 5799, 5561, 2190, 2279, 2391}"
111,1,676,0,1.4082702,"\int \frac{x^5 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^5*(a + b*ArcCsch[c*x]))/(d + e*x^2)^3,x]","\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^3}-\frac{b \text{PolyLog}\left(2,e^{2 \text{csch}^{-1}(c x)}\right)}{2 e^3}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^3}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 e^3}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^3}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 e^3}-\frac{a+b \text{csch}^{-1}(c x)}{2 e^2 \left(\frac{d}{x^2}+e\right)}-\frac{a+b \text{csch}^{-1}(c x)}{4 e \left(\frac{d}{x^2}+e\right)^2}-\frac{\log \left(1-e^{2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{e^3}+\frac{b c d \sqrt{\frac{1}{c^2 x^2}+1}}{8 e^2 x \left(c^2 d-e\right) \left(\frac{d}{x^2}+e\right)}+\frac{b \tan ^{-1}\left(\frac{\sqrt{c^2 d-e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}+1}}\right)}{2 e^{5/2} \sqrt{c^2 d-e}}+\frac{b \left(c^2 d-2 e\right) \tan ^{-1}\left(\frac{\sqrt{c^2 d-e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}+1}}\right)}{8 e^{5/2} \left(c^2 d-e\right)^{3/2}}","\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^3}+\frac{b \text{PolyLog}\left(2,e^{-2 \text{csch}^{-1}(c x)}\right)}{2 e^3}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 e^3}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 e^3}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 e^3}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 e^3}-\frac{a+b \text{csch}^{-1}(c x)}{2 e^2 \left(\frac{d}{x^2}+e\right)}-\frac{a+b \text{csch}^{-1}(c x)}{4 e \left(\frac{d}{x^2}+e\right)^2}-\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{b e^3}-\frac{\log \left(1-e^{-2 \text{csch}^{-1}(c x)}\right) \left(a+b \text{csch}^{-1}(c x)\right)}{e^3}+\frac{b c d \sqrt{\frac{1}{c^2 x^2}+1}}{8 e^2 x \left(c^2 d-e\right) \left(\frac{d}{x^2}+e\right)}+\frac{b \tan ^{-1}\left(\frac{\sqrt{c^2 d-e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}+1}}\right)}{2 e^{5/2} \sqrt{c^2 d-e}}+\frac{b \left(c^2 d-2 e\right) \tan ^{-1}\left(\frac{\sqrt{c^2 d-e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}+1}}\right)}{8 e^{5/2} \left(c^2 d-e\right)^{3/2}}",1,"(b*c*d*Sqrt[1 + 1/(c^2*x^2)])/(8*(c^2*d - e)*e^2*(e + d/x^2)*x) - (a + b*ArcCsch[c*x])/(4*e*(e + d/x^2)^2) - (a + b*ArcCsch[c*x])/(2*e^2*(e + d/x^2)) + (b*(c^2*d - 2*e)*ArcTan[Sqrt[c^2*d - e]/(c*Sqrt[e]*Sqrt[1 + 1/(c^2*x^2)]*x)])/(8*(c^2*d - e)^(3/2)*e^(5/2)) + (b*ArcTan[Sqrt[c^2*d - e]/(c*Sqrt[e]*Sqrt[1 + 1/(c^2*x^2)]*x)])/(2*Sqrt[c^2*d - e]*e^(5/2)) + ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*e^3) + ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*e^3) + ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*e^3) + ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*e^3) - ((a + b*ArcCsch[c*x])*Log[1 - E^(2*ArcCsch[c*x])])/e^3 + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/(2*e^3) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*e^3) + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/(2*e^3) + (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*e^3) - (b*PolyLog[2, E^(2*ArcCsch[c*x])])/(2*e^3)","A",33,13,21,0.6190,0,"{6304, 5791, 5659, 3716, 2190, 2279, 2391, 5787, 382, 377, 205, 5799, 5561}"
112,1,167,0,0.2154717,"\int \frac{x^3 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^3*(a + b*ArcCsch[c*x]))/(d + e*x^2)^3,x]","\frac{x^4 \left(a+b \text{csch}^{-1}(c x)\right)}{4 d \left(d+e x^2\right)^2}+\frac{b c x \left(c^2 d-2 e\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{\sqrt{c^2 d-e}}\right)}{8 d e^{3/2} \sqrt{-c^2 x^2} \left(c^2 d-e\right)^{3/2}}-\frac{b c x \sqrt{-c^2 x^2-1}}{8 e \sqrt{-c^2 x^2} \left(c^2 d-e\right) \left(d+e x^2\right)}","\frac{x^4 \left(a+b \text{csch}^{-1}(c x)\right)}{4 d \left(d+e x^2\right)^2}+\frac{b c x \left(c^2 d-2 e\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{\sqrt{c^2 d-e}}\right)}{8 d e^{3/2} \sqrt{-c^2 x^2} \left(c^2 d-e\right)^{3/2}}-\frac{b c x \sqrt{-c^2 x^2-1}}{8 e \sqrt{-c^2 x^2} \left(c^2 d-e\right) \left(d+e x^2\right)}",1,"-(b*c*x*Sqrt[-1 - c^2*x^2])/(8*(c^2*d - e)*e*Sqrt[-(c^2*x^2)]*(d + e*x^2)) + (x^4*(a + b*ArcCsch[c*x]))/(4*d*(d + e*x^2)^2) + (b*c*(c^2*d - 2*e)*x*ArcTanh[(Sqrt[e]*Sqrt[-1 - c^2*x^2])/Sqrt[c^2*d - e]])/(8*d*(c^2*d - e)^(3/2)*e^(3/2)*Sqrt[-(c^2*x^2)])","A",6,7,21,0.3333,1,"{264, 6302, 12, 446, 78, 63, 208}"
113,1,205,0,0.2047168,"\int \frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x*(a + b*ArcCsch[c*x]))/(d + e*x^2)^3,x]","-\frac{a+b \text{csch}^{-1}(c x)}{4 e \left(d+e x^2\right)^2}+\frac{b c x \tan ^{-1}\left(\sqrt{-c^2 x^2-1}\right)}{4 d^2 e \sqrt{-c^2 x^2}}+\frac{b c x \left(3 c^2 d-2 e\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{\sqrt{c^2 d-e}}\right)}{8 d^2 \sqrt{e} \sqrt{-c^2 x^2} \left(c^2 d-e\right)^{3/2}}+\frac{b c x \sqrt{-c^2 x^2-1}}{8 d \sqrt{-c^2 x^2} \left(c^2 d-e\right) \left(d+e x^2\right)}","-\frac{a+b \text{csch}^{-1}(c x)}{4 e \left(d+e x^2\right)^2}+\frac{b c x \tan ^{-1}\left(\sqrt{-c^2 x^2-1}\right)}{4 d^2 e \sqrt{-c^2 x^2}}+\frac{b c x \left(3 c^2 d-2 e\right) \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{\sqrt{c^2 d-e}}\right)}{8 d^2 \sqrt{e} \sqrt{-c^2 x^2} \left(c^2 d-e\right)^{3/2}}+\frac{b c x \sqrt{-c^2 x^2-1}}{8 d \sqrt{-c^2 x^2} \left(c^2 d-e\right) \left(d+e x^2\right)}",1,"(b*c*x*Sqrt[-1 - c^2*x^2])/(8*d*(c^2*d - e)*Sqrt[-(c^2*x^2)]*(d + e*x^2)) - (a + b*ArcCsch[c*x])/(4*e*(d + e*x^2)^2) + (b*c*x*ArcTan[Sqrt[-1 - c^2*x^2]])/(4*d^2*e*Sqrt[-(c^2*x^2)]) + (b*c*(3*c^2*d - 2*e)*x*ArcTanh[(Sqrt[e]*Sqrt[-1 - c^2*x^2])/Sqrt[c^2*d - e]])/(8*d^2*(c^2*d - e)^(3/2)*Sqrt[e]*Sqrt[-(c^2*x^2)])","A",8,7,19,0.3684,1,"{6300, 446, 103, 156, 63, 205, 208}"
114,1,657,0,1.3221364,"\int \frac{a+b \text{csch}^{-1}(c x)}{x \left(d+e x^2\right)^3} \, dx","Int[(a + b*ArcCsch[c*x])/(x*(d + e*x^2)^3),x]","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d^3}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d^3}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 d^3}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d^3}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 d^3}+\frac{e^2 \left(a+b \text{csch}^{-1}(c x)\right)}{4 d^3 \left(\frac{d}{x^2}+e\right)^2}-\frac{e \left(a+b \text{csch}^{-1}(c x)\right)}{d^3 \left(\frac{d}{x^2}+e\right)}+\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{2 b d^3}-\frac{b c e \sqrt{\frac{1}{c^2 x^2}+1}}{8 d^2 x \left(c^2 d-e\right) \left(\frac{d}{x^2}+e\right)}+\frac{b \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{c^2 d-e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}+1}}\right)}{d^3 \sqrt{c^2 d-e}}-\frac{b \sqrt{e} \left(c^2 d-2 e\right) \tan ^{-1}\left(\frac{\sqrt{c^2 d-e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}+1}}\right)}{8 d^3 \left(c^2 d-e\right)^{3/2}}","-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d^3}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d^3}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{2 d^3}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{2 d^3}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}\right)}{2 d^3}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e-c^2 d}+\sqrt{e}}+1\right)}{2 d^3}+\frac{e^2 \left(a+b \text{csch}^{-1}(c x)\right)}{4 d^3 \left(\frac{d}{x^2}+e\right)^2}-\frac{e \left(a+b \text{csch}^{-1}(c x)\right)}{d^3 \left(\frac{d}{x^2}+e\right)}+\frac{\left(a+b \text{csch}^{-1}(c x)\right)^2}{2 b d^3}-\frac{b c e \sqrt{\frac{1}{c^2 x^2}+1}}{8 d^2 x \left(c^2 d-e\right) \left(\frac{d}{x^2}+e\right)}+\frac{b \sqrt{e} \tan ^{-1}\left(\frac{\sqrt{c^2 d-e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}+1}}\right)}{d^3 \sqrt{c^2 d-e}}-\frac{b \sqrt{e} \left(c^2 d-2 e\right) \tan ^{-1}\left(\frac{\sqrt{c^2 d-e}}{c \sqrt{e} x \sqrt{\frac{1}{c^2 x^2}+1}}\right)}{8 d^3 \left(c^2 d-e\right)^{3/2}}",1,"-(b*c*e*Sqrt[1 + 1/(c^2*x^2)])/(8*d^2*(c^2*d - e)*(e + d/x^2)*x) + (e^2*(a + b*ArcCsch[c*x]))/(4*d^3*(e + d/x^2)^2) - (e*(a + b*ArcCsch[c*x]))/(d^3*(e + d/x^2)) + (a + b*ArcCsch[c*x])^2/(2*b*d^3) - (b*(c^2*d - 2*e)*Sqrt[e]*ArcTan[Sqrt[c^2*d - e]/(c*Sqrt[e]*Sqrt[1 + 1/(c^2*x^2)]*x)])/(8*d^3*(c^2*d - e)^(3/2)) + (b*Sqrt[e]*ArcTan[Sqrt[c^2*d - e]/(c*Sqrt[e]*Sqrt[1 + 1/(c^2*x^2)]*x)])/(d^3*Sqrt[c^2*d - e]) - ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*d^3) - ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*d^3) - ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*d^3) - ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*d^3) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/(2*d^3) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(2*d^3) - (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/(2*d^3) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(2*d^3)","A",28,11,21,0.5238,1,"{6304, 5791, 5787, 382, 377, 205, 5799, 5561, 2190, 2279, 2391}"
115,1,1106,0,1.7407568,"\int \frac{x^4 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^4*(a + b*ArcCsch[c*x]))/(d + e*x^2)^3,x]","-\frac{b \sqrt{-d} \sqrt{1+\frac{1}{c^2 x^2}} c}{16 \left(c^2 d-e\right) e^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{b \sqrt{-d} \sqrt{1+\frac{1}{c^2 x^2}} c}{16 \left(c^2 d-e\right) e^{3/2} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{3 \left(a+b \text{csch}^{-1}(c x)\right)}{16 e^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{3 \left(a+b \text{csch}^{-1}(c x)\right)}{16 e^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{\sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right)}{16 e^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{\sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right)}{16 e^{3/2} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}+\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 \sqrt{d} \left(c^2 d-e\right)^{3/2} e}-\frac{3 b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 \sqrt{d} \sqrt{c^2 d-e} e^2}+\frac{b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 \sqrt{d} \left(c^2 d-e\right)^{3/2} e}-\frac{3 b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 \sqrt{d} \sqrt{c^2 d-e} e^2}+\frac{3 \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{csch}^{-1}(c x)} c}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{csch}^{-1}(c x)} c}{\sqrt{e}+\sqrt{e-c^2 d}}+1\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 \sqrt{-d} e^{5/2}}","-\frac{b \sqrt{-d} \sqrt{1+\frac{1}{c^2 x^2}} c}{16 \left(c^2 d-e\right) e^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{b \sqrt{-d} \sqrt{1+\frac{1}{c^2 x^2}} c}{16 \left(c^2 d-e\right) e^{3/2} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{3 \left(a+b \text{csch}^{-1}(c x)\right)}{16 e^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{3 \left(a+b \text{csch}^{-1}(c x)\right)}{16 e^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{\sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right)}{16 e^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{\sqrt{-d} \left(a+b \text{csch}^{-1}(c x)\right)}{16 e^{3/2} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}+\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 \sqrt{d} \left(c^2 d-e\right)^{3/2} e}-\frac{3 b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 \sqrt{d} \sqrt{c^2 d-e} e^2}+\frac{b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 \sqrt{d} \left(c^2 d-e\right)^{3/2} e}-\frac{3 b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 \sqrt{d} \sqrt{c^2 d-e} e^2}+\frac{3 \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{csch}^{-1}(c x)} c}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{csch}^{-1}(c x)} c}{\sqrt{e}+\sqrt{e-c^2 d}}+1\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 \sqrt{-d} e^{5/2}}-\frac{3 b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 \sqrt{-d} e^{5/2}}+\frac{3 b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 \sqrt{-d} e^{5/2}}",1,"-(b*c*Sqrt[-d]*Sqrt[1 + 1/(c^2*x^2)])/(16*(c^2*d - e)*e^(3/2)*(Sqrt[-d]*Sqrt[e] - d/x)) - (b*c*Sqrt[-d]*Sqrt[1 + 1/(c^2*x^2)])/(16*(c^2*d - e)*e^(3/2)*(Sqrt[-d]*Sqrt[e] + d/x)) + (Sqrt[-d]*(a + b*ArcCsch[c*x]))/(16*e^(3/2)*(Sqrt[-d]*Sqrt[e] - d/x)^2) + (3*(a + b*ArcCsch[c*x]))/(16*e^2*(Sqrt[-d]*Sqrt[e] - d/x)) - (Sqrt[-d]*(a + b*ArcCsch[c*x]))/(16*e^(3/2)*(Sqrt[-d]*Sqrt[e] + d/x)^2) - (3*(a + b*ArcCsch[c*x]))/(16*e^2*(Sqrt[-d]*Sqrt[e] + d/x)) - (3*b*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(16*Sqrt[d]*Sqrt[c^2*d - e]*e^2) + (b*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(16*Sqrt[d]*(c^2*d - e)^(3/2)*e) - (3*b*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(16*Sqrt[d]*Sqrt[c^2*d - e]*e^2) + (b*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(16*Sqrt[d]*(c^2*d - e)^(3/2)*e) + (3*(a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(16*Sqrt[-d]*e^(5/2)) - (3*(a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(16*Sqrt[-d]*e^(5/2)) + (3*(a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(16*Sqrt[-d]*e^(5/2)) - (3*(a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(16*Sqrt[-d]*e^(5/2)) - (3*b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/(16*Sqrt[-d]*e^(5/2)) + (3*b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(16*Sqrt[-d]*e^(5/2)) - (3*b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/(16*Sqrt[-d]*e^(5/2)) + (3*b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(16*Sqrt[-d]*e^(5/2))","A",35,11,21,0.5238,1,"{6304, 5706, 5801, 731, 725, 206, 5799, 5561, 2190, 2279, 2391}"
116,1,1106,0,3.0461376,"\int \frac{x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^3} \, dx","Int[(x^2*(a + b*ArcCsch[c*x]))/(d + e*x^2)^3,x]","-\frac{b \sqrt{1+\frac{1}{c^2 x^2}} c}{16 \sqrt{-d} \left(c^2 d-e\right) \sqrt{e} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{b \sqrt{1+\frac{1}{c^2 x^2}} c}{16 \sqrt{-d} \left(c^2 d-e\right) \sqrt{e} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{a+b \text{csch}^{-1}(c x)}{16 d e \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{a+b \text{csch}^{-1}(c x)}{16 d e \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{a+b \text{csch}^{-1}(c x)}{16 \sqrt{-d} \sqrt{e} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{a+b \text{csch}^{-1}(c x)}{16 \sqrt{-d} \sqrt{e} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}-\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 d^{3/2} \sqrt{c^2 d-e} e}-\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 d^{3/2} \left(c^2 d-e\right)^{3/2}}-\frac{b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 d^{3/2} \sqrt{c^2 d-e} e}-\frac{b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 d^{3/2} \left(c^2 d-e\right)^{3/2}}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{csch}^{-1}(c x)} c}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{csch}^{-1}(c x)} c}{\sqrt{e}+\sqrt{e-c^2 d}}+1\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 (-d)^{3/2} e^{3/2}}","-\frac{b \sqrt{1+\frac{1}{c^2 x^2}} c}{16 \sqrt{-d} \left(c^2 d-e\right) \sqrt{e} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{b \sqrt{1+\frac{1}{c^2 x^2}} c}{16 \sqrt{-d} \left(c^2 d-e\right) \sqrt{e} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{a+b \text{csch}^{-1}(c x)}{16 d e \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{a+b \text{csch}^{-1}(c x)}{16 d e \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{a+b \text{csch}^{-1}(c x)}{16 \sqrt{-d} \sqrt{e} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{a+b \text{csch}^{-1}(c x)}{16 \sqrt{-d} \sqrt{e} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}-\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 d^{3/2} \sqrt{c^2 d-e} e}-\frac{b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 d^{3/2} \left(c^2 d-e\right)^{3/2}}-\frac{b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 d^{3/2} \sqrt{c^2 d-e} e}-\frac{b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 d^{3/2} \left(c^2 d-e\right)^{3/2}}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{csch}^{-1}(c x)} c}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{\left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{csch}^{-1}(c x)} c}{\sqrt{e}+\sqrt{e-c^2 d}}+1\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 (-d)^{3/2} e^{3/2}}+\frac{b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 (-d)^{3/2} e^{3/2}}-\frac{b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 (-d)^{3/2} e^{3/2}}",1,"-(b*c*Sqrt[1 + 1/(c^2*x^2)])/(16*Sqrt[-d]*(c^2*d - e)*Sqrt[e]*(Sqrt[-d]*Sqrt[e] - d/x)) - (b*c*Sqrt[1 + 1/(c^2*x^2)])/(16*Sqrt[-d]*(c^2*d - e)*Sqrt[e]*(Sqrt[-d]*Sqrt[e] + d/x)) + (a + b*ArcCsch[c*x])/(16*Sqrt[-d]*Sqrt[e]*(Sqrt[-d]*Sqrt[e] - d/x)^2) + (a + b*ArcCsch[c*x])/(16*d*e*(Sqrt[-d]*Sqrt[e] - d/x)) - (a + b*ArcCsch[c*x])/(16*Sqrt[-d]*Sqrt[e]*(Sqrt[-d]*Sqrt[e] + d/x)^2) - (a + b*ArcCsch[c*x])/(16*d*e*(Sqrt[-d]*Sqrt[e] + d/x)) - (b*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(16*d^(3/2)*(c^2*d - e)^(3/2)) - (b*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(16*d^(3/2)*Sqrt[c^2*d - e]*e) - (b*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(16*d^(3/2)*(c^2*d - e)^(3/2)) - (b*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(16*d^(3/2)*Sqrt[c^2*d - e]*e) - ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(16*(-d)^(3/2)*e^(3/2)) + ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(16*(-d)^(3/2)*e^(3/2)) - ((a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(16*(-d)^(3/2)*e^(3/2)) + ((a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(16*(-d)^(3/2)*e^(3/2)) + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/(16*(-d)^(3/2)*e^(3/2)) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(16*(-d)^(3/2)*e^(3/2)) + (b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/(16*(-d)^(3/2)*e^(3/2)) - (b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(16*(-d)^(3/2)*e^(3/2))","A",63,12,21,0.5714,1,"{6304, 5791, 5706, 5801, 731, 725, 206, 5799, 5561, 2190, 2279, 2391}"
117,1,1096,0,3.7426364,"\int \frac{a+b \text{csch}^{-1}(c x)}{\left(d+e x^2\right)^3} \, dx","Int[(a + b*ArcCsch[c*x])/(d + e*x^2)^3,x]","-\frac{b \sqrt{e} \sqrt{1+\frac{1}{c^2 x^2}} c}{16 (-d)^{3/2} \left(c^2 d-e\right) \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{b \sqrt{e} \sqrt{1+\frac{1}{c^2 x^2}} c}{16 (-d)^{3/2} \left(c^2 d-e\right) \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}-\frac{5 \left(a+b \text{csch}^{-1}(c x)\right)}{16 d^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{5 \left(a+b \text{csch}^{-1}(c x)\right)}{16 d^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{\sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right)}{16 (-d)^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{\sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right)}{16 (-d)^{3/2} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}+\frac{b e \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 d^{5/2} \left(c^2 d-e\right)^{3/2}}+\frac{5 b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 d^{5/2} \sqrt{c^2 d-e}}+\frac{b e \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 d^{5/2} \left(c^2 d-e\right)^{3/2}}+\frac{5 b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 d^{5/2} \sqrt{c^2 d-e}}+\frac{3 \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{csch}^{-1}(c x)} c}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{csch}^{-1}(c x)} c}{\sqrt{e}+\sqrt{e-c^2 d}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 (-d)^{5/2} \sqrt{e}}","-\frac{b \sqrt{e} \sqrt{1+\frac{1}{c^2 x^2}} c}{16 (-d)^{3/2} \left(c^2 d-e\right) \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}-\frac{b \sqrt{e} \sqrt{1+\frac{1}{c^2 x^2}} c}{16 (-d)^{3/2} \left(c^2 d-e\right) \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}-\frac{5 \left(a+b \text{csch}^{-1}(c x)\right)}{16 d^2 \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)}+\frac{5 \left(a+b \text{csch}^{-1}(c x)\right)}{16 d^2 \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)}+\frac{\sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right)}{16 (-d)^{3/2} \left(\sqrt{-d} \sqrt{e}-\frac{d}{x}\right)^2}-\frac{\sqrt{e} \left(a+b \text{csch}^{-1}(c x)\right)}{16 (-d)^{3/2} \left(\frac{d}{x}+\sqrt{-d} \sqrt{e}\right)^2}+\frac{b e \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 d^{5/2} \left(c^2 d-e\right)^{3/2}}+\frac{5 b \tanh ^{-1}\left(\frac{c^2 d-\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 d^{5/2} \sqrt{c^2 d-e}}+\frac{b e \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 d^{5/2} \left(c^2 d-e\right)^{3/2}}+\frac{5 b \tanh ^{-1}\left(\frac{d c^2+\frac{\sqrt{-d} \sqrt{e}}{x}}{c \sqrt{d} \sqrt{c^2 d-e} \sqrt{1+\frac{1}{c^2 x^2}}}\right)}{16 d^{5/2} \sqrt{c^2 d-e}}+\frac{3 \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{csch}^{-1}(c x)} c}{\sqrt{e}-\sqrt{e-c^2 d}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 \left(a+b \text{csch}^{-1}(c x)\right) \log \left(1-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 \left(a+b \text{csch}^{-1}(c x)\right) \log \left(\frac{\sqrt{-d} e^{\text{csch}^{-1}(c x)} c}{\sqrt{e}+\sqrt{e-c^2 d}}+1\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}-\sqrt{e-c^2 d}}\right)}{16 (-d)^{5/2} \sqrt{e}}-\frac{3 b \text{PolyLog}\left(2,-\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 (-d)^{5/2} \sqrt{e}}+\frac{3 b \text{PolyLog}\left(2,\frac{c \sqrt{-d} e^{\text{csch}^{-1}(c x)}}{\sqrt{e}+\sqrt{e-c^2 d}}\right)}{16 (-d)^{5/2} \sqrt{e}}",1,"-(b*c*Sqrt[e]*Sqrt[1 + 1/(c^2*x^2)])/(16*(-d)^(3/2)*(c^2*d - e)*(Sqrt[-d]*Sqrt[e] - d/x)) - (b*c*Sqrt[e]*Sqrt[1 + 1/(c^2*x^2)])/(16*(-d)^(3/2)*(c^2*d - e)*(Sqrt[-d]*Sqrt[e] + d/x)) + (Sqrt[e]*(a + b*ArcCsch[c*x]))/(16*(-d)^(3/2)*(Sqrt[-d]*Sqrt[e] - d/x)^2) - (5*(a + b*ArcCsch[c*x]))/(16*d^2*(Sqrt[-d]*Sqrt[e] - d/x)) - (Sqrt[e]*(a + b*ArcCsch[c*x]))/(16*(-d)^(3/2)*(Sqrt[-d]*Sqrt[e] + d/x)^2) + (5*(a + b*ArcCsch[c*x]))/(16*d^2*(Sqrt[-d]*Sqrt[e] + d/x)) + (5*b*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(16*d^(5/2)*Sqrt[c^2*d - e]) + (b*e*ArcTanh[(c^2*d - (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(16*d^(5/2)*(c^2*d - e)^(3/2)) + (5*b*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(16*d^(5/2)*Sqrt[c^2*d - e]) + (b*e*ArcTanh[(c^2*d + (Sqrt[-d]*Sqrt[e])/x)/(c*Sqrt[d]*Sqrt[c^2*d - e]*Sqrt[1 + 1/(c^2*x^2)])])/(16*d^(5/2)*(c^2*d - e)^(3/2)) + (3*(a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*(a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(16*(-d)^(5/2)*Sqrt[e]) + (3*(a + b*ArcCsch[c*x])*Log[1 - (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*(a + b*ArcCsch[c*x])*Log[1 + (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e]))])/(16*(-d)^(5/2)*Sqrt[e]) + (3*b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] - Sqrt[-(c^2*d) + e])])/(16*(-d)^(5/2)*Sqrt[e]) - (3*b*PolyLog[2, -((c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e]))])/(16*(-d)^(5/2)*Sqrt[e]) + (3*b*PolyLog[2, (c*Sqrt[-d]*E^ArcCsch[c*x])/(Sqrt[e] + Sqrt[-(c^2*d) + e])])/(16*(-d)^(5/2)*Sqrt[e])","A",81,12,18,0.6667,1,"{6294, 5791, 5706, 5801, 731, 725, 206, 5799, 5561, 2190, 2279, 2391}"
118,1,413,0,1.4122032,"\int x^5 \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^5*Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]),x]","\frac{d^2 \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^3}-\frac{2 d \left(d+e x^2\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e^3}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \text{csch}^{-1}(c x)\right)}{7 e^3}-\frac{b x \sqrt{-c^2 x^2-1} \left(23 c^4 d^2-12 c^2 d e-75 e^2\right) \sqrt{d+e x^2}}{1680 c^5 e^2 \sqrt{-c^2 x^2}}+\frac{8 b c d^{7/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{105 e^3 \sqrt{-c^2 x^2}}+\frac{b x \left(35 c^4 d^2 e+105 c^6 d^3+63 c^2 d e^2-75 e^3\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{1680 c^6 e^{5/2} \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(d+e x^2\right)^{5/2}}{42 c e^2 \sqrt{-c^2 x^2}}-\frac{b x \sqrt{-c^2 x^2-1} \left(29 c^2 d+25 e\right) \left(d+e x^2\right)^{3/2}}{840 c^3 e^2 \sqrt{-c^2 x^2}}","\frac{d^2 \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^3}-\frac{2 d \left(d+e x^2\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e^3}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \text{csch}^{-1}(c x)\right)}{7 e^3}-\frac{b x \sqrt{-c^2 x^2-1} \left(23 c^4 d^2-12 c^2 d e-75 e^2\right) \sqrt{d+e x^2}}{1680 c^5 e^2 \sqrt{-c^2 x^2}}+\frac{8 b c d^{7/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{105 e^3 \sqrt{-c^2 x^2}}+\frac{b x \left(35 c^4 d^2 e+105 c^6 d^3+63 c^2 d e^2-75 e^3\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{1680 c^6 e^{5/2} \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(d+e x^2\right)^{5/2}}{42 c e^2 \sqrt{-c^2 x^2}}-\frac{b x \sqrt{-c^2 x^2-1} \left(29 c^2 d+25 e\right) \left(d+e x^2\right)^{3/2}}{840 c^3 e^2 \sqrt{-c^2 x^2}}",1,"-(b*(23*c^4*d^2 - 12*c^2*d*e - 75*e^2)*x*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(1680*c^5*e^2*Sqrt[-(c^2*x^2)]) - (b*(29*c^2*d + 25*e)*x*Sqrt[-1 - c^2*x^2]*(d + e*x^2)^(3/2))/(840*c^3*e^2*Sqrt[-(c^2*x^2)]) + (b*x*Sqrt[-1 - c^2*x^2]*(d + e*x^2)^(5/2))/(42*c*e^2*Sqrt[-(c^2*x^2)]) + (d^2*(d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/(3*e^3) - (2*d*(d + e*x^2)^(5/2)*(a + b*ArcCsch[c*x]))/(5*e^3) + ((d + e*x^2)^(7/2)*(a + b*ArcCsch[c*x]))/(7*e^3) + (b*(105*c^6*d^3 + 35*c^4*d^2*e + 63*c^2*d*e^2 - 75*e^3)*x*ArcTan[(Sqrt[e]*Sqrt[-1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(1680*c^6*e^(5/2)*Sqrt[-(c^2*x^2)]) + (8*b*c*d^(7/2)*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 - c^2*x^2])])/(105*e^3*Sqrt[-(c^2*x^2)])","A",12,12,23,0.5217,1,"{266, 43, 6302, 12, 1615, 154, 157, 63, 217, 203, 93, 204}"
119,1,302,0,0.4336569,"\int x^3 \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^3*Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]),x]","-\frac{d \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^2}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e^2}-\frac{2 b c d^{5/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{15 e^2 \sqrt{-c^2 x^2}}-\frac{b x \left(15 c^4 d^2+10 c^2 d e-9 e^2\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{120 c^4 e^{3/2} \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{20 c e \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(c^2 d-9 e\right) \sqrt{d+e x^2}}{120 c^3 e \sqrt{-c^2 x^2}}","-\frac{d \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^2}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e^2}-\frac{2 b c d^{5/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{15 e^2 \sqrt{-c^2 x^2}}-\frac{b x \left(15 c^4 d^2+10 c^2 d e-9 e^2\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{120 c^4 e^{3/2} \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{20 c e \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(c^2 d-9 e\right) \sqrt{d+e x^2}}{120 c^3 e \sqrt{-c^2 x^2}}",1,"(b*(c^2*d - 9*e)*x*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(120*c^3*e*Sqrt[-(c^2*x^2)]) + (b*x*Sqrt[-1 - c^2*x^2]*(d + e*x^2)^(3/2))/(20*c*e*Sqrt[-(c^2*x^2)]) - (d*(d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/(3*e^2) + ((d + e*x^2)^(5/2)*(a + b*ArcCsch[c*x]))/(5*e^2) - (b*(15*c^4*d^2 + 10*c^2*d*e - 9*e^2)*x*ArcTan[(Sqrt[e]*Sqrt[-1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(120*c^4*e^(3/2)*Sqrt[-(c^2*x^2)]) - (2*b*c*d^(5/2)*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 - c^2*x^2])])/(15*e^2*Sqrt[-(c^2*x^2)])","A",11,12,23,0.5217,1,"{266, 43, 6302, 12, 573, 154, 157, 63, 217, 203, 93, 204}"
120,1,203,0,0.2056431,"\int x \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x*Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]),x]","\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e}+\frac{b c d^{3/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{3 e \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \sqrt{d+e x^2}}{6 c \sqrt{-c^2 x^2}}+\frac{b x \left(3 c^2 d-e\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{6 c^2 \sqrt{e} \sqrt{-c^2 x^2}}","\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e}+\frac{b c d^{3/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{3 e \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \sqrt{d+e x^2}}{6 c \sqrt{-c^2 x^2}}+\frac{b x \left(3 c^2 d-e\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{6 c^2 \sqrt{e} \sqrt{-c^2 x^2}}",1,"(b*x*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(6*c*Sqrt[-(c^2*x^2)]) + ((d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/(3*e) + (b*(3*c^2*d - e)*x*ArcTan[(Sqrt[e]*Sqrt[-1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(6*c^2*Sqrt[e]*Sqrt[-(c^2*x^2)]) + (b*c*d^(3/2)*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 - c^2*x^2])])/(3*e*Sqrt[-(c^2*x^2)])","A",9,9,21,0.4286,1,"{6300, 446, 102, 157, 63, 217, 203, 93, 204}"
121,0,0,0,0.0997737,"\int \frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{x} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/x,x]","\int \frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{x} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{x},x\right)",0,"Defer[Int][(Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/x, x]","A",0,0,0,0,-1,"{}"
122,0,0,0,0.10563,"\int \frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^3} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/x^3,x]","\int \frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^3} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^3},x\right)",0,"Defer[Int][(Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/x^3, x]","A",0,0,0,0,-1,"{}"
123,0,0,0,0.1005643,"\int x^2 \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^2*Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]),x]","\int x^2 \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","\text{Int}\left(x^2 \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right),x\right)",0,"Defer[Int][x^2*Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]), x]","A",0,0,0,0,-1,"{}"
124,0,0,0,0.0368549,"\int \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]),x]","\int \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","\text{Int}\left(\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right),x\right)",0,"Defer[Int][Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]), x]","A",0,0,0,0,-1,"{}"
125,0,0,0,0.0898209,"\int \frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^2} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/x^2,x]","\int \frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^2} \, dx","\text{Int}\left(\frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^2},x\right)",0,"Defer[Int][(Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/x^2, x]","A",0,0,0,0,-1,"{}"
126,1,389,0,0.4270765,"\int \frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^4} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/x^4,x]","-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 d x^3}-\frac{b e x \left(c^2 d-3 e\right) \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{9 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}-\frac{2 b c^3 x^2 \left(c^2 d-2 e\right) \sqrt{d+e x^2}}{9 d \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}-\frac{2 b c \sqrt{-c^2 x^2-1} \left(c^2 d-2 e\right) \sqrt{d+e x^2}}{9 d \sqrt{-c^2 x^2}}+\frac{b c \sqrt{-c^2 x^2-1} \sqrt{d+e x^2}}{9 x^2 \sqrt{-c^2 x^2}}+\frac{2 b c^2 x \left(c^2 d-2 e\right) \sqrt{d+e x^2} E\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{9 d \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}","-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 d x^3}-\frac{b e x \left(c^2 d-3 e\right) \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{9 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}-\frac{2 b c^3 x^2 \left(c^2 d-2 e\right) \sqrt{d+e x^2}}{9 d \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}-\frac{2 b c \sqrt{-c^2 x^2-1} \left(c^2 d-2 e\right) \sqrt{d+e x^2}}{9 d \sqrt{-c^2 x^2}}+\frac{b c \sqrt{-c^2 x^2-1} \sqrt{d+e x^2}}{9 x^2 \sqrt{-c^2 x^2}}+\frac{2 b c^2 x \left(c^2 d-2 e\right) \sqrt{d+e x^2} E\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{9 d \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}",1,"(-2*b*c^3*(c^2*d - 2*e)*x^2*Sqrt[d + e*x^2])/(9*d*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]) - (2*b*c*(c^2*d - 2*e)*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(9*d*Sqrt[-(c^2*x^2)]) + (b*c*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(9*x^2*Sqrt[-(c^2*x^2)]) - ((d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/(3*d*x^3) + (2*b*c^2*(c^2*d - 2*e)*x*Sqrt[d + e*x^2]*EllipticE[ArcTan[c*x], 1 - e/(c^2*d)])/(9*d*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))]) - (b*(c^2*d - 3*e)*e*x*Sqrt[d + e*x^2]*EllipticF[ArcTan[c*x], 1 - e/(c^2*d)])/(9*d^2*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))])","A",8,9,23,0.3913,1,"{264, 6302, 12, 474, 583, 531, 418, 492, 411}"
127,1,527,0,0.6379921,"\int \frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^6} \, dx","Int[(Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/x^6,x]","\frac{2 e \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{15 d^2 x^3}-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 d x^5}+\frac{b c^3 x^2 \left(24 c^4 d^2-19 c^2 d e-31 e^2\right) \sqrt{d+e x^2}}{225 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}+\frac{b c \sqrt{-c^2 x^2-1} \left(24 c^4 d^2-19 c^2 d e-31 e^2\right) \sqrt{d+e x^2}}{225 d^2 \sqrt{-c^2 x^2}}+\frac{2 b e x \left(6 c^4 d^2-4 c^2 d e-15 e^2\right) \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{225 d^3 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}-\frac{b c^2 x \left(24 c^4 d^2-19 c^2 d e-31 e^2\right) \sqrt{d+e x^2} E\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{225 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}+\frac{b c \sqrt{-c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{25 d x^4 \sqrt{-c^2 x^2}}-\frac{b c \sqrt{-c^2 x^2-1} \left(12 c^2 d+e\right) \sqrt{d+e x^2}}{225 d x^2 \sqrt{-c^2 x^2}}","\frac{2 e \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{15 d^2 x^3}-\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 d x^5}+\frac{b c^3 x^2 \left(24 c^4 d^2-19 c^2 d e-31 e^2\right) \sqrt{d+e x^2}}{225 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}+\frac{b c \sqrt{-c^2 x^2-1} \left(24 c^4 d^2-19 c^2 d e-31 e^2\right) \sqrt{d+e x^2}}{225 d^2 \sqrt{-c^2 x^2}}+\frac{2 b e x \left(6 c^4 d^2-4 c^2 d e-15 e^2\right) \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{225 d^3 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}-\frac{b c^2 x \left(24 c^4 d^2-19 c^2 d e-31 e^2\right) \sqrt{d+e x^2} E\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{225 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}+\frac{b c \sqrt{-c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{25 d x^4 \sqrt{-c^2 x^2}}-\frac{b c \sqrt{-c^2 x^2-1} \left(12 c^2 d+e\right) \sqrt{d+e x^2}}{225 d x^2 \sqrt{-c^2 x^2}}",1,"(b*c^3*(24*c^4*d^2 - 19*c^2*d*e - 31*e^2)*x^2*Sqrt[d + e*x^2])/(225*d^2*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]) + (b*c*(24*c^4*d^2 - 19*c^2*d*e - 31*e^2)*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(225*d^2*Sqrt[-(c^2*x^2)]) - (b*c*(12*c^2*d + e)*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(225*d*x^2*Sqrt[-(c^2*x^2)]) + (b*c*Sqrt[-1 - c^2*x^2]*(d + e*x^2)^(3/2))/(25*d*x^4*Sqrt[-(c^2*x^2)]) - ((d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/(5*d*x^5) + (2*e*(d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/(15*d^2*x^3) - (b*c^2*(24*c^4*d^2 - 19*c^2*d*e - 31*e^2)*x*Sqrt[d + e*x^2]*EllipticE[ArcTan[c*x], 1 - e/(c^2*d)])/(225*d^2*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))]) + (2*b*e*(6*c^4*d^2 - 4*c^2*d*e - 15*e^2)*x*Sqrt[d + e*x^2]*EllipticF[ArcTan[c*x], 1 - e/(c^2*d)])/(225*d^3*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))])","A",9,10,23,0.4348,1,"{271, 264, 6302, 12, 580, 583, 531, 418, 492, 411}"
128,1,384,0,0.5142404,"\int x^3 \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^3*(d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]),x]","-\frac{d \left(d+e x^2\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e^2}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \text{csch}^{-1}(c x)\right)}{7 e^2}-\frac{b x \sqrt{-c^2 x^2-1} \left(3 c^4 d^2+38 c^2 d e-25 e^2\right) \sqrt{d+e x^2}}{560 c^5 e \sqrt{-c^2 x^2}}-\frac{2 b c d^{7/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{35 e^2 \sqrt{-c^2 x^2}}-\frac{b x \left(35 c^4 d^2 e+35 c^6 d^3-63 c^2 d e^2+25 e^3\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{560 c^6 e^{3/2} \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(d+e x^2\right)^{5/2}}{42 c e \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(13 c^2 d-25 e\right) \left(d+e x^2\right)^{3/2}}{840 c^3 e \sqrt{-c^2 x^2}}","-\frac{d \left(d+e x^2\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e^2}+\frac{\left(d+e x^2\right)^{7/2} \left(a+b \text{csch}^{-1}(c x)\right)}{7 e^2}-\frac{b x \sqrt{-c^2 x^2-1} \left(3 c^4 d^2+38 c^2 d e-25 e^2\right) \sqrt{d+e x^2}}{560 c^5 e \sqrt{-c^2 x^2}}-\frac{2 b c d^{7/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{35 e^2 \sqrt{-c^2 x^2}}-\frac{b x \left(35 c^4 d^2 e+35 c^6 d^3-63 c^2 d e^2+25 e^3\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{560 c^6 e^{3/2} \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(d+e x^2\right)^{5/2}}{42 c e \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(13 c^2 d-25 e\right) \left(d+e x^2\right)^{3/2}}{840 c^3 e \sqrt{-c^2 x^2}}",1,"-(b*(3*c^4*d^2 + 38*c^2*d*e - 25*e^2)*x*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(560*c^5*e*Sqrt[-(c^2*x^2)]) + (b*(13*c^2*d - 25*e)*x*Sqrt[-1 - c^2*x^2]*(d + e*x^2)^(3/2))/(840*c^3*e*Sqrt[-(c^2*x^2)]) + (b*x*Sqrt[-1 - c^2*x^2]*(d + e*x^2)^(5/2))/(42*c*e*Sqrt[-(c^2*x^2)]) - (d*(d + e*x^2)^(5/2)*(a + b*ArcCsch[c*x]))/(5*e^2) + ((d + e*x^2)^(7/2)*(a + b*ArcCsch[c*x]))/(7*e^2) - (b*(35*c^6*d^3 + 35*c^4*d^2*e - 63*c^2*d*e^2 + 25*e^3)*x*ArcTan[(Sqrt[e]*Sqrt[-1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(560*c^6*e^(3/2)*Sqrt[-(c^2*x^2)]) - (2*b*c*d^(7/2)*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 - c^2*x^2])])/(35*e^2*Sqrt[-(c^2*x^2)])","A",12,12,23,0.5217,1,"{266, 43, 6302, 12, 573, 154, 157, 63, 217, 203, 93, 204}"
129,1,270,0,0.2814692,"\int x \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x*(d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]),x]","\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e}+\frac{b x \left(15 c^4 d^2-10 c^2 d e+3 e^2\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{40 c^4 \sqrt{e} \sqrt{-c^2 x^2}}+\frac{b c d^{5/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{5 e \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{20 c \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(7 c^2 d-3 e\right) \sqrt{d+e x^2}}{40 c^3 \sqrt{-c^2 x^2}}","\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e}+\frac{b x \left(15 c^4 d^2-10 c^2 d e+3 e^2\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{40 c^4 \sqrt{e} \sqrt{-c^2 x^2}}+\frac{b c d^{5/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{5 e \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{20 c \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(7 c^2 d-3 e\right) \sqrt{d+e x^2}}{40 c^3 \sqrt{-c^2 x^2}}",1,"(b*(7*c^2*d - 3*e)*x*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(40*c^3*Sqrt[-(c^2*x^2)]) + (b*x*Sqrt[-1 - c^2*x^2]*(d + e*x^2)^(3/2))/(20*c*Sqrt[-(c^2*x^2)]) + ((d + e*x^2)^(5/2)*(a + b*ArcCsch[c*x]))/(5*e) + (b*(15*c^4*d^2 - 10*c^2*d*e + 3*e^2)*x*ArcTan[(Sqrt[e]*Sqrt[-1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(40*c^4*Sqrt[e]*Sqrt[-(c^2*x^2)]) + (b*c*d^(5/2)*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 - c^2*x^2])])/(5*e*Sqrt[-(c^2*x^2)])","A",10,10,21,0.4762,1,"{6300, 446, 102, 154, 157, 63, 217, 203, 93, 204}"
130,0,0,0,0.1170362,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{x} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/x,x]","\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{x} \, dx","\text{Int}\left(\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{x},x\right)",0,"Defer[Int][((d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/x, x]","A",0,0,0,0,-1,"{}"
131,0,0,0,0.1227836,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^3} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/x^3,x]","\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^3} \, dx","\text{Int}\left(\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^3},x\right)",0,"Defer[Int][((d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/x^3, x]","A",0,0,0,0,-1,"{}"
132,0,0,0,0.1196949,"\int x^2 \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[x^2*(d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]),x]","\int x^2 \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","\text{Int}\left(x^2 \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right),x\right)",0,"Defer[Int][x^2*(d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]), x]","A",0,0,0,0,-1,"{}"
133,0,0,0,0.0438619,"\int \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[(d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]),x]","\int \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","\text{Int}\left(\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right),x\right)",0,"Defer[Int][(d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]), x]","A",0,0,0,0,-1,"{}"
134,0,0,0,0.105802,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^2} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/x^2,x]","\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^2} \, dx","\text{Int}\left(\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^2},x\right)",0,"Defer[Int][((d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/x^2, x]","A",0,0,0,0,-1,"{}"
135,0,0,0,0.1079586,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^4} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/x^4,x]","\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^4} \, dx","\text{Int}\left(\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^4},x\right)",0,"Defer[Int][((d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/x^4, x]","A",0,0,0,0,-1,"{}"
136,1,492,0,0.5754719,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^6} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/x^6,x]","-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 d x^5}+\frac{b c^3 x^2 \left(8 c^4 d^2-23 c^2 d e+23 e^2\right) \sqrt{d+e x^2}}{75 d \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}+\frac{b c \sqrt{-c^2 x^2-1} \left(8 c^4 d^2-23 c^2 d e+23 e^2\right) \sqrt{d+e x^2}}{75 d \sqrt{-c^2 x^2}}+\frac{b e x \left(4 c^4 d^2-11 c^2 d e+15 e^2\right) \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{75 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}-\frac{b c^2 x \left(8 c^4 d^2-23 c^2 d e+23 e^2\right) \sqrt{d+e x^2} E\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{75 d \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}+\frac{b c \sqrt{-c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{25 x^4 \sqrt{-c^2 x^2}}-\frac{4 b c \sqrt{-c^2 x^2-1} \left(c^2 d-2 e\right) \sqrt{d+e x^2}}{75 x^2 \sqrt{-c^2 x^2}}","-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 d x^5}+\frac{b c^3 x^2 \left(8 c^4 d^2-23 c^2 d e+23 e^2\right) \sqrt{d+e x^2}}{75 d \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}+\frac{b c \sqrt{-c^2 x^2-1} \left(8 c^4 d^2-23 c^2 d e+23 e^2\right) \sqrt{d+e x^2}}{75 d \sqrt{-c^2 x^2}}+\frac{b e x \left(4 c^4 d^2-11 c^2 d e+15 e^2\right) \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{75 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}-\frac{b c^2 x \left(8 c^4 d^2-23 c^2 d e+23 e^2\right) \sqrt{d+e x^2} E\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{75 d \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}+\frac{b c \sqrt{-c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{25 x^4 \sqrt{-c^2 x^2}}-\frac{4 b c \sqrt{-c^2 x^2-1} \left(c^2 d-2 e\right) \sqrt{d+e x^2}}{75 x^2 \sqrt{-c^2 x^2}}",1,"(b*c^3*(8*c^4*d^2 - 23*c^2*d*e + 23*e^2)*x^2*Sqrt[d + e*x^2])/(75*d*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]) + (b*c*(8*c^4*d^2 - 23*c^2*d*e + 23*e^2)*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(75*d*Sqrt[-(c^2*x^2)]) - (4*b*c*(c^2*d - 2*e)*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(75*x^2*Sqrt[-(c^2*x^2)]) + (b*c*Sqrt[-1 - c^2*x^2]*(d + e*x^2)^(3/2))/(25*x^4*Sqrt[-(c^2*x^2)]) - ((d + e*x^2)^(5/2)*(a + b*ArcCsch[c*x]))/(5*d*x^5) - (b*c^2*(8*c^4*d^2 - 23*c^2*d*e + 23*e^2)*x*Sqrt[d + e*x^2]*EllipticE[ArcTan[c*x], 1 - e/(c^2*d)])/(75*d*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))]) + (b*e*(4*c^4*d^2 - 11*c^2*d*e + 15*e^2)*x*Sqrt[d + e*x^2]*EllipticF[ArcTan[c*x], 1 - e/(c^2*d)])/(75*d^2*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))])","A",9,10,23,0.4348,1,"{264, 6302, 12, 474, 580, 583, 531, 418, 492, 411}"
137,1,643,0,0.8660621,"\int \frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{x^8} \, dx","Int[((d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/x^8,x]","\frac{2 e \left(d+e x^2\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{35 d^2 x^5}-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{7 d x^7}-\frac{b c^3 x^2 \left(-528 c^4 d^2 e+240 c^6 d^3+193 c^2 d e^2+247 e^3\right) \sqrt{d+e x^2}}{3675 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}-\frac{b c \sqrt{-c^2 x^2-1} \left(-528 c^4 d^2 e+240 c^6 d^3+193 c^2 d e^2+247 e^3\right) \sqrt{d+e x^2}}{3675 d^2 \sqrt{-c^2 x^2}}+\frac{b c \sqrt{-c^2 x^2-1} \left(120 c^4 d^2-159 c^2 d e-37 e^2\right) \sqrt{d+e x^2}}{3675 d x^2 \sqrt{-c^2 x^2}}-\frac{b e x \left(-249 c^4 d^2 e+120 c^6 d^3+71 c^2 d e^2+210 e^3\right) \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{3675 d^3 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}+\frac{b c^2 x \left(-528 c^4 d^2 e+240 c^6 d^3+193 c^2 d e^2+247 e^3\right) \sqrt{d+e x^2} E\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{3675 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}+\frac{b c \sqrt{-c^2 x^2-1} \left(d+e x^2\right)^{5/2}}{49 d x^6 \sqrt{-c^2 x^2}}-\frac{b c \sqrt{-c^2 x^2-1} \left(30 c^2 d-11 e\right) \left(d+e x^2\right)^{3/2}}{1225 d x^4 \sqrt{-c^2 x^2}}","\frac{2 e \left(d+e x^2\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{35 d^2 x^5}-\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{7 d x^7}-\frac{b c^3 x^2 \left(-528 c^4 d^2 e+240 c^6 d^3+193 c^2 d e^2+247 e^3\right) \sqrt{d+e x^2}}{3675 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}-\frac{b c \sqrt{-c^2 x^2-1} \left(-528 c^4 d^2 e+240 c^6 d^3+193 c^2 d e^2+247 e^3\right) \sqrt{d+e x^2}}{3675 d^2 \sqrt{-c^2 x^2}}+\frac{b c \sqrt{-c^2 x^2-1} \left(120 c^4 d^2-159 c^2 d e-37 e^2\right) \sqrt{d+e x^2}}{3675 d x^2 \sqrt{-c^2 x^2}}-\frac{b e x \left(-249 c^4 d^2 e+120 c^6 d^3+71 c^2 d e^2+210 e^3\right) \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{3675 d^3 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}+\frac{b c^2 x \left(-528 c^4 d^2 e+240 c^6 d^3+193 c^2 d e^2+247 e^3\right) \sqrt{d+e x^2} E\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{3675 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}+\frac{b c \sqrt{-c^2 x^2-1} \left(d+e x^2\right)^{5/2}}{49 d x^6 \sqrt{-c^2 x^2}}-\frac{b c \sqrt{-c^2 x^2-1} \left(30 c^2 d-11 e\right) \left(d+e x^2\right)^{3/2}}{1225 d x^4 \sqrt{-c^2 x^2}}",1,"-(b*c^3*(240*c^6*d^3 - 528*c^4*d^2*e + 193*c^2*d*e^2 + 247*e^3)*x^2*Sqrt[d + e*x^2])/(3675*d^2*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]) - (b*c*(240*c^6*d^3 - 528*c^4*d^2*e + 193*c^2*d*e^2 + 247*e^3)*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(3675*d^2*Sqrt[-(c^2*x^2)]) + (b*c*(120*c^4*d^2 - 159*c^2*d*e - 37*e^2)*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(3675*d*x^2*Sqrt[-(c^2*x^2)]) - (b*c*(30*c^2*d - 11*e)*Sqrt[-1 - c^2*x^2]*(d + e*x^2)^(3/2))/(1225*d*x^4*Sqrt[-(c^2*x^2)]) + (b*c*Sqrt[-1 - c^2*x^2]*(d + e*x^2)^(5/2))/(49*d*x^6*Sqrt[-(c^2*x^2)]) - ((d + e*x^2)^(5/2)*(a + b*ArcCsch[c*x]))/(7*d*x^7) + (2*e*(d + e*x^2)^(5/2)*(a + b*ArcCsch[c*x]))/(35*d^2*x^5) + (b*c^2*(240*c^6*d^3 - 528*c^4*d^2*e + 193*c^2*d*e^2 + 247*e^3)*x*Sqrt[d + e*x^2]*EllipticE[ArcTan[c*x], 1 - e/(c^2*d)])/(3675*d^2*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))]) - (b*e*(120*c^6*d^3 - 249*c^4*d^2*e + 71*c^2*d*e^2 + 210*e^3)*x*Sqrt[d + e*x^2]*EllipticF[ArcTan[c*x], 1 - e/(c^2*d)])/(3675*d^3*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))])","A",10,10,23,0.4348,1,"{271, 264, 6302, 12, 580, 583, 531, 418, 492, 411}"
138,1,329,0,1.1793765,"\int \frac{x^5 \left(a+b \text{csch}^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x^5*(a + b*ArcCsch[c*x]))/Sqrt[d + e*x^2],x]","\frac{d^2 \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{e^3}-\frac{2 d \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^3}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e^3}+\frac{8 b c d^{5/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{15 e^3 \sqrt{-c^2 x^2}}+\frac{b x \left(45 c^4 d^2+10 c^2 d e+9 e^2\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{120 c^4 e^{5/2} \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{20 c e^2 \sqrt{-c^2 x^2}}-\frac{b x \sqrt{-c^2 x^2-1} \left(19 c^2 d+9 e\right) \sqrt{d+e x^2}}{120 c^3 e^2 \sqrt{-c^2 x^2}}","\frac{d^2 \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{e^3}-\frac{2 d \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^3}+\frac{\left(d+e x^2\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{5 e^3}+\frac{8 b c d^{5/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{15 e^3 \sqrt{-c^2 x^2}}+\frac{b x \left(45 c^4 d^2+10 c^2 d e+9 e^2\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{120 c^4 e^{5/2} \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \left(d+e x^2\right)^{3/2}}{20 c e^2 \sqrt{-c^2 x^2}}-\frac{b x \sqrt{-c^2 x^2-1} \left(19 c^2 d+9 e\right) \sqrt{d+e x^2}}{120 c^3 e^2 \sqrt{-c^2 x^2}}",1,"-(b*(19*c^2*d + 9*e)*x*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(120*c^3*e^2*Sqrt[-(c^2*x^2)]) + (b*x*Sqrt[-1 - c^2*x^2]*(d + e*x^2)^(3/2))/(20*c*e^2*Sqrt[-(c^2*x^2)]) + (d^2*Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/e^3 - (2*d*(d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/(3*e^3) + ((d + e*x^2)^(5/2)*(a + b*ArcCsch[c*x]))/(5*e^3) + (b*(45*c^4*d^2 + 10*c^2*d*e + 9*e^2)*x*ArcTan[(Sqrt[e]*Sqrt[-1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(120*c^4*e^(5/2)*Sqrt[-(c^2*x^2)]) + (8*b*c*d^(5/2)*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 - c^2*x^2])])/(15*e^3*Sqrt[-(c^2*x^2)])","A",11,12,23,0.5217,1,"{266, 43, 6302, 12, 1615, 154, 157, 63, 217, 203, 93, 204}"
139,1,229,0,0.3180053,"\int \frac{x^3 \left(a+b \text{csch}^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x^3*(a + b*ArcCsch[c*x]))/Sqrt[d + e*x^2],x]","-\frac{d \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{e^2}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^2}-\frac{2 b c d^{3/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{3 e^2 \sqrt{-c^2 x^2}}-\frac{b x \left(3 c^2 d+e\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{6 c^2 e^{3/2} \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \sqrt{d+e x^2}}{6 c e \sqrt{-c^2 x^2}}","-\frac{d \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{e^2}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^2}-\frac{2 b c d^{3/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{3 e^2 \sqrt{-c^2 x^2}}-\frac{b x \left(3 c^2 d+e\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{6 c^2 e^{3/2} \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \sqrt{d+e x^2}}{6 c e \sqrt{-c^2 x^2}}",1,"(b*x*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(6*c*e*Sqrt[-(c^2*x^2)]) - (d*Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/e^2 + ((d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/(3*e^2) - (b*(3*c^2*d + e)*x*ArcTan[(Sqrt[e]*Sqrt[-1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(6*c^2*e^(3/2)*Sqrt[-(c^2*x^2)]) - (2*b*c*d^(3/2)*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 - c^2*x^2])])/(3*e^2*Sqrt[-(c^2*x^2)])","A",10,12,23,0.5217,1,"{266, 43, 6302, 12, 573, 154, 157, 63, 217, 203, 93, 204}"
140,1,135,0,0.1536747,"\int \frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x*(a + b*ArcCsch[c*x]))/Sqrt[d + e*x^2],x]","\frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{e}+\frac{b x \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{\sqrt{e} \sqrt{-c^2 x^2}}+\frac{b c \sqrt{d} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{e \sqrt{-c^2 x^2}}","\frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{e}+\frac{b x \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{\sqrt{e} \sqrt{-c^2 x^2}}+\frac{b c \sqrt{d} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{e \sqrt{-c^2 x^2}}",1,"(Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/e + (b*x*ArcTan[(Sqrt[e]*Sqrt[-1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(Sqrt[e]*Sqrt[-(c^2*x^2)]) + (b*c*Sqrt[d]*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 - c^2*x^2])])/(e*Sqrt[-(c^2*x^2)])","A",8,8,21,0.3810,1,"{6300, 446, 105, 63, 217, 203, 93, 204}"
141,0,0,0,0.0958852,"\int \frac{a+b \text{csch}^{-1}(c x)}{x \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcCsch[c*x])/(x*Sqrt[d + e*x^2]),x]","\int \frac{a+b \text{csch}^{-1}(c x)}{x \sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{a+b \text{csch}^{-1}(c x)}{x \sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcCsch[c*x])/(x*Sqrt[d + e*x^2]), x]","A",0,0,0,0,-1,"{}"
142,0,0,0,0.1077698,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^3 \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcCsch[c*x])/(x^3*Sqrt[d + e*x^2]),x]","\int \frac{a+b \text{csch}^{-1}(c x)}{x^3 \sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{a+b \text{csch}^{-1}(c x)}{x^3 \sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcCsch[c*x])/(x^3*Sqrt[d + e*x^2]), x]","A",0,0,0,0,-1,"{}"
143,0,0,0,0.0915653,"\int \frac{x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[(x^2*(a + b*ArcCsch[c*x]))/Sqrt[d + e*x^2],x]","\int \frac{x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][(x^2*(a + b*ArcCsch[c*x]))/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
144,0,0,0,0.0312072,"\int \frac{a+b \text{csch}^{-1}(c x)}{\sqrt{d+e x^2}} \, dx","Int[(a + b*ArcCsch[c*x])/Sqrt[d + e*x^2],x]","\int \frac{a+b \text{csch}^{-1}(c x)}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{a+b \text{csch}^{-1}(c x)}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][(a + b*ArcCsch[c*x])/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
145,1,294,0,0.2509013,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^2 \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcCsch[c*x])/(x^2*Sqrt[d + e*x^2]),x]","-\frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{d x}+\frac{b e x \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}+\frac{b c^3 x^2 \sqrt{d+e x^2}}{d \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}+\frac{b c \sqrt{-c^2 x^2-1} \sqrt{d+e x^2}}{d \sqrt{-c^2 x^2}}-\frac{b c^2 x \sqrt{d+e x^2} E\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{d \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}","-\frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{d x}+\frac{b e x \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}+\frac{b c^3 x^2 \sqrt{d+e x^2}}{d \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}+\frac{b c \sqrt{-c^2 x^2-1} \sqrt{d+e x^2}}{d \sqrt{-c^2 x^2}}-\frac{b c^2 x \sqrt{d+e x^2} E\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{d \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}",1,"(b*c^3*x^2*Sqrt[d + e*x^2])/(d*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]) + (b*c*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(d*Sqrt[-(c^2*x^2)]) - (Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/(d*x) - (b*c^2*x*Sqrt[d + e*x^2]*EllipticE[ArcTan[c*x], 1 - e/(c^2*d)])/(d*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))]) + (b*e*x*Sqrt[d + e*x^2]*EllipticF[ArcTan[c*x], 1 - e/(c^2*d)])/(d^2*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))])","A",8,9,23,0.3913,1,"{264, 6302, 12, 475, 21, 422, 418, 492, 411}"
146,1,425,0,0.4864389,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^4 \sqrt{d+e x^2}} \, dx","Int[(a + b*ArcCsch[c*x])/(x^4*Sqrt[d + e*x^2]),x]","\frac{2 e \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 d^2 x}-\frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 d x^3}-\frac{b c^3 x^2 \left(2 c^2 d+5 e\right) \sqrt{d+e x^2}}{9 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}-\frac{b c \sqrt{-c^2 x^2-1} \left(2 c^2 d+5 e\right) \sqrt{d+e x^2}}{9 d^2 \sqrt{-c^2 x^2}}-\frac{b e x \left(c^2 d+6 e\right) \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{9 d^3 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}+\frac{b c^2 x \left(2 c^2 d+5 e\right) \sqrt{d+e x^2} E\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{9 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}+\frac{b c \sqrt{-c^2 x^2-1} \sqrt{d+e x^2}}{9 d x^2 \sqrt{-c^2 x^2}}","\frac{2 e \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 d^2 x}-\frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 d x^3}-\frac{b c^3 x^2 \left(2 c^2 d+5 e\right) \sqrt{d+e x^2}}{9 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}-\frac{b c \sqrt{-c^2 x^2-1} \left(2 c^2 d+5 e\right) \sqrt{d+e x^2}}{9 d^2 \sqrt{-c^2 x^2}}-\frac{b e x \left(c^2 d+6 e\right) \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{9 d^3 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}+\frac{b c^2 x \left(2 c^2 d+5 e\right) \sqrt{d+e x^2} E\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{9 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}+\frac{b c \sqrt{-c^2 x^2-1} \sqrt{d+e x^2}}{9 d x^2 \sqrt{-c^2 x^2}}",1,"-(b*c^3*(2*c^2*d + 5*e)*x^2*Sqrt[d + e*x^2])/(9*d^2*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]) - (b*c*(2*c^2*d + 5*e)*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(9*d^2*Sqrt[-(c^2*x^2)]) + (b*c*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(9*d*x^2*Sqrt[-(c^2*x^2)]) - (Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/(3*d*x^3) + (2*e*Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/(3*d^2*x) + (b*c^2*(2*c^2*d + 5*e)*x*Sqrt[d + e*x^2]*EllipticE[ArcTan[c*x], 1 - e/(c^2*d)])/(9*d^2*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))]) - (b*e*(c^2*d + 6*e)*x*Sqrt[d + e*x^2]*EllipticF[ArcTan[c*x], 1 - e/(c^2*d)])/(9*d^3*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))])","A",8,10,23,0.4348,1,"{271, 264, 6302, 12, 580, 583, 531, 418, 492, 411}"
147,1,256,0,1.1345861,"\int \frac{x^5 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^5*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(3/2),x]","-\frac{d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{e^3 \sqrt{d+e x^2}}-\frac{2 d \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{e^3}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^3}-\frac{8 b c d^{3/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{3 e^3 \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \sqrt{d+e x^2}}{6 c e^2 \sqrt{-c^2 x^2}}-\frac{b x \left(9 c^2 d+e\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{6 c^2 e^{5/2} \sqrt{-c^2 x^2}}","-\frac{d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{e^3 \sqrt{d+e x^2}}-\frac{2 d \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{e^3}+\frac{\left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^3}-\frac{8 b c d^{3/2} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{3 e^3 \sqrt{-c^2 x^2}}+\frac{b x \sqrt{-c^2 x^2-1} \sqrt{d+e x^2}}{6 c e^2 \sqrt{-c^2 x^2}}-\frac{b x \left(9 c^2 d+e\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{6 c^2 e^{5/2} \sqrt{-c^2 x^2}}",1,"(b*x*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(6*c*e^2*Sqrt[-(c^2*x^2)]) - (d^2*(a + b*ArcCsch[c*x]))/(e^3*Sqrt[d + e*x^2]) - (2*d*Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/e^3 + ((d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]))/(3*e^3) - (b*(9*c^2*d + e)*x*ArcTan[(Sqrt[e]*Sqrt[-1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(6*c^2*e^(5/2)*Sqrt[-(c^2*x^2)]) - (8*b*c*d^(3/2)*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 - c^2*x^2])])/(3*e^3*Sqrt[-(c^2*x^2)])","A",10,11,23,0.4783,1,"{266, 43, 6302, 12, 1615, 157, 63, 217, 203, 93, 204}"
148,1,160,0,0.2751381,"\int \frac{x^3 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^3*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(3/2),x]","\frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{e^2}+\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{e^2 \sqrt{d+e x^2}}+\frac{b x \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{e^{3/2} \sqrt{-c^2 x^2}}+\frac{2 b c \sqrt{d} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{e^2 \sqrt{-c^2 x^2}}","\frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{e^2}+\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{e^2 \sqrt{d+e x^2}}+\frac{b x \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{e^{3/2} \sqrt{-c^2 x^2}}+\frac{2 b c \sqrt{d} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{e^2 \sqrt{-c^2 x^2}}",1,"(d*(a + b*ArcCsch[c*x]))/(e^2*Sqrt[d + e*x^2]) + (Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/e^2 + (b*x*ArcTan[(Sqrt[e]*Sqrt[-1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(e^(3/2)*Sqrt[-(c^2*x^2)]) + (2*b*c*Sqrt[d]*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 - c^2*x^2])])/(e^2*Sqrt[-(c^2*x^2)])","A",9,11,23,0.4783,1,"{266, 43, 6302, 12, 573, 157, 63, 217, 203, 93, 204}"
149,1,82,0,0.11148,"\int \frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(3/2),x]","-\frac{a+b \text{csch}^{-1}(c x)}{e \sqrt{d+e x^2}}-\frac{b c x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{\sqrt{d} e \sqrt{-c^2 x^2}}","-\frac{a+b \text{csch}^{-1}(c x)}{e \sqrt{d+e x^2}}-\frac{b c x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{\sqrt{d} e \sqrt{-c^2 x^2}}",1,"-((a + b*ArcCsch[c*x])/(e*Sqrt[d + e*x^2])) - (b*c*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 - c^2*x^2])])/(Sqrt[d]*e*Sqrt[-(c^2*x^2)])","A",4,4,21,0.1905,1,"{6300, 446, 93, 204}"
150,0,0,0,0.1208812,"\int \frac{a+b \text{csch}^{-1}(c x)}{x \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCsch[c*x])/(x*(d + e*x^2)^(3/2)),x]","\int \frac{a+b \text{csch}^{-1}(c x)}{x \left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{a+b \text{csch}^{-1}(c x)}{x \left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(a + b*ArcCsch[c*x])/(x*(d + e*x^2)^(3/2)), x]","A",0,0,0,0,-1,"{}"
151,0,0,0,0.1327131,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^3 \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCsch[c*x])/(x^3*(d + e*x^2)^(3/2)),x]","\int \frac{a+b \text{csch}^{-1}(c x)}{x^3 \left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{a+b \text{csch}^{-1}(c x)}{x^3 \left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(a + b*ArcCsch[c*x])/(x^3*(d + e*x^2)^(3/2)), x]","A",0,0,0,0,-1,"{}"
152,0,0,0,0.1113341,"\int \frac{x^4 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^4*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(3/2),x]","\int \frac{x^4 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{x^4 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(x^4*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
153,0,0,0,0.1070161,"\int \frac{x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(x^2*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(3/2),x]","\int \frac{x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][(x^2*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
154,1,111,0,0.075112,"\int \frac{a+b \text{csch}^{-1}(c x)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCsch[c*x])/(d + e*x^2)^(3/2),x]","\frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{d \sqrt{d+e x^2}}-\frac{b x \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}","\frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{d \sqrt{d+e x^2}}-\frac{b x \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}",1,"(x*(a + b*ArcCsch[c*x]))/(d*Sqrt[d + e*x^2]) - (b*x*Sqrt[d + e*x^2]*EllipticF[ArcTan[c*x], 1 - e/(c^2*d)])/(d^2*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))])","A",3,4,20,0.2000,1,"{191, 6292, 12, 418}"
155,1,321,0,0.319709,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^2 \left(d+e x^2\right)^{3/2}} \, dx","Int[(a + b*ArcCsch[c*x])/(x^2*(d + e*x^2)^(3/2)),x]","-\frac{2 e x \left(a+b \text{csch}^{-1}(c x)\right)}{d^2 \sqrt{d+e x^2}}-\frac{a+b \text{csch}^{-1}(c x)}{d x \sqrt{d+e x^2}}+\frac{b c^3 x^2 \sqrt{d+e x^2}}{d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}+\frac{b c \sqrt{-c^2 x^2-1} \sqrt{d+e x^2}}{d^2 \sqrt{-c^2 x^2}}+\frac{2 b e x \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{d^3 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}-\frac{b c^2 x \sqrt{d+e x^2} E\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}","-\frac{2 e x \left(a+b \text{csch}^{-1}(c x)\right)}{d^2 \sqrt{d+e x^2}}-\frac{a+b \text{csch}^{-1}(c x)}{d x \sqrt{d+e x^2}}+\frac{b c^3 x^2 \sqrt{d+e x^2}}{d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}+\frac{b c \sqrt{-c^2 x^2-1} \sqrt{d+e x^2}}{d^2 \sqrt{-c^2 x^2}}+\frac{2 b e x \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{d^3 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}-\frac{b c^2 x \sqrt{d+e x^2} E\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}",1,"(b*c^3*x^2*Sqrt[d + e*x^2])/(d^2*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]) + (b*c*Sqrt[-1 - c^2*x^2]*Sqrt[d + e*x^2])/(d^2*Sqrt[-(c^2*x^2)]) - (a + b*ArcCsch[c*x])/(d*x*Sqrt[d + e*x^2]) - (2*e*x*(a + b*ArcCsch[c*x]))/(d^2*Sqrt[d + e*x^2]) - (b*c^2*x*Sqrt[d + e*x^2]*EllipticE[ArcTan[c*x], 1 - e/(c^2*d)])/(d^2*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))]) + (2*b*e*x*Sqrt[d + e*x^2]*EllipticF[ArcTan[c*x], 1 - e/(c^2*d)])/(d^3*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))])","A",7,9,23,0.3913,1,"{271, 191, 6302, 12, 583, 531, 418, 492, 411}"
156,1,251,0,1.2293504,"\int \frac{x^5 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^5*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(5/2),x]","-\frac{d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^3 \left(d+e x^2\right)^{3/2}}+\frac{2 d \left(a+b \text{csch}^{-1}(c x)\right)}{e^3 \sqrt{d+e x^2}}+\frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{e^3}+\frac{b c d x \sqrt{-c^2 x^2-1}}{3 e^2 \sqrt{-c^2 x^2} \left(c^2 d-e\right) \sqrt{d+e x^2}}+\frac{8 b c \sqrt{d} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{3 e^3 \sqrt{-c^2 x^2}}+\frac{b x \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{e^{5/2} \sqrt{-c^2 x^2}}","-\frac{d^2 \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^3 \left(d+e x^2\right)^{3/2}}+\frac{2 d \left(a+b \text{csch}^{-1}(c x)\right)}{e^3 \sqrt{d+e x^2}}+\frac{\sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right)}{e^3}+\frac{b c d x \sqrt{-c^2 x^2-1}}{3 e^2 \sqrt{-c^2 x^2} \left(c^2 d-e\right) \sqrt{d+e x^2}}+\frac{8 b c \sqrt{d} x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{3 e^3 \sqrt{-c^2 x^2}}+\frac{b x \tan ^{-1}\left(\frac{\sqrt{e} \sqrt{-c^2 x^2-1}}{c \sqrt{d+e x^2}}\right)}{e^{5/2} \sqrt{-c^2 x^2}}",1,"(b*c*d*x*Sqrt[-1 - c^2*x^2])/(3*(c^2*d - e)*e^2*Sqrt[-(c^2*x^2)]*Sqrt[d + e*x^2]) - (d^2*(a + b*ArcCsch[c*x]))/(3*e^3*(d + e*x^2)^(3/2)) + (2*d*(a + b*ArcCsch[c*x]))/(e^3*Sqrt[d + e*x^2]) + (Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]))/e^3 + (b*x*ArcTan[(Sqrt[e]*Sqrt[-1 - c^2*x^2])/(c*Sqrt[d + e*x^2])])/(e^(5/2)*Sqrt[-(c^2*x^2)]) + (8*b*c*Sqrt[d]*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 - c^2*x^2])])/(3*e^3*Sqrt[-(c^2*x^2)])","A",10,11,23,0.4783,1,"{266, 43, 6302, 12, 1614, 157, 63, 217, 203, 93, 204}"
157,1,169,0,0.2681624,"\int \frac{x^3 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^3*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(5/2),x]","-\frac{a+b \text{csch}^{-1}(c x)}{e^2 \sqrt{d+e x^2}}+\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^2 \left(d+e x^2\right)^{3/2}}-\frac{2 b c x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{3 \sqrt{d} e^2 \sqrt{-c^2 x^2}}-\frac{b c x \sqrt{-c^2 x^2-1}}{3 e \sqrt{-c^2 x^2} \left(c^2 d-e\right) \sqrt{d+e x^2}}","-\frac{a+b \text{csch}^{-1}(c x)}{e^2 \sqrt{d+e x^2}}+\frac{d \left(a+b \text{csch}^{-1}(c x)\right)}{3 e^2 \left(d+e x^2\right)^{3/2}}-\frac{2 b c x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{3 \sqrt{d} e^2 \sqrt{-c^2 x^2}}-\frac{b c x \sqrt{-c^2 x^2-1}}{3 e \sqrt{-c^2 x^2} \left(c^2 d-e\right) \sqrt{d+e x^2}}",1,"-(b*c*x*Sqrt[-1 - c^2*x^2])/(3*(c^2*d - e)*e*Sqrt[-(c^2*x^2)]*Sqrt[d + e*x^2]) + (d*(a + b*ArcCsch[c*x]))/(3*e^2*(d + e*x^2)^(3/2)) - (a + b*ArcCsch[c*x])/(e^2*Sqrt[d + e*x^2]) - (2*b*c*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 - c^2*x^2])])/(3*Sqrt[d]*e^2*Sqrt[-(c^2*x^2)])","A",7,8,23,0.3478,1,"{266, 43, 6302, 12, 573, 152, 93, 204}"
158,1,144,0,0.1438878,"\int \frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(5/2),x]","-\frac{a+b \text{csch}^{-1}(c x)}{3 e \left(d+e x^2\right)^{3/2}}-\frac{b c x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{3 d^{3/2} e \sqrt{-c^2 x^2}}+\frac{b c x \sqrt{-c^2 x^2-1}}{3 d \sqrt{-c^2 x^2} \left(c^2 d-e\right) \sqrt{d+e x^2}}","-\frac{a+b \text{csch}^{-1}(c x)}{3 e \left(d+e x^2\right)^{3/2}}-\frac{b c x \tan ^{-1}\left(\frac{\sqrt{d+e x^2}}{\sqrt{d} \sqrt{-c^2 x^2-1}}\right)}{3 d^{3/2} e \sqrt{-c^2 x^2}}+\frac{b c x \sqrt{-c^2 x^2-1}}{3 d \sqrt{-c^2 x^2} \left(c^2 d-e\right) \sqrt{d+e x^2}}",1,"(b*c*x*Sqrt[-1 - c^2*x^2])/(3*d*(c^2*d - e)*Sqrt[-(c^2*x^2)]*Sqrt[d + e*x^2]) - (a + b*ArcCsch[c*x])/(3*e*(d + e*x^2)^(3/2)) - (b*c*x*ArcTan[Sqrt[d + e*x^2]/(Sqrt[d]*Sqrt[-1 - c^2*x^2])])/(3*d^(3/2)*e*Sqrt[-(c^2*x^2)])","A",5,5,21,0.2381,1,"{6300, 446, 96, 93, 204}"
159,0,0,0,0.1240755,"\int \frac{a+b \text{csch}^{-1}(c x)}{x \left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCsch[c*x])/(x*(d + e*x^2)^(5/2)),x]","\int \frac{a+b \text{csch}^{-1}(c x)}{x \left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{a+b \text{csch}^{-1}(c x)}{x \left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(a + b*ArcCsch[c*x])/(x*(d + e*x^2)^(5/2)), x]","A",0,0,0,0,-1,"{}"
160,0,0,0,0.1523062,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^3 \left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCsch[c*x])/(x^3*(d + e*x^2)^(5/2)),x]","\int \frac{a+b \text{csch}^{-1}(c x)}{x^3 \left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{a+b \text{csch}^{-1}(c x)}{x^3 \left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(a + b*ArcCsch[c*x])/(x^3*(d + e*x^2)^(5/2)), x]","A",0,0,0,0,-1,"{}"
161,0,0,0,0.1316733,"\int \frac{x^6 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^6*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(5/2),x]","\int \frac{x^6 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{x^6 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(x^6*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(5/2), x]","A",0,0,0,0,-1,"{}"
162,0,0,0,0.1098748,"\int \frac{x^4 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^4*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(5/2),x]","\int \frac{x^4 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","\text{Int}\left(\frac{x^4 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}},x\right)",0,"Defer[Int][(x^4*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(5/2), x]","A",0,0,0,0,-1,"{}"
163,1,359,0,0.3077251,"\int \frac{x^2 \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(x^2*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(5/2),x]","\frac{x^3 \left(a+b \text{csch}^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}+\frac{b x \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{3 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \left(c^2 d-e\right) \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}+\frac{b c^3 x^2 \sqrt{d+e x^2}}{3 d e \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \left(c^2 d-e\right)}+\frac{b c x^2 \sqrt{-c^2 x^2-1}}{3 d \sqrt{-c^2 x^2} \left(c^2 d-e\right) \sqrt{d+e x^2}}-\frac{b c^2 x \sqrt{d+e x^2} E\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{3 d e \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \left(c^2 d-e\right) \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}","\frac{x^3 \left(a+b \text{csch}^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}+\frac{b x \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{3 d^2 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \left(c^2 d-e\right) \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}+\frac{b c^3 x^2 \sqrt{d+e x^2}}{3 d e \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \left(c^2 d-e\right)}+\frac{b c x^2 \sqrt{-c^2 x^2-1}}{3 d \sqrt{-c^2 x^2} \left(c^2 d-e\right) \sqrt{d+e x^2}}-\frac{b c^2 x \sqrt{d+e x^2} E\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{3 d e \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \left(c^2 d-e\right) \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}",1,"(b*c*x^2*Sqrt[-1 - c^2*x^2])/(3*d*(c^2*d - e)*Sqrt[-(c^2*x^2)]*Sqrt[d + e*x^2]) + (b*c^3*x^2*Sqrt[d + e*x^2])/(3*d*(c^2*d - e)*e*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]) + (x^3*(a + b*ArcCsch[c*x]))/(3*d*(d + e*x^2)^(3/2)) - (b*c^2*x*Sqrt[d + e*x^2]*EllipticE[ArcTan[c*x], 1 - e/(c^2*d)])/(3*d*(c^2*d - e)*e*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))]) + (b*x*Sqrt[d + e*x^2]*EllipticF[ArcTan[c*x], 1 - e/(c^2*d)])/(3*d^2*(c^2*d - e)*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))])","A",7,8,23,0.3478,1,"{264, 6302, 12, 471, 422, 418, 492, 411}"
164,1,278,0,0.1765788,"\int \frac{a+b \text{csch}^{-1}(c x)}{\left(d+e x^2\right)^{5/2}} \, dx","Int[(a + b*ArcCsch[c*x])/(d + e*x^2)^(5/2),x]","\frac{2 x \left(a+b \text{csch}^{-1}(c x)\right)}{3 d^2 \sqrt{d+e x^2}}+\frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}-\frac{b x \left(3 c^2 d-2 e\right) \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{3 d^3 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \left(c^2 d-e\right) \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}-\frac{b c \sqrt{e} x \sqrt{-c^2 x^2-1} E\left(\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)|1-\frac{c^2 d}{e}\right)}{3 d^{3/2} \sqrt{-c^2 x^2} \left(c^2 d-e\right) \sqrt{d+e x^2} \sqrt{\frac{d \left(c^2 x^2+1\right)}{d+e x^2}}}","\frac{2 x \left(a+b \text{csch}^{-1}(c x)\right)}{3 d^2 \sqrt{d+e x^2}}+\frac{x \left(a+b \text{csch}^{-1}(c x)\right)}{3 d \left(d+e x^2\right)^{3/2}}-\frac{b x \left(3 c^2 d-2 e\right) \sqrt{d+e x^2} F\left(\tan ^{-1}(c x)|1-\frac{e}{c^2 d}\right)}{3 d^3 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1} \left(c^2 d-e\right) \sqrt{\frac{d+e x^2}{d \left(c^2 x^2+1\right)}}}-\frac{b c \sqrt{e} x \sqrt{-c^2 x^2-1} E\left(\tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)|1-\frac{c^2 d}{e}\right)}{3 d^{3/2} \sqrt{-c^2 x^2} \left(c^2 d-e\right) \sqrt{d+e x^2} \sqrt{\frac{d \left(c^2 x^2+1\right)}{d+e x^2}}}",1,"(x*(a + b*ArcCsch[c*x]))/(3*d*(d + e*x^2)^(3/2)) + (2*x*(a + b*ArcCsch[c*x]))/(3*d^2*Sqrt[d + e*x^2]) - (b*c*Sqrt[e]*x*Sqrt[-1 - c^2*x^2]*EllipticE[ArcTan[(Sqrt[e]*x)/Sqrt[d]], 1 - (c^2*d)/e])/(3*d^(3/2)*(c^2*d - e)*Sqrt[-(c^2*x^2)]*Sqrt[(d*(1 + c^2*x^2))/(d + e*x^2)]*Sqrt[d + e*x^2]) - (b*(3*c^2*d - 2*e)*x*Sqrt[d + e*x^2]*EllipticF[ArcTan[c*x], 1 - e/(c^2*d)])/(3*d^3*(c^2*d - e)*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2]*Sqrt[(d + e*x^2)/(d*(1 + c^2*x^2))])","A",5,7,20,0.3500,1,"{192, 191, 6292, 12, 525, 418, 411}"
165,1,577,0,2.5749731,"\int (f x)^m \left(d+e x^2\right)^3 \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^3*(a + b*ArcCsch[c*x]),x]","\frac{3 d^2 e (f x)^{m+3} \left(a+b \text{csch}^{-1}(c x)\right)}{f^3 (m+3)}+\frac{d^3 (f x)^{m+1} \left(a+b \text{csch}^{-1}(c x)\right)}{f (m+1)}+\frac{3 d e^2 (f x)^{m+5} \left(a+b \text{csch}^{-1}(c x)\right)}{f^5 (m+5)}+\frac{e^3 (f x)^{m+7} \left(a+b \text{csch}^{-1}(c x)\right)}{f^7 (m+7)}-\frac{b c x \sqrt{c^2 x^2+1} (f x)^{m+1} \left(\frac{d^3}{(m+1)^2}-\frac{e \left(3 c^4 d^2 \left(m^4+22 m^3+179 m^2+638 m+840\right)-3 c^2 d e (m+3)^2 \left(m^2+13 m+42\right)+e^2 \left(m^2+8 m+15\right)^2\right)}{c^6 (m+2) (m+3) (m+4) (m+5) (m+6) (m+7)}\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-c^2 x^2\right)}{f \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}+\frac{b e x \sqrt{-c^2 x^2-1} (f x)^{m+1} \left(3 c^4 d^2 \left(m^4+22 m^3+179 m^2+638 m+840\right)-3 c^2 d e (m+3)^2 \left(m^2+13 m+42\right)+e^2 \left(m^2+8 m+15\right)^2\right)}{c^5 f (m+2) (m+3) (m+4) (m+5) (m+6) (m+7) \sqrt{-c^2 x^2}}-\frac{b e^2 x \sqrt{-c^2 x^2-1} (f x)^{m+3} \left(e (m+5)^2-3 c^2 d \left(m^2+13 m+42\right)\right)}{c^3 f^3 (m+4) (m+5) (m+6) (m+7) \sqrt{-c^2 x^2}}+\frac{b e^3 x \sqrt{-c^2 x^2-1} (f x)^{m+5}}{c f^5 (m+6) (m+7) \sqrt{-c^2 x^2}}","\frac{3 d^2 e (f x)^{m+3} \left(a+b \text{csch}^{-1}(c x)\right)}{f^3 (m+3)}+\frac{d^3 (f x)^{m+1} \left(a+b \text{csch}^{-1}(c x)\right)}{f (m+1)}+\frac{3 d e^2 (f x)^{m+5} \left(a+b \text{csch}^{-1}(c x)\right)}{f^5 (m+5)}+\frac{e^3 (f x)^{m+7} \left(a+b \text{csch}^{-1}(c x)\right)}{f^7 (m+7)}-\frac{b x \sqrt{c^2 x^2+1} (f x)^{m+1} \left(\frac{c^6 d^3 (m+2) (m+4) (m+6)}{m+1}-\frac{e (m+1) \left(3 c^4 d^2 \left(m^4+22 m^3+179 m^2+638 m+840\right)-3 c^2 d e (m+3)^2 \left(m^2+13 m+42\right)+e^2 \left(m^2+8 m+15\right)^2\right)}{(m+3) (m+5) (m+7)}\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-c^2 x^2\right)}{c^5 f (m+1) (m+2) (m+4) (m+6) \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}+\frac{b e x \sqrt{-c^2 x^2-1} (f x)^{m+1} \left(3 c^4 d^2 \left(m^4+22 m^3+179 m^2+638 m+840\right)-3 c^2 d e (m+3)^2 \left(m^2+13 m+42\right)+e^2 \left(m^2+8 m+15\right)^2\right)}{c^5 f (m+2) (m+3) (m+4) (m+5) (m+6) (m+7) \sqrt{-c^2 x^2}}-\frac{b e^2 x \sqrt{-c^2 x^2-1} (f x)^{m+3} \left(e (m+5)^2-3 c^2 d \left(m^2+13 m+42\right)\right)}{c^3 f^3 (m+4) (m+5) (m+6) (m+7) \sqrt{-c^2 x^2}}+\frac{b e^3 x \sqrt{-c^2 x^2-1} (f x)^{m+5}}{c f^5 (m+6) (m+7) \sqrt{-c^2 x^2}}",1,"(b*e*(e^2*(15 + 8*m + m^2)^2 - 3*c^2*d*e*(3 + m)^2*(42 + 13*m + m^2) + 3*c^4*d^2*(840 + 638*m + 179*m^2 + 22*m^3 + m^4))*x*(f*x)^(1 + m)*Sqrt[-1 - c^2*x^2])/(c^5*f*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(7 + m)*Sqrt[-(c^2*x^2)]) - (b*e^2*(e*(5 + m)^2 - 3*c^2*d*(42 + 13*m + m^2))*x*(f*x)^(3 + m)*Sqrt[-1 - c^2*x^2])/(c^3*f^3*(4 + m)*(5 + m)*(6 + m)*(7 + m)*Sqrt[-(c^2*x^2)]) + (b*e^3*x*(f*x)^(5 + m)*Sqrt[-1 - c^2*x^2])/(c*f^5*(6 + m)*(7 + m)*Sqrt[-(c^2*x^2)]) + (d^3*(f*x)^(1 + m)*(a + b*ArcCsch[c*x]))/(f*(1 + m)) + (3*d^2*e*(f*x)^(3 + m)*(a + b*ArcCsch[c*x]))/(f^3*(3 + m)) + (3*d*e^2*(f*x)^(5 + m)*(a + b*ArcCsch[c*x]))/(f^5*(5 + m)) + (e^3*(f*x)^(7 + m)*(a + b*ArcCsch[c*x]))/(f^7*(7 + m)) - (b*c*(d^3/(1 + m)^2 - (e*(e^2*(15 + 8*m + m^2)^2 - 3*c^2*d*e*(3 + m)^2*(42 + 13*m + m^2) + 3*c^4*d^2*(840 + 638*m + 179*m^2 + 22*m^3 + m^4)))/(c^6*(2 + m)*(3 + m)*(4 + m)*(5 + m)*(6 + m)*(7 + m)))*x*(f*x)^(1 + m)*Sqrt[1 + c^2*x^2]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -(c^2*x^2)])/(f*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2])","A",6,7,23,0.3043,1,"{270, 6302, 1809, 1267, 459, 365, 364}"
166,1,360,0,0.4912816,"\int (f x)^m \left(d+e x^2\right)^2 \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^2*(a + b*ArcCsch[c*x]),x]","\frac{d^2 (f x)^{m+1} \left(a+b \text{csch}^{-1}(c x)\right)}{f (m+1)}+\frac{2 d e (f x)^{m+3} \left(a+b \text{csch}^{-1}(c x)\right)}{f^3 (m+3)}+\frac{e^2 (f x)^{m+5} \left(a+b \text{csch}^{-1}(c x)\right)}{f^5 (m+5)}-\frac{b c x \sqrt{c^2 x^2+1} (f x)^{m+1} \left(\frac{e \left(e (m+3)^2-2 c^2 d \left(m^2+9 m+20\right)\right)}{c^4 (m+2) (m+3) (m+4) (m+5)}+\frac{d^2}{(m+1)^2}\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-c^2 x^2\right)}{f \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}-\frac{b e x \sqrt{-c^2 x^2-1} (f x)^{m+1} \left(e (m+3)^2-2 c^2 d \left(m^2+9 m+20\right)\right)}{c^3 f (m+2) (m+3) (m+4) (m+5) \sqrt{-c^2 x^2}}+\frac{b e^2 x \sqrt{-c^2 x^2-1} (f x)^{m+3}}{c f^3 (m+4) (m+5) \sqrt{-c^2 x^2}}","\frac{d^2 (f x)^{m+1} \left(a+b \text{csch}^{-1}(c x)\right)}{f (m+1)}+\frac{2 d e (f x)^{m+3} \left(a+b \text{csch}^{-1}(c x)\right)}{f^3 (m+3)}+\frac{e^2 (f x)^{m+5} \left(a+b \text{csch}^{-1}(c x)\right)}{f^5 (m+5)}-\frac{b x \sqrt{c^2 x^2+1} (f x)^{m+1} \left(c^4 d^2 (m+2) (m+3) (m+4) (m+5)+e (m+1)^2 \left(e (m+3)^2-2 c^2 d \left(m^2+9 m+20\right)\right)\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-c^2 x^2\right)}{c^3 f (m+1)^2 (m+2) (m+3) (m+4) (m+5) \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}-\frac{b e x \sqrt{-c^2 x^2-1} (f x)^{m+1} \left(e (m+3)^2-2 c^2 d \left(m^2+9 m+20\right)\right)}{c^3 f (m+2) (m+3) (m+4) (m+5) \sqrt{-c^2 x^2}}+\frac{b e^2 x \sqrt{-c^2 x^2-1} (f x)^{m+3}}{c f^3 (m+4) (m+5) \sqrt{-c^2 x^2}}",1,"-((b*e*(e*(3 + m)^2 - 2*c^2*d*(20 + 9*m + m^2))*x*(f*x)^(1 + m)*Sqrt[-1 - c^2*x^2])/(c^3*f*(2 + m)*(3 + m)*(4 + m)*(5 + m)*Sqrt[-(c^2*x^2)])) + (b*e^2*x*(f*x)^(3 + m)*Sqrt[-1 - c^2*x^2])/(c*f^3*(4 + m)*(5 + m)*Sqrt[-(c^2*x^2)]) + (d^2*(f*x)^(1 + m)*(a + b*ArcCsch[c*x]))/(f*(1 + m)) + (2*d*e*(f*x)^(3 + m)*(a + b*ArcCsch[c*x]))/(f^3*(3 + m)) + (e^2*(f*x)^(5 + m)*(a + b*ArcCsch[c*x]))/(f^5*(5 + m)) - (b*c*(d^2/(1 + m)^2 + (e*(e*(3 + m)^2 - 2*c^2*d*(20 + 9*m + m^2)))/(c^4*(2 + m)*(3 + m)*(4 + m)*(5 + m)))*x*(f*x)^(1 + m)*Sqrt[1 + c^2*x^2]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -(c^2*x^2)])/(f*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2])","A",6,7,23,0.3043,1,"{270, 6302, 12, 1267, 459, 365, 364}"
167,1,208,0,0.2195704,"\int (f x)^m \left(d+e x^2\right) \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)*(a + b*ArcCsch[c*x]),x]","\frac{d (f x)^{m+1} \left(a+b \text{csch}^{-1}(c x)\right)}{f (m+1)}+\frac{e (f x)^{m+3} \left(a+b \text{csch}^{-1}(c x)\right)}{f^3 (m+3)}-\frac{b c x \sqrt{c^2 x^2+1} (f x)^{m+1} \left(\frac{d}{(m+1)^2}-\frac{e}{c^2 (m+2) (m+3)}\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-c^2 x^2\right)}{f \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}+\frac{b e x \sqrt{-c^2 x^2-1} (f x)^{m+1}}{c f \left(m^2+5 m+6\right) \sqrt{-c^2 x^2}}","\frac{d (f x)^{m+1} \left(a+b \text{csch}^{-1}(c x)\right)}{f (m+1)}+\frac{e (f x)^{m+3} \left(a+b \text{csch}^{-1}(c x)\right)}{f^3 (m+3)}+\frac{b x \sqrt{c^2 x^2+1} (f x)^{m+1} \left(e (m+1)^2-c^2 d (m+2) (m+3)\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-c^2 x^2\right)}{c f (m+1)^2 (m+2) (m+3) \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}+\frac{b e x \sqrt{-c^2 x^2-1} (f x)^{m+1}}{c f \left(m^2+5 m+6\right) \sqrt{-c^2 x^2}}",1,"(b*e*x*(f*x)^(1 + m)*Sqrt[-1 - c^2*x^2])/(c*f*(6 + 5*m + m^2)*Sqrt[-(c^2*x^2)]) + (d*(f*x)^(1 + m)*(a + b*ArcCsch[c*x]))/(f*(1 + m)) + (e*(f*x)^(3 + m)*(a + b*ArcCsch[c*x]))/(f^3*(3 + m)) - (b*c*(d/(1 + m)^2 - e/(c^2*(2 + m)*(3 + m)))*x*(f*x)^(1 + m)*Sqrt[1 + c^2*x^2]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -(c^2*x^2)])/(f*Sqrt[-(c^2*x^2)]*Sqrt[-1 - c^2*x^2])","A",5,6,21,0.2857,1,"{14, 6302, 12, 459, 365, 364}"
168,0,0,0,0.0785348,"\int \frac{(f x)^m \left(a+b \text{csch}^{-1}(c x)\right)}{d+e x^2} \, dx","Int[((f*x)^m*(a + b*ArcCsch[c*x]))/(d + e*x^2),x]","\int \frac{(f x)^m \left(a+b \text{csch}^{-1}(c x)\right)}{d+e x^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \text{csch}^{-1}(c x)\right)}{d+e x^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcCsch[c*x]))/(d + e*x^2), x]","A",0,0,0,0,-1,"{}"
169,0,0,0,0.0760004,"\int \frac{(f x)^m \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","Int[((f*x)^m*(a + b*ArcCsch[c*x]))/(d + e*x^2)^2,x]","\int \frac{(f x)^m \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^2} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^2},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcCsch[c*x]))/(d + e*x^2)^2, x]","A",0,0,0,0,-1,"{}"
170,0,0,0,0.1162835,"\int (f x)^m \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[(f*x)^m*(d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]),x]","\int (f x)^m \left(d+e x^2\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","\text{Int}\left(\left(d+e x^2\right)^{3/2} (f x)^m \left(a+b \text{csch}^{-1}(c x)\right),x\right)",0,"Defer[Int][(f*x)^m*(d + e*x^2)^(3/2)*(a + b*ArcCsch[c*x]), x]","A",0,0,0,0,-1,"{}"
171,0,0,0,0.1041744,"\int (f x)^m \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","Int[(f*x)^m*Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]),x]","\int (f x)^m \sqrt{d+e x^2} \left(a+b \text{csch}^{-1}(c x)\right) \, dx","\text{Int}\left(\sqrt{d+e x^2} (f x)^m \left(a+b \text{csch}^{-1}(c x)\right),x\right)",0,"Defer[Int][(f*x)^m*Sqrt[d + e*x^2]*(a + b*ArcCsch[c*x]), x]","A",0,0,0,0,-1,"{}"
172,0,0,0,0.1034372,"\int \frac{(f x)^m \left(a+b \text{csch}^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","Int[((f*x)^m*(a + b*ArcCsch[c*x]))/Sqrt[d + e*x^2],x]","\int \frac{(f x)^m \left(a+b \text{csch}^{-1}(c x)\right)}{\sqrt{d+e x^2}} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \text{csch}^{-1}(c x)\right)}{\sqrt{d+e x^2}},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcCsch[c*x]))/Sqrt[d + e*x^2], x]","A",0,0,0,0,-1,"{}"
173,0,0,0,0.1149558,"\int \frac{(f x)^m \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","Int[((f*x)^m*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(3/2),x]","\int \frac{(f x)^m \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}} \, dx","\text{Int}\left(\frac{(f x)^m \left(a+b \text{csch}^{-1}(c x)\right)}{\left(d+e x^2\right)^{3/2}},x\right)",0,"Defer[Int][((f*x)^m*(a + b*ArcCsch[c*x]))/(d + e*x^2)^(3/2), x]","A",0,0,0,0,-1,"{}"
174,1,395,0,2.3444023,"\int \frac{x^{11} \left(a+b \text{csch}^{-1}(c x)\right)}{\sqrt{1-c^4 x^4}} \, dx","Int[(x^11*(a + b*ArcCsch[c*x]))/Sqrt[1 - c^4*x^4],x]","-\frac{\left(1-c^4 x^4\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{10 c^{12}}+\frac{\left(1-c^4 x^4\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 c^{12}}-\frac{\sqrt{1-c^4 x^4} \left(a+b \text{csch}^{-1}(c x)\right)}{2 c^{12}}-\frac{b \sqrt{c^2 x^2+1} \left(1-c^2 x^2\right)^{9/2}}{90 c^{13} x \sqrt{\frac{1}{c^2 x^2}+1}}+\frac{3 b \sqrt{c^2 x^2+1} \left(1-c^2 x^2\right)^{7/2}}{70 c^{13} x \sqrt{\frac{1}{c^2 x^2}+1}}-\frac{13 b \sqrt{c^2 x^2+1} \left(1-c^2 x^2\right)^{5/2}}{150 c^{13} x \sqrt{\frac{1}{c^2 x^2}+1}}+\frac{7 b \sqrt{c^2 x^2+1} \left(1-c^2 x^2\right)^{3/2}}{90 c^{13} x \sqrt{\frac{1}{c^2 x^2}+1}}-\frac{4 b \sqrt{c^2 x^2+1} \sqrt{1-c^2 x^2}}{15 c^{13} x \sqrt{\frac{1}{c^2 x^2}+1}}+\frac{4 b \sqrt{c^2 x^2+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{15 c^{13} x \sqrt{\frac{1}{c^2 x^2}+1}}","-\frac{\left(1-c^4 x^4\right)^{5/2} \left(a+b \text{csch}^{-1}(c x)\right)}{10 c^{12}}+\frac{\left(1-c^4 x^4\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{3 c^{12}}-\frac{\sqrt{1-c^4 x^4} \left(a+b \text{csch}^{-1}(c x)\right)}{2 c^{12}}-\frac{b \sqrt{c^2 x^2+1} \left(1-c^2 x^2\right)^{9/2}}{90 c^{13} x \sqrt{\frac{1}{c^2 x^2}+1}}+\frac{3 b \sqrt{c^2 x^2+1} \left(1-c^2 x^2\right)^{7/2}}{70 c^{13} x \sqrt{\frac{1}{c^2 x^2}+1}}-\frac{13 b \sqrt{c^2 x^2+1} \left(1-c^2 x^2\right)^{5/2}}{150 c^{13} x \sqrt{\frac{1}{c^2 x^2}+1}}+\frac{7 b \sqrt{c^2 x^2+1} \left(1-c^2 x^2\right)^{3/2}}{90 c^{13} x \sqrt{\frac{1}{c^2 x^2}+1}}-\frac{4 b \sqrt{c^2 x^2+1} \sqrt{1-c^2 x^2}}{15 c^{13} x \sqrt{\frac{1}{c^2 x^2}+1}}+\frac{4 b \sqrt{c^2 x^2+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{15 c^{13} x \sqrt{\frac{1}{c^2 x^2}+1}}",1,"(-4*b*Sqrt[1 - c^2*x^2]*Sqrt[1 + c^2*x^2])/(15*c^13*Sqrt[1 + 1/(c^2*x^2)]*x) + (7*b*(1 - c^2*x^2)^(3/2)*Sqrt[1 + c^2*x^2])/(90*c^13*Sqrt[1 + 1/(c^2*x^2)]*x) - (13*b*(1 - c^2*x^2)^(5/2)*Sqrt[1 + c^2*x^2])/(150*c^13*Sqrt[1 + 1/(c^2*x^2)]*x) + (3*b*(1 - c^2*x^2)^(7/2)*Sqrt[1 + c^2*x^2])/(70*c^13*Sqrt[1 + 1/(c^2*x^2)]*x) - (b*(1 - c^2*x^2)^(9/2)*Sqrt[1 + c^2*x^2])/(90*c^13*Sqrt[1 + 1/(c^2*x^2)]*x) - (Sqrt[1 - c^4*x^4]*(a + b*ArcCsch[c*x]))/(2*c^12) + ((1 - c^4*x^4)^(3/2)*(a + b*ArcCsch[c*x]))/(3*c^12) - ((1 - c^4*x^4)^(5/2)*(a + b*ArcCsch[c*x]))/(10*c^12) + (4*b*Sqrt[1 + c^2*x^2]*ArcTanh[Sqrt[1 - c^2*x^2]])/(15*c^13*Sqrt[1 + 1/(c^2*x^2)]*x)","A",16,11,26,0.4231,1,"{266, 43, 6310, 12, 6721, 6742, 848, 50, 63, 208, 783}"
175,1,264,0,1.916145,"\int \frac{x^7 \left(a+b \text{csch}^{-1}(c x)\right)}{\sqrt{1-c^4 x^4}} \, dx","Int[(x^7*(a + b*ArcCsch[c*x]))/Sqrt[1 - c^4*x^4],x]","\frac{\left(1-c^4 x^4\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{6 c^8}-\frac{\sqrt{1-c^4 x^4} \left(a+b \text{csch}^{-1}(c x)\right)}{2 c^8}-\frac{b \sqrt{c^2 x^2+1} \left(1-c^2 x^2\right)^{5/2}}{30 c^9 x \sqrt{\frac{1}{c^2 x^2}+1}}+\frac{b \sqrt{c^2 x^2+1} \left(1-c^2 x^2\right)^{3/2}}{18 c^9 x \sqrt{\frac{1}{c^2 x^2}+1}}-\frac{b \sqrt{c^2 x^2+1} \sqrt{1-c^2 x^2}}{3 c^9 x \sqrt{\frac{1}{c^2 x^2}+1}}+\frac{b \sqrt{c^2 x^2+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{3 c^9 x \sqrt{\frac{1}{c^2 x^2}+1}}","\frac{\left(1-c^4 x^4\right)^{3/2} \left(a+b \text{csch}^{-1}(c x)\right)}{6 c^8}-\frac{\sqrt{1-c^4 x^4} \left(a+b \text{csch}^{-1}(c x)\right)}{2 c^8}-\frac{b \sqrt{c^2 x^2+1} \left(1-c^2 x^2\right)^{5/2}}{30 c^9 x \sqrt{\frac{1}{c^2 x^2}+1}}+\frac{b \sqrt{c^2 x^2+1} \left(1-c^2 x^2\right)^{3/2}}{18 c^9 x \sqrt{\frac{1}{c^2 x^2}+1}}-\frac{b \sqrt{c^2 x^2+1} \sqrt{1-c^2 x^2}}{3 c^9 x \sqrt{\frac{1}{c^2 x^2}+1}}+\frac{b \sqrt{c^2 x^2+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{3 c^9 x \sqrt{\frac{1}{c^2 x^2}+1}}",1,"-(b*Sqrt[1 - c^2*x^2]*Sqrt[1 + c^2*x^2])/(3*c^9*Sqrt[1 + 1/(c^2*x^2)]*x) + (b*(1 - c^2*x^2)^(3/2)*Sqrt[1 + c^2*x^2])/(18*c^9*Sqrt[1 + 1/(c^2*x^2)]*x) - (b*(1 - c^2*x^2)^(5/2)*Sqrt[1 + c^2*x^2])/(30*c^9*Sqrt[1 + 1/(c^2*x^2)]*x) - (Sqrt[1 - c^4*x^4]*(a + b*ArcCsch[c*x]))/(2*c^8) + ((1 - c^4*x^4)^(3/2)*(a + b*ArcCsch[c*x]))/(6*c^8) + (b*Sqrt[1 + c^2*x^2]*ArcTanh[Sqrt[1 - c^2*x^2]])/(3*c^9*Sqrt[1 + 1/(c^2*x^2)]*x)","A",13,11,26,0.4231,1,"{266, 43, 6310, 12, 6721, 6742, 848, 50, 63, 208, 783}"
176,1,133,0,0.2141168,"\int \frac{x^3 \left(a+b \text{csch}^{-1}(c x)\right)}{\sqrt{1-c^4 x^4}} \, dx","Int[(x^3*(a + b*ArcCsch[c*x]))/Sqrt[1 - c^4*x^4],x]","-\frac{\sqrt{1-c^4 x^4} \left(a+b \text{csch}^{-1}(c x)\right)}{2 c^4}-\frac{b \sqrt{1-c^2 x^2} \sqrt{c^2 x^2+1}}{2 c^5 x \sqrt{\frac{1}{c^2 x^2}+1}}+\frac{b \sqrt{c^2 x^2+1} \tanh ^{-1}\left(\sqrt{1-c^2 x^2}\right)}{2 c^5 x \sqrt{\frac{1}{c^2 x^2}+1}}","-\frac{\sqrt{1-c^4 x^4} \left(a+b \text{csch}^{-1}(c x)\right)}{2 c^4}+\frac{b x \sqrt{1-c^4 x^4}}{2 c^3 \sqrt{-c^2 x^2} \sqrt{-c^2 x^2-1}}-\frac{b x \tan ^{-1}\left(\frac{\sqrt{1-c^4 x^4}}{\sqrt{-c^2 x^2-1}}\right)}{2 c^3 \sqrt{-c^2 x^2}}",1,"-(b*Sqrt[1 - c^2*x^2]*Sqrt[1 + c^2*x^2])/(2*c^5*Sqrt[1 + 1/(c^2*x^2)]*x) - (Sqrt[1 - c^4*x^4]*(a + b*ArcCsch[c*x]))/(2*c^4) + (b*Sqrt[1 + c^2*x^2]*ArcTanh[Sqrt[1 - c^2*x^2]])/(2*c^5*Sqrt[1 + 1/(c^2*x^2)]*x)","A",8,9,26,0.3462,1,"{261, 6310, 12, 1572, 1252, 848, 50, 63, 208}"
177,0,0,0,0.0906919,"\int \frac{a+b \text{csch}^{-1}(c x)}{x \sqrt{1-c^4 x^4}} \, dx","Int[(a + b*ArcCsch[c*x])/(x*Sqrt[1 - c^4*x^4]),x]","\int \frac{a+b \text{csch}^{-1}(c x)}{x \sqrt{1-c^4 x^4}} \, dx","\text{Int}\left(\frac{a+b \text{csch}^{-1}(c x)}{x \sqrt{1-c^4 x^4}},x\right)",0,"Defer[Int][(a + b*ArcCsch[c*x])/(x*Sqrt[1 - c^4*x^4]), x]","A",0,0,0,0,-1,"{}"
178,0,0,0,0.1038476,"\int \frac{a+b \text{csch}^{-1}(c x)}{x^5 \sqrt{1-c^4 x^4}} \, dx","Int[(a + b*ArcCsch[c*x])/(x^5*Sqrt[1 - c^4*x^4]),x]","\int \frac{a+b \text{csch}^{-1}(c x)}{x^5 \sqrt{1-c^4 x^4}} \, dx","\text{Int}\left(\frac{a+b \text{csch}^{-1}(c x)}{x^5 \sqrt{1-c^4 x^4}},x\right)",0,"Defer[Int][(a + b*ArcCsch[c*x])/(x^5*Sqrt[1 - c^4*x^4]), x]","A",0,0,0,0,-1,"{}"