1,1,153,183,0.2672165,"\int (d+e x)^3 \cosh ^{-1}(c x) \, dx","Integrate[(d + e*x)^3*ArcCosh[c*x],x]","-\frac{-24 c^4 x \cosh ^{-1}(c x) \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)+9 \left(8 c^2 d^2 e+e^3\right) \log \left(c x+\sqrt{c x-1} \sqrt{c x+1}\right)+c \sqrt{c x-1} \sqrt{c x+1} \left(c^2 \left(96 d^3+72 d^2 e x+32 d e^2 x^2+6 e^3 x^3\right)+e^2 (64 d+9 e x)\right)}{96 c^4}","-\frac{\left(8 c^4 d^4+24 c^2 d^2 e^2+3 e^4\right) \cosh ^{-1}(c x)}{32 c^4 e}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(e x \left(26 c^2 d^2+9 e^2\right)+4 d \left(19 c^2 d^2+16 e^2\right)\right)}{96 c^3}-\frac{\sqrt{c x-1} \sqrt{c x+1} (d+e x)^3}{16 c}-\frac{7 d \sqrt{c x-1} \sqrt{c x+1} (d+e x)^2}{48 c}+\frac{\cosh ^{-1}(c x) (d+e x)^4}{4 e}",1,"-1/96*(c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(e^2*(64*d + 9*e*x) + c^2*(96*d^3 + 72*d^2*e*x + 32*d*e^2*x^2 + 6*e^3*x^3)) - 24*c^4*x*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3)*ArcCosh[c*x] + 9*(8*c^2*d^2*e + e^3)*Log[c*x + Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/c^4","A",1
2,1,113,123,0.2058082,"\int (d+e x)^2 \cosh ^{-1}(c x) \, dx","Integrate[(d + e*x)^2*ArcCosh[c*x],x]","-\frac{-6 c^3 x \cosh ^{-1}(c x) \left(3 d^2+3 d e x+e^2 x^2\right)+\sqrt{c x-1} \sqrt{c x+1} \left(c^2 \left(18 d^2+9 d e x+2 e^2 x^2\right)+4 e^2\right)+9 c d e \log \left(c x+\sqrt{c x-1} \sqrt{c x+1}\right)}{18 c^3}","-\frac{1}{6} d \left(\frac{3 e}{c^2}+\frac{2 d^2}{e}\right) \cosh ^{-1}(c x)-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(4 \left(4 c^2 d^2+e^2\right)+5 c^2 d e x\right)}{18 c^3}-\frac{\sqrt{c x-1} \sqrt{c x+1} (d+e x)^2}{9 c}+\frac{\cosh ^{-1}(c x) (d+e x)^3}{3 e}",1,"-1/18*(Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(4*e^2 + c^2*(18*d^2 + 9*d*e*x + 2*e^2*x^2)) - 6*c^3*x*(3*d^2 + 3*d*e*x + e^2*x^2)*ArcCosh[c*x] + 9*c*d*e*Log[c*x + Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/c^3","A",1
3,1,73,97,0.0780148,"\int (d+e x) \cosh ^{-1}(c x) \, dx","Integrate[(d + e*x)*ArcCosh[c*x],x]","-\frac{-2 c^2 x \cosh ^{-1}(c x) (2 d+e x)+c \sqrt{c x-1} \sqrt{c x+1} (4 d+e x)+2 e \tanh ^{-1}\left(\sqrt{\frac{c x-1}{c x+1}}\right)}{4 c^2}","-\frac{1}{4} \left(\frac{e}{c^2}+\frac{2 d^2}{e}\right) \cosh ^{-1}(c x)-\frac{\sqrt{c x-1} \sqrt{c x+1} (d+e x)}{4 c}+\frac{\cosh ^{-1}(c x) (d+e x)^2}{2 e}-\frac{3 d \sqrt{c x-1} \sqrt{c x+1}}{4 c}",1,"-1/4*(c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(4*d + e*x) - 2*c^2*x*(2*d + e*x)*ArcCosh[c*x] + 2*e*ArcTanh[Sqrt[(-1 + c*x)/(1 + c*x)]])/c^2","A",0
4,1,176,178,0.0113671,"\int \frac{\cosh ^{-1}(c x)}{d+e x} \, dx","Integrate[ArcCosh[c*x]/(d + e*x),x]","\frac{\text{Li}_2\left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}-c d}\right)}{e}+\frac{\text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{\cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e}+\frac{\cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e}-\frac{\cosh ^{-1}(c x)^2}{2 e}","\frac{\text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{\text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{\cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e}+\frac{\cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e}-\frac{\cosh ^{-1}(c x)^2}{2 e}",1,"-1/2*ArcCosh[c*x]^2/e + (ArcCosh[c*x]*Log[1 + (e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2])])/e + (ArcCosh[c*x]*Log[1 + (e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2])])/e + PolyLog[2, (e*E^ArcCosh[c*x])/(-(c*d) + Sqrt[c^2*d^2 - e^2])]/e + PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2]))]/e","A",1
5,1,92,83,0.0998842,"\int \frac{\cosh ^{-1}(c x)}{(d+e x)^2} \, dx","Integrate[ArcCosh[c*x]/(d + e*x)^2,x]","\frac{\frac{c \left(\log (d+e x)-\log \left(-\sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d^2-e^2}+c^2 d x+e\right)\right)}{\sqrt{c^2 d^2-e^2}}-\frac{\cosh ^{-1}(c x)}{d+e x}}{e}","\frac{2 c \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{e \sqrt{c d-e} \sqrt{c d+e}}-\frac{\cosh ^{-1}(c x)}{e (d+e x)}",1,"(-(ArcCosh[c*x]/(d + e*x)) + (c*(Log[d + e*x] - Log[e + c^2*d*x - Sqrt[c^2*d^2 - e^2]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]]))/Sqrt[c^2*d^2 - e^2])/e","A",1
6,1,190,132,0.1932656,"\int \frac{\cosh ^{-1}(c x)}{(d+e x)^3} \, dx","Integrate[ArcCosh[c*x]/(d + e*x)^3,x]","\frac{c (d+e x) \left(-e \sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d^2-e^2}-c^2 d (d+e x) \log \left(-\sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d^2-e^2}+c^2 d x+e\right)+c^2 d (d+e x) \log (d+e x)\right)-\left(c^2 d^2-e^2\right)^{3/2} \cosh ^{-1}(c x)}{2 e (c d-e) (c d+e) \sqrt{c^2 d^2-e^2} (d+e x)^2}","\frac{c^3 d \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{e (c d-e)^{3/2} (c d+e)^{3/2}}-\frac{c \sqrt{c x-1} \sqrt{c x+1}}{2 \left(c^2 d^2-e^2\right) (d+e x)}-\frac{\cosh ^{-1}(c x)}{2 e (d+e x)^2}",1,"(-((c^2*d^2 - e^2)^(3/2)*ArcCosh[c*x]) + c*(d + e*x)*(-(e*Sqrt[c^2*d^2 - e^2]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + c^2*d*(d + e*x)*Log[d + e*x] - c^2*d*(d + e*x)*Log[e + c^2*d*x - Sqrt[c^2*d^2 - e^2]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]]))/(2*(c*d - e)*e*(c*d + e)*Sqrt[c^2*d^2 - e^2]*(d + e*x)^2)","A",1
7,1,244,195,0.5567289,"\int \frac{\cosh ^{-1}(c x)}{(d+e x)^4} \, dx","Integrate[ArcCosh[c*x]/(d + e*x)^4,x]","\frac{1}{6} \left(\frac{c \sqrt{c x-1} \sqrt{c x+1} \left(e^2-c^2 d (4 d+3 e x)\right)}{\left(e^2-c^2 d^2\right)^2 (d+e x)^2}-\frac{i c^3 \left(2 c^2 d^2+e^2\right) \log \left(\frac{12 e^2 (e-c d)^2 (c d+e)^2 \left(\sqrt{c x-1} \sqrt{c x+1} \sqrt{e^2-c^2 d^2}-i c^2 d x-i e\right)}{c^3 \sqrt{e^2-c^2 d^2} \left(2 c^2 d^2+e^2\right) (d+e x)}\right)}{e (e-c d)^2 (c d+e)^2 \sqrt{e^2-c^2 d^2}}-\frac{2 \cosh ^{-1}(c x)}{e (d+e x)^3}\right)","-\frac{c^3 d \sqrt{c x-1} \sqrt{c x+1}}{2 (c d-e)^2 (c d+e)^2 (d+e x)}-\frac{c \sqrt{c x-1} \sqrt{c x+1}}{6 \left(c^2 d^2-e^2\right) (d+e x)^2}+\frac{c^3 \left(2 c^2 d^2+e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{3 e (c d-e)^{5/2} (c d+e)^{5/2}}-\frac{\cosh ^{-1}(c x)}{3 e (d+e x)^3}",1,"((c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(e^2 - c^2*d*(4*d + 3*e*x)))/((-(c^2*d^2) + e^2)^2*(d + e*x)^2) - (2*ArcCosh[c*x])/(e*(d + e*x)^3) - (I*c^3*(2*c^2*d^2 + e^2)*Log[(12*e^2*(-(c*d) + e)^2*(c*d + e)^2*((-I)*e - I*c^2*d*x + Sqrt[-(c^2*d^2) + e^2]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]))/(c^3*Sqrt[-(c^2*d^2) + e^2]*(2*c^2*d^2 + e^2)*(d + e*x))])/(e*(-(c*d) + e)^2*(c*d + e)^2*Sqrt[-(c^2*d^2) + e^2]))/6","C",1
8,1,191,334,0.2707593,"\int (d+e x)^3 \cosh ^{-1}(c x)^2 \, dx","Integrate[(d + e*x)^3*ArcCosh[c*x]^2,x]","\frac{c^2 x \left(c^2 \left(576 d^3+216 d^2 e x+64 d e^2 x^2+9 e^3 x^3\right)+3 e^2 (128 d+9 e x)\right)-6 c \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x) \left(c^2 \left(96 d^3+72 d^2 e x+32 d e^2 x^2+6 e^3 x^3\right)+e^2 (64 d+9 e x)\right)+9 \cosh ^{-1}(c x)^2 \left(8 c^4 x \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)-24 c^2 d^2 e-3 e^3\right)}{288 c^4}","-\frac{3 e^3 \cosh ^{-1}(c x)^2}{32 c^4}-\frac{4 d e^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{3 c^3}-\frac{3 e^3 x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{16 c^3}-\frac{3 d^2 e \cosh ^{-1}(c x)^2}{4 c^2}+\frac{4 d e^2 x}{3 c^2}+\frac{3 e^3 x^2}{32 c^2}-\frac{d^4 \cosh ^{-1}(c x)^2}{4 e}-\frac{2 d^3 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c}-\frac{3 d^2 e x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{2 c}-\frac{2 d e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{3 c}+\frac{\cosh ^{-1}(c x)^2 (d+e x)^4}{4 e}-\frac{e^3 x^3 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{8 c}+2 d^3 x+\frac{3}{4} d^2 e x^2+\frac{2}{9} d e^2 x^3+\frac{e^3 x^4}{32}",1,"(c^2*x*(3*e^2*(128*d + 9*e*x) + c^2*(576*d^3 + 216*d^2*e*x + 64*d*e^2*x^2 + 9*e^3*x^3)) - 6*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(e^2*(64*d + 9*e*x) + c^2*(96*d^3 + 72*d^2*e*x + 32*d*e^2*x^2 + 6*e^3*x^3))*ArcCosh[c*x] + 9*(-24*c^2*d^2*e - 3*e^3 + 8*c^4*x*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3))*ArcCosh[c*x]^2)/(288*c^4)","A",1
9,1,131,215,0.1896741,"\int (d+e x)^2 \cosh ^{-1}(c x)^2 \, dx","Integrate[(d + e*x)^2*ArcCosh[c*x]^2,x]","\frac{9 \cosh ^{-1}(c x)^2 \left(2 c^3 x \left(3 d^2+3 d e x+e^2 x^2\right)-3 c d e\right)+c x \left(c^2 \left(108 d^2+27 d e x+4 e^2 x^2\right)+24 e^2\right)-6 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x) \left(c^2 \left(18 d^2+9 d e x+2 e^2 x^2\right)+4 e^2\right)}{54 c^3}","-\frac{4 e^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{9 c^3}-\frac{d e \cosh ^{-1}(c x)^2}{2 c^2}+\frac{4 e^2 x}{9 c^2}-\frac{d^3 \cosh ^{-1}(c x)^2}{3 e}-\frac{2 d^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c}-\frac{d e x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c}+\frac{\cosh ^{-1}(c x)^2 (d+e x)^3}{3 e}-\frac{2 e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{9 c}+2 d^2 x+\frac{1}{2} d e x^2+\frac{2 e^2 x^3}{27}",1,"(c*x*(24*e^2 + c^2*(108*d^2 + 27*d*e*x + 4*e^2*x^2)) - 6*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(4*e^2 + c^2*(18*d^2 + 9*d*e*x + 2*e^2*x^2))*ArcCosh[c*x] + 9*(-3*c*d*e + 2*c^3*x*(3*d^2 + 3*d*e*x + e^2*x^2))*ArcCosh[c*x]^2)/(54*c^3)","A",1
10,1,105,122,0.0758161,"\int (d+e x) \cosh ^{-1}(c x)^2 \, dx","Integrate[(d + e*x)*ArcCosh[c*x]^2,x]","\frac{e \left(2 c^2 x^2-1\right) \cosh ^{-1}(c x)^2}{4 c^2}+d x \cosh ^{-1}(c x)^2-\frac{2 d \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c}-\frac{e x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{2 c}+2 d x+\frac{e x^2}{4}","-\frac{e \cosh ^{-1}(c x)^2}{4 c^2}-\frac{d^2 \cosh ^{-1}(c x)^2}{2 e}+\frac{\cosh ^{-1}(c x)^2 (d+e x)^2}{2 e}-\frac{2 d \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{c}-\frac{e x \sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)}{2 c}+2 d x+\frac{e x^2}{4}",1,"2*d*x + (e*x^2)/4 - (2*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/c - (e*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x])/(2*c) + d*x*ArcCosh[c*x]^2 + (e*(-1 + 2*c^2*x^2)*ArcCosh[c*x]^2)/(4*c^2)","A",1
11,1,252,272,0.163395,"\int \frac{\cosh ^{-1}(c x)^2}{d+e x} \, dx","Integrate[ArcCosh[c*x]^2/(d + e*x),x]","-\frac{-6 \cosh ^{-1}(c x) \text{Li}_2\left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}-c d}\right)-6 \cosh ^{-1}(c x) \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)+6 \text{Li}_3\left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}-c d}\right)+6 \text{Li}_3\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)-3 \cosh ^{-1}(c x)^2 \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)-3 \cosh ^{-1}(c x)^2 \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)+\cosh ^{-1}(c x)^3}{3 e}","\frac{2 \cosh ^{-1}(c x) \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{2 \cosh ^{-1}(c x) \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e}-\frac{2 \text{Li}_3\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}-\frac{2 \text{Li}_3\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{\cosh ^{-1}(c x)^2 \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e}+\frac{\cosh ^{-1}(c x)^2 \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e}-\frac{\cosh ^{-1}(c x)^3}{3 e}",1,"-1/3*(ArcCosh[c*x]^3 - 3*ArcCosh[c*x]^2*Log[1 + (e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2])] - 3*ArcCosh[c*x]^2*Log[1 + (e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2])] - 6*ArcCosh[c*x]*PolyLog[2, (e*E^ArcCosh[c*x])/(-(c*d) + Sqrt[c^2*d^2 - e^2])] - 6*ArcCosh[c*x]*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2]))] + 6*PolyLog[3, (e*E^ArcCosh[c*x])/(-(c*d) + Sqrt[c^2*d^2 - e^2])] + 6*PolyLog[3, -((e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2]))])/e","A",1
12,1,848,259,3.4306489,"\int \frac{\cosh ^{-1}(c x)^2}{(d+e x)^2} \, dx","Integrate[ArcCosh[c*x]^2/(d + e*x)^2,x]","-\frac{c \left(\frac{\cosh ^{-1}(c x)^2}{c d+c e x}+\frac{2 \left(2 \cosh ^{-1}(c x) \tan ^{-1}\left(\frac{(c d+e) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)-2 i \cos ^{-1}\left(-\frac{c d}{e}\right) \tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)+\left(\cos ^{-1}\left(-\frac{c d}{e}\right)+2 \left(\tan ^{-1}\left(\frac{(c d+e) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)+\tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)\right)\right) \log \left(\frac{\sqrt{e^2-c^2 d^2} e^{-\frac{1}{2} \cosh ^{-1}(c x)}}{\sqrt{2} \sqrt{e} \sqrt{c d+c e x}}\right)+\left(\cos ^{-1}\left(-\frac{c d}{e}\right)-2 \left(\tan ^{-1}\left(\frac{(c d+e) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)+\tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)\right)\right) \log \left(\frac{\sqrt{e^2-c^2 d^2} e^{\frac{1}{2} \cosh ^{-1}(c x)}}{\sqrt{2} \sqrt{e} \sqrt{c d+c e x}}\right)-\left(\cos ^{-1}\left(-\frac{c d}{e}\right)+2 \tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)\right) \log \left(\frac{(c d+e) \left(c d-e+i \sqrt{e^2-c^2 d^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)-1\right)}{e \left(c d+e+i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\left(\cos ^{-1}\left(-\frac{c d}{e}\right)-2 \tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)\right) \log \left(\frac{(c d+e) \left(-c d+e+i \sqrt{e^2-c^2 d^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)+1\right)}{e \left(c d+e+i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)+i \left(\text{Li}_2\left(\frac{\left(c d-i \sqrt{e^2-c^2 d^2}\right) \left(c d+e-i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{e \left(c d+e+i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\text{Li}_2\left(\frac{\left(c d+i \sqrt{e^2-c^2 d^2}\right) \left(c d+e-i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{e \left(c d+e+i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)\right)\right)}{\sqrt{e^2-c^2 d^2}}\right)}{e}","\frac{2 c \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{2 c \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e \sqrt{c^2 d^2-e^2}}+\frac{2 c \cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{2 c \cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{\cosh ^{-1}(c x)^2}{e (d+e x)}",1,"-((c*(ArcCosh[c*x]^2/(c*d + c*e*x) + (2*(2*ArcCosh[c*x]*ArcTan[((c*d + e)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]] - (2*I)*ArcCos[-((c*d)/e)]*ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]] + (ArcCos[-((c*d)/e)] + 2*(ArcTan[((c*d + e)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]] + ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]]))*Log[Sqrt[-(c^2*d^2) + e^2]/(Sqrt[2]*Sqrt[e]*E^(ArcCosh[c*x]/2)*Sqrt[c*d + c*e*x])] + (ArcCos[-((c*d)/e)] - 2*(ArcTan[((c*d + e)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]] + ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]]))*Log[(Sqrt[-(c^2*d^2) + e^2]*E^(ArcCosh[c*x]/2))/(Sqrt[2]*Sqrt[e]*Sqrt[c*d + c*e*x])] - (ArcCos[-((c*d)/e)] + 2*ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]])*Log[((c*d + e)*(c*d - e + I*Sqrt[-(c^2*d^2) + e^2])*(-1 + Tanh[ArcCosh[c*x]/2]))/(e*(c*d + e + I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))] - (ArcCos[-((c*d)/e)] - 2*ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]])*Log[((c*d + e)*(-(c*d) + e + I*Sqrt[-(c^2*d^2) + e^2])*(1 + Tanh[ArcCosh[c*x]/2]))/(e*(c*d + e + I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))] + I*(PolyLog[2, ((c*d - I*Sqrt[-(c^2*d^2) + e^2])*(c*d + e - I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))/(e*(c*d + e + I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))] - PolyLog[2, ((c*d + I*Sqrt[-(c^2*d^2) + e^2])*(c*d + e - I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))/(e*(c*d + e + I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))])))/Sqrt[-(c^2*d^2) + e^2]))/e)","C",0
13,1,936,352,4.526809,"\int \frac{\cosh ^{-1}(c x)^2}{(d+e x)^3} \, dx","Integrate[ArcCosh[c*x]^2/(d + e*x)^3,x]","c^2 \left(-\frac{\cosh ^{-1}(c x)^2}{2 e (c d+c e x)^2}-\frac{\sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)}{(c d-e) (c d+e) (c d+c e x)}+\frac{\log \left(\frac{e x}{d}+1\right)}{c^2 d^2 e-e^3}+\frac{c d \left(2 \cosh ^{-1}(c x) \tan ^{-1}\left(\frac{(c d+e) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)-2 i \cos ^{-1}\left(-\frac{c d}{e}\right) \tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)+\left(\cos ^{-1}\left(-\frac{c d}{e}\right)+2 \left(\tan ^{-1}\left(\frac{(c d+e) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)+\tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)\right)\right) \log \left(\frac{\sqrt{e^2-c^2 d^2} e^{-\frac{1}{2} \cosh ^{-1}(c x)}}{\sqrt{2} \sqrt{e} \sqrt{c d+c e x}}\right)+\left(\cos ^{-1}\left(-\frac{c d}{e}\right)-2 \left(\tan ^{-1}\left(\frac{(c d+e) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)+\tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)\right)\right) \log \left(\frac{\sqrt{e^2-c^2 d^2} e^{\frac{1}{2} \cosh ^{-1}(c x)}}{\sqrt{2} \sqrt{e} \sqrt{c d+c e x}}\right)-\left(\cos ^{-1}\left(-\frac{c d}{e}\right)+2 \tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)\right) \log \left(\frac{(c d+e) \left(c d-e+i \sqrt{e^2-c^2 d^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)-1\right)}{e \left(c d+e+i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\left(\cos ^{-1}\left(-\frac{c d}{e}\right)-2 \tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)\right) \log \left(\frac{(c d+e) \left(-c d+e+i \sqrt{e^2-c^2 d^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)+1\right)}{e \left(c d+e+i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)+i \left(\text{Li}_2\left(\frac{\left(c d-i \sqrt{e^2-c^2 d^2}\right) \left(c d+e-i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{e \left(c d+e+i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\text{Li}_2\left(\frac{\left(c d+i \sqrt{e^2-c^2 d^2}\right) \left(c d+e-i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{e \left(c d+e+i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)\right)\right)}{e \left(e^2-c^2 d^2\right)^{3/2}}\right)","\frac{c^2 \log (d+e x)}{e \left(c^2 d^2-e^2\right)}-\frac{c \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \cosh ^{-1}(c x)}{\left(c^2 d^2-e^2\right) (d+e x)}+\frac{c^3 d \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{c^3 d \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}+\frac{c^3 d \cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{c^3 d \cosh ^{-1}(c x) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{\cosh ^{-1}(c x)^2}{2 e (d+e x)^2}",1,"c^2*(-((Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x])/((c*d - e)*(c*d + e)*(c*d + c*e*x))) - ArcCosh[c*x]^2/(2*e*(c*d + c*e*x)^2) + Log[1 + (e*x)/d]/(c^2*d^2*e - e^3) + (c*d*(2*ArcCosh[c*x]*ArcTan[((c*d + e)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]] - (2*I)*ArcCos[-((c*d)/e)]*ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]] + (ArcCos[-((c*d)/e)] + 2*(ArcTan[((c*d + e)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]] + ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]]))*Log[Sqrt[-(c^2*d^2) + e^2]/(Sqrt[2]*Sqrt[e]*E^(ArcCosh[c*x]/2)*Sqrt[c*d + c*e*x])] + (ArcCos[-((c*d)/e)] - 2*(ArcTan[((c*d + e)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]] + ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]]))*Log[(Sqrt[-(c^2*d^2) + e^2]*E^(ArcCosh[c*x]/2))/(Sqrt[2]*Sqrt[e]*Sqrt[c*d + c*e*x])] - (ArcCos[-((c*d)/e)] + 2*ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]])*Log[((c*d + e)*(c*d - e + I*Sqrt[-(c^2*d^2) + e^2])*(-1 + Tanh[ArcCosh[c*x]/2]))/(e*(c*d + e + I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))] - (ArcCos[-((c*d)/e)] - 2*ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]])*Log[((c*d + e)*(-(c*d) + e + I*Sqrt[-(c^2*d^2) + e^2])*(1 + Tanh[ArcCosh[c*x]/2]))/(e*(c*d + e + I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))] + I*(PolyLog[2, ((c*d - I*Sqrt[-(c^2*d^2) + e^2])*(c*d + e - I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))/(e*(c*d + e + I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))] - PolyLog[2, ((c*d + I*Sqrt[-(c^2*d^2) + e^2])*(c*d + e - I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))/(e*(c*d + e + I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))])))/(e*(-(c^2*d^2) + e^2)^(3/2)))","C",0
14,1,193,191,0.2962236,"\int (d+e x)^3 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[(d + e*x)^3*(a + b*ArcCosh[c*x]),x]","\frac{24 a c^4 x \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)+24 b c^4 x \cosh ^{-1}(c x) \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)-9 b e \left(8 c^2 d^2+e^2\right) \log \left(c x+\sqrt{c x-1} \sqrt{c x+1}\right)-b c \sqrt{c x-1} \sqrt{c x+1} \left(c^2 \left(96 d^3+72 d^2 e x+32 d e^2 x^2+6 e^3 x^3\right)+e^2 (64 d+9 e x)\right)}{96 c^4}","\frac{(d+e x)^4 \left(a+b \cosh ^{-1}(c x)\right)}{4 e}-\frac{b \left(8 c^4 d^4+24 c^2 d^2 e^2+3 e^4\right) \cosh ^{-1}(c x)}{32 c^4 e}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \left(e x \left(26 c^2 d^2+9 e^2\right)+4 d \left(19 c^2 d^2+16 e^2\right)\right)}{96 c^3}-\frac{b \sqrt{c x-1} \sqrt{c x+1} (d+e x)^3}{16 c}-\frac{7 b d \sqrt{c x-1} \sqrt{c x+1} (d+e x)^2}{48 c}",1,"(24*a*c^4*x*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3) - b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(e^2*(64*d + 9*e*x) + c^2*(96*d^3 + 72*d^2*e*x + 32*d*e^2*x^2 + 6*e^3*x^3)) + 24*b*c^4*x*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3)*ArcCosh[c*x] - 9*b*e*(8*c^2*d^2 + e^2)*Log[c*x + Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/(96*c^4)","A",1
15,1,142,132,0.2102024,"\int (d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[(d + e*x)^2*(a + b*ArcCosh[c*x]),x]","a d^2 x+a d e x^2+\frac{1}{3} a e^2 x^3-\frac{b d e \log \left(c x+\sqrt{c x-1} \sqrt{c x+1}\right)}{2 c^2}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \left(c^2 \left(18 d^2+9 d e x+2 e^2 x^2\right)+4 e^2\right)}{18 c^3}+\frac{1}{3} b x \cosh ^{-1}(c x) \left(3 d^2+3 d e x+e^2 x^2\right)","\frac{(d+e x)^3 \left(a+b \cosh ^{-1}(c x)\right)}{3 e}-\frac{b d \left(\frac{3 e^2}{c^2}+2 d^2\right) \cosh ^{-1}(c x)}{6 e}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \left(4 \left(4 c^2 d^2+e^2\right)+5 c^2 d e x\right)}{18 c^3}-\frac{b \sqrt{c x-1} \sqrt{c x+1} (d+e x)^2}{9 c}",1,"a*d^2*x + a*d*e*x^2 + (a*e^2*x^3)/3 - (b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(4*e^2 + c^2*(18*d^2 + 9*d*e*x + 2*e^2*x^2)))/(18*c^3) + (b*x*(3*d^2 + 3*d*e*x + e^2*x^2)*ArcCosh[c*x])/3 - (b*d*e*Log[c*x + Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/(2*c^2)","A",1
16,1,117,106,0.1009409,"\int (d+e x) \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[(d + e*x)*(a + b*ArcCosh[c*x]),x]","a d x+\frac{1}{2} a e x^2-\frac{b e \tanh ^{-1}\left(\frac{\sqrt{c x-1}}{\sqrt{c x+1}}\right)}{2 c^2}-\frac{b d \sqrt{c x-1} \sqrt{c x+1}}{c}+b d x \cosh ^{-1}(c x)+\frac{1}{2} b e x^2 \cosh ^{-1}(c x)-\frac{b e x \sqrt{c x-1} \sqrt{c x+1}}{4 c}","\frac{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 e}-\frac{b \left(\frac{e^2}{c^2}+2 d^2\right) \cosh ^{-1}(c x)}{4 e}-\frac{b \sqrt{c x-1} \sqrt{c x+1} (d+e x)}{4 c}-\frac{3 b d \sqrt{c x-1} \sqrt{c x+1}}{4 c}",1,"a*d*x + (a*e*x^2)/2 - (b*d*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/c - (b*e*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(4*c) + b*d*x*ArcCosh[c*x] + (b*e*x^2*ArcCosh[c*x])/2 - (b*e*ArcTanh[Sqrt[-1 + c*x]/Sqrt[1 + c*x]])/(2*c^2)","A",1
17,1,183,195,0.1414994,"\int \frac{a+b \cosh ^{-1}(c x)}{d+e x} \, dx","Integrate[(a + b*ArcCosh[c*x])/(d + e*x),x]","\frac{-\left(a+b \cosh ^{-1}(c x)\right) \left(a-2 b \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)-2 b \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)+b \cosh ^{-1}(c x)\right)+2 b^2 \text{Li}_2\left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}-c d}\right)+2 b^2 \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{2 b e}","\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e}+\frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 b e}+\frac{b \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{b \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e}",1,"(-((a + b*ArcCosh[c*x])*(a + b*ArcCosh[c*x] - 2*b*Log[1 + (e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2])] - 2*b*Log[1 + (e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2])])) + 2*b^2*PolyLog[2, (e*E^ArcCosh[c*x])/(-(c*d) + Sqrt[c^2*d^2 - e^2])] + 2*b^2*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2]))])/(2*b*e)","A",1
18,1,121,88,0.2051867,"\int \frac{a+b \cosh ^{-1}(c x)}{(d+e x)^2} \, dx","Integrate[(a + b*ArcCosh[c*x])/(d + e*x)^2,x]","-\frac{\frac{a}{d+e x}-\frac{b c \log (d+e x)}{\sqrt{c^2 d^2-e^2}}+\frac{b c \log \left(-\sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d^2-e^2}+c^2 d x+e\right)}{\sqrt{c^2 d^2-e^2}}+\frac{b \cosh ^{-1}(c x)}{d+e x}}{e}","\frac{2 b c \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{e \sqrt{c d-e} \sqrt{c d+e}}-\frac{a+b \cosh ^{-1}(c x)}{e (d+e x)}",1,"-((a/(d + e*x) + (b*ArcCosh[c*x])/(d + e*x) - (b*c*Log[d + e*x])/Sqrt[c^2*d^2 - e^2] + (b*c*Log[e + c^2*d*x - Sqrt[c^2*d^2 - e^2]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/Sqrt[c^2*d^2 - e^2])/e)","A",1
19,1,184,138,0.3922903,"\int \frac{a+b \cosh ^{-1}(c x)}{(d+e x)^3} \, dx","Integrate[(a + b*ArcCosh[c*x])/(d + e*x)^3,x]","\frac{1}{2} \left(-\frac{a}{e (d+e x)^2}-\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{\left(c^2 d^2-e^2\right) (d+e x)}+\frac{b c^3 d \log (d+e x)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b c^3 d \log \left(-\sqrt{c x-1} \sqrt{c x+1} \sqrt{c^2 d^2-e^2}+c^2 d x+e\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b \cosh ^{-1}(c x)}{e (d+e x)^2}\right)","-\frac{a+b \cosh ^{-1}(c x)}{2 e (d+e x)^2}+\frac{b c^3 d \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{e (c d-e)^{3/2} (c d+e)^{3/2}}-\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{2 \left(c^2 d^2-e^2\right) (d+e x)}",1,"(-(a/(e*(d + e*x)^2)) - (b*c*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/((c^2*d^2 - e^2)*(d + e*x)) - (b*ArcCosh[c*x])/(e*(d + e*x)^2) + (b*c^3*d*Log[d + e*x])/(e*(c^2*d^2 - e^2)^(3/2)) - (b*c^3*d*Log[e + c^2*d*x - Sqrt[c^2*d^2 - e^2]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/(e*(c^2*d^2 - e^2)^(3/2)))/2","A",1
20,1,259,202,0.9808324,"\int \frac{a+b \cosh ^{-1}(c x)}{(d+e x)^4} \, dx","Integrate[(a + b*ArcCosh[c*x])/(d + e*x)^4,x]","-\frac{\frac{2 a+\frac{b c e \sqrt{c x-1} \sqrt{c x+1} (d+e x) \left(c^2 d (4 d+3 e x)-e^2\right)}{\left(e^2-c^2 d^2\right)^2}}{(d+e x)^3}+\frac{i b c^3 \left(2 c^2 d^2+e^2\right) \log \left(\frac{12 e^2 (e-c d)^2 (c d+e)^2 \left(\sqrt{c x-1} \sqrt{c x+1} \sqrt{e^2-c^2 d^2}-i c^2 d x-i e\right)}{b c^3 \sqrt{e^2-c^2 d^2} \left(2 c^2 d^2+e^2\right) (d+e x)}\right)}{(e-c d)^2 (c d+e)^2 \sqrt{e^2-c^2 d^2}}+\frac{2 b \cosh ^{-1}(c x)}{(d+e x)^3}}{6 e}","-\frac{a+b \cosh ^{-1}(c x)}{3 e (d+e x)^3}-\frac{b c^3 d \sqrt{c x-1} \sqrt{c x+1}}{2 (c d-e)^2 (c d+e)^2 (d+e x)}-\frac{b c \sqrt{c x-1} \sqrt{c x+1}}{6 \left(c^2 d^2-e^2\right) (d+e x)^2}+\frac{b c^3 \left(2 c^2 d^2+e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c x+1} \sqrt{c d+e}}{\sqrt{c x-1} \sqrt{c d-e}}\right)}{3 e (c d-e)^{5/2} (c d+e)^{5/2}}",1,"-1/6*((2*a + (b*c*e*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(d + e*x)*(-e^2 + c^2*d*(4*d + 3*e*x)))/(-(c^2*d^2) + e^2)^2)/(d + e*x)^3 + (2*b*ArcCosh[c*x])/(d + e*x)^3 + (I*b*c^3*(2*c^2*d^2 + e^2)*Log[(12*e^2*(-(c*d) + e)^2*(c*d + e)^2*((-I)*e - I*c^2*d*x + Sqrt[-(c^2*d^2) + e^2]*Sqrt[-1 + c*x]*Sqrt[1 + c*x]))/(b*c^3*Sqrt[-(c^2*d^2) + e^2]*(2*c^2*d^2 + e^2)*(d + e*x))])/((-(c*d) + e)^2*(c*d + e)^2*Sqrt[-(c^2*d^2) + e^2]))/e","C",1
21,1,386,398,0.8511766,"\int (d+e x)^3 \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Integrate[(d + e*x)^3*(a + b*ArcCosh[c*x])^2,x]","\frac{c \left(72 a^2 c^3 x \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)-6 a b \sqrt{c x-1} \sqrt{c x+1} \left(c^2 \left(96 d^3+72 d^2 e x+32 d e^2 x^2+6 e^3 x^3\right)+e^2 (64 d+9 e x)\right)+b^2 c x \left(c^2 \left(576 d^3+216 d^2 e x+64 d e^2 x^2+9 e^3 x^3\right)+3 e^2 (128 d+9 e x)\right)\right)-54 a b e \left(8 c^2 d^2+e^2\right) \log \left(c x+\sqrt{c x-1} \sqrt{c x+1}\right)-6 b c \cosh ^{-1}(c x) \left(b \sqrt{c x-1} \sqrt{c x+1} \left(c^2 \left(96 d^3+72 d^2 e x+32 d e^2 x^2+6 e^3 x^3\right)+e^2 (64 d+9 e x)\right)-24 a c^3 x \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)\right)+9 b^2 \cosh ^{-1}(c x)^2 \left(8 c^4 x \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)-24 c^2 d^2 e-3 e^3\right)}{288 c^4}","-\frac{3 e^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{32 c^4}-\frac{4 b d e^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^3}-\frac{3 b e^3 x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{16 c^3}-\frac{3 d^2 e \left(a+b \cosh ^{-1}(c x)\right)^2}{4 c^2}-\frac{d^4 \left(a+b \cosh ^{-1}(c x)\right)^2}{4 e}-\frac{2 b d^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}-\frac{3 b d^2 e x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{2 c}-\frac{2 b d e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{3 c}+\frac{(d+e x)^4 \left(a+b \cosh ^{-1}(c x)\right)^2}{4 e}-\frac{b e^3 x^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{8 c}+\frac{4 b^2 d e^2 x}{3 c^2}+\frac{3 b^2 e^3 x^2}{32 c^2}+2 b^2 d^3 x+\frac{3}{4} b^2 d^2 e x^2+\frac{2}{9} b^2 d e^2 x^3+\frac{1}{32} b^2 e^3 x^4",1,"(c*(72*a^2*c^3*x*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3) - 6*a*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(e^2*(64*d + 9*e*x) + c^2*(96*d^3 + 72*d^2*e*x + 32*d*e^2*x^2 + 6*e^3*x^3)) + b^2*c*x*(3*e^2*(128*d + 9*e*x) + c^2*(576*d^3 + 216*d^2*e*x + 64*d*e^2*x^2 + 9*e^3*x^3))) - 6*b*c*(-24*a*c^3*x*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3) + b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(e^2*(64*d + 9*e*x) + c^2*(96*d^3 + 72*d^2*e*x + 32*d*e^2*x^2 + 6*e^3*x^3)))*ArcCosh[c*x] + 9*b^2*(-24*c^2*d^2*e - 3*e^3 + 8*c^4*x*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3))*ArcCosh[c*x]^2 - 54*a*b*e*(8*c^2*d^2 + e^2)*Log[c*x + Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/(288*c^4)","A",1
22,1,360,259,0.660742,"\int (d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Integrate[(d + e*x)^2*(a + b*ArcCosh[c*x])^2,x]","a^2 d^2 x+a^2 d e x^2+\frac{1}{3} a^2 e^2 x^3-\frac{4 a b e^2 \sqrt{c x-1} \sqrt{c x+1}}{9 c^3}-\frac{a b d e \log \left(c x+\sqrt{c x-1} \sqrt{c x+1}\right)}{c^2}-\frac{b \cosh ^{-1}(c x) \left(b \sqrt{c x-1} \sqrt{c x+1} \left(c^2 \left(18 d^2+9 d e x+2 e^2 x^2\right)+4 e^2\right)-6 a c^3 x \left(3 d^2+3 d e x+e^2 x^2\right)\right)}{9 c^3}-\frac{2 a b d^2 \sqrt{c x-1} \sqrt{c x+1}}{c}-\frac{a b d e x \sqrt{c x-1} \sqrt{c x+1}}{c}-\frac{2 a b e^2 x^2 \sqrt{c x-1} \sqrt{c x+1}}{9 c}+\frac{1}{6} b^2 \cosh ^{-1}(c x)^2 \left(2 x \left(3 d^2+3 d e x+e^2 x^2\right)-\frac{3 d e}{c^2}\right)+\frac{4 b^2 e^2 x}{9 c^2}+2 b^2 d^2 x+\frac{1}{2} b^2 d e x^2+\frac{2}{27} b^2 e^2 x^3","-\frac{4 b e^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{9 c^3}-\frac{d e \left(a+b \cosh ^{-1}(c x)\right)^2}{2 c^2}-\frac{d^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 e}-\frac{2 b d^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}-\frac{b d e x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}+\frac{(d+e x)^3 \left(a+b \cosh ^{-1}(c x)\right)^2}{3 e}-\frac{2 b e^2 x^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{9 c}+\frac{4 b^2 e^2 x}{9 c^2}+2 b^2 d^2 x+\frac{1}{2} b^2 d e x^2+\frac{2}{27} b^2 e^2 x^3",1,"a^2*d^2*x + 2*b^2*d^2*x + (4*b^2*e^2*x)/(9*c^2) + a^2*d*e*x^2 + (b^2*d*e*x^2)/2 + (a^2*e^2*x^3)/3 + (2*b^2*e^2*x^3)/27 - (2*a*b*d^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/c - (4*a*b*e^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(9*c^3) - (a*b*d*e*x*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/c - (2*a*b*e^2*x^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])/(9*c) - (b*(-6*a*c^3*x*(3*d^2 + 3*d*e*x + e^2*x^2) + b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(4*e^2 + c^2*(18*d^2 + 9*d*e*x + 2*e^2*x^2)))*ArcCosh[c*x])/(9*c^3) + (b^2*((-3*d*e)/c^2 + 2*x*(3*d^2 + 3*d*e*x + e^2*x^2))*ArcCosh[c*x]^2)/6 - (a*b*d*e*Log[c*x + Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/c^2","A",1
23,1,174,150,0.4321045,"\int (d+e x) \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Integrate[(d + e*x)*(a + b*ArcCosh[c*x])^2,x]","\frac{c \left(2 a^2 c x (2 d+e x)-2 a b \sqrt{c x-1} \sqrt{c x+1} (4 d+e x)+b^2 c x (8 d+e x)\right)-2 b c \cosh ^{-1}(c x) \left(b \sqrt{c x-1} \sqrt{c x+1} (4 d+e x)-2 a c x (2 d+e x)\right)-2 a b e \log \left(c x+\sqrt{c x-1} \sqrt{c x+1}\right)+b^2 \cosh ^{-1}(c x)^2 \left(4 c^2 d x+e \left(2 c^2 x^2-1\right)\right)}{4 c^2}","-\frac{e \left(a+b \cosh ^{-1}(c x)\right)^2}{4 c^2}-\frac{d^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{2 e}+\frac{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)^2}{2 e}-\frac{2 b d \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{c}-\frac{b e x \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)}{2 c}+2 b^2 d x+\frac{1}{4} b^2 e x^2",1,"(c*(2*a^2*c*x*(2*d + e*x) - 2*a*b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(4*d + e*x) + b^2*c*x*(8*d + e*x)) - 2*b*c*(-2*a*c*x*(2*d + e*x) + b*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(4*d + e*x))*ArcCosh[c*x] + b^2*(4*c^2*d*x + e*(-1 + 2*c^2*x^2))*ArcCosh[c*x]^2 - 2*a*b*e*Log[c*x + Sqrt[-1 + c*x]*Sqrt[1 + c*x]])/(4*c^2)","A",1
24,1,285,303,0.2785487,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{d+e x} \, dx","Integrate[(a + b*ArcCosh[c*x])^2/(d + e*x),x]","\frac{6 b \left(a+b \cosh ^{-1}(c x)\right) \text{Li}_2\left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}-c d}\right)+6 b \left(a+b \cosh ^{-1}(c x)\right) \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)+3 \left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)+3 \left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)-\frac{\left(a+b \cosh ^{-1}(c x)\right)^3}{b}-6 b^2 \text{Li}_3\left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}-c d}\right)-6 b^2 \text{Li}_3\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{3 e}","\frac{2 b \left(a+b \cosh ^{-1}(c x)\right) \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{2 b \left(a+b \cosh ^{-1}(c x)\right) \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e}+\frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^3}{3 b e}-\frac{2 b^2 \text{Li}_3\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e}-\frac{2 b^2 \text{Li}_3\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e}",1,"(-((a + b*ArcCosh[c*x])^3/b) + 3*(a + b*ArcCosh[c*x])^2*Log[1 + (e*E^ArcCosh[c*x])/(c*d - Sqrt[c^2*d^2 - e^2])] + 3*(a + b*ArcCosh[c*x])^2*Log[1 + (e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2])] + 6*b*(a + b*ArcCosh[c*x])*PolyLog[2, (e*E^ArcCosh[c*x])/(-(c*d) + Sqrt[c^2*d^2 - e^2])] + 6*b*(a + b*ArcCosh[c*x])*PolyLog[2, -((e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2]))] - 6*b^2*PolyLog[3, (e*E^ArcCosh[c*x])/(-(c*d) + Sqrt[c^2*d^2 - e^2])] - 6*b^2*PolyLog[3, -((e*E^ArcCosh[c*x])/(c*d + Sqrt[c^2*d^2 - e^2]))])/(3*e)","A",1
25,1,961,279,4.6007618,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{(d+e x)^2} \, dx","Integrate[(a + b*ArcCosh[c*x])^2/(d + e*x)^2,x]","-\frac{a^2}{e (d+e x)}+2 b c \left(\frac{2 \tanh ^{-1}\left(\frac{\sqrt{(c d-e) e} \sqrt{\frac{c x-1}{c x+1}}}{\sqrt{e (c d+e)}}\right)}{\sqrt{(c d-e) e} \sqrt{e (c d+e)}}-\frac{\cosh ^{-1}(c x)}{e (c d+c e x)}\right) a-\frac{b^2 c \left(\frac{\cosh ^{-1}(c x)^2}{c d+c e x}+\frac{2 \left(2 \cosh ^{-1}(c x) \tan ^{-1}\left(\frac{(c d+e) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)-2 i \cos ^{-1}\left(-\frac{c d}{e}\right) \tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)+\left(\cos ^{-1}\left(-\frac{c d}{e}\right)+2 \left(\tan ^{-1}\left(\frac{(c d+e) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)+\tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)\right)\right) \log \left(\frac{\sqrt{e^2-c^2 d^2} e^{-\frac{1}{2} \cosh ^{-1}(c x)}}{\sqrt{2} \sqrt{e} \sqrt{c d+c e x}}\right)+\left(\cos ^{-1}\left(-\frac{c d}{e}\right)-2 \left(\tan ^{-1}\left(\frac{(c d+e) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)+\tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)\right)\right) \log \left(\frac{\sqrt{e^2-c^2 d^2} e^{\frac{1}{2} \cosh ^{-1}(c x)}}{\sqrt{2} \sqrt{e} \sqrt{c d+c e x}}\right)-\left(\cos ^{-1}\left(-\frac{c d}{e}\right)+2 \tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)\right) \log \left(\frac{(c d+e) \left(c d-e+i \sqrt{e^2-c^2 d^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)-1\right)}{e \left(c d+e+i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\left(\cos ^{-1}\left(-\frac{c d}{e}\right)-2 \tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)\right) \log \left(\frac{(c d+e) \left(-c d+e+i \sqrt{e^2-c^2 d^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)+1\right)}{e \left(c d+e+i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)+i \left(\text{Li}_2\left(\frac{\left(c d-i \sqrt{e^2-c^2 d^2}\right) \left(c d+e-i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{e \left(c d+e+i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\text{Li}_2\left(\frac{\left(c d+i \sqrt{e^2-c^2 d^2}\right) \left(c d+e-i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{e \left(c d+e+i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)\right)\right)}{\sqrt{e^2-c^2 d^2}}\right)}{e}","\frac{2 b c \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{2 b c \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{e (d+e x)}+\frac{2 b^2 c \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \sqrt{c^2 d^2-e^2}}-\frac{2 b^2 c \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e \sqrt{c^2 d^2-e^2}}",1,"-(a^2/(e*(d + e*x))) + 2*a*b*c*(-(ArcCosh[c*x]/(e*(c*d + c*e*x))) + (2*ArcTanh[(Sqrt[(c*d - e)*e]*Sqrt[(-1 + c*x)/(1 + c*x)])/Sqrt[e*(c*d + e)]])/(Sqrt[(c*d - e)*e]*Sqrt[e*(c*d + e)])) - (b^2*c*(ArcCosh[c*x]^2/(c*d + c*e*x) + (2*(2*ArcCosh[c*x]*ArcTan[((c*d + e)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]] - (2*I)*ArcCos[-((c*d)/e)]*ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]] + (ArcCos[-((c*d)/e)] + 2*(ArcTan[((c*d + e)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]] + ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]]))*Log[Sqrt[-(c^2*d^2) + e^2]/(Sqrt[2]*Sqrt[e]*E^(ArcCosh[c*x]/2)*Sqrt[c*d + c*e*x])] + (ArcCos[-((c*d)/e)] - 2*(ArcTan[((c*d + e)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]] + ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]]))*Log[(Sqrt[-(c^2*d^2) + e^2]*E^(ArcCosh[c*x]/2))/(Sqrt[2]*Sqrt[e]*Sqrt[c*d + c*e*x])] - (ArcCos[-((c*d)/e)] + 2*ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]])*Log[((c*d + e)*(c*d - e + I*Sqrt[-(c^2*d^2) + e^2])*(-1 + Tanh[ArcCosh[c*x]/2]))/(e*(c*d + e + I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))] - (ArcCos[-((c*d)/e)] - 2*ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]])*Log[((c*d + e)*(-(c*d) + e + I*Sqrt[-(c^2*d^2) + e^2])*(1 + Tanh[ArcCosh[c*x]/2]))/(e*(c*d + e + I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))] + I*(PolyLog[2, ((c*d - I*Sqrt[-(c^2*d^2) + e^2])*(c*d + e - I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))/(e*(c*d + e + I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))] - PolyLog[2, ((c*d + I*Sqrt[-(c^2*d^2) + e^2])*(c*d + e - I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))/(e*(c*d + e + I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))])))/Sqrt[-(c^2*d^2) + e^2]))/e","C",0
26,1,1093,380,7.7803227,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{(d+e x)^3} \, dx","Integrate[(a + b*ArcCosh[c*x])^2/(d + e*x)^3,x]","-\frac{a^2}{2 e (d+e x)^2}+b c^2 \left(-\frac{\cosh ^{-1}(c x)}{e (c d+c e x)^2}+\frac{2 c d \tanh ^{-1}\left(\frac{\sqrt{c d-e} \sqrt{\frac{c x-1}{c x+1}}}{\sqrt{c d+e}}\right)}{(c d-e)^{3/2} e (c d+e)^{3/2}}-\frac{\sqrt{c x-1} \sqrt{c x+1}}{(c d-e) (c d+e) (c d+c e x)}\right) a+b^2 c^2 \left(-\frac{\cosh ^{-1}(c x)^2}{2 e (c d+c e x)^2}-\frac{\sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)}{(c d-e) (c d+e) (c d+c e x)}+\frac{\log \left(\frac{e x}{d}+1\right)}{c^2 d^2 e-e^3}+\frac{c d \left(2 \cosh ^{-1}(c x) \tan ^{-1}\left(\frac{(c d+e) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)-2 i \cos ^{-1}\left(-\frac{c d}{e}\right) \tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)+\left(\cos ^{-1}\left(-\frac{c d}{e}\right)+2 \left(\tan ^{-1}\left(\frac{(c d+e) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)+\tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)\right)\right) \log \left(\frac{\sqrt{e^2-c^2 d^2} e^{-\frac{1}{2} \cosh ^{-1}(c x)}}{\sqrt{2} \sqrt{e} \sqrt{c (d+e x)}}\right)+\left(\cos ^{-1}\left(-\frac{c d}{e}\right)-2 \left(\tan ^{-1}\left(\frac{(c d+e) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)+\tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)\right)\right) \log \left(\frac{\sqrt{e^2-c^2 d^2} e^{\frac{1}{2} \cosh ^{-1}(c x)}}{\sqrt{2} \sqrt{e} \sqrt{c (d+e x)}}\right)-\left(\cos ^{-1}\left(-\frac{c d}{e}\right)+2 \tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)\right) \log \left(\frac{(c d+e) \left(c d-e+i \sqrt{e^2-c^2 d^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)-1\right)}{e \left(c d+e+i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\left(\cos ^{-1}\left(-\frac{c d}{e}\right)-2 \tan ^{-1}\left(\frac{(e-c d) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{e^2-c^2 d^2}}\right)\right) \log \left(\frac{(c d+e) \left(-c d+e+i \sqrt{e^2-c^2 d^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)+1\right)}{e \left(c d+e+i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)+i \left(\text{Li}_2\left(\frac{\left(c d-i \sqrt{e^2-c^2 d^2}\right) \left(c d+e-i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{e \left(c d+e+i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\text{Li}_2\left(\frac{\left(c d+i \sqrt{e^2-c^2 d^2}\right) \left(c d+e-i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{e \left(c d+e+i \sqrt{e^2-c^2 d^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)\right)\right)}{e \left(e^2-c^2 d^2\right)^{3/2}}\right)","-\frac{b c \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{\left(c^2 d^2-e^2\right) (d+e x)}+\frac{b c^3 d \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}+1\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b c^3 d \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{e e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 d^2-e^2}+c d}+1\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{2 e (d+e x)^2}+\frac{b^2 c^2 \log (d+e x)}{e \left(c^2 d^2-e^2\right)}+\frac{b^2 c^3 d \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d-\sqrt{c^2 d^2-e^2}}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}-\frac{b^2 c^3 d \text{Li}_2\left(-\frac{e e^{\cosh ^{-1}(c x)}}{c d+\sqrt{c^2 d^2-e^2}}\right)}{e \left(c^2 d^2-e^2\right)^{3/2}}",1,"-1/2*a^2/(e*(d + e*x)^2) + a*b*c^2*(-((Sqrt[-1 + c*x]*Sqrt[1 + c*x])/((c*d - e)*(c*d + e)*(c*d + c*e*x))) - ArcCosh[c*x]/(e*(c*d + c*e*x)^2) + (2*c*d*ArcTanh[(Sqrt[c*d - e]*Sqrt[(-1 + c*x)/(1 + c*x)])/Sqrt[c*d + e]])/((c*d - e)^(3/2)*e*(c*d + e)^(3/2))) + b^2*c^2*(-((Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x])/((c*d - e)*(c*d + e)*(c*d + c*e*x))) - ArcCosh[c*x]^2/(2*e*(c*d + c*e*x)^2) + Log[1 + (e*x)/d]/(c^2*d^2*e - e^3) + (c*d*(2*ArcCosh[c*x]*ArcTan[((c*d + e)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]] - (2*I)*ArcCos[-((c*d)/e)]*ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]] + (ArcCos[-((c*d)/e)] + 2*(ArcTan[((c*d + e)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]] + ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]]))*Log[Sqrt[-(c^2*d^2) + e^2]/(Sqrt[2]*Sqrt[e]*E^(ArcCosh[c*x]/2)*Sqrt[c*(d + e*x)])] + (ArcCos[-((c*d)/e)] - 2*(ArcTan[((c*d + e)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]] + ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]]))*Log[(Sqrt[-(c^2*d^2) + e^2]*E^(ArcCosh[c*x]/2))/(Sqrt[2]*Sqrt[e]*Sqrt[c*(d + e*x)])] - (ArcCos[-((c*d)/e)] + 2*ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]])*Log[((c*d + e)*(c*d - e + I*Sqrt[-(c^2*d^2) + e^2])*(-1 + Tanh[ArcCosh[c*x]/2]))/(e*(c*d + e + I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))] - (ArcCos[-((c*d)/e)] - 2*ArcTan[((-(c*d) + e)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*d^2) + e^2]])*Log[((c*d + e)*(-(c*d) + e + I*Sqrt[-(c^2*d^2) + e^2])*(1 + Tanh[ArcCosh[c*x]/2]))/(e*(c*d + e + I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))] + I*(PolyLog[2, ((c*d - I*Sqrt[-(c^2*d^2) + e^2])*(c*d + e - I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))/(e*(c*d + e + I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))] - PolyLog[2, ((c*d + I*Sqrt[-(c^2*d^2) + e^2])*(c*d + e - I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))/(e*(c*d + e + I*Sqrt[-(c^2*d^2) + e^2]*Tanh[ArcCosh[c*x]/2]))])))/(e*(-(c^2*d^2) + e^2)^(3/2)))","C",0
27,1,287,394,0.6138231,"\int \frac{(d+e x)^3}{a+b \cosh ^{-1}(c x)} \, dx","Integrate[(d + e*x)^3/(a + b*ArcCosh[c*x]),x]","\frac{8 c^3 d^3 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)-2 c d \sinh \left(\frac{a}{b}\right) \left(4 c^2 d^2+3 e^2\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)-2 e \sinh \left(\frac{2 a}{b}\right) \left(6 c^2 d^2+e^2\right) \text{Chi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)+12 c^2 d^2 e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)-6 c d e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)-e^3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(4 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)+6 c d e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)+6 c d e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)+2 e^3 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)+e^3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(4 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)}{8 b c^4}","-\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{4 b c^4}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{8 b c^4}+\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{4 b c^4}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 a}{b}+4 \cosh ^{-1}(c x)\right)}{8 b c^4}-\frac{3 d e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^3}-\frac{3 d e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b c^3}+\frac{3 d e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^3}+\frac{3 d e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b c^3}-\frac{3 d^2 e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c^2}+\frac{3 d^2 e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c^2}-\frac{d^3 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}+\frac{d^3 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}",1,"(-2*c*d*(4*c^2*d^2 + 3*e^2)*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b] - 2*e*(6*c^2*d^2 + e^2)*CoshIntegral[2*(a/b + ArcCosh[c*x])]*Sinh[(2*a)/b] - 6*c*d*e^2*CoshIntegral[3*(a/b + ArcCosh[c*x])]*Sinh[(3*a)/b] - e^3*CoshIntegral[4*(a/b + ArcCosh[c*x])]*Sinh[(4*a)/b] + 8*c^3*d^3*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]] + 6*c*d*e^2*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]] + 12*c^2*d^2*e*Cosh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c*x])] + 2*e^3*Cosh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c*x])] + 6*c*d*e^2*Cosh[(3*a)/b]*SinhIntegral[3*(a/b + ArcCosh[c*x])] + e^3*Cosh[(4*a)/b]*SinhIntegral[4*(a/b + ArcCosh[c*x])])/(8*b*c^4)","A",1
28,1,187,245,0.3304513,"\int \frac{(d+e x)^2}{a+b \cosh ^{-1}(c x)} \, dx","Integrate[(d + e*x)^2/(a + b*ArcCosh[c*x]),x]","\frac{-\sinh \left(\frac{a}{b}\right) \left(4 c^2 d^2+e^2\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)+4 c^2 d^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)-4 c d e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)-e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)+4 c d e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)+e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)+e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)}{4 b c^3}","-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^3}-\frac{e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b c^3}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{4 b c^3}+\frac{e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 a}{b}+3 \cosh ^{-1}(c x)\right)}{4 b c^3}-\frac{d e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b c^2}+\frac{d e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{b c^2}-\frac{d^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}+\frac{d^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}",1,"(-((4*c^2*d^2 + e^2)*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b]) - 4*c*d*e*CoshIntegral[2*(a/b + ArcCosh[c*x])]*Sinh[(2*a)/b] - e^2*CoshIntegral[3*(a/b + ArcCosh[c*x])]*Sinh[(3*a)/b] + 4*c^2*d^2*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]] + e^2*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]] + 4*c*d*e*Cosh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c*x])] + e^2*Cosh[(3*a)/b]*SinhIntegral[3*(a/b + ArcCosh[c*x])])/(4*b*c^3)","A",1
29,1,98,116,0.1416233,"\int \frac{d+e x}{a+b \cosh ^{-1}(c x)} \, dx","Integrate[(d + e*x)/(a + b*ArcCosh[c*x]),x]","\frac{-2 c d \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)-e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)+2 c d \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)+e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)}{2 b c^2}","-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c^2}+\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c x)\right)}{2 b c^2}-\frac{d \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}+\frac{d \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)}{b c}",1,"(-2*c*d*CoshIntegral[a/b + ArcCosh[c*x]]*Sinh[a/b] - e*CoshIntegral[2*(a/b + ArcCosh[c*x])]*Sinh[(2*a)/b] + 2*c*d*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]] + e*Cosh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c*x])])/(2*b*c^2)","A",1
30,0,0,21,0.2152247,"\int \frac{1}{(d+e x) \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Integrate[1/((d + e*x)*(a + b*ArcCosh[c*x])),x]","\int \frac{1}{(d+e x) \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{(d+e x) \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"Integrate[1/((d + e*x)*(a + b*ArcCosh[c*x])), x]","A",-1
31,0,0,21,0.402666,"\int \frac{1}{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Integrate[1/((d + e*x)^2*(a + b*ArcCosh[c*x])),x]","\int \frac{1}{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\text{Int}\left(\frac{1}{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)},x\right)",0,"Integrate[1/((d + e*x)^2*(a + b*ArcCosh[c*x])), x]","A",-1
32,1,530,374,1.4641513,"\int \frac{(d+e x)^2}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Integrate[(d + e*x)^2/(a + b*ArcCosh[c*x])^2,x]","-\frac{-\cosh \left(\frac{a}{b}\right) \left(4 c^2 d^2+e^2\right) \left(a+b \cosh ^{-1}(c x)\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)+4 a c^2 d^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)+4 b c^2 d^2 \sinh \left(\frac{a}{b}\right) \cosh ^{-1}(c x) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)-8 c d e \cosh \left(\frac{2 a}{b}\right) \left(a+b \cosh ^{-1}(c x)\right) \text{Chi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)-3 a e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)-3 b e^2 \cosh \left(\frac{3 a}{b}\right) \cosh ^{-1}(c x) \text{Chi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)+8 a c d e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)+8 b c d e \sinh \left(\frac{2 a}{b}\right) \cosh ^{-1}(c x) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)+a e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)+b e^2 \sinh \left(\frac{a}{b}\right) \cosh ^{-1}(c x) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)+3 a e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)+3 b e^2 \sinh \left(\frac{3 a}{b}\right) \cosh ^{-1}(c x) \text{Shi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)+4 b c^3 d^2 x \sqrt{\frac{c x-1}{c x+1}}+8 b c^3 d e x^2 \sqrt{\frac{c x-1}{c x+1}}+4 b c^3 e^2 x^3 \sqrt{\frac{c x-1}{c x+1}}+4 b c^2 d^2 \sqrt{\frac{c x-1}{c x+1}}+8 b c^2 d e x \sqrt{\frac{c x-1}{c x+1}}+4 b c^2 e^2 x^2 \sqrt{\frac{c x-1}{c x+1}}}{4 b^2 c^3 \left(a+b \cosh ^{-1}(c x)\right)}","\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b^2 c^3}+\frac{3 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^3}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{4 b^2 c^3}-\frac{3 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{4 b^2 c^3}+\frac{2 d e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b^2 c^2}-\frac{2 d e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b^2 c^2}+\frac{d^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{d^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{d^2 \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}-\frac{2 d e x \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}-\frac{e^2 x^2 \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}",1,"-1/4*(4*b*c^2*d^2*Sqrt[(-1 + c*x)/(1 + c*x)] + 4*b*c^3*d^2*x*Sqrt[(-1 + c*x)/(1 + c*x)] + 8*b*c^2*d*e*x*Sqrt[(-1 + c*x)/(1 + c*x)] + 8*b*c^3*d*e*x^2*Sqrt[(-1 + c*x)/(1 + c*x)] + 4*b*c^2*e^2*x^2*Sqrt[(-1 + c*x)/(1 + c*x)] + 4*b*c^3*e^2*x^3*Sqrt[(-1 + c*x)/(1 + c*x)] - (4*c^2*d^2 + e^2)*(a + b*ArcCosh[c*x])*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]] - 8*c*d*e*(a + b*ArcCosh[c*x])*Cosh[(2*a)/b]*CoshIntegral[2*(a/b + ArcCosh[c*x])] - 3*a*e^2*Cosh[(3*a)/b]*CoshIntegral[3*(a/b + ArcCosh[c*x])] - 3*b*e^2*ArcCosh[c*x]*Cosh[(3*a)/b]*CoshIntegral[3*(a/b + ArcCosh[c*x])] + 4*a*c^2*d^2*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]] + a*e^2*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]] + 4*b*c^2*d^2*ArcCosh[c*x]*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]] + b*e^2*ArcCosh[c*x]*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]] + 8*a*c*d*e*Sinh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c*x])] + 8*b*c*d*e*ArcCosh[c*x]*Sinh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c*x])] + 3*a*e^2*Sinh[(3*a)/b]*SinhIntegral[3*(a/b + ArcCosh[c*x])] + 3*b*e^2*ArcCosh[c*x]*Sinh[(3*a)/b]*SinhIntegral[3*(a/b + ArcCosh[c*x])])/(b^2*c^3*(a + b*ArcCosh[c*x]))","A",0
33,1,268,190,0.7946428,"\int \frac{d+e x}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Integrate[(d + e*x)/(a + b*ArcCosh[c*x])^2,x]","-\frac{-c d \cosh \left(\frac{a}{b}\right) \left(a+b \cosh ^{-1}(c x)\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)-e \cosh \left(\frac{2 a}{b}\right) \left(a+b \cosh ^{-1}(c x)\right) \text{Chi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)+a c d \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)+b c d \sinh \left(\frac{a}{b}\right) \cosh ^{-1}(c x) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c x)\right)+a e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)+b e \sinh \left(\frac{2 a}{b}\right) \cosh ^{-1}(c x) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)+b c^2 d x \sqrt{\frac{c x-1}{c x+1}}+b c^2 e x^2 \sqrt{\frac{c x-1}{c x+1}}+b c d \sqrt{\frac{c x-1}{c x+1}}+b c e x \sqrt{\frac{c x-1}{c x+1}}}{b^2 c^2 \left(a+b \cosh ^{-1}(c x)\right)}","\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b^2 c^2}-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c x)\right)}{b}\right)}{b^2 c^2}+\frac{d \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{d \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{b^2 c}-\frac{d \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}-\frac{e x \sqrt{c x-1} \sqrt{c x+1}}{b c \left(a+b \cosh ^{-1}(c x)\right)}",1,"-((b*c*d*Sqrt[(-1 + c*x)/(1 + c*x)] + b*c^2*d*x*Sqrt[(-1 + c*x)/(1 + c*x)] + b*c*e*x*Sqrt[(-1 + c*x)/(1 + c*x)] + b*c^2*e*x^2*Sqrt[(-1 + c*x)/(1 + c*x)] - c*d*(a + b*ArcCosh[c*x])*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c*x]] - e*(a + b*ArcCosh[c*x])*Cosh[(2*a)/b]*CoshIntegral[2*(a/b + ArcCosh[c*x])] + a*c*d*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]] + b*c*d*ArcCosh[c*x]*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c*x]] + a*e*Sinh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c*x])] + b*e*ArcCosh[c*x]*Sinh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c*x])])/(b^2*c^2*(a + b*ArcCosh[c*x])))","A",0
34,0,0,21,10.1707169,"\int \frac{1}{(d+e x) \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Integrate[1/((d + e*x)*(a + b*ArcCosh[c*x])^2),x]","\int \frac{1}{(d+e x) \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{(d+e x) \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"Integrate[1/((d + e*x)*(a + b*ArcCosh[c*x])^2), x]","A",-1
35,0,0,21,103.1768325,"\int \frac{1}{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Integrate[1/((d + e*x)^2*(a + b*ArcCosh[c*x])^2),x]","\int \frac{1}{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{1}{(d+e x)^2 \left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"Integrate[1/((d + e*x)^2*(a + b*ArcCosh[c*x])^2), x]","A",-1
36,0,0,82,6.7031944,"\int (d+e x)^m \left(a+b \cosh ^{-1}(c x)\right)^3 \, dx","Integrate[(d + e*x)^m*(a + b*ArcCosh[c*x])^3,x]","\int (d+e x)^m \left(a+b \cosh ^{-1}(c x)\right)^3 \, dx","\frac{(d+e x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{e (m+1)}-\frac{3 b c \text{Int}\left(\frac{(d+e x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{\sqrt{c x-1} \sqrt{c x+1}},x\right)}{e (m+1)}",0,"Integrate[(d + e*x)^m*(a + b*ArcCosh[c*x])^3, x]","A",-1
37,0,0,80,0.1974752,"\int (d+e x)^m \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","Integrate[(d + e*x)^m*(a + b*ArcCosh[c*x])^2,x]","\int (d+e x)^m \left(a+b \cosh ^{-1}(c x)\right)^2 \, dx","\frac{(d+e x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{e (m+1)}-\frac{2 b c \text{Int}\left(\frac{(d+e x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{c x-1} \sqrt{c x+1}},x\right)}{e (m+1)}",0,"Integrate[(d + e*x)^m*(a + b*ArcCosh[c*x])^2, x]","A",-1
38,1,177,125,0.2349607,"\int (d+e x)^m \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[(d + e*x)^m*(a + b*ArcCosh[c*x]),x]","\frac{(d+e x)^m \left(\frac{c (d+e x)}{c d+e}\right)^{-m} \left(c (d+e x) \left(a+b \cosh ^{-1}(c x)\right) \left(\frac{c (d+e x)}{c d+e}\right)^m-2 b e \sqrt{2 c x-2} F_1\left(\frac{1}{2};-\frac{1}{2},-m;\frac{3}{2};\frac{1}{2}-\frac{c x}{2},\frac{e-c e x}{c d+e}\right)+b \sqrt{2 c x-2} (e-c d) F_1\left(\frac{1}{2};\frac{1}{2},-m;\frac{3}{2};\frac{1}{2}-\frac{c x}{2},\frac{e-c e x}{c d+e}\right)\right)}{c e (m+1)}","\frac{(d+e x)^{m+1} \left(a+b \cosh ^{-1}(c x)\right)}{e (m+1)}-\frac{\sqrt{2} b \sqrt{c x-1} (c d+e) (d+e x)^m \left(\frac{c (d+e x)}{c d+e}\right)^{-m} F_1\left(\frac{1}{2};\frac{1}{2},-m-1;\frac{3}{2};\frac{1}{2} (1-c x),\frac{e (1-c x)}{c d+e}\right)}{c e (m+1)}",1,"((d + e*x)^m*(-2*b*e*Sqrt[-2 + 2*c*x]*AppellF1[1/2, -1/2, -m, 3/2, 1/2 - (c*x)/2, (e - c*e*x)/(c*d + e)] + b*(-(c*d) + e)*Sqrt[-2 + 2*c*x]*AppellF1[1/2, 1/2, -m, 3/2, 1/2 - (c*x)/2, (e - c*e*x)/(c*d + e)] + c*(d + e*x)*((c*(d + e*x))/(c*d + e))^m*(a + b*ArcCosh[c*x])))/(c*e*(1 + m)*((c*(d + e*x))/(c*d + e))^m)","A",0
39,0,0,21,0.3874212,"\int \frac{(d+e x)^m}{a+b \cosh ^{-1}(c x)} \, dx","Integrate[(d + e*x)^m/(a + b*ArcCosh[c*x]),x]","\int \frac{(d+e x)^m}{a+b \cosh ^{-1}(c x)} \, dx","\text{Int}\left(\frac{(d+e x)^m}{a+b \cosh ^{-1}(c x)},x\right)",0,"Integrate[(d + e*x)^m/(a + b*ArcCosh[c*x]), x]","A",-1
40,0,0,21,0.8379915,"\int \frac{(d+e x)^m}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","Integrate[(d + e*x)^m/(a + b*ArcCosh[c*x])^2,x]","\int \frac{(d+e x)^m}{\left(a+b \cosh ^{-1}(c x)\right)^2} \, dx","\text{Int}\left(\frac{(d+e x)^m}{\left(a+b \cosh ^{-1}(c x)\right)^2},x\right)",0,"Integrate[(d + e*x)^m/(a + b*ArcCosh[c*x])^2, x]","A",-1
41,1,216,370,0.3055351,"\int \left(c+d x^2\right)^4 \cosh ^{-1}(a x) \, dx","Integrate[(c + d*x^2)^4*ArcCosh[a*x],x]","\frac{1}{315} x \cosh ^{-1}(a x) \left(315 c^4+420 c^3 d x^2+378 c^2 d^2 x^4+180 c d^3 x^6+35 d^4 x^8\right)-\frac{\sqrt{a x-1} \sqrt{a x+1} \left(a^8 \left(99225 c^4+44100 c^3 d x^2+23814 c^2 d^2 x^4+8100 c d^3 x^6+1225 d^4 x^8\right)+8 a^6 d \left(11025 c^3+3969 c^2 d x^2+1215 c d^2 x^4+175 d^3 x^6\right)+48 a^4 d^2 \left(1323 c^2+270 c d x^2+35 d^2 x^4\right)+320 a^2 d^3 \left(81 c+7 d x^2\right)+4480 d^4\right)}{99225 a^9}","-\frac{4 d^3 \left(1-a^2 x^2\right)^4 \left(9 a^2 c+7 d\right)}{441 a^9 \sqrt{a x-1} \sqrt{a x+1}}+\frac{d^4 \left(1-a^2 x^2\right)^5}{81 a^9 \sqrt{a x-1} \sqrt{a x+1}}+\frac{2 d^2 \left(1-a^2 x^2\right)^3 \left(63 a^4 c^2+90 a^2 c d+35 d^2\right)}{525 a^9 \sqrt{a x-1} \sqrt{a x+1}}-\frac{4 d \left(1-a^2 x^2\right)^2 \left(105 a^6 c^3+189 a^4 c^2 d+135 a^2 c d^2+35 d^3\right)}{945 a^9 \sqrt{a x-1} \sqrt{a x+1}}+\frac{\left(1-a^2 x^2\right) \left(315 a^8 c^4+420 a^6 c^3 d+378 a^4 c^2 d^2+180 a^2 c d^3+35 d^4\right)}{315 a^9 \sqrt{a x-1} \sqrt{a x+1}}+c^4 x \cosh ^{-1}(a x)+\frac{4}{3} c^3 d x^3 \cosh ^{-1}(a x)+\frac{6}{5} c^2 d^2 x^5 \cosh ^{-1}(a x)+\frac{4}{7} c d^3 x^7 \cosh ^{-1}(a x)+\frac{1}{9} d^4 x^9 \cosh ^{-1}(a x)",1,"-1/99225*(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(4480*d^4 + 320*a^2*d^3*(81*c + 7*d*x^2) + 48*a^4*d^2*(1323*c^2 + 270*c*d*x^2 + 35*d^2*x^4) + 8*a^6*d*(11025*c^3 + 3969*c^2*d*x^2 + 1215*c*d^2*x^4 + 175*d^3*x^6) + a^8*(99225*c^4 + 44100*c^3*d*x^2 + 23814*c^2*d^2*x^4 + 8100*c*d^3*x^6 + 1225*d^4*x^8)))/a^9 + (x*(315*c^4 + 420*c^3*d*x^2 + 378*c^2*d^2*x^4 + 180*c*d^3*x^6 + 35*d^4*x^8)*ArcCosh[a*x])/315","A",1
42,1,154,267,0.2084338,"\int \left(c+d x^2\right)^3 \cosh ^{-1}(a x) \, dx","Integrate[(c + d*x^2)^3*ArcCosh[a*x],x]","\frac{1}{35} x \cosh ^{-1}(a x) \left(35 c^3+35 c^2 d x^2+21 c d^2 x^4+5 d^3 x^6\right)-\frac{\sqrt{a x-1} \sqrt{a x+1} \left(a^6 \left(3675 c^3+1225 c^2 d x^2+441 c d^2 x^4+75 d^3 x^6\right)+2 a^4 d \left(1225 c^2+294 c d x^2+45 d^2 x^4\right)+24 a^2 d^2 \left(49 c+5 d x^2\right)+240 d^3\right)}{3675 a^7}","\frac{3 d^2 \left(1-a^2 x^2\right)^3 \left(7 a^2 c+5 d\right)}{175 a^7 \sqrt{a x-1} \sqrt{a x+1}}-\frac{d^3 \left(1-a^2 x^2\right)^4}{49 a^7 \sqrt{a x-1} \sqrt{a x+1}}-\frac{d \left(1-a^2 x^2\right)^2 \left(35 a^4 c^2+42 a^2 c d+15 d^2\right)}{105 a^7 \sqrt{a x-1} \sqrt{a x+1}}+\frac{\left(1-a^2 x^2\right) \left(35 a^6 c^3+35 a^4 c^2 d+21 a^2 c d^2+5 d^3\right)}{35 a^7 \sqrt{a x-1} \sqrt{a x+1}}+c^3 x \cosh ^{-1}(a x)+c^2 d x^3 \cosh ^{-1}(a x)+\frac{3}{5} c d^2 x^5 \cosh ^{-1}(a x)+\frac{1}{7} d^3 x^7 \cosh ^{-1}(a x)",1,"-1/3675*(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(240*d^3 + 24*a^2*d^2*(49*c + 5*d*x^2) + 2*a^4*d*(1225*c^2 + 294*c*d*x^2 + 45*d^2*x^4) + a^6*(3675*c^3 + 1225*c^2*d*x^2 + 441*c*d^2*x^4 + 75*d^3*x^6)))/a^7 + (x*(35*c^3 + 35*c^2*d*x^2 + 21*c*d^2*x^4 + 5*d^3*x^6)*ArcCosh[a*x])/35","A",1
43,1,103,181,0.1617354,"\int \left(c+d x^2\right)^2 \cosh ^{-1}(a x) \, dx","Integrate[(c + d*x^2)^2*ArcCosh[a*x],x]","\cosh ^{-1}(a x) \left(c^2 x+\frac{2}{3} c d x^3+\frac{d^2 x^5}{5}\right)-\frac{\sqrt{a x-1} \sqrt{a x+1} \left(a^4 \left(225 c^2+50 c d x^2+9 d^2 x^4\right)+4 a^2 d \left(25 c+3 d x^2\right)+24 d^2\right)}{225 a^5}","-\frac{2 d \left(1-a^2 x^2\right)^2 \left(5 a^2 c+3 d\right)}{45 a^5 \sqrt{a x-1} \sqrt{a x+1}}+\frac{d^2 \left(1-a^2 x^2\right)^3}{25 a^5 \sqrt{a x-1} \sqrt{a x+1}}+\frac{\left(1-a^2 x^2\right) \left(15 a^4 c^2+10 a^2 c d+3 d^2\right)}{15 a^5 \sqrt{a x-1} \sqrt{a x+1}}+c^2 x \cosh ^{-1}(a x)+\frac{2}{3} c d x^3 \cosh ^{-1}(a x)+\frac{1}{5} d^2 x^5 \cosh ^{-1}(a x)",1,"-1/225*(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(24*d^2 + 4*a^2*d*(25*c + 3*d*x^2) + a^4*(225*c^2 + 50*c*d*x^2 + 9*d^2*x^4)))/a^5 + (c^2*x + (2*c*d*x^3)/3 + (d^2*x^5)/5)*ArcCosh[a*x]","A",1
44,1,60,84,0.0643921,"\int \left(c+d x^2\right) \cosh ^{-1}(a x) \, dx","Integrate[(c + d*x^2)*ArcCosh[a*x],x]","\cosh ^{-1}(a x) \left(c x+\frac{d x^3}{3}\right)-\frac{\sqrt{a x-1} \sqrt{a x+1} \left(a^2 \left(9 c+d x^2\right)+2 d\right)}{9 a^3}","-\frac{\sqrt{a x-1} \sqrt{a x+1} \left(9 a^2 c+2 d\right)}{9 a^3}+c x \cosh ^{-1}(a x)+\frac{1}{3} d x^3 \cosh ^{-1}(a x)-\frac{d x^2 \sqrt{a x-1} \sqrt{a x+1}}{9 a}",1,"-1/9*(Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(2*d + a^2*(9*c + d*x^2)))/a^3 + (c*x + (d*x^3)/3)*ArcCosh[a*x]","A",1
45,1,375,481,0.4009723,"\int \frac{\cosh ^{-1}(a x)}{c+d x^2} \, dx","Integrate[ArcCosh[a*x]/(c + d*x^2),x]","\frac{\text{Li}_2\left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{-c a^2-d}}\right)-\text{Li}_2\left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{-c a^2-d}-a \sqrt{-c}}\right)-\text{Li}_2\left(-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{-c} a+\sqrt{-c a^2-d}}\right)+\text{Li}_2\left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{-c} a+\sqrt{-c a^2-d}}\right)-\cosh ^{-1}(a x) \log \left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}+1\right)+\cosh ^{-1}(a x) \log \left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}-a \sqrt{-c}}+1\right)+\cosh ^{-1}(a x) \log \left(1-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}\right)-\cosh ^{-1}(a x) \log \left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}+1\right)}{2 \sqrt{-c} \sqrt{d}}","-\frac{\text{Li}_2\left(-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{-c a^2-d}}\right)}{2 \sqrt{-c} \sqrt{d}}+\frac{\text{Li}_2\left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{-c a^2-d}}\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\text{Li}_2\left(-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{-c} a+\sqrt{-c a^2-d}}\right)}{2 \sqrt{-c} \sqrt{d}}+\frac{\text{Li}_2\left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{-c} a+\sqrt{-c a^2-d}}\right)}{2 \sqrt{-c} \sqrt{d}}+\frac{\cosh ^{-1}(a x) \log \left(1-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\cosh ^{-1}(a x) \log \left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}+1\right)}{2 \sqrt{-c} \sqrt{d}}+\frac{\cosh ^{-1}(a x) \log \left(1-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\cosh ^{-1}(a x) \log \left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}+1\right)}{2 \sqrt{-c} \sqrt{d}}",1,"(-(ArcCosh[a*x]*Log[1 + (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] - Sqrt[-(a^2*c) - d])]) + ArcCosh[a*x]*Log[1 + (Sqrt[d]*E^ArcCosh[a*x])/(-(a*Sqrt[-c]) + Sqrt[-(a^2*c) - d])] + ArcCosh[a*x]*Log[1 - (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] + Sqrt[-(a^2*c) - d])] - ArcCosh[a*x]*Log[1 + (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] + Sqrt[-(a^2*c) - d])] + PolyLog[2, (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] - Sqrt[-(a^2*c) - d])] - PolyLog[2, (Sqrt[d]*E^ArcCosh[a*x])/(-(a*Sqrt[-c]) + Sqrt[-(a^2*c) - d])] - PolyLog[2, -((Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] + Sqrt[-(a^2*c) - d]))] + PolyLog[2, (Sqrt[d]*E^ArcCosh[a*x])/(a*Sqrt[-c] + Sqrt[-(a^2*c) - d])])/(2*Sqrt[-c]*Sqrt[d])","A",1
46,1,687,774,1.3771386,"\int \frac{\cosh ^{-1}(a x)}{\left(c+d x^2\right)^2} \, dx","Integrate[ArcCosh[a*x]/(c + d*x^2)^2,x]","\frac{i \left(2 \text{Li}_2\left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{-c a^2-d}-i a \sqrt{c}}\right)+2 \text{Li}_2\left(-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{i \sqrt{c} a+\sqrt{-c a^2-d}}\right)+\cosh ^{-1}(a x) \left(-\cosh ^{-1}(a x)+2 \left(\log \left(1+\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{-\sqrt{a^2 (-c)-d}+i a \sqrt{c}}\right)+\log \left(1+\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+i a \sqrt{c}}\right)\right)\right)\right)-i \left(2 \text{Li}_2\left(-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{-c a^2-d}-i a \sqrt{c}}\right)+2 \text{Li}_2\left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{i \sqrt{c} a+\sqrt{-c a^2-d}}\right)+\cosh ^{-1}(a x) \left(-\cosh ^{-1}(a x)+2 \left(\log \left(1+\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}-i a \sqrt{c}}\right)+\log \left(1-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+i a \sqrt{c}}\right)\right)\right)\right)+2 \sqrt{c} \left(\frac{a \log \left(\frac{2 d \left(-i \sqrt{a x-1} \sqrt{a x+1} \sqrt{a^2 (-c)-d}+a^2 \sqrt{c} x+i \sqrt{d}\right)}{a \sqrt{a^2 (-c)-d} \left(\sqrt{c}+i \sqrt{d} x\right)}\right)}{\sqrt{a^2 (-c)-d}}+\frac{\cosh ^{-1}(a x)}{\sqrt{d} x-i \sqrt{c}}\right)-2 \sqrt{c} \left(-\frac{a \log \left(\frac{2 d \left(\sqrt{a x-1} \sqrt{a x+1} \sqrt{a^2 (-c)-d}-i a^2 \sqrt{c} x-\sqrt{d}\right)}{a \sqrt{a^2 (-c)-d} \left(\sqrt{d} x+i \sqrt{c}\right)}\right)}{\sqrt{a^2 (-c)-d}}-\frac{\cosh ^{-1}(a x)}{\sqrt{d} x+i \sqrt{c}}\right)}{8 c^{3/2} \sqrt{d}}","\frac{\text{Li}_2\left(-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{-c a^2-d}}\right)}{4 (-c)^{3/2} \sqrt{d}}-\frac{\text{Li}_2\left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{-c a^2-d}}\right)}{4 (-c)^{3/2} \sqrt{d}}+\frac{\text{Li}_2\left(-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{-c} a+\sqrt{-c a^2-d}}\right)}{4 (-c)^{3/2} \sqrt{d}}-\frac{\text{Li}_2\left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{-c} a+\sqrt{-c a^2-d}}\right)}{4 (-c)^{3/2} \sqrt{d}}-\frac{\cosh ^{-1}(a x) \log \left(1-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}\right)}{4 (-c)^{3/2} \sqrt{d}}+\frac{\cosh ^{-1}(a x) \log \left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{a \sqrt{-c}-\sqrt{a^2 (-c)-d}}+1\right)}{4 (-c)^{3/2} \sqrt{d}}-\frac{\cosh ^{-1}(a x) \log \left(1-\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}\right)}{4 (-c)^{3/2} \sqrt{d}}+\frac{\cosh ^{-1}(a x) \log \left(\frac{\sqrt{d} e^{\cosh ^{-1}(a x)}}{\sqrt{a^2 (-c)-d}+a \sqrt{-c}}+1\right)}{4 (-c)^{3/2} \sqrt{d}}-\frac{\cosh ^{-1}(a x)}{4 c \sqrt{d} \left(\sqrt{-c}-\sqrt{d} x\right)}+\frac{\cosh ^{-1}(a x)}{4 c \sqrt{d} \left(\sqrt{-c}+\sqrt{d} x\right)}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{a x+1} \sqrt{a \sqrt{-c}-\sqrt{d}}}{\sqrt{a x-1} \sqrt{a \sqrt{-c}+\sqrt{d}}}\right)}{2 c \sqrt{d} \sqrt{a \sqrt{-c}-\sqrt{d}} \sqrt{a \sqrt{-c}+\sqrt{d}}}-\frac{a \tanh ^{-1}\left(\frac{\sqrt{a x+1} \sqrt{a \sqrt{-c}+\sqrt{d}}}{\sqrt{a x-1} \sqrt{a \sqrt{-c}-\sqrt{d}}}\right)}{2 c \sqrt{d} \sqrt{a \sqrt{-c}-\sqrt{d}} \sqrt{a \sqrt{-c}+\sqrt{d}}}",1,"(2*Sqrt[c]*(ArcCosh[a*x]/((-I)*Sqrt[c] + Sqrt[d]*x) + (a*Log[(2*d*(I*Sqrt[d] + a^2*Sqrt[c]*x - I*Sqrt[-(a^2*c) - d]*Sqrt[-1 + a*x]*Sqrt[1 + a*x]))/(a*Sqrt[-(a^2*c) - d]*(Sqrt[c] + I*Sqrt[d]*x))])/Sqrt[-(a^2*c) - d]) - 2*Sqrt[c]*(-(ArcCosh[a*x]/(I*Sqrt[c] + Sqrt[d]*x)) - (a*Log[(2*d*(-Sqrt[d] - I*a^2*Sqrt[c]*x + Sqrt[-(a^2*c) - d]*Sqrt[-1 + a*x]*Sqrt[1 + a*x]))/(a*Sqrt[-(a^2*c) - d]*(I*Sqrt[c] + Sqrt[d]*x))])/Sqrt[-(a^2*c) - d]) + I*(ArcCosh[a*x]*(-ArcCosh[a*x] + 2*(Log[1 + (Sqrt[d]*E^ArcCosh[a*x])/(I*a*Sqrt[c] - Sqrt[-(a^2*c) - d])] + Log[1 + (Sqrt[d]*E^ArcCosh[a*x])/(I*a*Sqrt[c] + Sqrt[-(a^2*c) - d])])) + 2*PolyLog[2, (Sqrt[d]*E^ArcCosh[a*x])/((-I)*a*Sqrt[c] + Sqrt[-(a^2*c) - d])] + 2*PolyLog[2, -((Sqrt[d]*E^ArcCosh[a*x])/(I*a*Sqrt[c] + Sqrt[-(a^2*c) - d]))]) - I*(ArcCosh[a*x]*(-ArcCosh[a*x] + 2*(Log[1 + (Sqrt[d]*E^ArcCosh[a*x])/((-I)*a*Sqrt[c] + Sqrt[-(a^2*c) - d])] + Log[1 - (Sqrt[d]*E^ArcCosh[a*x])/(I*a*Sqrt[c] + Sqrt[-(a^2*c) - d])])) + 2*PolyLog[2, -((Sqrt[d]*E^ArcCosh[a*x])/((-I)*a*Sqrt[c] + Sqrt[-(a^2*c) - d]))] + 2*PolyLog[2, (Sqrt[d]*E^ArcCosh[a*x])/(I*a*Sqrt[c] + Sqrt[-(a^2*c) - d])]))/(8*c^(3/2)*Sqrt[d])","C",0
47,0,0,19,3.0506009,"\int \sqrt{c+d x^2} \cosh ^{-1}(a x) \, dx","Integrate[Sqrt[c + d*x^2]*ArcCosh[a*x],x]","\int \sqrt{c+d x^2} \cosh ^{-1}(a x) \, dx","\text{Int}\left(\cosh ^{-1}(a x) \sqrt{c+d x^2},x\right)",0,"Integrate[Sqrt[c + d*x^2]*ArcCosh[a*x], x]","A",-1
48,0,0,19,1.973694,"\int \frac{\cosh ^{-1}(a x)}{\sqrt{c+d x^2}} \, dx","Integrate[ArcCosh[a*x]/Sqrt[c + d*x^2],x]","\int \frac{\cosh ^{-1}(a x)}{\sqrt{c+d x^2}} \, dx","\text{Int}\left(\frac{\cosh ^{-1}(a x)}{\sqrt{c+d x^2}},x\right)",0,"Integrate[ArcCosh[a*x]/Sqrt[c + d*x^2], x]","A",-1
49,1,551,96,3.2283768,"\int \frac{\cosh ^{-1}(a x)}{\left(c+d x^2\right)^{3/2}} \, dx","Integrate[ArcCosh[a*x]/(c + d*x^2)^(3/2),x]","\frac{x \cosh ^{-1}(a x)+\frac{2 (a x-1)^{3/2} \sqrt{\frac{(a x+1) \left(a \sqrt{c}-i \sqrt{d}\right)}{(a x-1) \left(a \sqrt{c}+i \sqrt{d}\right)}} \left(a \sqrt{c} \left(-a \sqrt{c}+i \sqrt{d}\right) \sqrt{\frac{\left(a^2 c+d\right) \left(c+d x^2\right)}{c d (a x-1)^2}} \sqrt{-\frac{a \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)+\frac{i \sqrt{d} x}{\sqrt{c}}-1}{1-a x}} \Pi \left(\frac{2 a \sqrt{c}}{\sqrt{c} a+i \sqrt{d}};\sin ^{-1}\left(\sqrt{-\frac{\frac{i \sqrt{d} x}{\sqrt{c}}+a \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)-1}{2-2 a x}}\right)|\frac{4 i a \sqrt{c} \sqrt{d}}{\left(\sqrt{c} a+i \sqrt{d}\right)^2}\right)+\frac{a \left(\sqrt{d}-i a \sqrt{c}\right) \left(\sqrt{d} x+i \sqrt{c}\right) \sqrt{\frac{\frac{i a \sqrt{c}}{\sqrt{d}}+a (-x)+\frac{i \sqrt{d} x}{\sqrt{c}}+1}{1-a x}} F\left(\sin ^{-1}\left(\sqrt{-\frac{\frac{i \sqrt{d} x}{\sqrt{c}}+a \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)-1}{2-2 a x}}\right)|\frac{4 i a \sqrt{c} \sqrt{d}}{\left(\sqrt{c} a+i \sqrt{d}\right)^2}\right)}{a x-1}\right)}{a \sqrt{a x+1} \left(a^2 c+d\right) \sqrt{-\frac{a \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)+\frac{i \sqrt{d} x}{\sqrt{c}}-1}{1-a x}}}}{c \sqrt{c+d x^2}}","\frac{x \cosh ^{-1}(a x)}{c \sqrt{c+d x^2}}-\frac{\sqrt{a^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a^2 x^2-1}}{a \sqrt{c+d x^2}}\right)}{c \sqrt{d} \sqrt{a x-1} \sqrt{a x+1}}",1,"(x*ArcCosh[a*x] + (2*(-1 + a*x)^(3/2)*Sqrt[((a*Sqrt[c] - I*Sqrt[d])*(1 + a*x))/((a*Sqrt[c] + I*Sqrt[d])*(-1 + a*x))]*((a*((-I)*a*Sqrt[c] + Sqrt[d])*(I*Sqrt[c] + Sqrt[d]*x)*Sqrt[(1 + (I*a*Sqrt[c])/Sqrt[d] - a*x + (I*Sqrt[d]*x)/Sqrt[c])/(1 - a*x)]*EllipticF[ArcSin[Sqrt[-((-1 + (I*Sqrt[d]*x)/Sqrt[c] + a*((I*Sqrt[c])/Sqrt[d] + x))/(2 - 2*a*x))]], ((4*I)*a*Sqrt[c]*Sqrt[d])/(a*Sqrt[c] + I*Sqrt[d])^2])/(-1 + a*x) + a*Sqrt[c]*(-(a*Sqrt[c]) + I*Sqrt[d])*Sqrt[((a^2*c + d)*(c + d*x^2))/(c*d*(-1 + a*x)^2)]*Sqrt[-((-1 + (I*Sqrt[d]*x)/Sqrt[c] + a*((I*Sqrt[c])/Sqrt[d] + x))/(1 - a*x))]*EllipticPi[(2*a*Sqrt[c])/(a*Sqrt[c] + I*Sqrt[d]), ArcSin[Sqrt[-((-1 + (I*Sqrt[d]*x)/Sqrt[c] + a*((I*Sqrt[c])/Sqrt[d] + x))/(2 - 2*a*x))]], ((4*I)*a*Sqrt[c]*Sqrt[d])/(a*Sqrt[c] + I*Sqrt[d])^2]))/(a*(a^2*c + d)*Sqrt[1 + a*x]*Sqrt[-((-1 + (I*Sqrt[d]*x)/Sqrt[c] + a*((I*Sqrt[c])/Sqrt[d] + x))/(1 - a*x))]))/(c*Sqrt[c + d*x^2])","C",1
50,1,609,180,2.213533,"\int \frac{\cosh ^{-1}(a x)}{\left(c+d x^2\right)^{5/2}} \, dx","Integrate[ArcCosh[a*x]/(c + d*x^2)^(5/2),x]","\frac{-\frac{a c \sqrt{a x+1} \sqrt{a x-1} \left(c+d x^2\right)}{a^2 c+d}+\frac{4 (a x-1)^{3/2} \left(c+d x^2\right) \sqrt{\frac{(a x+1) \left(a \sqrt{c}-i \sqrt{d}\right)}{(a x-1) \left(a \sqrt{c}+i \sqrt{d}\right)}} \left(a \sqrt{c} \left(-a \sqrt{c}+i \sqrt{d}\right) \sqrt{\frac{\left(a^2 c+d\right) \left(c+d x^2\right)}{c d (a x-1)^2}} \sqrt{-\frac{a \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)+\frac{i \sqrt{d} x}{\sqrt{c}}-1}{1-a x}} \Pi \left(\frac{2 a \sqrt{c}}{\sqrt{c} a+i \sqrt{d}};\sin ^{-1}\left(\sqrt{-\frac{\frac{i \sqrt{d} x}{\sqrt{c}}+a \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)-1}{2-2 a x}}\right)|\frac{4 i a \sqrt{c} \sqrt{d}}{\left(\sqrt{c} a+i \sqrt{d}\right)^2}\right)+\frac{a \left(\sqrt{d}-i a \sqrt{c}\right) \left(\sqrt{d} x+i \sqrt{c}\right) \sqrt{\frac{\frac{i a \sqrt{c}}{\sqrt{d}}+a (-x)+\frac{i \sqrt{d} x}{\sqrt{c}}+1}{1-a x}} F\left(\sin ^{-1}\left(\sqrt{-\frac{\frac{i \sqrt{d} x}{\sqrt{c}}+a \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)-1}{2-2 a x}}\right)|\frac{4 i a \sqrt{c} \sqrt{d}}{\left(\sqrt{c} a+i \sqrt{d}\right)^2}\right)}{a x-1}\right)}{a \sqrt{a x+1} \left(a^2 c+d\right) \sqrt{-\frac{a \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)+\frac{i \sqrt{d} x}{\sqrt{c}}-1}{1-a x}}}+x \cosh ^{-1}(a x) \left(3 c+2 d x^2\right)}{3 c^2 \left(c+d x^2\right)^{3/2}}","-\frac{2 \sqrt{a^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a^2 x^2-1}}{a \sqrt{c+d x^2}}\right)}{3 c^2 \sqrt{d} \sqrt{a x-1} \sqrt{a x+1}}+\frac{a \left(1-a^2 x^2\right)}{3 c \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right) \sqrt{c+d x^2}}+\frac{2 x \cosh ^{-1}(a x)}{3 c^2 \sqrt{c+d x^2}}+\frac{x \cosh ^{-1}(a x)}{3 c \left(c+d x^2\right)^{3/2}}",1,"(-((a*c*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(c + d*x^2))/(a^2*c + d)) + x*(3*c + 2*d*x^2)*ArcCosh[a*x] + (4*(-1 + a*x)^(3/2)*Sqrt[((a*Sqrt[c] - I*Sqrt[d])*(1 + a*x))/((a*Sqrt[c] + I*Sqrt[d])*(-1 + a*x))]*(c + d*x^2)*((a*((-I)*a*Sqrt[c] + Sqrt[d])*(I*Sqrt[c] + Sqrt[d]*x)*Sqrt[(1 + (I*a*Sqrt[c])/Sqrt[d] - a*x + (I*Sqrt[d]*x)/Sqrt[c])/(1 - a*x)]*EllipticF[ArcSin[Sqrt[-((-1 + (I*Sqrt[d]*x)/Sqrt[c] + a*((I*Sqrt[c])/Sqrt[d] + x))/(2 - 2*a*x))]], ((4*I)*a*Sqrt[c]*Sqrt[d])/(a*Sqrt[c] + I*Sqrt[d])^2])/(-1 + a*x) + a*Sqrt[c]*(-(a*Sqrt[c]) + I*Sqrt[d])*Sqrt[((a^2*c + d)*(c + d*x^2))/(c*d*(-1 + a*x)^2)]*Sqrt[-((-1 + (I*Sqrt[d]*x)/Sqrt[c] + a*((I*Sqrt[c])/Sqrt[d] + x))/(1 - a*x))]*EllipticPi[(2*a*Sqrt[c])/(a*Sqrt[c] + I*Sqrt[d]), ArcSin[Sqrt[-((-1 + (I*Sqrt[d]*x)/Sqrt[c] + a*((I*Sqrt[c])/Sqrt[d] + x))/(2 - 2*a*x))]], ((4*I)*a*Sqrt[c]*Sqrt[d])/(a*Sqrt[c] + I*Sqrt[d])^2]))/(a*(a^2*c + d)*Sqrt[1 + a*x]*Sqrt[-((-1 + (I*Sqrt[d]*x)/Sqrt[c] + a*((I*Sqrt[c])/Sqrt[d] + x))/(1 - a*x))]))/(3*c^2*(c + d*x^2)^(3/2))","C",1
51,1,655,269,3.5146467,"\int \frac{\cosh ^{-1}(a x)}{\left(c+d x^2\right)^{7/2}} \, dx","Integrate[ArcCosh[a*x]/(c + d*x^2)^(7/2),x]","\frac{\frac{16 (a x-1)^{3/2} \left(c+d x^2\right)^2 \sqrt{\frac{(a x+1) \left(a \sqrt{c}-i \sqrt{d}\right)}{(a x-1) \left(a \sqrt{c}+i \sqrt{d}\right)}} \left(a \sqrt{c} \left(-a \sqrt{c}+i \sqrt{d}\right) \sqrt{\frac{\left(a^2 c+d\right) \left(c+d x^2\right)}{c d (a x-1)^2}} \sqrt{-\frac{a \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)+\frac{i \sqrt{d} x}{\sqrt{c}}-1}{1-a x}} \Pi \left(\frac{2 a \sqrt{c}}{\sqrt{c} a+i \sqrt{d}};\sin ^{-1}\left(\sqrt{-\frac{\frac{i \sqrt{d} x}{\sqrt{c}}+a \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)-1}{2-2 a x}}\right)|\frac{4 i a \sqrt{c} \sqrt{d}}{\left(\sqrt{c} a+i \sqrt{d}\right)^2}\right)+\frac{a \left(\sqrt{d}-i a \sqrt{c}\right) \left(\sqrt{d} x+i \sqrt{c}\right) \sqrt{\frac{\frac{i a \sqrt{c}}{\sqrt{d}}+a (-x)+\frac{i \sqrt{d} x}{\sqrt{c}}+1}{1-a x}} F\left(\sin ^{-1}\left(\sqrt{-\frac{\frac{i \sqrt{d} x}{\sqrt{c}}+a \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)-1}{2-2 a x}}\right)|\frac{4 i a \sqrt{c} \sqrt{d}}{\left(\sqrt{c} a+i \sqrt{d}\right)^2}\right)}{a x-1}\right)}{a c^3 \sqrt{a x+1} \left(a^2 c+d\right) \sqrt{-\frac{a \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)+\frac{i \sqrt{d} x}{\sqrt{c}}-1}{1-a x}}}-\frac{a \sqrt{a x-1} \sqrt{a x+1} \left(c+d x^2\right) \left(a^2 c \left(7 c+6 d x^2\right)+d \left(5 c+4 d x^2\right)\right)}{c^2 \left(a^2 c+d\right)^2}+\frac{x \cosh ^{-1}(a x) \left(15 c^2+20 c d x^2+8 d^2 x^4\right)}{c^3}}{15 \left(c+d x^2\right)^{5/2}}","-\frac{8 \sqrt{a^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a^2 x^2-1}}{a \sqrt{c+d x^2}}\right)}{15 c^3 \sqrt{d} \sqrt{a x-1} \sqrt{a x+1}}+\frac{2 a \left(1-a^2 x^2\right) \left(3 a^2 c+2 d\right)}{15 c^2 \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right)^2 \sqrt{c+d x^2}}+\frac{a \left(1-a^2 x^2\right)}{15 c \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right) \left(c+d x^2\right)^{3/2}}+\frac{8 x \cosh ^{-1}(a x)}{15 c^3 \sqrt{c+d x^2}}+\frac{4 x \cosh ^{-1}(a x)}{15 c^2 \left(c+d x^2\right)^{3/2}}+\frac{x \cosh ^{-1}(a x)}{5 c \left(c+d x^2\right)^{5/2}}",1,"(-((a*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*(c + d*x^2)*(d*(5*c + 4*d*x^2) + a^2*c*(7*c + 6*d*x^2)))/(c^2*(a^2*c + d)^2)) + (x*(15*c^2 + 20*c*d*x^2 + 8*d^2*x^4)*ArcCosh[a*x])/c^3 + (16*(-1 + a*x)^(3/2)*Sqrt[((a*Sqrt[c] - I*Sqrt[d])*(1 + a*x))/((a*Sqrt[c] + I*Sqrt[d])*(-1 + a*x))]*(c + d*x^2)^2*((a*((-I)*a*Sqrt[c] + Sqrt[d])*(I*Sqrt[c] + Sqrt[d]*x)*Sqrt[(1 + (I*a*Sqrt[c])/Sqrt[d] - a*x + (I*Sqrt[d]*x)/Sqrt[c])/(1 - a*x)]*EllipticF[ArcSin[Sqrt[-((-1 + (I*Sqrt[d]*x)/Sqrt[c] + a*((I*Sqrt[c])/Sqrt[d] + x))/(2 - 2*a*x))]], ((4*I)*a*Sqrt[c]*Sqrt[d])/(a*Sqrt[c] + I*Sqrt[d])^2])/(-1 + a*x) + a*Sqrt[c]*(-(a*Sqrt[c]) + I*Sqrt[d])*Sqrt[((a^2*c + d)*(c + d*x^2))/(c*d*(-1 + a*x)^2)]*Sqrt[-((-1 + (I*Sqrt[d]*x)/Sqrt[c] + a*((I*Sqrt[c])/Sqrt[d] + x))/(1 - a*x))]*EllipticPi[(2*a*Sqrt[c])/(a*Sqrt[c] + I*Sqrt[d]), ArcSin[Sqrt[-((-1 + (I*Sqrt[d]*x)/Sqrt[c] + a*((I*Sqrt[c])/Sqrt[d] + x))/(2 - 2*a*x))]], ((4*I)*a*Sqrt[c]*Sqrt[d])/(a*Sqrt[c] + I*Sqrt[d])^2]))/(a*c^3*(a^2*c + d)*Sqrt[1 + a*x]*Sqrt[-((-1 + (I*Sqrt[d]*x)/Sqrt[c] + a*((I*Sqrt[c])/Sqrt[d] + x))/(1 - a*x))]))/(15*(c + d*x^2)^(5/2))","C",1
52,1,844,369,6.2734978,"\int \frac{\cosh ^{-1}(a x)}{\left(c+d x^2\right)^{9/2}} \, dx","Integrate[ArcCosh[a*x]/(c + d*x^2)^(9/2),x]","\frac{32 \sqrt{\frac{\left(a \sqrt{c}-i \sqrt{d}\right) \left(1+\frac{2}{a x-1}\right)}{\sqrt{c} a+i \sqrt{d}}} \left(\left(\sqrt{c} a+i \sqrt{d}\right) \sqrt{-\frac{i \left(\frac{c a^2}{a x-1}+i \sqrt{c} \sqrt{d} a+d+\frac{d}{a x-1}\right)}{a \sqrt{c} \sqrt{d}}} \left(\frac{a \sqrt{c}}{a x-1}-i \sqrt{d} \left(1+\frac{1}{a x-1}\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{i \left(\frac{c a^2}{a x-1}-i \sqrt{c} \sqrt{d} a+d+\frac{d}{a x-1}\right)}{a \sqrt{c} \sqrt{d}}}}{\sqrt{2}}\right)|\frac{4 i a \sqrt{c} \sqrt{d}}{\left(\sqrt{c} a+i \sqrt{d}\right)^2}\right)+a \sqrt{c} \left(i \sqrt{d}-a \sqrt{c}\right) \sqrt{\frac{i \left(\frac{c a^2}{a x-1}-i \sqrt{c} \sqrt{d} a+d+\frac{d}{a x-1}\right)}{a \sqrt{c} \sqrt{d}}} \sqrt{\frac{\left(c a^2+d\right) \left(\frac{c a^2}{(a x-1)^2}+d \left(1+\frac{1}{a x-1}\right)^2\right)}{a^2 c d}} \Pi \left(\frac{2 a \sqrt{c}}{\sqrt{c} a+i \sqrt{d}};\sin ^{-1}\left(\frac{\sqrt{\frac{i \left(\frac{c a^2}{a x-1}-i \sqrt{c} \sqrt{d} a+d+\frac{d}{a x-1}\right)}{a \sqrt{c} \sqrt{d}}}}{\sqrt{2}}\right)|\frac{4 i a \sqrt{c} \sqrt{d}}{\left(\sqrt{c} a+i \sqrt{d}\right)^2}\right)\right) (a x-1)^{3/2}}{35 a c^4 \left(c a^2+d\right) \sqrt{a x+1} \sqrt{\frac{i \left(\frac{c a^2}{a x-1}-i \sqrt{c} \sqrt{d} a+d+\frac{d}{a x-1}\right)}{a \sqrt{c} \sqrt{d}}} \sqrt{\frac{d (a x-1)^2 \left(1+\frac{1}{a x-1}\right)^2}{a^2}+c}}+\sqrt{a x+1} \sqrt{d x^2+c} \left(-\frac{4 \left(11 c^2 a^4+15 c d a^2+6 d^2\right) a}{105 c^3 \left(c a^2+d\right)^3 \left(d x^2+c\right)}-\frac{2 \left(5 c a^2+3 d\right) a}{105 c^2 \left(c a^2+d\right)^2 \left(d x^2+c\right)^2}-\frac{a}{35 c \left(c a^2+d\right) \left(d x^2+c\right)^3}\right) \sqrt{a x-1}+\frac{x \left(16 d^3 x^6+56 c d^2 x^4+70 c^2 d x^2+35 c^3\right) \cosh ^{-1}(a x)}{35 c^4 \left(d x^2+c\right)^{7/2}}","-\frac{16 \sqrt{a^2 x^2-1} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a^2 x^2-1}}{a \sqrt{c+d x^2}}\right)}{35 c^4 \sqrt{d} \sqrt{a x-1} \sqrt{a x+1}}+\frac{2 a \left(1-a^2 x^2\right) \left(5 a^2 c+3 d\right)}{105 c^2 \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right)^2 \left(c+d x^2\right)^{3/2}}+\frac{a \left(1-a^2 x^2\right)}{35 c \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right) \left(c+d x^2\right)^{5/2}}+\frac{4 a \left(1-a^2 x^2\right) \left(11 a^4 c^2+15 a^2 c d+6 d^2\right)}{105 c^3 \sqrt{a x-1} \sqrt{a x+1} \left(a^2 c+d\right)^3 \sqrt{c+d x^2}}+\frac{16 x \cosh ^{-1}(a x)}{35 c^4 \sqrt{c+d x^2}}+\frac{8 x \cosh ^{-1}(a x)}{35 c^3 \left(c+d x^2\right)^{3/2}}+\frac{6 x \cosh ^{-1}(a x)}{35 c^2 \left(c+d x^2\right)^{5/2}}+\frac{x \cosh ^{-1}(a x)}{7 c \left(c+d x^2\right)^{7/2}}",1,"Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Sqrt[c + d*x^2]*(-1/35*a/(c*(a^2*c + d)*(c + d*x^2)^3) - (2*a*(5*a^2*c + 3*d))/(105*c^2*(a^2*c + d)^2*(c + d*x^2)^2) - (4*a*(11*a^4*c^2 + 15*a^2*c*d + 6*d^2))/(105*c^3*(a^2*c + d)^3*(c + d*x^2))) + (x*(35*c^3 + 70*c^2*d*x^2 + 56*c*d^2*x^4 + 16*d^3*x^6)*ArcCosh[a*x])/(35*c^4*(c + d*x^2)^(7/2)) + (32*(-1 + a*x)^(3/2)*Sqrt[((a*Sqrt[c] - I*Sqrt[d])*(1 + 2/(-1 + a*x)))/(a*Sqrt[c] + I*Sqrt[d])]*((a*Sqrt[c] + I*Sqrt[d])*Sqrt[((-I)*(I*a*Sqrt[c]*Sqrt[d] + d + (a^2*c)/(-1 + a*x) + d/(-1 + a*x)))/(a*Sqrt[c]*Sqrt[d])]*((a*Sqrt[c])/(-1 + a*x) - I*Sqrt[d]*(1 + (-1 + a*x)^(-1)))*EllipticF[ArcSin[Sqrt[(I*((-I)*a*Sqrt[c]*Sqrt[d] + d + (a^2*c)/(-1 + a*x) + d/(-1 + a*x)))/(a*Sqrt[c]*Sqrt[d])]/Sqrt[2]], ((4*I)*a*Sqrt[c]*Sqrt[d])/(a*Sqrt[c] + I*Sqrt[d])^2] + a*Sqrt[c]*(-(a*Sqrt[c]) + I*Sqrt[d])*Sqrt[(I*((-I)*a*Sqrt[c]*Sqrt[d] + d + (a^2*c)/(-1 + a*x) + d/(-1 + a*x)))/(a*Sqrt[c]*Sqrt[d])]*Sqrt[((a^2*c + d)*((a^2*c)/(-1 + a*x)^2 + d*(1 + (-1 + a*x)^(-1))^2))/(a^2*c*d)]*EllipticPi[(2*a*Sqrt[c])/(a*Sqrt[c] + I*Sqrt[d]), ArcSin[Sqrt[(I*((-I)*a*Sqrt[c]*Sqrt[d] + d + (a^2*c)/(-1 + a*x) + d/(-1 + a*x)))/(a*Sqrt[c]*Sqrt[d])]/Sqrt[2]], ((4*I)*a*Sqrt[c]*Sqrt[d])/(a*Sqrt[c] + I*Sqrt[d])^2]))/(35*a*c^4*(a^2*c + d)*Sqrt[1 + a*x]*Sqrt[(I*((-I)*a*Sqrt[c]*Sqrt[d] + d + (a^2*c)/(-1 + a*x) + d/(-1 + a*x)))/(a*Sqrt[c]*Sqrt[d])]*Sqrt[c + (d*(-1 + a*x)^2*(1 + (-1 + a*x)^(-1))^2)/a^2])","C",1
53,1,491,713,1.9707425,"\int (f+g x)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[(f + g*x)^3*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]),x]","\frac{-3600 a c \sqrt{d} f \sqrt{\frac{c x-1}{c x+1}} (c x+1) \left(4 c^2 f^2+3 g^2\right) \tan ^{-1}\left(\frac{c x \sqrt{d-c^2 d x^2}}{\sqrt{d} \left(c^2 x^2-1\right)}\right)+240 a \sqrt{\frac{c x-1}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2} \left(6 c^4 x \left(10 f^3+20 f^2 g x+15 f g^2 x^2+4 g^3 x^3\right)-c^2 g \left(120 f^2+45 f g x+8 g^2 x^2\right)-16 g^3\right)+2400 b c^2 f^2 g \sqrt{d-c^2 d x^2} \left(9 c x+12 \left(\frac{c x-1}{c x+1}\right)^{3/2} (c x+1)^3 \cosh ^{-1}(c x)-\cosh \left(3 \cosh ^{-1}(c x)\right)\right)-675 b c f g^2 \sqrt{d-c^2 d x^2} \left(8 \cosh ^{-1}(c x)^2+\cosh \left(4 \cosh ^{-1}(c x)\right)-4 \cosh ^{-1}(c x) \sinh \left(4 \cosh ^{-1}(c x)\right)\right)+8 b g^3 \sqrt{d-c^2 d x^2} \left(450 c x-450 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)-25 \cosh \left(3 \cosh ^{-1}(c x)\right)-9 \cosh \left(5 \cosh ^{-1}(c x)\right)+75 \cosh ^{-1}(c x) \sinh \left(3 \cosh ^{-1}(c x)\right)+45 \cosh ^{-1}(c x) \sinh \left(5 \cosh ^{-1}(c x)\right)\right)-3600 b c^3 f^3 \sqrt{d-c^2 d x^2} \left(\cosh \left(2 \cosh ^{-1}(c x)\right)+2 \cosh ^{-1}(c x) \left(\cosh ^{-1}(c x)-\sinh \left(2 \cosh ^{-1}(c x)\right)\right)\right)}{28800 c^4 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}","\frac{1}{2} f^3 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{f^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{f^2 g (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{c^2}-\frac{3 f g^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 c^2}+\frac{3}{4} f g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{g^3 x^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^2}-\frac{2 g^3 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{15 c^4}-\frac{3 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c f^3 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b f^2 g x \sqrt{d-c^2 d x^2}}{c \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c f^2 g x^3 \sqrt{d-c^2 d x^2}}{3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b f g^2 x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c f g^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c g^3 x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b g^3 x^3 \sqrt{d-c^2 d x^2}}{45 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b g^3 x \sqrt{d-c^2 d x^2}}{15 c^3 \sqrt{c x-1} \sqrt{c x+1}}",1,"(240*a*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(-16*g^3 - c^2*g*(120*f^2 + 45*f*g*x + 8*g^2*x^2) + 6*c^4*x*(10*f^3 + 20*f^2*g*x + 15*f*g^2*x^2 + 4*g^3*x^3)) - 3600*a*c*Sqrt[d]*f*(4*c^2*f^2 + 3*g^2)*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcTan[(c*x*Sqrt[d - c^2*d*x^2])/(Sqrt[d]*(-1 + c^2*x^2))] + 2400*b*c^2*f^2*g*Sqrt[d - c^2*d*x^2]*(9*c*x + 12*((-1 + c*x)/(1 + c*x))^(3/2)*(1 + c*x)^3*ArcCosh[c*x] - Cosh[3*ArcCosh[c*x]]) - 3600*b*c^3*f^3*Sqrt[d - c^2*d*x^2]*(Cosh[2*ArcCosh[c*x]] + 2*ArcCosh[c*x]*(ArcCosh[c*x] - Sinh[2*ArcCosh[c*x]])) - 675*b*c*f*g^2*Sqrt[d - c^2*d*x^2]*(8*ArcCosh[c*x]^2 + Cosh[4*ArcCosh[c*x]] - 4*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]]) + 8*b*g^3*Sqrt[d - c^2*d*x^2]*(450*c*x - 450*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x] - 25*Cosh[3*ArcCosh[c*x]] - 9*Cosh[5*ArcCosh[c*x]] + 75*ArcCosh[c*x]*Sinh[3*ArcCosh[c*x]] + 45*ArcCosh[c*x]*Sinh[5*ArcCosh[c*x]]))/(28800*c^4*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x))","A",0
54,1,356,479,1.2068814,"\int (f+g x)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[(f + g*x)^2*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]),x]","\frac{48 a c \sqrt{\frac{c x-1}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2} \left(12 c^2 f^2 x+16 f g \left(c^2 x^2-1\right)+3 g^2 x \left(2 c^2 x^2-1\right)\right)-144 a \sqrt{d} \sqrt{\frac{c x-1}{c x+1}} (c x+1) \left(4 c^2 f^2+g^2\right) \tan ^{-1}\left(\frac{c x \sqrt{d-c^2 d x^2}}{\sqrt{d} \left(c^2 x^2-1\right)}\right)-144 b c^2 f^2 \sqrt{d-c^2 d x^2} \left(\cosh \left(2 \cosh ^{-1}(c x)\right)+2 \cosh ^{-1}(c x) \left(\cosh ^{-1}(c x)-\sinh \left(2 \cosh ^{-1}(c x)\right)\right)\right)+64 b c f g \sqrt{d-c^2 d x^2} \left(9 c x+12 \left(\frac{c x-1}{c x+1}\right)^{3/2} (c x+1)^3 \cosh ^{-1}(c x)-\cosh \left(3 \cosh ^{-1}(c x)\right)\right)-9 b g^2 \sqrt{d-c^2 d x^2} \left(8 \cosh ^{-1}(c x)^2+\cosh \left(4 \cosh ^{-1}(c x)\right)-4 \cosh ^{-1}(c x) \sinh \left(4 \cosh ^{-1}(c x)\right)\right)}{1152 c^3 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}","\frac{1}{2} f^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{f^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 f g (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2}-\frac{g^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{8 c^2}+\frac{1}{4} g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c f^2 x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b f g x \sqrt{d-c^2 d x^2}}{3 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c f g x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b g^2 x^2 \sqrt{d-c^2 d x^2}}{16 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c g^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}",1,"(48*a*c*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(12*c^2*f^2*x + 16*f*g*(-1 + c^2*x^2) + 3*g^2*x*(-1 + 2*c^2*x^2)) - 144*a*Sqrt[d]*(4*c^2*f^2 + g^2)*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcTan[(c*x*Sqrt[d - c^2*d*x^2])/(Sqrt[d]*(-1 + c^2*x^2))] + 64*b*c*f*g*Sqrt[d - c^2*d*x^2]*(9*c*x + 12*((-1 + c*x)/(1 + c*x))^(3/2)*(1 + c*x)^3*ArcCosh[c*x] - Cosh[3*ArcCosh[c*x]]) - 144*b*c^2*f^2*Sqrt[d - c^2*d*x^2]*(Cosh[2*ArcCosh[c*x]] + 2*ArcCosh[c*x]*(ArcCosh[c*x] - Sinh[2*ArcCosh[c*x]])) - 9*b*g^2*Sqrt[d - c^2*d*x^2]*(8*ArcCosh[c*x]^2 + Cosh[4*ArcCosh[c*x]] - 4*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]]))/(1152*c^3*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x))","A",0
55,1,251,255,1.0515104,"\int (f+g x) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[(f + g*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]),x]","\frac{12 a \sqrt{d-c^2 d x^2} \left(3 c^2 f x+2 g \left(c^2 x^2-1\right)\right)-36 a c \sqrt{d} f \tan ^{-1}\left(\frac{c x \sqrt{d-c^2 d x^2}}{\sqrt{d} \left(c^2 x^2-1\right)}\right)-\frac{9 b c f \sqrt{d-c^2 d x^2} \left(2 \cosh ^{-1}(c x)^2+\cosh \left(2 \cosh ^{-1}(c x)\right)-2 \cosh ^{-1}(c x) \sinh \left(2 \cosh ^{-1}(c x)\right)\right)}{\sqrt{\frac{c x-1}{c x+1}} (c x+1)}+\frac{2 b g \sqrt{d-c^2 d x^2} \left(9 c x+12 \left(\frac{c x-1}{c x+1}\right)^{3/2} (c x+1)^3 \cosh ^{-1}(c x)-\cosh \left(3 \cosh ^{-1}(c x)\right)\right)}{\sqrt{\frac{c x-1}{c x+1}} (c x+1)}}{72 c^2}","\frac{1}{2} f x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{f \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{g (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2}-\frac{b c f x^2 \sqrt{d-c^2 d x^2}}{4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b g x \sqrt{d-c^2 d x^2}}{3 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c g x^3 \sqrt{d-c^2 d x^2}}{9 \sqrt{c x-1} \sqrt{c x+1}}",1,"(12*a*Sqrt[d - c^2*d*x^2]*(3*c^2*f*x + 2*g*(-1 + c^2*x^2)) - 36*a*c*Sqrt[d]*f*ArcTan[(c*x*Sqrt[d - c^2*d*x^2])/(Sqrt[d]*(-1 + c^2*x^2))] + (2*b*g*Sqrt[d - c^2*d*x^2]*(9*c*x + 12*((-1 + c*x)/(1 + c*x))^(3/2)*(1 + c*x)^3*ArcCosh[c*x] - Cosh[3*ArcCosh[c*x]]))/(Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) - (9*b*c*f*Sqrt[d - c^2*d*x^2]*(2*ArcCosh[c*x]^2 + Cosh[2*ArcCosh[c*x]] - 2*ArcCosh[c*x]*Sinh[2*ArcCosh[c*x]]))/(Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)))/(72*c^2)","A",0
56,1,1121,785,4.0270367,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{f+g x} \, dx","Integrate[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(f + g*x),x]","\frac{2 a \sqrt{d-c^2 d x^2} g-2 a c \sqrt{d} f \tan ^{-1}\left(\frac{c x \sqrt{d-c^2 d x^2}}{\sqrt{d} \left(c^2 x^2-1\right)}\right)+2 a \sqrt{d} \sqrt{g^2-c^2 f^2} \log (f+g x)-2 a \sqrt{d} \sqrt{g^2-c^2 f^2} \log \left(d \left(f x c^2+g\right)+\sqrt{d} \sqrt{g^2-c^2 f^2} \sqrt{d-c^2 d x^2}\right)+b \sqrt{d-c^2 d x^2} \left(\frac{c f \sqrt{\frac{c x-1}{c x+1}} \cosh ^{-1}(c x)^2}{1-c x}+2 g \cosh ^{-1}(c x)+\frac{2 (g-c f) (c f+g) \left(2 \cosh ^{-1}(c x) \tan ^{-1}\left(\frac{(c f+g) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)-2 i \cos ^{-1}\left(-\frac{c f}{g}\right) \tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)+\left(\cos ^{-1}\left(-\frac{c f}{g}\right)+2 \left(\tan ^{-1}\left(\frac{(c f+g) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)+\tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right)\right) \log \left(\frac{e^{-\frac{1}{2} \cosh ^{-1}(c x)} \sqrt{g^2-c^2 f^2}}{\sqrt{2} \sqrt{g} \sqrt{c (f+g x)}}\right)+\left(\cos ^{-1}\left(-\frac{c f}{g}\right)-2 \left(\tan ^{-1}\left(\frac{(c f+g) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)+\tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right)\right) \log \left(\frac{e^{\frac{1}{2} \cosh ^{-1}(c x)} \sqrt{g^2-c^2 f^2}}{\sqrt{2} \sqrt{g} \sqrt{c (f+g x)}}\right)-\left(\cos ^{-1}\left(-\frac{c f}{g}\right)+2 \tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right) \log \left(\frac{(c f+g) \left(c f-g+i \sqrt{g^2-c^2 f^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)-1\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\left(\cos ^{-1}\left(-\frac{c f}{g}\right)-2 \tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right) \log \left(\frac{(c f+g) \left(-c f+g+i \sqrt{g^2-c^2 f^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)+1\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)+i \left(\text{Li}_2\left(\frac{\left(c f-i \sqrt{g^2-c^2 f^2}\right) \left(c f+g-i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\text{Li}_2\left(\frac{\left(c f+i \sqrt{g^2-c^2 f^2}\right) \left(c f+g-i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)\right)\right)}{\sqrt{g^2-c^2 f^2} \sqrt{\frac{c x-1}{c x+1}} (c x+1)}+\frac{2 c g x \sqrt{\frac{c x-1}{c x+1}}}{1-c x}\right)}{2 g^2}","\frac{\sqrt{d-c^2 d x^2} \left(1-\frac{c^2 f^2}{g^2}\right) \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c \sqrt{c x-1} \sqrt{c x+1} (f+g x)}-\frac{\left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c \sqrt{c x-1} \sqrt{c x+1} (f+g x)}-\frac{c x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b g \sqrt{c x-1} \sqrt{c x+1}}-\frac{a \sqrt{c^2 x^2-1} \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \tanh ^{-1}\left(\frac{c^2 f x+g}{\sqrt{c^2 x^2-1} \sqrt{c^2 f^2-g^2}}\right)}{g^2 (1-c x) (c x+1)}+\frac{a \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{g (1-c x) (c x+1)}+\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \cosh ^{-1}(c x) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2} \cosh ^{-1}(c x) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c x \sqrt{d-c^2 d x^2}}{g \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{g}",1,"(2*a*g*Sqrt[d - c^2*d*x^2] - 2*a*c*Sqrt[d]*f*ArcTan[(c*x*Sqrt[d - c^2*d*x^2])/(Sqrt[d]*(-1 + c^2*x^2))] + 2*a*Sqrt[d]*Sqrt[-(c^2*f^2) + g^2]*Log[f + g*x] - 2*a*Sqrt[d]*Sqrt[-(c^2*f^2) + g^2]*Log[d*(g + c^2*f*x) + Sqrt[d]*Sqrt[-(c^2*f^2) + g^2]*Sqrt[d - c^2*d*x^2]] + b*Sqrt[d - c^2*d*x^2]*((2*c*g*x*Sqrt[(-1 + c*x)/(1 + c*x)])/(1 - c*x) + 2*g*ArcCosh[c*x] + (c*f*Sqrt[(-1 + c*x)/(1 + c*x)]*ArcCosh[c*x]^2)/(1 - c*x) + (2*(-(c*f) + g)*(c*f + g)*(2*ArcCosh[c*x]*ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] - (2*I)*ArcCos[-((c*f)/g)]*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + (ArcCos[-((c*f)/g)] + 2*(ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]]))*Log[Sqrt[-(c^2*f^2) + g^2]/(Sqrt[2]*E^(ArcCosh[c*x]/2)*Sqrt[g]*Sqrt[c*(f + g*x)])] + (ArcCos[-((c*f)/g)] - 2*(ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]]))*Log[(E^(ArcCosh[c*x]/2)*Sqrt[-(c^2*f^2) + g^2])/(Sqrt[2]*Sqrt[g]*Sqrt[c*(f + g*x)])] - (ArcCos[-((c*f)/g)] + 2*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]])*Log[((c*f + g)*(c*f - g + I*Sqrt[-(c^2*f^2) + g^2])*(-1 + Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] - (ArcCos[-((c*f)/g)] - 2*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]])*Log[((c*f + g)*(-(c*f) + g + I*Sqrt[-(c^2*f^2) + g^2])*(1 + Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] + I*(PolyLog[2, ((c*f - I*Sqrt[-(c^2*f^2) + g^2])*(c*f + g - I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] - PolyLog[2, ((c*f + I*Sqrt[-(c^2*f^2) + g^2])*(c*f + g - I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))])))/(Sqrt[-(c^2*f^2) + g^2]*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x))))/(2*g^2)","C",0
57,1,1139,918,7.3112509,"\int \frac{\sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{(f+g x)^2} \, dx","Integrate[(Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(f + g*x)^2,x]","\frac{\frac{2 a \sqrt{d} f \log (f+g x) c^2}{\sqrt{g^2-c^2 f^2}}-\frac{2 a \sqrt{d} f \log \left(d \left(f x c^2+g\right)+\sqrt{d} \sqrt{g^2-c^2 f^2} \sqrt{d-c^2 d x^2}\right) c^2}{\sqrt{g^2-c^2 f^2}}+2 a \sqrt{d} \tan ^{-1}\left(\frac{c x \sqrt{d-c^2 d x^2}}{\sqrt{d} \left(c^2 x^2-1\right)}\right) c+b \sqrt{d-c^2 d x^2} \left(\frac{\cosh ^{-1}(c x)^2}{\sqrt{\frac{c x-1}{c x+1}} (c x+1)}-\frac{2 g \cosh ^{-1}(c x)}{c f+c g x}+\frac{2 \log \left(\frac{g x}{f}+1\right)}{\sqrt{\frac{c x-1}{c x+1}} (c x+1)}+\frac{2 c f \left(2 \cosh ^{-1}(c x) \tan ^{-1}\left(\frac{(c f+g) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)-2 i \cos ^{-1}\left(-\frac{c f}{g}\right) \tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)+\left(\cos ^{-1}\left(-\frac{c f}{g}\right)+2 \left(\tan ^{-1}\left(\frac{(c f+g) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)+\tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right)\right) \log \left(\frac{e^{-\frac{1}{2} \cosh ^{-1}(c x)} \sqrt{g^2-c^2 f^2}}{\sqrt{2} \sqrt{g} \sqrt{c (f+g x)}}\right)+\left(\cos ^{-1}\left(-\frac{c f}{g}\right)-2 \left(\tan ^{-1}\left(\frac{(c f+g) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)+\tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right)\right) \log \left(\frac{e^{\frac{1}{2} \cosh ^{-1}(c x)} \sqrt{g^2-c^2 f^2}}{\sqrt{2} \sqrt{g} \sqrt{c (f+g x)}}\right)-\left(\cos ^{-1}\left(-\frac{c f}{g}\right)+2 \tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right) \log \left(\frac{(c f+g) \left(c f-g+i \sqrt{g^2-c^2 f^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)-1\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\left(\cos ^{-1}\left(-\frac{c f}{g}\right)-2 \tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right) \log \left(\frac{(c f+g) \left(-c f+g+i \sqrt{g^2-c^2 f^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)+1\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)+i \left(\text{Li}_2\left(\frac{\left(c f-i \sqrt{g^2-c^2 f^2}\right) \left(c f+g-i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\text{Li}_2\left(\frac{\left(c f+i \sqrt{g^2-c^2 f^2}\right) \left(c f+g-i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)\right)\right)}{\sqrt{g^2-c^2 f^2} \sqrt{\frac{c x-1}{c x+1}} (c x+1)}\right) c-\frac{2 a g \sqrt{d-c^2 d x^2}}{f+g x}}{2 g^2}","\frac{b f^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)^2 c^3}{2 g^2 \left(c^2 f^2-g^2\right) \sqrt{c x-1} \sqrt{c x+1}}+\frac{a f^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) c^3}{g^2 \left(c^2 f^2-g^2\right) \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 a f \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(\frac{\sqrt{c f+g} \sqrt{c x+1}}{\sqrt{c f-g} \sqrt{c x-1}}\right) c^2}{\sqrt{c f-g} g^2 \sqrt{c f+g} \sqrt{c x-1} \sqrt{c x+1}}-\frac{b f \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) \log \left(\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}+1\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b f \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) \log \left(\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}+1\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{c x-1} \sqrt{c x+1}}-\frac{b f \sqrt{d-c^2 d x^2} \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b f \sqrt{d-c^2 d x^2} \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right) c^2}{g^2 \sqrt{c^2 f^2-g^2} \sqrt{c x-1} \sqrt{c x+1}}+\frac{b \sqrt{d-c^2 d x^2} \log (f+g x) c}{g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b \sqrt{-\frac{1-c x}{c x+1}} \sqrt{c x+1} \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{g \sqrt{c x-1} (f+g x)}-\frac{a \sqrt{d-c^2 d x^2}}{g (f+g x)}-\frac{\left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b \sqrt{c x-1} \sqrt{c x+1} (f+g x)^2 c}-\frac{\left(f x c^2+g\right)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b \left(c^2 f^2-g^2\right) \sqrt{c x-1} \sqrt{c x+1} (f+g x)^2 c}",1,"((-2*a*g*Sqrt[d - c^2*d*x^2])/(f + g*x) + 2*a*c*Sqrt[d]*ArcTan[(c*x*Sqrt[d - c^2*d*x^2])/(Sqrt[d]*(-1 + c^2*x^2))] + (2*a*c^2*Sqrt[d]*f*Log[f + g*x])/Sqrt[-(c^2*f^2) + g^2] - (2*a*c^2*Sqrt[d]*f*Log[d*(g + c^2*f*x) + Sqrt[d]*Sqrt[-(c^2*f^2) + g^2]*Sqrt[d - c^2*d*x^2]])/Sqrt[-(c^2*f^2) + g^2] + b*c*Sqrt[d - c^2*d*x^2]*((-2*g*ArcCosh[c*x])/(c*f + c*g*x) + ArcCosh[c*x]^2/(Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) + (2*Log[1 + (g*x)/f])/(Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) + (2*c*f*(2*ArcCosh[c*x]*ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] - (2*I)*ArcCos[-((c*f)/g)]*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + (ArcCos[-((c*f)/g)] + 2*(ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]]))*Log[Sqrt[-(c^2*f^2) + g^2]/(Sqrt[2]*E^(ArcCosh[c*x]/2)*Sqrt[g]*Sqrt[c*(f + g*x)])] + (ArcCos[-((c*f)/g)] - 2*(ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]]))*Log[(E^(ArcCosh[c*x]/2)*Sqrt[-(c^2*f^2) + g^2])/(Sqrt[2]*Sqrt[g]*Sqrt[c*(f + g*x)])] - (ArcCos[-((c*f)/g)] + 2*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]])*Log[((c*f + g)*(c*f - g + I*Sqrt[-(c^2*f^2) + g^2])*(-1 + Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] - (ArcCos[-((c*f)/g)] - 2*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]])*Log[((c*f + g)*(-(c*f) + g + I*Sqrt[-(c^2*f^2) + g^2])*(1 + Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] + I*(PolyLog[2, ((c*f - I*Sqrt[-(c^2*f^2) + g^2])*(c*f + g - I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] - PolyLog[2, ((c*f + I*Sqrt[-(c^2*f^2) + g^2])*(c*f + g - I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))])))/(Sqrt[-(c^2*f^2) + g^2]*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x))))/(2*g^2)","C",0
58,1,901,1029,4.4480233,"\int (f+g x)^3 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[(f + g*x)^3*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]),x]","\frac{-352800 b c^3 d \sqrt{d-c^2 d x^2} \left(\cosh \left(2 \cosh ^{-1}(c x)\right)+2 \cosh ^{-1}(c x) \left(\cosh ^{-1}(c x)-\sinh \left(2 \cosh ^{-1}(c x)\right)\right)\right) f^3+22050 b c^3 d \sqrt{d-c^2 d x^2} \left(8 \cosh ^{-1}(c x)^2-4 \sinh \left(4 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)+\cosh \left(4 \cosh ^{-1}(c x)\right)\right) f^3+235200 b c^2 d g \sqrt{d-c^2 d x^2} \left(12 \left(\frac{c x-1}{c x+1}\right)^{3/2} \cosh ^{-1}(c x) (c x+1)^3+9 c x-\cosh \left(3 \cosh ^{-1}(c x)\right)\right) f^2-2352 b c^2 d g \sqrt{d-c^2 d x^2} \left(450 c x-450 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)-25 \cosh \left(3 \cosh ^{-1}(c x)\right)-9 \cosh \left(5 \cosh ^{-1}(c x)\right)+75 \cosh ^{-1}(c x) \sinh \left(3 \cosh ^{-1}(c x)\right)+45 \cosh ^{-1}(c x) \sinh \left(5 \cosh ^{-1}(c x)\right)\right) f^2-529200 a c d^{3/2} \left(2 c^2 f^2+g^2\right) \sqrt{\frac{c x-1}{c x+1}} (c x+1) \tan ^{-1}\left(\frac{c x \sqrt{d-c^2 d x^2}}{\sqrt{d} \left(c^2 x^2-1\right)}\right) f-66150 b c d g^2 \sqrt{d-c^2 d x^2} \left(8 \cosh ^{-1}(c x)^2-4 \sinh \left(4 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)+\cosh \left(4 \cosh ^{-1}(c x)\right)\right) f-3675 b c d g^2 \sqrt{d-c^2 d x^2} \left(-72 \cosh ^{-1}(c x)^2+12 \left(-3 \sinh \left(2 \cosh ^{-1}(c x)\right)+3 \sinh \left(4 \cosh ^{-1}(c x)\right)+\sinh \left(6 \cosh ^{-1}(c x)\right)\right) \cosh ^{-1}(c x)+18 \cosh \left(2 \cosh ^{-1}(c x)\right)-9 \cosh \left(4 \cosh ^{-1}(c x)\right)-2 \cosh \left(6 \cosh ^{-1}(c x)\right)\right) f-5040 a d \sqrt{\frac{c x-1}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2} \left(4 x^3 \left(35 f^3+84 g x f^2+70 g^2 x^2 f+20 g^3 x^3\right) c^6-2 x \left(175 f^3+336 g x f^2+245 g^2 x^2 f+64 g^3 x^3\right) c^4+g \left(336 f^2+105 g x f+16 g^2 x^2\right) c^2+32 g^3\right)+784 b d g^3 \sqrt{d-c^2 d x^2} \left(450 c x-450 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)-25 \cosh \left(3 \cosh ^{-1}(c x)\right)-9 \cosh \left(5 \cosh ^{-1}(c x)\right)+75 \cosh ^{-1}(c x) \sinh \left(3 \cosh ^{-1}(c x)\right)+45 \cosh ^{-1}(c x) \sinh \left(5 \cosh ^{-1}(c x)\right)\right)-4 b d g^3 \sqrt{d-c^2 d x^2} \left(55125 c x-55125 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)-1225 \cosh \left(3 \cosh ^{-1}(c x)\right)-1323 \cosh \left(5 \cosh ^{-1}(c x)\right)-225 \cosh \left(7 \cosh ^{-1}(c x)\right)+3675 \cosh ^{-1}(c x) \sinh \left(3 \cosh ^{-1}(c x)\right)+6615 \cosh ^{-1}(c x) \sinh \left(5 \cosh ^{-1}(c x)\right)+1575 \cosh ^{-1}(c x) \sinh \left(7 \cosh ^{-1}(c x)\right)\right)}{2822400 c^4 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}","\frac{b c^3 d g^3 \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d f g^2 \sqrt{d-c^2 d x^2} x^6}{12 \sqrt{c x-1} \sqrt{c x+1}}-\frac{8 b c d g^3 \sqrt{d-c^2 d x^2} x^5}{175 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b c^3 d f^2 g \sqrt{d-c^2 d x^2} x^5}{25 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d f^3 \sqrt{d-c^2 d x^2} x^4}{16 \sqrt{c x-1} \sqrt{c x+1}}-\frac{7 b c d f g^2 \sqrt{d-c^2 d x^2} x^4}{32 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3}{8} d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{1}{2} d f g^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{b d g^3 \sqrt{d-c^2 d x^2} x^3}{105 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c d f^2 g \sqrt{d-c^2 d x^2} x^3}{5 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d g^3 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^2}{7 c^2}-\frac{5 b c d f^3 \sqrt{d-c^2 d x^2} x^2}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b d f g^2 \sqrt{d-c^2 d x^2} x^2}{32 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{3}{8} d f^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x-\frac{3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x}{16 c^2}+\frac{1}{4} d f^3 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x+\frac{2 b d g^3 \sqrt{d-c^2 d x^2} x}{35 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b d f^2 g \sqrt{d-c^2 d x^2} x}{5 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 d f^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 d f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 d g^3 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{35 c^4}-\frac{3 d f^2 g (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^2}",1,"(-5040*a*d*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(32*g^3 + c^2*g*(336*f^2 + 105*f*g*x + 16*g^2*x^2) + 4*c^6*x^3*(35*f^3 + 84*f^2*g*x + 70*f*g^2*x^2 + 20*g^3*x^3) - 2*c^4*x*(175*f^3 + 336*f^2*g*x + 245*f*g^2*x^2 + 64*g^3*x^3)) - 529200*a*c*d^(3/2)*f*(2*c^2*f^2 + g^2)*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcTan[(c*x*Sqrt[d - c^2*d*x^2])/(Sqrt[d]*(-1 + c^2*x^2))] + 235200*b*c^2*d*f^2*g*Sqrt[d - c^2*d*x^2]*(9*c*x + 12*((-1 + c*x)/(1 + c*x))^(3/2)*(1 + c*x)^3*ArcCosh[c*x] - Cosh[3*ArcCosh[c*x]]) - 352800*b*c^3*d*f^3*Sqrt[d - c^2*d*x^2]*(Cosh[2*ArcCosh[c*x]] + 2*ArcCosh[c*x]*(ArcCosh[c*x] - Sinh[2*ArcCosh[c*x]])) + 22050*b*c^3*d*f^3*Sqrt[d - c^2*d*x^2]*(8*ArcCosh[c*x]^2 + Cosh[4*ArcCosh[c*x]] - 4*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]]) - 66150*b*c*d*f*g^2*Sqrt[d - c^2*d*x^2]*(8*ArcCosh[c*x]^2 + Cosh[4*ArcCosh[c*x]] - 4*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]]) - 2352*b*c^2*d*f^2*g*Sqrt[d - c^2*d*x^2]*(450*c*x - 450*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x] - 25*Cosh[3*ArcCosh[c*x]] - 9*Cosh[5*ArcCosh[c*x]] + 75*ArcCosh[c*x]*Sinh[3*ArcCosh[c*x]] + 45*ArcCosh[c*x]*Sinh[5*ArcCosh[c*x]]) + 784*b*d*g^3*Sqrt[d - c^2*d*x^2]*(450*c*x - 450*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x] - 25*Cosh[3*ArcCosh[c*x]] - 9*Cosh[5*ArcCosh[c*x]] + 75*ArcCosh[c*x]*Sinh[3*ArcCosh[c*x]] + 45*ArcCosh[c*x]*Sinh[5*ArcCosh[c*x]]) - 3675*b*c*d*f*g^2*Sqrt[d - c^2*d*x^2]*(-72*ArcCosh[c*x]^2 + 18*Cosh[2*ArcCosh[c*x]] - 9*Cosh[4*ArcCosh[c*x]] - 2*Cosh[6*ArcCosh[c*x]] + 12*ArcCosh[c*x]*(-3*Sinh[2*ArcCosh[c*x]] + 3*Sinh[4*ArcCosh[c*x]] + Sinh[6*ArcCosh[c*x]])) - 4*b*d*g^3*Sqrt[d - c^2*d*x^2]*(55125*c*x - 55125*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x] - 1225*Cosh[3*ArcCosh[c*x]] - 1323*Cosh[5*ArcCosh[c*x]] - 225*Cosh[7*ArcCosh[c*x]] + 3675*ArcCosh[c*x]*Sinh[3*ArcCosh[c*x]] + 6615*ArcCosh[c*x]*Sinh[5*ArcCosh[c*x]] + 1575*ArcCosh[c*x]*Sinh[7*ArcCosh[c*x]]))/(2822400*c^4*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x))","A",0
59,1,623,725,2.8003899,"\int (f+g x)^2 \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[(f + g*x)^2*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]),x]","\frac{-3600 a d^{3/2} \sqrt{\frac{c x-1}{c x+1}} (c x+1) \left(6 c^2 f^2+g^2\right) \tan ^{-1}\left(\frac{c x \sqrt{d-c^2 d x^2}}{\sqrt{d} \left(c^2 x^2-1\right)}\right)-240 a c d \sqrt{\frac{c x-1}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2} \left(30 c^2 f^2 x \left(2 c^2 x^2-5\right)+96 f g \left(c^2 x^2-1\right)^2+5 g^2 x \left(8 c^4 x^4-14 c^2 x^2+3\right)\right)-7200 b c^2 d f^2 \sqrt{d-c^2 d x^2} \left(\cosh \left(2 \cosh ^{-1}(c x)\right)+2 \cosh ^{-1}(c x) \left(\cosh ^{-1}(c x)-\sinh \left(2 \cosh ^{-1}(c x)\right)\right)\right)+450 b c^2 d f^2 \sqrt{d-c^2 d x^2} \left(8 \cosh ^{-1}(c x)^2+\cosh \left(4 \cosh ^{-1}(c x)\right)-4 \cosh ^{-1}(c x) \sinh \left(4 \cosh ^{-1}(c x)\right)\right)+3200 b c d f g \sqrt{d-c^2 d x^2} \left(9 c x+12 \left(\frac{c x-1}{c x+1}\right)^{3/2} (c x+1)^3 \cosh ^{-1}(c x)-\cosh \left(3 \cosh ^{-1}(c x)\right)\right)-32 b c d f g \sqrt{d-c^2 d x^2} \left(450 c x-450 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)-25 \cosh \left(3 \cosh ^{-1}(c x)\right)-9 \cosh \left(5 \cosh ^{-1}(c x)\right)+75 \cosh ^{-1}(c x) \sinh \left(3 \cosh ^{-1}(c x)\right)+45 \cosh ^{-1}(c x) \sinh \left(5 \cosh ^{-1}(c x)\right)\right)-450 b d g^2 \sqrt{d-c^2 d x^2} \left(8 \cosh ^{-1}(c x)^2+\cosh \left(4 \cosh ^{-1}(c x)\right)-4 \cosh ^{-1}(c x) \sinh \left(4 \cosh ^{-1}(c x)\right)\right)-25 b d g^2 \sqrt{d-c^2 d x^2} \left(-72 \cosh ^{-1}(c x)^2+18 \cosh \left(2 \cosh ^{-1}(c x)\right)-9 \cosh \left(4 \cosh ^{-1}(c x)\right)-2 \cosh \left(6 \cosh ^{-1}(c x)\right)+12 \cosh ^{-1}(c x) \left(-3 \sinh \left(2 \cosh ^{-1}(c x)\right)+3 \sinh \left(4 \cosh ^{-1}(c x)\right)+\sinh \left(6 \cosh ^{-1}(c x)\right)\right)\right)}{57600 c^3 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}","\frac{3}{8} d f^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} d f^2 x (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{3 d f^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 d f g (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^2}-\frac{d g^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{16 c^2}+\frac{1}{8} d g^2 x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{6} d g^2 x^3 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{d g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 b c d f^2 x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d f g x \sqrt{d-c^2 d x^2}}{5 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{4 b c d f g x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d g^2 x^2 \sqrt{d-c^2 d x^2}}{32 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{7 b c d g^2 x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d f^2 x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b c^3 d f g x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d g^2 x^6 \sqrt{d-c^2 d x^2}}{36 \sqrt{c x-1} \sqrt{c x+1}}",1,"(-240*a*c*d*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(96*f*g*(-1 + c^2*x^2)^2 + 30*c^2*f^2*x*(-5 + 2*c^2*x^2) + 5*g^2*x*(3 - 14*c^2*x^2 + 8*c^4*x^4)) - 3600*a*d^(3/2)*(6*c^2*f^2 + g^2)*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcTan[(c*x*Sqrt[d - c^2*d*x^2])/(Sqrt[d]*(-1 + c^2*x^2))] + 3200*b*c*d*f*g*Sqrt[d - c^2*d*x^2]*(9*c*x + 12*((-1 + c*x)/(1 + c*x))^(3/2)*(1 + c*x)^3*ArcCosh[c*x] - Cosh[3*ArcCosh[c*x]]) - 7200*b*c^2*d*f^2*Sqrt[d - c^2*d*x^2]*(Cosh[2*ArcCosh[c*x]] + 2*ArcCosh[c*x]*(ArcCosh[c*x] - Sinh[2*ArcCosh[c*x]])) + 450*b*c^2*d*f^2*Sqrt[d - c^2*d*x^2]*(8*ArcCosh[c*x]^2 + Cosh[4*ArcCosh[c*x]] - 4*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]]) - 450*b*d*g^2*Sqrt[d - c^2*d*x^2]*(8*ArcCosh[c*x]^2 + Cosh[4*ArcCosh[c*x]] - 4*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]]) - 32*b*c*d*f*g*Sqrt[d - c^2*d*x^2]*(450*c*x - 450*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x] - 25*Cosh[3*ArcCosh[c*x]] - 9*Cosh[5*ArcCosh[c*x]] + 75*ArcCosh[c*x]*Sinh[3*ArcCosh[c*x]] + 45*ArcCosh[c*x]*Sinh[5*ArcCosh[c*x]]) - 25*b*d*g^2*Sqrt[d - c^2*d*x^2]*(-72*ArcCosh[c*x]^2 + 18*Cosh[2*ArcCosh[c*x]] - 9*Cosh[4*ArcCosh[c*x]] - 2*Cosh[6*ArcCosh[c*x]] + 12*ArcCosh[c*x]*(-3*Sinh[2*ArcCosh[c*x]] + 3*Sinh[4*ArcCosh[c*x]] + Sinh[6*ArcCosh[c*x]])))/(57600*c^3*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x))","A",0
60,1,432,398,1.6115573,"\int (f+g x) \left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[(f + g*x)*(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]),x]","\frac{-10800 a c d^{3/2} f \sqrt{\frac{c x-1}{c x+1}} (c x+1) \tan ^{-1}\left(\frac{c x \sqrt{d-c^2 d x^2}}{\sqrt{d} \left(c^2 x^2-1\right)}\right)-720 a d \sqrt{\frac{c x-1}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2} \left(5 c^2 f x \left(2 c^2 x^2-5\right)+8 g \left(c^2 x^2-1\right)^2\right)-3600 b c d f \sqrt{d-c^2 d x^2} \left(\cosh \left(2 \cosh ^{-1}(c x)\right)+2 \cosh ^{-1}(c x) \left(\cosh ^{-1}(c x)-\sinh \left(2 \cosh ^{-1}(c x)\right)\right)\right)+225 b c d f \sqrt{d-c^2 d x^2} \left(8 \cosh ^{-1}(c x)^2+\cosh \left(4 \cosh ^{-1}(c x)\right)-4 \cosh ^{-1}(c x) \sinh \left(4 \cosh ^{-1}(c x)\right)\right)+800 b d g \sqrt{d-c^2 d x^2} \left(9 c x+12 \left(\frac{c x-1}{c x+1}\right)^{3/2} (c x+1)^3 \cosh ^{-1}(c x)-\cosh \left(3 \cosh ^{-1}(c x)\right)\right)-8 b d g \sqrt{d-c^2 d x^2} \left(450 c x-450 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)-25 \cosh \left(3 \cosh ^{-1}(c x)\right)-9 \cosh \left(5 \cosh ^{-1}(c x)\right)+75 \cosh ^{-1}(c x) \sinh \left(3 \cosh ^{-1}(c x)\right)+45 \cosh ^{-1}(c x) \sinh \left(5 \cosh ^{-1}(c x)\right)\right)}{28800 c^2 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}","\frac{3}{8} d f x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{1}{4} d f x (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{3 d f \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{16 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d g (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{5 c^2}-\frac{5 b c d f x^2 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d g x \sqrt{d-c^2 d x^2}}{5 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c d g x^3 \sqrt{d-c^2 d x^2}}{15 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d f x^4 \sqrt{d-c^2 d x^2}}{16 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c^3 d g x^5 \sqrt{d-c^2 d x^2}}{25 \sqrt{c x-1} \sqrt{c x+1}}",1,"(-720*a*d*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(8*g*(-1 + c^2*x^2)^2 + 5*c^2*f*x*(-5 + 2*c^2*x^2)) - 10800*a*c*d^(3/2)*f*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcTan[(c*x*Sqrt[d - c^2*d*x^2])/(Sqrt[d]*(-1 + c^2*x^2))] + 800*b*d*g*Sqrt[d - c^2*d*x^2]*(9*c*x + 12*((-1 + c*x)/(1 + c*x))^(3/2)*(1 + c*x)^3*ArcCosh[c*x] - Cosh[3*ArcCosh[c*x]]) - 3600*b*c*d*f*Sqrt[d - c^2*d*x^2]*(Cosh[2*ArcCosh[c*x]] + 2*ArcCosh[c*x]*(ArcCosh[c*x] - Sinh[2*ArcCosh[c*x]])) + 225*b*c*d*f*Sqrt[d - c^2*d*x^2]*(8*ArcCosh[c*x]^2 + Cosh[4*ArcCosh[c*x]] - 4*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]]) - 8*b*d*g*Sqrt[d - c^2*d*x^2]*(450*c*x - 450*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x] - 25*Cosh[3*ArcCosh[c*x]] - 9*Cosh[5*ArcCosh[c*x]] + 75*ArcCosh[c*x]*Sinh[3*ArcCosh[c*x]] + 45*ArcCosh[c*x]*Sinh[5*ArcCosh[c*x]]))/(28800*c^2*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x))","A",0
61,1,3068,1270,11.6932128,"\int \frac{\left(d-c^2 d x^2\right)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{f+g x} \, dx","Integrate[((d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x]))/(f + g*x),x]","\text{Result too large to show}","-\frac{b c^2 d (c f-g) \sqrt{d-c^2 d x^2} x^2}{4 g^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{c d (c f-g) (c f+g) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 x}{2 b g^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{c d (c f-g) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x}{2 g^2}+\frac{b c d \left(4 c^2 x^2-9 c x-12\right) \sqrt{d-c^2 d x^2} x}{36 g \sqrt{c x-1} \sqrt{c x+1}}+\frac{b c d (c f-g) (c f+g) \sqrt{d-c^2 d x^2} x}{g^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)^2}{4 g \sqrt{c x-1} \sqrt{c x+1}}+\frac{d (c f-g) (c f+g) \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c g^2 \sqrt{c x-1} \sqrt{c x+1} (f+g x)}-\frac{d (c f-g) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b g^2 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d (c f-g)^2 (c f+g)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c g^4 \sqrt{c x-1} \sqrt{c x+1} (f+g x)}-\frac{b d (c f-g) (c f+g) \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{g^3}+\frac{b d \left(-2 c^2 x^2+3 c x+2\right) \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{6 g}-\frac{a d \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{2 g \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 a d (c f-g)^{3/2} (c f+g)^{3/2} \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(\frac{\sqrt{c f+g} \sqrt{c x+1}}{\sqrt{c f-g} \sqrt{c x-1}}\right)}{g^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d (c f-g) (c f+g) \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) \log \left(\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{g^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d (c f-g) (c f+g) \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) \log \left(\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}+1\right)}{g^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d (c f-g) (c f+g) \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d (c f-g) (c f+g) \sqrt{c^2 f^2-g^2} \sqrt{d-c^2 d x^2} \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{a d (c f-g) (c f+g) \sqrt{d-c^2 d x^2}}{g^3}+\frac{a d \left(-2 c^2 x^2+3 c x+2\right) \sqrt{d-c^2 d x^2}}{6 g}",1,"Sqrt[-(d*(-1 + c^2*x^2))]*((a*d*(-3*c^2*f^2 + 4*g^2))/(3*g^3) + (a*c^2*d*f*x)/(2*g^2) - (a*c^2*d*x^2)/(3*g)) + (a*c*d^(3/2)*f*(2*c^2*f^2 - 3*g^2)*ArcTan[(c*x*Sqrt[-(d*(-1 + c^2*x^2))])/(Sqrt[d]*(-1 + c^2*x^2))])/(2*g^4) + (a*d^(3/2)*(-(c^2*f^2) + g^2)^(3/2)*Log[f + g*x])/g^4 - (a*d^(3/2)*(-(c^2*f^2) + g^2)^(3/2)*Log[d*g + c^2*d*f*x + Sqrt[d]*Sqrt[-(c^2*f^2) + g^2]*Sqrt[-(d*(-1 + c^2*x^2))]])/g^4 + (b*d*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*((-2*c*g*x)/(Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) + 2*g*ArcCosh[c*x] - (c*f*ArcCosh[c*x]^2)/(Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) + (2*(-(c*f) + g)*(c*f + g)*(2*ArcCosh[c*x]*ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] - (2*I)*ArcCos[-((c*f)/g)]*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + (ArcCos[-((c*f)/g)] + 2*(ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]]))*Log[Sqrt[-(c^2*f^2) + g^2]/(Sqrt[2]*E^(ArcCosh[c*x]/2)*Sqrt[g]*Sqrt[c*f + c*g*x])] + (ArcCos[-((c*f)/g)] - 2*(ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]]))*Log[(E^(ArcCosh[c*x]/2)*Sqrt[-(c^2*f^2) + g^2])/(Sqrt[2]*Sqrt[g]*Sqrt[c*f + c*g*x])] - (ArcCos[-((c*f)/g)] + 2*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]])*Log[((c*f + g)*(c*f - g + I*Sqrt[-(c^2*f^2) + g^2])*(-1 + Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] - (ArcCos[-((c*f)/g)] - 2*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]])*Log[((c*f + g)*(-(c*f) + g + I*Sqrt[-(c^2*f^2) + g^2])*(1 + Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] + I*(PolyLog[2, ((c*f - I*Sqrt[-(c^2*f^2) + g^2])*(c*f + g - I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] - PolyLog[2, ((c*f + I*Sqrt[-(c^2*f^2) + g^2])*(c*f + g - I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))])))/(Sqrt[-(c^2*f^2) + g^2]*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x))))/(2*g^2) - (b*d*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*((-9*(-2*ArcCosh[c*x]*ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + (2*I)*ArcCos[-((c*f)/g)]*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] - (ArcCos[-((c*f)/g)] + 2*(ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]]))*Log[Sqrt[-(c^2*f^2) + g^2]/(Sqrt[2]*E^(ArcCosh[c*x]/2)*Sqrt[g]*Sqrt[c*f + c*g*x])] - (ArcCos[-((c*f)/g)] - 2*(ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]]))*Log[(E^(ArcCosh[c*x]/2)*Sqrt[-(c^2*f^2) + g^2])/(Sqrt[2]*Sqrt[g]*Sqrt[c*f + c*g*x])] + (ArcCos[-((c*f)/g)] + 2*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]])*Log[((c*f + g)*(c*f - g + I*Sqrt[-(c^2*f^2) + g^2])*(-1 + Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] + (ArcCos[-((c*f)/g)] - 2*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]])*Log[((c*f + g)*(-(c*f) + g + I*Sqrt[-(c^2*f^2) + g^2])*(1 + Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] - I*(PolyLog[2, ((c*f - I*Sqrt[-(c^2*f^2) + g^2])*(c*f + g - I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] - PolyLog[2, ((c*f + I*Sqrt[-(c^2*f^2) + g^2])*(c*f + g - I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))])))/Sqrt[-(c^2*f^2) + g^2] - (-18*c*g*(-4*c^2*f^2 + g^2)*x + 18*g*(-4*c^2*f^2 + g^2)*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x] + 18*c*f*(2*c^2*f^2 - g^2)*ArcCosh[c*x]^2 - 9*c*f*g^2*Cosh[2*ArcCosh[c*x]] + 2*g^3*Cosh[3*ArcCosh[c*x]] + (9*(8*c^4*f^4 - 8*c^2*f^2*g^2 + g^4)*(2*ArcCosh[c*x]*ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] - (2*I)*ArcCos[-((c*f)/g)]*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + (ArcCos[-((c*f)/g)] + 2*(ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]]))*Log[Sqrt[-(c^2*f^2) + g^2]/(Sqrt[2]*E^(ArcCosh[c*x]/2)*Sqrt[g]*Sqrt[c*f + c*g*x])] + (ArcCos[-((c*f)/g)] - 2*(ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]]))*Log[(E^(ArcCosh[c*x]/2)*Sqrt[-(c^2*f^2) + g^2])/(Sqrt[2]*Sqrt[g]*Sqrt[c*f + c*g*x])] - (ArcCos[-((c*f)/g)] + 2*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]])*Log[((c*f + g)*(c*f - g + I*Sqrt[-(c^2*f^2) + g^2])*(-1 + Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] - (ArcCos[-((c*f)/g)] - 2*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]])*Log[((c*f + g)*(-(c*f) + g + I*Sqrt[-(c^2*f^2) + g^2])*(1 + Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] + I*(PolyLog[2, ((c*f - I*Sqrt[-(c^2*f^2) + g^2])*(c*f + g - I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] - PolyLog[2, ((c*f + I*Sqrt[-(c^2*f^2) + g^2])*(c*f + g - I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))])))/Sqrt[-(c^2*f^2) + g^2] + 18*c*f*g^2*ArcCosh[c*x]*Sinh[2*ArcCosh[c*x]] - 6*g^3*ArcCosh[c*x]*Sinh[3*ArcCosh[c*x]])/g^4))/(72*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x))","C",0
62,1,1802,1385,7.9758169,"\int (f+g x)^3 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[(f + g*x)^3*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]),x]","-\frac{b d^2 \sqrt{-d (c x-1) (c x+1)} \left(\cosh \left(2 \cosh ^{-1}(c x)\right)+2 \cosh ^{-1}(c x) \left(\cosh ^{-1}(c x)-\sinh \left(2 \cosh ^{-1}(c x)\right)\right)\right) f^3}{8 c \sqrt{\frac{c x-1}{c x+1}} (c x+1)}+\frac{b d^2 \sqrt{-d (c x-1) (c x+1)} \left(8 \cosh ^{-1}(c x)^2-4 \sinh \left(4 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)+\cosh \left(4 \cosh ^{-1}(c x)\right)\right) f^3}{64 c \sqrt{\frac{c x-1}{c x+1}} (c x+1)}+\frac{b d^2 \sqrt{-d (c x-1) (c x+1)} \left(18 \cosh \left(2 \cosh ^{-1}(c x)\right)-9 \cosh \left(4 \cosh ^{-1}(c x)\right)-2 \left(36 \cosh ^{-1}(c x)^2+18 \sinh \left(2 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-18 \sinh \left(4 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-6 \sinh \left(6 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)+\cosh \left(6 \cosh ^{-1}(c x)\right)\right)\right) f^3}{2304 c \sqrt{\frac{c x-1}{c x+1}} (c x+1)}-\frac{b d^2 g \sqrt{-d (c x-1) (c x+1)} \left(-12 \left(\frac{c x-1}{c x+1}\right)^{3/2} \cosh ^{-1}(c x) (c x+1)^3-9 c x+\cosh \left(3 \cosh ^{-1}(c x)\right)\right) f^2}{12 c^2 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}+\frac{b d^2 g \sqrt{-d (c x-1) (c x+1)} \left(-450 c x+450 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)+25 \cosh \left(3 \cosh ^{-1}(c x)\right)+9 \cosh \left(5 \cosh ^{-1}(c x)\right)-75 \cosh ^{-1}(c x) \sinh \left(3 \cosh ^{-1}(c x)\right)-45 \cosh ^{-1}(c x) \sinh \left(5 \cosh ^{-1}(c x)\right)\right) f^2}{600 c^2 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}-\frac{b d^2 g \sqrt{-d (c x-1) (c x+1)} \left(-55125 c x+1225 \cosh \left(3 \cosh ^{-1}(c x)\right)+3 \left(18375 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)-1225 \sinh \left(3 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-2205 \sinh \left(5 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-525 \sinh \left(7 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)+441 \cosh \left(5 \cosh ^{-1}(c x)\right)+75 \cosh \left(7 \cosh ^{-1}(c x)\right)\right)\right) f^2}{235200 c^2 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}-\frac{5 a d^{5/2} \left(8 c^2 f^2+3 g^2\right) \tan ^{-1}\left(\frac{c x \sqrt{-d \left(c^2 x^2-1\right)}}{\sqrt{d} \left(c^2 x^2-1\right)}\right) f}{128 c^3}-\frac{3 b d^2 g^2 \sqrt{-d (c x-1) (c x+1)} \left(8 \cosh ^{-1}(c x)^2-4 \sinh \left(4 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)+\cosh \left(4 \cosh ^{-1}(c x)\right)\right) f}{128 c^3 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}-\frac{b d^2 g^2 \sqrt{-d (c x-1) (c x+1)} \left(18 \cosh \left(2 \cosh ^{-1}(c x)\right)-9 \cosh \left(4 \cosh ^{-1}(c x)\right)-2 \left(36 \cosh ^{-1}(c x)^2+18 \sinh \left(2 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-18 \sinh \left(4 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-6 \sinh \left(6 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)+\cosh \left(6 \cosh ^{-1}(c x)\right)\right)\right) f}{384 c^3 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}-\frac{b d^2 g^2 \sqrt{-d (c x-1) (c x+1)} \left(1440 \cosh ^{-1}(c x)^2+1152 \sinh \left(2 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-576 \sinh \left(4 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-384 \sinh \left(6 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-72 \sinh \left(8 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-576 \cosh \left(2 \cosh ^{-1}(c x)\right)+144 \cosh \left(4 \cosh ^{-1}(c x)\right)+64 \cosh \left(6 \cosh ^{-1}(c x)\right)+9 \cosh \left(8 \cosh ^{-1}(c x)\right)\right) f}{24576 c^3 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}+\sqrt{-d \left(c^2 x^2-1\right)} \left(\frac{1}{9} a c^4 d^2 g^3 x^8+\frac{3}{8} a c^4 d^2 f g^2 x^7-\frac{1}{63} a c^2 d^2 g \left(19 g^2-27 c^2 f^2\right) x^6+\frac{1}{48} a c^2 d^2 f \left(8 c^2 f^2-51 g^2\right) x^5+\frac{1}{21} a d^2 g \left(5 g^2-27 c^2 f^2\right) x^4-\frac{1}{192} a d^2 f \left(104 c^2 f^2-177 g^2\right) x^3-\frac{a d^2 g \left(g^2-81 c^2 f^2\right) x^2}{63 c^2}+\frac{a d^2 f \left(88 c^2 f^2-15 g^2\right) x}{128 c^2}-\frac{a d^2 g \left(27 c^2 f^2+2 g^2\right)}{63 c^4}\right)-\frac{b d^2 g^3 \sqrt{-d (c x-1) (c x+1)} \left(-450 c x+450 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)+25 \cosh \left(3 \cosh ^{-1}(c x)\right)+9 \cosh \left(5 \cosh ^{-1}(c x)\right)-75 \cosh ^{-1}(c x) \sinh \left(3 \cosh ^{-1}(c x)\right)-45 \cosh ^{-1}(c x) \sinh \left(5 \cosh ^{-1}(c x)\right)\right)}{3600 c^4 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}+\frac{b d^2 g^3 \sqrt{-d (c x-1) (c x+1)} \left(-55125 c x+1225 \cosh \left(3 \cosh ^{-1}(c x)\right)+3 \left(18375 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)-1225 \sinh \left(3 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-2205 \sinh \left(5 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-525 \sinh \left(7 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)+441 \cosh \left(5 \cosh ^{-1}(c x)\right)+75 \cosh \left(7 \cosh ^{-1}(c x)\right)\right)\right)}{352800 c^4 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}-\frac{b d^2 g^3 \sqrt{-d (c x-1) (c x+1)} \left(-1389150 c x+31752 \cosh \left(5 \cosh ^{-1}(c x)\right)+5 \left(2025 \cosh \left(7 \cosh ^{-1}(c x)\right)+245 \cosh \left(9 \cosh ^{-1}(c x)\right)-63 \cosh ^{-1}(c x) \left(-4410 \sqrt{\frac{c x-1}{c x+1}} (c x+1)+504 \sinh \left(5 \cosh ^{-1}(c x)\right)+225 \sinh \left(7 \cosh ^{-1}(c x)\right)+35 \sinh \left(9 \cosh ^{-1}(c x)\right)\right)\right)\right)}{25401600 c^4 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}","-\frac{b c^5 d^2 g^3 \sqrt{d-c^2 d x^2} x^9}{81 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c^5 d^2 f g^2 \sqrt{d-c^2 d x^2} x^8}{64 \sqrt{c x-1} \sqrt{c x+1}}+\frac{19 b c^3 d^2 g^3 \sqrt{d-c^2 d x^2} x^7}{441 \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c^5 d^2 f^2 g \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{c x-1} \sqrt{c x+1}}+\frac{17 b c^3 d^2 f g^2 \sqrt{d-c^2 d x^2} x^6}{96 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 g^3 \sqrt{d-c^2 d x^2} x^5}{21 \sqrt{c x-1} \sqrt{c x+1}}+\frac{9 b c^3 d^2 f^2 g \sqrt{d-c^2 d x^2} x^5}{35 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c^3 d^2 f^3 \sqrt{d-c^2 d x^2} x^4}{96 \sqrt{c x-1} \sqrt{c x+1}}-\frac{59 b c d^2 f g^2 \sqrt{d-c^2 d x^2} x^4}{256 \sqrt{c x-1} \sqrt{c x+1}}+\frac{15}{64} d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{3}{8} d^2 f g^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{5}{16} d^2 f g^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{b d^2 g^3 \sqrt{d-c^2 d x^2} x^3}{189 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{3 b c d^2 f^2 g \sqrt{d-c^2 d x^2} x^3}{7 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 g^3 (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^2}{9 c^2}-\frac{25 b c d^2 f^3 \sqrt{d-c^2 d x^2} x^2}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{15 b d^2 f g^2 \sqrt{d-c^2 d x^2} x^2}{256 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{5}{16} d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x-\frac{15 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^3 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^3 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x+\frac{2 b d^2 g^3 \sqrt{d-c^2 d x^2} x}{63 c^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b d^2 f^2 g \sqrt{d-c^2 d x^2} x}{7 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 f^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{15 d^2 f g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 d^2 g^3 (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{63 c^4}-\frac{3 d^2 f^2 g (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^2}+\frac{b d^2 f^3 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{36 c \sqrt{c x-1} \sqrt{c x+1}}",1,"Sqrt[-(d*(-1 + c^2*x^2))]*(-1/63*(a*d^2*g*(27*c^2*f^2 + 2*g^2))/c^4 + (a*d^2*f*(88*c^2*f^2 - 15*g^2)*x)/(128*c^2) - (a*d^2*g*(-81*c^2*f^2 + g^2)*x^2)/(63*c^2) - (a*d^2*f*(104*c^2*f^2 - 177*g^2)*x^3)/192 + (a*d^2*g*(-27*c^2*f^2 + 5*g^2)*x^4)/21 + (a*c^2*d^2*f*(8*c^2*f^2 - 51*g^2)*x^5)/48 - (a*c^2*d^2*g*(-27*c^2*f^2 + 19*g^2)*x^6)/63 + (3*a*c^4*d^2*f*g^2*x^7)/8 + (a*c^4*d^2*g^3*x^8)/9) - (5*a*d^(5/2)*f*(8*c^2*f^2 + 3*g^2)*ArcTan[(c*x*Sqrt[-(d*(-1 + c^2*x^2))])/(Sqrt[d]*(-1 + c^2*x^2))])/(128*c^3) - (b*d^2*f^2*g*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(-9*c*x - 12*((-1 + c*x)/(1 + c*x))^(3/2)*(1 + c*x)^3*ArcCosh[c*x] + Cosh[3*ArcCosh[c*x]]))/(12*c^2*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) - (b*d^2*f^3*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(Cosh[2*ArcCosh[c*x]] + 2*ArcCosh[c*x]*(ArcCosh[c*x] - Sinh[2*ArcCosh[c*x]])))/(8*c*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) + (b*d^2*f^3*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(8*ArcCosh[c*x]^2 + Cosh[4*ArcCosh[c*x]] - 4*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]]))/(64*c*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) - (3*b*d^2*f*g^2*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(8*ArcCosh[c*x]^2 + Cosh[4*ArcCosh[c*x]] - 4*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]]))/(128*c^3*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) + (b*d^2*f^2*g*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(-450*c*x + 450*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x] + 25*Cosh[3*ArcCosh[c*x]] + 9*Cosh[5*ArcCosh[c*x]] - 75*ArcCosh[c*x]*Sinh[3*ArcCosh[c*x]] - 45*ArcCosh[c*x]*Sinh[5*ArcCosh[c*x]]))/(600*c^2*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) - (b*d^2*g^3*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(-450*c*x + 450*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x] + 25*Cosh[3*ArcCosh[c*x]] + 9*Cosh[5*ArcCosh[c*x]] - 75*ArcCosh[c*x]*Sinh[3*ArcCosh[c*x]] - 45*ArcCosh[c*x]*Sinh[5*ArcCosh[c*x]]))/(3600*c^4*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) + (b*d^2*f^3*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(18*Cosh[2*ArcCosh[c*x]] - 9*Cosh[4*ArcCosh[c*x]] - 2*(36*ArcCosh[c*x]^2 + Cosh[6*ArcCosh[c*x]] + 18*ArcCosh[c*x]*Sinh[2*ArcCosh[c*x]] - 18*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]] - 6*ArcCosh[c*x]*Sinh[6*ArcCosh[c*x]])))/(2304*c*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) - (b*d^2*f*g^2*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(18*Cosh[2*ArcCosh[c*x]] - 9*Cosh[4*ArcCosh[c*x]] - 2*(36*ArcCosh[c*x]^2 + Cosh[6*ArcCosh[c*x]] + 18*ArcCosh[c*x]*Sinh[2*ArcCosh[c*x]] - 18*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]] - 6*ArcCosh[c*x]*Sinh[6*ArcCosh[c*x]])))/(384*c^3*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) - (b*d^2*f^2*g*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(-55125*c*x + 1225*Cosh[3*ArcCosh[c*x]] + 3*(18375*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x] + 441*Cosh[5*ArcCosh[c*x]] + 75*Cosh[7*ArcCosh[c*x]] - 1225*ArcCosh[c*x]*Sinh[3*ArcCosh[c*x]] - 2205*ArcCosh[c*x]*Sinh[5*ArcCosh[c*x]] - 525*ArcCosh[c*x]*Sinh[7*ArcCosh[c*x]])))/(235200*c^2*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) + (b*d^2*g^3*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(-55125*c*x + 1225*Cosh[3*ArcCosh[c*x]] + 3*(18375*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x] + 441*Cosh[5*ArcCosh[c*x]] + 75*Cosh[7*ArcCosh[c*x]] - 1225*ArcCosh[c*x]*Sinh[3*ArcCosh[c*x]] - 2205*ArcCosh[c*x]*Sinh[5*ArcCosh[c*x]] - 525*ArcCosh[c*x]*Sinh[7*ArcCosh[c*x]])))/(352800*c^4*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) - (b*d^2*f*g^2*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(1440*ArcCosh[c*x]^2 - 576*Cosh[2*ArcCosh[c*x]] + 144*Cosh[4*ArcCosh[c*x]] + 64*Cosh[6*ArcCosh[c*x]] + 9*Cosh[8*ArcCosh[c*x]] + 1152*ArcCosh[c*x]*Sinh[2*ArcCosh[c*x]] - 576*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]] - 384*ArcCosh[c*x]*Sinh[6*ArcCosh[c*x]] - 72*ArcCosh[c*x]*Sinh[8*ArcCosh[c*x]]))/(24576*c^3*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) - (b*d^2*g^3*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(-1389150*c*x + 31752*Cosh[5*ArcCosh[c*x]] + 5*(2025*Cosh[7*ArcCosh[c*x]] + 245*Cosh[9*ArcCosh[c*x]] - 63*ArcCosh[c*x]*(-4410*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x) + 504*Sinh[5*ArcCosh[c*x]] + 225*Sinh[7*ArcCosh[c*x]] + 35*Sinh[9*ArcCosh[c*x]]))))/(25401600*c^4*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x))","A",0
63,1,1282,1015,7.3912091,"\int (f+g x)^2 \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[(f + g*x)^2*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]),x]","-\frac{5 a \left(8 c^2 f^2+g^2\right) \tan ^{-1}\left(\frac{c x \sqrt{-d \left(c^2 x^2-1\right)}}{\sqrt{d} \left(c^2 x^2-1\right)}\right) d^{5/2}}{128 c^3}-\frac{b f g \sqrt{-d (c x-1) (c x+1)} \left(-12 \left(\frac{c x-1}{c x+1}\right)^{3/2} \cosh ^{-1}(c x) (c x+1)^3-9 c x+\cosh \left(3 \cosh ^{-1}(c x)\right)\right) d^2}{18 c^2 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}-\frac{b f^2 \sqrt{-d (c x-1) (c x+1)} \left(\cosh \left(2 \cosh ^{-1}(c x)\right)+2 \cosh ^{-1}(c x) \left(\cosh ^{-1}(c x)-\sinh \left(2 \cosh ^{-1}(c x)\right)\right)\right) d^2}{8 c \sqrt{\frac{c x-1}{c x+1}} (c x+1)}+\frac{b f^2 \sqrt{-d (c x-1) (c x+1)} \left(8 \cosh ^{-1}(c x)^2-4 \sinh \left(4 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)+\cosh \left(4 \cosh ^{-1}(c x)\right)\right) d^2}{64 c \sqrt{\frac{c x-1}{c x+1}} (c x+1)}-\frac{b g^2 \sqrt{-d (c x-1) (c x+1)} \left(8 \cosh ^{-1}(c x)^2-4 \sinh \left(4 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)+\cosh \left(4 \cosh ^{-1}(c x)\right)\right) d^2}{128 c^3 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}+\frac{b f g \sqrt{-d (c x-1) (c x+1)} \left(-450 c x+450 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)+25 \cosh \left(3 \cosh ^{-1}(c x)\right)+9 \cosh \left(5 \cosh ^{-1}(c x)\right)-75 \cosh ^{-1}(c x) \sinh \left(3 \cosh ^{-1}(c x)\right)-45 \cosh ^{-1}(c x) \sinh \left(5 \cosh ^{-1}(c x)\right)\right) d^2}{900 c^2 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}+\frac{b f^2 \sqrt{-d (c x-1) (c x+1)} \left(18 \cosh \left(2 \cosh ^{-1}(c x)\right)-9 \cosh \left(4 \cosh ^{-1}(c x)\right)-2 \left(36 \cosh ^{-1}(c x)^2+18 \sinh \left(2 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-18 \sinh \left(4 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-6 \sinh \left(6 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)+\cosh \left(6 \cosh ^{-1}(c x)\right)\right)\right) d^2}{2304 c \sqrt{\frac{c x-1}{c x+1}} (c x+1)}-\frac{b g^2 \sqrt{-d (c x-1) (c x+1)} \left(18 \cosh \left(2 \cosh ^{-1}(c x)\right)-9 \cosh \left(4 \cosh ^{-1}(c x)\right)-2 \left(36 \cosh ^{-1}(c x)^2+18 \sinh \left(2 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-18 \sinh \left(4 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-6 \sinh \left(6 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)+\cosh \left(6 \cosh ^{-1}(c x)\right)\right)\right) d^2}{1152 c^3 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}-\frac{b f g \sqrt{-d (c x-1) (c x+1)} \left(-55125 c x+1225 \cosh \left(3 \cosh ^{-1}(c x)\right)+3 \left(18375 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)-1225 \sinh \left(3 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-2205 \sinh \left(5 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-525 \sinh \left(7 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)+441 \cosh \left(5 \cosh ^{-1}(c x)\right)+75 \cosh \left(7 \cosh ^{-1}(c x)\right)\right)\right) d^2}{352800 c^2 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}-\frac{b g^2 \sqrt{-d (c x-1) (c x+1)} \left(1440 \cosh ^{-1}(c x)^2+1152 \sinh \left(2 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-576 \sinh \left(4 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-384 \sinh \left(6 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-72 \sinh \left(8 \cosh ^{-1}(c x)\right) \cosh ^{-1}(c x)-576 \cosh \left(2 \cosh ^{-1}(c x)\right)+144 \cosh \left(4 \cosh ^{-1}(c x)\right)+64 \cosh \left(6 \cosh ^{-1}(c x)\right)+9 \cosh \left(8 \cosh ^{-1}(c x)\right)\right) d^2}{73728 c^3 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}+\sqrt{-d \left(c^2 x^2-1\right)} \left(\frac{1}{8} a c^4 d^2 g^2 x^7+\frac{2}{7} a c^4 d^2 f g x^6+\frac{1}{48} a c^2 d^2 \left(8 c^2 f^2-17 g^2\right) x^5-\frac{6}{7} a c^2 d^2 f g x^4+\frac{1}{192} a d^2 \left(59 g^2-104 c^2 f^2\right) x^3+\frac{6}{7} a d^2 f g x^2+\frac{a d^2 \left(88 c^2 f^2-5 g^2\right) x}{128 c^2}-\frac{2 a d^2 f g}{7 c^2}\right)","-\frac{b c^5 d^2 g^2 \sqrt{d-c^2 d x^2} x^8}{64 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 b c^5 d^2 f g \sqrt{d-c^2 d x^2} x^7}{49 \sqrt{c x-1} \sqrt{c x+1}}+\frac{17 b c^3 d^2 g^2 \sqrt{d-c^2 d x^2} x^6}{288 \sqrt{c x-1} \sqrt{c x+1}}+\frac{6 b c^3 d^2 f g \sqrt{d-c^2 d x^2} x^5}{35 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c^3 d^2 f^2 \sqrt{d-c^2 d x^2} x^4}{96 \sqrt{c x-1} \sqrt{c x+1}}-\frac{59 b c d^2 g^2 \sqrt{d-c^2 d x^2} x^4}{768 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5}{64} d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{1}{8} d^2 g^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3+\frac{5}{48} d^2 g^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x^3-\frac{2 b c d^2 f g \sqrt{d-c^2 d x^2} x^3}{7 \sqrt{c x-1} \sqrt{c x+1}}-\frac{25 b c d^2 f^2 \sqrt{d-c^2 d x^2} x^2}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b d^2 g^2 \sqrt{d-c^2 d x^2} x^2}{256 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{5}{16} d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x-\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x}{128 c^2}+\frac{1}{6} d^2 f^2 (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x+\frac{5}{24} d^2 f^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) x+\frac{2 b d^2 f g \sqrt{d-c^2 d x^2} x}{7 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 f^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{5 d^2 g^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{256 b c^3 \sqrt{c x-1} \sqrt{c x+1}}-\frac{2 d^2 f g (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^2}+\frac{b d^2 f^2 \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{36 c \sqrt{c x-1} \sqrt{c x+1}}",1,"Sqrt[-(d*(-1 + c^2*x^2))]*((-2*a*d^2*f*g)/(7*c^2) + (a*d^2*(88*c^2*f^2 - 5*g^2)*x)/(128*c^2) + (6*a*d^2*f*g*x^2)/7 + (a*d^2*(-104*c^2*f^2 + 59*g^2)*x^3)/192 - (6*a*c^2*d^2*f*g*x^4)/7 + (a*c^2*d^2*(8*c^2*f^2 - 17*g^2)*x^5)/48 + (2*a*c^4*d^2*f*g*x^6)/7 + (a*c^4*d^2*g^2*x^7)/8) - (5*a*d^(5/2)*(8*c^2*f^2 + g^2)*ArcTan[(c*x*Sqrt[-(d*(-1 + c^2*x^2))])/(Sqrt[d]*(-1 + c^2*x^2))])/(128*c^3) - (b*d^2*f*g*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(-9*c*x - 12*((-1 + c*x)/(1 + c*x))^(3/2)*(1 + c*x)^3*ArcCosh[c*x] + Cosh[3*ArcCosh[c*x]]))/(18*c^2*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) - (b*d^2*f^2*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(Cosh[2*ArcCosh[c*x]] + 2*ArcCosh[c*x]*(ArcCosh[c*x] - Sinh[2*ArcCosh[c*x]])))/(8*c*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) + (b*d^2*f^2*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(8*ArcCosh[c*x]^2 + Cosh[4*ArcCosh[c*x]] - 4*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]]))/(64*c*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) - (b*d^2*g^2*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(8*ArcCosh[c*x]^2 + Cosh[4*ArcCosh[c*x]] - 4*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]]))/(128*c^3*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) + (b*d^2*f*g*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(-450*c*x + 450*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x] + 25*Cosh[3*ArcCosh[c*x]] + 9*Cosh[5*ArcCosh[c*x]] - 75*ArcCosh[c*x]*Sinh[3*ArcCosh[c*x]] - 45*ArcCosh[c*x]*Sinh[5*ArcCosh[c*x]]))/(900*c^2*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) + (b*d^2*f^2*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(18*Cosh[2*ArcCosh[c*x]] - 9*Cosh[4*ArcCosh[c*x]] - 2*(36*ArcCosh[c*x]^2 + Cosh[6*ArcCosh[c*x]] + 18*ArcCosh[c*x]*Sinh[2*ArcCosh[c*x]] - 18*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]] - 6*ArcCosh[c*x]*Sinh[6*ArcCosh[c*x]])))/(2304*c*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) - (b*d^2*g^2*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(18*Cosh[2*ArcCosh[c*x]] - 9*Cosh[4*ArcCosh[c*x]] - 2*(36*ArcCosh[c*x]^2 + Cosh[6*ArcCosh[c*x]] + 18*ArcCosh[c*x]*Sinh[2*ArcCosh[c*x]] - 18*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]] - 6*ArcCosh[c*x]*Sinh[6*ArcCosh[c*x]])))/(1152*c^3*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) - (b*d^2*f*g*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(-55125*c*x + 1225*Cosh[3*ArcCosh[c*x]] + 3*(18375*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x] + 441*Cosh[5*ArcCosh[c*x]] + 75*Cosh[7*ArcCosh[c*x]] - 1225*ArcCosh[c*x]*Sinh[3*ArcCosh[c*x]] - 2205*ArcCosh[c*x]*Sinh[5*ArcCosh[c*x]] - 525*ArcCosh[c*x]*Sinh[7*ArcCosh[c*x]])))/(352800*c^2*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)) - (b*d^2*g^2*Sqrt[-(d*(-1 + c*x)*(1 + c*x))]*(1440*ArcCosh[c*x]^2 - 576*Cosh[2*ArcCosh[c*x]] + 144*Cosh[4*ArcCosh[c*x]] + 64*Cosh[6*ArcCosh[c*x]] + 9*Cosh[8*ArcCosh[c*x]] + 1152*ArcCosh[c*x]*Sinh[2*ArcCosh[c*x]] - 576*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]] - 384*ArcCosh[c*x]*Sinh[6*ArcCosh[c*x]] - 72*ArcCosh[c*x]*Sinh[8*ArcCosh[c*x]]))/(73728*c^3*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x))","A",0
64,1,644,568,6.2055449,"\int (f+g x) \left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right) \, dx","Integrate[(f + g*x)*(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]),x]","\frac{d^2 \left(-882000 a c \sqrt{d} f \sqrt{\frac{c x-1}{c x+1}} (c x+1) \tan ^{-1}\left(\frac{c x \sqrt{d-c^2 d x^2}}{\sqrt{d} \left(c^2 x^2-1\right)}\right)+8400 a \sqrt{\frac{c x-1}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2} \left(48 g \left(c^2 x^2-1\right)^3+7 c^2 f x \left(8 c^4 x^4-26 c^2 x^2+33\right)\right)-352800 b c f \sqrt{d-c^2 d x^2} \left(\cosh \left(2 \cosh ^{-1}(c x)\right)+2 \cosh ^{-1}(c x) \left(\cosh ^{-1}(c x)-\sinh \left(2 \cosh ^{-1}(c x)\right)\right)\right)+44100 b c f \sqrt{d-c^2 d x^2} \left(8 \cosh ^{-1}(c x)^2+\cosh \left(4 \cosh ^{-1}(c x)\right)-4 \cosh ^{-1}(c x) \sinh \left(4 \cosh ^{-1}(c x)\right)\right)+1225 b c f \sqrt{d-c^2 d x^2} \left(-72 \cosh ^{-1}(c x)^2+18 \cosh \left(2 \cosh ^{-1}(c x)\right)-9 \cosh \left(4 \cosh ^{-1}(c x)\right)-2 \cosh \left(6 \cosh ^{-1}(c x)\right)+12 \cosh ^{-1}(c x) \left(-3 \sinh \left(2 \cosh ^{-1}(c x)\right)+3 \sinh \left(4 \cosh ^{-1}(c x)\right)+\sinh \left(6 \cosh ^{-1}(c x)\right)\right)\right)+78400 b g \sqrt{d-c^2 d x^2} \left(9 c x+12 \left(\frac{c x-1}{c x+1}\right)^{3/2} (c x+1)^3 \cosh ^{-1}(c x)-\cosh \left(3 \cosh ^{-1}(c x)\right)\right)-1568 b g \sqrt{d-c^2 d x^2} \left(450 c x-450 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)-25 \cosh \left(3 \cosh ^{-1}(c x)\right)-9 \cosh \left(5 \cosh ^{-1}(c x)\right)+75 \cosh ^{-1}(c x) \sinh \left(3 \cosh ^{-1}(c x)\right)+45 \cosh ^{-1}(c x) \sinh \left(5 \cosh ^{-1}(c x)\right)\right)+4 b g \sqrt{d-c^2 d x^2} \left(55125 c x-55125 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)-1225 \cosh \left(3 \cosh ^{-1}(c x)\right)-1323 \cosh \left(5 \cosh ^{-1}(c x)\right)-225 \cosh \left(7 \cosh ^{-1}(c x)\right)+3675 \cosh ^{-1}(c x) \sinh \left(3 \cosh ^{-1}(c x)\right)+6615 \cosh ^{-1}(c x) \sinh \left(5 \cosh ^{-1}(c x)\right)+1575 \cosh ^{-1}(c x) \sinh \left(7 \cosh ^{-1}(c x)\right)\right)\right)}{2822400 c^2 \sqrt{\frac{c x-1}{c x+1}} (c x+1)}","\frac{1}{6} d^2 f x (1-c x)^2 (c x+1)^2 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{5}{16} d^2 f x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)+\frac{5}{24} d^2 f x (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)-\frac{5 d^2 f \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{32 b c \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 g (1-c x)^3 (c x+1)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{7 c^2}-\frac{25 b c d^2 f x^2 \sqrt{d-c^2 d x^2}}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 f \left(1-c^2 x^2\right)^3 \sqrt{d-c^2 d x^2}}{36 c \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 g x \sqrt{d-c^2 d x^2}}{7 c \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c d^2 g x^3 \sqrt{d-c^2 d x^2}}{7 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b c^5 d^2 g x^7 \sqrt{d-c^2 d x^2}}{49 \sqrt{c x-1} \sqrt{c x+1}}+\frac{5 b c^3 d^2 f x^4 \sqrt{d-c^2 d x^2}}{96 \sqrt{c x-1} \sqrt{c x+1}}+\frac{3 b c^3 d^2 g x^5 \sqrt{d-c^2 d x^2}}{35 \sqrt{c x-1} \sqrt{c x+1}}",1,"(d^2*(8400*a*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*Sqrt[d - c^2*d*x^2]*(48*g*(-1 + c^2*x^2)^3 + 7*c^2*f*x*(33 - 26*c^2*x^2 + 8*c^4*x^4)) - 882000*a*c*Sqrt[d]*f*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcTan[(c*x*Sqrt[d - c^2*d*x^2])/(Sqrt[d]*(-1 + c^2*x^2))] + 78400*b*g*Sqrt[d - c^2*d*x^2]*(9*c*x + 12*((-1 + c*x)/(1 + c*x))^(3/2)*(1 + c*x)^3*ArcCosh[c*x] - Cosh[3*ArcCosh[c*x]]) - 352800*b*c*f*Sqrt[d - c^2*d*x^2]*(Cosh[2*ArcCosh[c*x]] + 2*ArcCosh[c*x]*(ArcCosh[c*x] - Sinh[2*ArcCosh[c*x]])) + 44100*b*c*f*Sqrt[d - c^2*d*x^2]*(8*ArcCosh[c*x]^2 + Cosh[4*ArcCosh[c*x]] - 4*ArcCosh[c*x]*Sinh[4*ArcCosh[c*x]]) - 1568*b*g*Sqrt[d - c^2*d*x^2]*(450*c*x - 450*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x] - 25*Cosh[3*ArcCosh[c*x]] - 9*Cosh[5*ArcCosh[c*x]] + 75*ArcCosh[c*x]*Sinh[3*ArcCosh[c*x]] + 45*ArcCosh[c*x]*Sinh[5*ArcCosh[c*x]]) + 1225*b*c*f*Sqrt[d - c^2*d*x^2]*(-72*ArcCosh[c*x]^2 + 18*Cosh[2*ArcCosh[c*x]] - 9*Cosh[4*ArcCosh[c*x]] - 2*Cosh[6*ArcCosh[c*x]] + 12*ArcCosh[c*x]*(-3*Sinh[2*ArcCosh[c*x]] + 3*Sinh[4*ArcCosh[c*x]] + Sinh[6*ArcCosh[c*x]])) + 4*b*g*Sqrt[d - c^2*d*x^2]*(55125*c*x - 55125*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x] - 1225*Cosh[3*ArcCosh[c*x]] - 1323*Cosh[5*ArcCosh[c*x]] - 225*Cosh[7*ArcCosh[c*x]] + 3675*ArcCosh[c*x]*Sinh[3*ArcCosh[c*x]] + 6615*ArcCosh[c*x]*Sinh[5*ArcCosh[c*x]] + 1575*ArcCosh[c*x]*Sinh[7*ArcCosh[c*x]])))/(2822400*c^2*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x))","A",0
65,1,6244,1744,18.357979,"\int \frac{\left(d-c^2 d x^2\right)^{5/2} \left(a+b \cosh ^{-1}(c x)\right)}{f+g x} \, dx","Integrate[((d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x]))/(f + g*x),x]","\text{Result too large to show}","-\frac{b d^2 x^5 \sqrt{d-c^2 d x^2} c^5}{25 g \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 f x^4 \sqrt{d-c^2 d x^2} c^5}{16 g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 f x^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c^4}{4 g^2}-\frac{b d^2 \left(c^2 f^2-2 g^2\right) x^3 \sqrt{d-c^2 d x^2} c^3}{9 g^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 x^3 \sqrt{d-c^2 d x^2} c^3}{45 g \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 f \left(c^2 f^2-2 g^2\right) x^2 \sqrt{d-c^2 d x^2} c^3}{4 g^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^2 f x^2 \sqrt{d-c^2 d x^2} c^3}{16 g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 f \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c^2}{2 g^4}+\frac{d^2 f x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c^2}{8 g^2}-\frac{d^2 x^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right) c^2}{5 g}+\frac{d^2 f \left(c^2 f^2-2 g^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 c}{4 b g^4 \sqrt{c x-1} \sqrt{c x+1}}-\frac{d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 c}{2 b g^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{d^2 f \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2 c}{16 b g^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^2 \left(c^2 f^2-g^2\right)^2 x \sqrt{d-c^2 d x^2} c}{g^5 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 \left(c^2 f^2-2 g^2\right) x \sqrt{d-c^2 d x^2} c}{3 g^3 \sqrt{c x-1} \sqrt{c x+1}}+\frac{2 b d^2 x \sqrt{d-c^2 d x^2} c}{15 g \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 \left(c^2 f^2-g^2\right)^2 \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x)}{g^5}-\frac{d^2 \left(c^2 f^2-2 g^2\right) (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{3 g^3}-\frac{2 d^2 (1-c x) (c x+1) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)}{15 g}-\frac{a d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{c^2 x^2-1} \sqrt{d-c^2 d x^2} \tanh ^{-1}\left(\frac{f x c^2+g}{\sqrt{c^2 f^2-g^2} \sqrt{c^2 x^2-1}}\right)}{g^6 (1-c x) (c x+1)}+\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) \log \left(\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{g^6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \cosh ^{-1}(c x) \log \left(\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}+1\right)}{g^6 \sqrt{c x-1} \sqrt{c x+1}}+\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{c x-1} \sqrt{c x+1}}-\frac{b d^2 \left(c^2 f^2-g^2\right)^{5/2} \sqrt{d-c^2 d x^2} \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{g^6 \sqrt{c x-1} \sqrt{c x+1}}+\frac{a d^2 \left(c^2 f^2-g^2\right)^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2}}{g^5 (1-c x) (c x+1)}-\frac{d^2 \left(c^2 f^2-g^2\right)^2 \left(1-c^2 x^2\right) \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b g^4 \sqrt{c x-1} \sqrt{c x+1} (f+g x) c}-\frac{d^2 \left(c^2 f^2-g^2\right)^3 \sqrt{d-c^2 d x^2} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b g^6 \sqrt{c x-1} \sqrt{c x+1} (f+g x) c}",1,"Result too large to show","C",0
66,1,405,478,2.0941795,"\int \frac{(f+g x)^3 \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Integrate[((f + g*x)^3*(a + b*ArcCosh[c*x]))/Sqrt[d - c^2*d*x^2],x]","\frac{-\frac{36 a c f \left(2 c^2 f^2+3 g^2\right) \tan ^{-1}\left(\frac{c x \sqrt{d-c^2 d x^2}}{\sqrt{d} \left(c^2 x^2-1\right)}\right)}{\sqrt{d}}-\frac{12 a \sqrt{d-c^2 d x^2} \left(c^2 g \left(18 f^2+9 f g x+2 g^2 x^2\right)+4 g^3\right)}{d}+\frac{216 b c^2 f^2 g \sqrt{d-c^2 d x^2} \left(c x-\sqrt{c x-1} \sqrt{c x+1} \cosh ^{-1}(c x)\right)}{d \sqrt{c x-1} \sqrt{c x+1}}+\frac{27 b c f g^2 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \left(2 \cosh ^{-1}(c x) \left(\cosh ^{-1}(c x)+\sinh \left(2 \cosh ^{-1}(c x)\right)\right)-\cosh \left(2 \cosh ^{-1}(c x)\right)\right)}{\sqrt{d-c^2 d x^2}}+\frac{8 b g^3 \sqrt{d-c^2 d x^2} \left(c x \left(c^2 x^2+6\right)-3 \sqrt{c x-1} \sqrt{c x+1} \left(c^2 x^2+2\right) \cosh ^{-1}(c x)\right)}{d \sqrt{c x-1} \sqrt{c x+1}}+\frac{36 b c^3 f^3 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)^2}{\sqrt{d-c^2 d x^2}}}{72 c^4}","\frac{f^3 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{3 f^2 g (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}-\frac{3 f g^2 x (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{2 c^2 \sqrt{d-c^2 d x^2}}-\frac{g^3 x^2 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^2 \sqrt{d-c^2 d x^2}}-\frac{2 g^3 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{3 c^4 \sqrt{d-c^2 d x^2}}+\frac{3 f g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c^3 \sqrt{d-c^2 d x^2}}-\frac{3 b f^2 g x \sqrt{c x-1} \sqrt{c x+1}}{c \sqrt{d-c^2 d x^2}}-\frac{3 b f g^2 x^2 \sqrt{c x-1} \sqrt{c x+1}}{4 c \sqrt{d-c^2 d x^2}}-\frac{b g^3 x^3 \sqrt{c x-1} \sqrt{c x+1}}{9 c \sqrt{d-c^2 d x^2}}-\frac{2 b g^3 x \sqrt{c x-1} \sqrt{c x+1}}{3 c^3 \sqrt{d-c^2 d x^2}}",1,"((-12*a*Sqrt[d - c^2*d*x^2]*(4*g^3 + c^2*g*(18*f^2 + 9*f*g*x + 2*g^2*x^2)))/d + (36*b*c^3*f^3*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x]^2)/Sqrt[d - c^2*d*x^2] + (216*b*c^2*f^2*g*Sqrt[d - c^2*d*x^2]*(c*x - Sqrt[-1 + c*x]*Sqrt[1 + c*x]*ArcCosh[c*x]))/(d*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) + (8*b*g^3*Sqrt[d - c^2*d*x^2]*(c*x*(6 + c^2*x^2) - 3*Sqrt[-1 + c*x]*Sqrt[1 + c*x]*(2 + c^2*x^2)*ArcCosh[c*x]))/(d*Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - (36*a*c*f*(2*c^2*f^2 + 3*g^2)*ArcTan[(c*x*Sqrt[d - c^2*d*x^2])/(Sqrt[d]*(-1 + c^2*x^2))])/Sqrt[d] + (27*b*c*f*g^2*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*(-Cosh[2*ArcCosh[c*x]] + 2*ArcCosh[c*x]*(ArcCosh[c*x] + Sinh[2*ArcCosh[c*x]])))/Sqrt[d - c^2*d*x^2])/(72*c^4)","A",0
67,1,267,288,1.5879255,"\int \frac{(f+g x)^2 \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Integrate[((f + g*x)^2*(a + b*ArcCosh[c*x]))/Sqrt[d - c^2*d*x^2],x]","\frac{-\frac{4 a \left(2 c^2 f^2+g^2\right) \tan ^{-1}\left(\frac{c x \sqrt{d-c^2 d x^2}}{\sqrt{d} \left(c^2 x^2-1\right)}\right)}{\sqrt{d}}-\frac{4 a c g \sqrt{d-c^2 d x^2} (4 f+g x)}{d}+\frac{4 b c^2 f^2 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)^2}{\sqrt{d-c^2 d x^2}}+\frac{16 b c f g \sqrt{d-c^2 d x^2} \left(\frac{c x}{\sqrt{c x-1} \sqrt{c x+1}}-\cosh ^{-1}(c x)\right)}{d}+\frac{b g^2 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \left(2 \cosh ^{-1}(c x) \left(\cosh ^{-1}(c x)+\sinh \left(2 \cosh ^{-1}(c x)\right)\right)-\cosh \left(2 \cosh ^{-1}(c x)\right)\right)}{\sqrt{d-c^2 d x^2}}}{8 c^3}","\frac{f^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{2 f g (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}-\frac{g^2 x (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{2 c^2 \sqrt{d-c^2 d x^2}}+\frac{g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{4 b c^3 \sqrt{d-c^2 d x^2}}-\frac{2 b f g x \sqrt{c x-1} \sqrt{c x+1}}{c \sqrt{d-c^2 d x^2}}-\frac{b g^2 x^2 \sqrt{c x-1} \sqrt{c x+1}}{4 c \sqrt{d-c^2 d x^2}}",1,"((-4*a*c*g*(4*f + g*x)*Sqrt[d - c^2*d*x^2])/d + (16*b*c*f*g*Sqrt[d - c^2*d*x^2]*((c*x)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ArcCosh[c*x]))/d + (4*b*c^2*f^2*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x]^2)/Sqrt[d - c^2*d*x^2] - (4*a*(2*c^2*f^2 + g^2)*ArcTan[(c*x*Sqrt[d - c^2*d*x^2])/(Sqrt[d]*(-1 + c^2*x^2))])/Sqrt[d] + (b*g^2*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*(-Cosh[2*ArcCosh[c*x]] + 2*ArcCosh[c*x]*(ArcCosh[c*x] + Sinh[2*ArcCosh[c*x]])))/Sqrt[d - c^2*d*x^2])/(8*c^3)","A",0
68,1,172,136,0.696112,"\int \frac{(f+g x) \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2}} \, dx","Integrate[((f + g*x)*(a + b*ArcCosh[c*x]))/Sqrt[d - c^2*d*x^2],x]","\frac{-\frac{2 a c f \tan ^{-1}\left(\frac{c x \sqrt{d-c^2 d x^2}}{\sqrt{d} \left(c^2 x^2-1\right)}\right)}{\sqrt{d}}-\frac{2 a g \sqrt{d-c^2 d x^2}}{d}+\frac{b c f \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)^2}{\sqrt{d-c^2 d x^2}}+\frac{2 b g \sqrt{d-c^2 d x^2} \left(\frac{c x}{\sqrt{c x-1} \sqrt{c x+1}}-\cosh ^{-1}(c x)\right)}{d}}{2 c^2}","\frac{f \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c \sqrt{d-c^2 d x^2}}-\frac{g (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 \sqrt{d-c^2 d x^2}}-\frac{b g x \sqrt{c x-1} \sqrt{c x+1}}{c \sqrt{d-c^2 d x^2}}",1,"((-2*a*g*Sqrt[d - c^2*d*x^2])/d + (2*b*g*Sqrt[d - c^2*d*x^2]*((c*x)/(Sqrt[-1 + c*x]*Sqrt[1 + c*x]) - ArcCosh[c*x]))/d + (b*c*f*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x]^2)/Sqrt[d - c^2*d*x^2] - (2*a*c*f*ArcTan[(c*x*Sqrt[d - c^2*d*x^2])/(Sqrt[d]*(-1 + c^2*x^2))])/Sqrt[d])/(2*c^2)","A",1
69,1,932,365,1.8659754,"\int \frac{a+b \cosh ^{-1}(c x)}{(f+g x) \sqrt{d-c^2 d x^2}} \, dx","Integrate[(a + b*ArcCosh[c*x])/((f + g*x)*Sqrt[d - c^2*d*x^2]),x]","\frac{\frac{a \log (f+g x)}{\sqrt{d}}-\frac{a \log \left(d \left(f x c^2+g\right)+\sqrt{d} \sqrt{g^2-c^2 f^2} \sqrt{d-c^2 d x^2}\right)}{\sqrt{d}}-\frac{b \sqrt{\frac{c x-1}{c x+1}} (c x+1) \left(2 \cosh ^{-1}(c x) \tan ^{-1}\left(\frac{(c f+g) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)-2 i \cos ^{-1}\left(-\frac{c f}{g}\right) \tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)+\left(\cos ^{-1}\left(-\frac{c f}{g}\right)+2 \left(\tan ^{-1}\left(\frac{(c f+g) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)+\tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right)\right) \log \left(\frac{e^{-\frac{1}{2} \cosh ^{-1}(c x)} \sqrt{g^2-c^2 f^2}}{\sqrt{2} \sqrt{g} \sqrt{c (f+g x)}}\right)+\left(\cos ^{-1}\left(-\frac{c f}{g}\right)-2 \left(\tan ^{-1}\left(\frac{(c f+g) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)+\tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right)\right) \log \left(\frac{e^{\frac{1}{2} \cosh ^{-1}(c x)} \sqrt{g^2-c^2 f^2}}{\sqrt{2} \sqrt{g} \sqrt{c (f+g x)}}\right)-\left(\cos ^{-1}\left(-\frac{c f}{g}\right)+2 \tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right) \log \left(\frac{(c f+g) \left(c f-g+i \sqrt{g^2-c^2 f^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)-1\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\left(\cos ^{-1}\left(-\frac{c f}{g}\right)-2 \tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right) \log \left(\frac{(c f+g) \left(-c f+g+i \sqrt{g^2-c^2 f^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)+1\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)+i \left(\text{Li}_2\left(\frac{\left(c f-i \sqrt{g^2-c^2 f^2}\right) \left(c f+g-i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\text{Li}_2\left(\frac{\left(c f+i \sqrt{g^2-c^2 f^2}\right) \left(c f+g-i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)\right)\right)}{\sqrt{d-c^2 d x^2}}}{\sqrt{g^2-c^2 f^2}}","\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}-\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}+\frac{b \sqrt{c x-1} \sqrt{c x+1} \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}-\frac{b \sqrt{c x-1} \sqrt{c x+1} \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \sqrt{c^2 f^2-g^2}}",1,"((a*Log[f + g*x])/Sqrt[d] - (a*Log[d*(g + c^2*f*x) + Sqrt[d]*Sqrt[-(c^2*f^2) + g^2]*Sqrt[d - c^2*d*x^2]])/Sqrt[d] - (b*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*(2*ArcCosh[c*x]*ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] - (2*I)*ArcCos[-((c*f)/g)]*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + (ArcCos[-((c*f)/g)] + 2*(ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]]))*Log[Sqrt[-(c^2*f^2) + g^2]/(Sqrt[2]*E^(ArcCosh[c*x]/2)*Sqrt[g]*Sqrt[c*(f + g*x)])] + (ArcCos[-((c*f)/g)] - 2*(ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]]))*Log[(E^(ArcCosh[c*x]/2)*Sqrt[-(c^2*f^2) + g^2])/(Sqrt[2]*Sqrt[g]*Sqrt[c*(f + g*x)])] - (ArcCos[-((c*f)/g)] + 2*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]])*Log[((c*f + g)*(c*f - g + I*Sqrt[-(c^2*f^2) + g^2])*(-1 + Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] - (ArcCos[-((c*f)/g)] - 2*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]])*Log[((c*f + g)*(-(c*f) + g + I*Sqrt[-(c^2*f^2) + g^2])*(1 + Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] + I*(PolyLog[2, ((c*f - I*Sqrt[-(c^2*f^2) + g^2])*(c*f + g - I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] - PolyLog[2, ((c*f + I*Sqrt[-(c^2*f^2) + g^2])*(c*f + g - I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))])))/Sqrt[d - c^2*d*x^2])/Sqrt[-(c^2*f^2) + g^2]","C",0
70,1,1115,523,5.8437872,"\int \frac{a+b \cosh ^{-1}(c x)}{(f+g x)^2 \sqrt{d-c^2 d x^2}} \, dx","Integrate[(a + b*ArcCosh[c*x])/((f + g*x)^2*Sqrt[d - c^2*d*x^2]),x]","-\frac{a f \log (f+g x) c^2}{\sqrt{d} \left(g^2-c^2 f^2\right)^{3/2}}-\frac{a f \log \left(d \left(f x c^2+g\right)+\sqrt{d} \sqrt{g^2-c^2 f^2} \sqrt{d-c^2 d x^2}\right) c^2}{\sqrt{d} (c f-g) (c f+g) \sqrt{g^2-c^2 f^2}}+\frac{b \sqrt{\frac{c x-1}{c x+1}} (c x+1) \left(-\frac{g \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)}{(c f-g) (c f+g) (c f+c g x)}+\frac{\log \left(\frac{g x}{f}+1\right)}{c^2 f^2-g^2}+\frac{c f \left(2 \cosh ^{-1}(c x) \tan ^{-1}\left(\frac{(c f+g) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)-2 i \cos ^{-1}\left(-\frac{c f}{g}\right) \tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)+\left(\cos ^{-1}\left(-\frac{c f}{g}\right)+2 \left(\tan ^{-1}\left(\frac{(c f+g) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)+\tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right)\right) \log \left(\frac{e^{-\frac{1}{2} \cosh ^{-1}(c x)} \sqrt{g^2-c^2 f^2}}{\sqrt{2} \sqrt{g} \sqrt{c (f+g x)}}\right)+\left(\cos ^{-1}\left(-\frac{c f}{g}\right)-2 \left(\tan ^{-1}\left(\frac{(c f+g) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)+\tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right)\right) \log \left(\frac{e^{\frac{1}{2} \cosh ^{-1}(c x)} \sqrt{g^2-c^2 f^2}}{\sqrt{2} \sqrt{g} \sqrt{c (f+g x)}}\right)-\left(\cos ^{-1}\left(-\frac{c f}{g}\right)+2 \tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right) \log \left(\frac{(c f+g) \left(c f-g+i \sqrt{g^2-c^2 f^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)-1\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\left(\cos ^{-1}\left(-\frac{c f}{g}\right)-2 \tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right) \log \left(\frac{(c f+g) \left(-c f+g+i \sqrt{g^2-c^2 f^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)+1\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)+i \left(\text{Li}_2\left(\frac{\left(c f-i \sqrt{g^2-c^2 f^2}\right) \left(c f+g-i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\text{Li}_2\left(\frac{\left(c f+i \sqrt{g^2-c^2 f^2}\right) \left(c f+g-i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)\right)\right)}{\left(g^2-c^2 f^2\right)^{3/2}}\right) c}{\sqrt{d-c^2 d x^2}}-\frac{a g \sqrt{d-c^2 d x^2}}{d \left(g^2-c^2 f^2\right) (f+g x)}","-\frac{g \sqrt{c x-1} \sqrt{-\frac{1-c x}{c x+1}} (c x+1)^{3/2} \left(a+b \cosh ^{-1}(c x)\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right) (f+g x)}+\frac{c^2 f \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{c^2 f \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{b c^2 f \sqrt{c x-1} \sqrt{c x+1} \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{b c^2 f \sqrt{c x-1} \sqrt{c x+1} \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{b c \sqrt{c x-1} \sqrt{c x+1} \log (f+g x)}{\sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)}",1,"-((a*g*Sqrt[d - c^2*d*x^2])/(d*(-(c^2*f^2) + g^2)*(f + g*x))) - (a*c^2*f*Log[f + g*x])/(Sqrt[d]*(-(c^2*f^2) + g^2)^(3/2)) - (a*c^2*f*Log[d*(g + c^2*f*x) + Sqrt[d]*Sqrt[-(c^2*f^2) + g^2]*Sqrt[d - c^2*d*x^2]])/(Sqrt[d]*(c*f - g)*(c*f + g)*Sqrt[-(c^2*f^2) + g^2]) + (b*c*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*(-((g*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x])/((c*f - g)*(c*f + g)*(c*f + c*g*x))) + Log[1 + (g*x)/f]/(c^2*f^2 - g^2) + (c*f*(2*ArcCosh[c*x]*ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] - (2*I)*ArcCos[-((c*f)/g)]*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + (ArcCos[-((c*f)/g)] + 2*(ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]]))*Log[Sqrt[-(c^2*f^2) + g^2]/(Sqrt[2]*E^(ArcCosh[c*x]/2)*Sqrt[g]*Sqrt[c*(f + g*x)])] + (ArcCos[-((c*f)/g)] - 2*(ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]]))*Log[(E^(ArcCosh[c*x]/2)*Sqrt[-(c^2*f^2) + g^2])/(Sqrt[2]*Sqrt[g]*Sqrt[c*(f + g*x)])] - (ArcCos[-((c*f)/g)] + 2*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]])*Log[((c*f + g)*(c*f - g + I*Sqrt[-(c^2*f^2) + g^2])*(-1 + Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] - (ArcCos[-((c*f)/g)] - 2*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]])*Log[((c*f + g)*(-(c*f) + g + I*Sqrt[-(c^2*f^2) + g^2])*(1 + Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] + I*(PolyLog[2, ((c*f - I*Sqrt[-(c^2*f^2) + g^2])*(c*f + g - I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] - PolyLog[2, ((c*f + I*Sqrt[-(c^2*f^2) + g^2])*(c*f + g - I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))])))/(-(c^2*f^2) + g^2)^(3/2)))/Sqrt[d - c^2*d*x^2]","C",0
71,1,353,549,1.9516741,"\int \frac{(f+g x)^3 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Integrate[((f + g*x)^3*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(3/2),x]","\frac{-2 \sqrt{d} \left(-a \left(c^4 f^3 x+c^2 g \left(3 f^2+3 f g x-g^2 x^2\right)+2 g^3\right)+b c f \sqrt{\frac{c x-1}{c x+1}} (c x+1) \left(c^2 f^2+3 g^2\right) \log \left(\sqrt{\frac{c x-1}{c x+1}} (c x+1)\right)+b g \sqrt{\frac{c x-1}{c x+1}} (c x+1) \left(3 c^2 f^2+g^2\right) \log \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)\right)+6 a c f g^2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{c x \sqrt{d-c^2 d x^2}}{\sqrt{d} \left(c^2 x^2-1\right)}\right)+b \sqrt{d} \cosh ^{-1}(c x) \left(2 c^4 f^3 x+6 c^2 f g (f+g x)-g^3 \cosh \left(2 \cosh ^{-1}(c x)\right)+3 g^3\right)-3 b c \sqrt{d} f g^2 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)^2+b \sqrt{d} g^3 \sinh \left(2 \cosh ^{-1}(c x)\right)}{2 c^4 d^{3/2} \sqrt{d-c^2 d x^2}}","-\frac{(1-c x) (c f-g)^3 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^4 d \sqrt{d-c^2 d x^2}}+\frac{(c x+1) (c f+g)^3 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^4 d \sqrt{d-c^2 d x^2}}+\frac{g^3 (1-c x) (c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{c^4 d \sqrt{d-c^2 d x^2}}-\frac{3 f g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c^3 d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f-g)^3 \log \left(\frac{2}{c x+1}\right)}{2 c^4 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f+g)^3 \log \left(\sqrt{-\frac{1-c x}{c x+1}}\right)}{c^4 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f+g)^3 \log \left(\frac{2}{c x+1}\right)}{2 c^4 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b g^3 x \sqrt{c x-1} \sqrt{c x+1}}{c^3 d \sqrt{d-c^2 d x^2}}",1,"(-3*b*c*Sqrt[d]*f*g^2*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x]^2 + 6*a*c*f*g^2*Sqrt[d - c^2*d*x^2]*ArcTan[(c*x*Sqrt[d - c^2*d*x^2])/(Sqrt[d]*(-1 + c^2*x^2))] + b*Sqrt[d]*ArcCosh[c*x]*(3*g^3 + 2*c^4*f^3*x + 6*c^2*f*g*(f + g*x) - g^3*Cosh[2*ArcCosh[c*x]]) - 2*Sqrt[d]*(-(a*(2*g^3 + c^4*f^3*x + c^2*g*(3*f^2 + 3*f*g*x - g^2*x^2))) + b*c*f*(c^2*f^2 + 3*g^2)*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*Log[Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)] + b*g*(3*c^2*f^2 + g^2)*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*Log[Tanh[ArcCosh[c*x]/2]]) + b*Sqrt[d]*g^3*Sinh[2*ArcCosh[c*x]])/(2*c^4*d^(3/2)*Sqrt[d - c^2*d*x^2])","A",0
72,1,281,459,1.0818985,"\int \frac{(f+g x)^2 \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Integrate[((f + g*x)^2*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(3/2),x]","\frac{2 \sqrt{d} \left(a c \left(c^2 f^2 x+2 f g+g^2 x\right)-b \sqrt{\frac{c x-1}{c x+1}} (c x+1) \left(c^2 f^2+g^2\right) \log \left(\sqrt{\frac{c x-1}{c x+1}} (c x+1)\right)-2 b c f g \sqrt{\frac{c x-1}{c x+1}} (c x+1) \log \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)\right)+2 a g^2 \sqrt{d-c^2 d x^2} \tan ^{-1}\left(\frac{c x \sqrt{d-c^2 d x^2}}{\sqrt{d} \left(c^2 x^2-1\right)}\right)+2 b c \sqrt{d} \cosh ^{-1}(c x) \left(c^2 f^2 x+2 f g+g^2 x\right)-b \sqrt{d} g^2 \sqrt{\frac{c x-1}{c x+1}} (c x+1) \cosh ^{-1}(c x)^2}{2 c^3 d^{3/2} \sqrt{d-c^2 d x^2}}","-\frac{(1-c x) (c f-g)^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^3 d \sqrt{d-c^2 d x^2}}+\frac{(c x+1) (c f+g)^2 \left(a+b \cosh ^{-1}(c x)\right)}{2 c^3 d \sqrt{d-c^2 d x^2}}-\frac{g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2}{2 b c^3 d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f-g)^2 \log \left(\frac{2}{c x+1}\right)}{2 c^3 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}+\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f+g)^2 \log \left(\sqrt{-\frac{1-c x}{c x+1}}\right)}{c^3 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} (c f+g)^2 \log \left(\frac{2}{c x+1}\right)}{2 c^3 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2}}",1,"(2*b*c*Sqrt[d]*(2*f*g + c^2*f^2*x + g^2*x)*ArcCosh[c*x] - b*Sqrt[d]*g^2*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*ArcCosh[c*x]^2 + 2*a*g^2*Sqrt[d - c^2*d*x^2]*ArcTan[(c*x*Sqrt[d - c^2*d*x^2])/(Sqrt[d]*(-1 + c^2*x^2))] + 2*Sqrt[d]*(a*c*(2*f*g + c^2*f^2*x + g^2*x) - b*(c^2*f^2 + g^2)*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*Log[Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)] - 2*b*c*f*g*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*Log[Tanh[ArcCosh[c*x]/2]]))/(2*c^3*d^(3/2)*Sqrt[d - c^2*d*x^2])","A",0
73,1,123,142,0.3858314,"\int \frac{(f+g x) \left(a+b \cosh ^{-1}(c x)\right)}{\left(d-c^2 d x^2\right)^{3/2}} \, dx","Integrate[((f + g*x)*(a + b*ArcCosh[c*x]))/(d - c^2*d*x^2)^(3/2),x]","\frac{b \sqrt{d-c^2 d x^2} ((c f+g) \log (1-c x)+(c f-g) \log (c x+1))}{2 c^2 d^2 \sqrt{c x-1} \sqrt{c x+1}}-\frac{\sqrt{d-c^2 d x^2} \left(c^2 f x+g\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 d^2 \left(c^2 x^2-1\right)}","\frac{\left(c^2 f x+g\right) \left(a+b \cosh ^{-1}(c x)\right)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{b \sqrt{c x-1} \sqrt{c x+1} (c f-g) \tanh ^{-1}(c x)}{c^2 d \sqrt{d-c^2 d x^2}}-\frac{b f \sqrt{c x-1} \sqrt{c x+1} \log (1-c x)}{c d \sqrt{d-c^2 d x^2}}",1,"-(((g + c^2*f*x)*Sqrt[d - c^2*d*x^2]*(a + b*ArcCosh[c*x]))/(c^2*d^2*(-1 + c^2*x^2))) + (b*Sqrt[d - c^2*d*x^2]*((c*f + g)*Log[1 - c*x] + (c*f - g)*Log[1 + c*x]))/(2*c^2*d^2*Sqrt[-1 + c*x]*Sqrt[1 + c*x])","A",1
74,1,1203,773,9.7348399,"\int \frac{a+b \cosh ^{-1}(c x)}{(f+g x) \left(d-c^2 d x^2\right)^{3/2}} \, dx","Integrate[(a + b*ArcCosh[c*x])/((f + g*x)*(d - c^2*d*x^2)^(3/2)),x]","\frac{a \log (f+g x) g^2}{d^{3/2} (g-c f) (c f+g) \sqrt{g^2-c^2 f^2}}-\frac{a \log \left(d f x c^2+d g+\sqrt{d} \sqrt{g^2-c^2 f^2} \sqrt{-d \left(c^2 x^2-1\right)}\right) g^2}{d^{3/2} (g-c f) (c f+g) \sqrt{g^2-c^2 f^2}}-\frac{b \sqrt{\frac{c x-1}{c x+1}} (c x+1) \left(\frac{2 \left(2 \cosh ^{-1}(c x) \tan ^{-1}\left(\frac{(c f+g) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)-2 i \cos ^{-1}\left(-\frac{c f}{g}\right) \tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)+\left(\cos ^{-1}\left(-\frac{c f}{g}\right)+2 \left(\tan ^{-1}\left(\frac{(c f+g) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)+\tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right)\right) \log \left(\frac{e^{-\frac{1}{2} \cosh ^{-1}(c x)} \sqrt{g^2-c^2 f^2}}{\sqrt{2} \sqrt{g} \sqrt{c f+c g x}}\right)+\left(\cos ^{-1}\left(-\frac{c f}{g}\right)-2 \left(\tan ^{-1}\left(\frac{(c f+g) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)+\tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right)\right) \log \left(\frac{e^{\frac{1}{2} \cosh ^{-1}(c x)} \sqrt{g^2-c^2 f^2}}{\sqrt{2} \sqrt{g} \sqrt{c f+c g x}}\right)-\left(\cos ^{-1}\left(-\frac{c f}{g}\right)+2 \tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right) \log \left(\frac{(c f+g) \left(c f-g+i \sqrt{g^2-c^2 f^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)-1\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\left(\cos ^{-1}\left(-\frac{c f}{g}\right)-2 \tan ^{-1}\left(\frac{(g-c f) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{\sqrt{g^2-c^2 f^2}}\right)\right) \log \left(\frac{(c f+g) \left(-c f+g+i \sqrt{g^2-c^2 f^2}\right) \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)+1\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)+i \left(\text{Li}_2\left(\frac{\left(c f-i \sqrt{g^2-c^2 f^2}\right) \left(c f+g-i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)-\text{Li}_2\left(\frac{\left(c f+i \sqrt{g^2-c^2 f^2}\right) \left(c f+g-i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}{g \left(c f+g+i \sqrt{g^2-c^2 f^2} \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right)}\right)\right)\right) g^2}{(g-c f) (c f+g) \sqrt{g^2-c^2 f^2}}+\frac{2 \log \left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)\right) g}{g^2-c^2 f^2}-\frac{\cosh ^{-1}(c x) \coth \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{c f+g}+\frac{2 c f \log \left(\sqrt{\frac{c x-1}{c x+1}} (c x+1)\right)}{c^2 f^2-g^2}-\frac{\cosh ^{-1}(c x) \tanh \left(\frac{1}{2} \cosh ^{-1}(c x)\right)}{c f-g}\right)}{2 d \sqrt{-d (c x-1) (c x+1)}}+\frac{\left(a c^2 f x-a g\right) \sqrt{-d \left(c^2 x^2-1\right)}}{d^2 \left(g^2-c^2 f^2\right) \left(c^2 x^2-1\right)}","-\frac{g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{g^2 \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}-\frac{(1-c x) \left(a+b \cosh ^{-1}(c x)\right)}{2 d \sqrt{d-c^2 d x^2} (c f-g)}+\frac{(c x+1) \left(a+b \cosh ^{-1}(c x)\right)}{2 d \sqrt{d-c^2 d x^2} (c f+g)}-\frac{b g^2 \sqrt{c x-1} \sqrt{c x+1} \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{b g^2 \sqrt{c x-1} \sqrt{c x+1} \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{d \sqrt{d-c^2 d x^2} \left(c^2 f^2-g^2\right)^{3/2}}+\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} \log \left(\sqrt{-\frac{1-c x}{c x+1}}\right)}{d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2} (c f+g)}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} \log \left(\frac{2}{c x+1}\right)}{2 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2} (c f-g)}-\frac{b \sqrt{(1-c x) (c x+1)} \sqrt{1-c^2 x^2} \log \left(\frac{2}{c x+1}\right)}{2 d \sqrt{-\frac{1-c x}{c x+1}} (c x+1) \sqrt{d-c^2 d x^2} (c f+g)}",1,"((-(a*g) + a*c^2*f*x)*Sqrt[-(d*(-1 + c^2*x^2))])/(d^2*(-(c^2*f^2) + g^2)*(-1 + c^2*x^2)) + (a*g^2*Log[f + g*x])/(d^(3/2)*(-(c*f) + g)*(c*f + g)*Sqrt[-(c^2*f^2) + g^2]) - (a*g^2*Log[d*g + c^2*d*f*x + Sqrt[d]*Sqrt[-(c^2*f^2) + g^2]*Sqrt[-(d*(-1 + c^2*x^2))]])/(d^(3/2)*(-(c*f) + g)*(c*f + g)*Sqrt[-(c^2*f^2) + g^2]) - (b*Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*(-((ArcCosh[c*x]*Coth[ArcCosh[c*x]/2])/(c*f + g)) + (2*c*f*Log[Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)])/(c^2*f^2 - g^2) + (2*g*Log[Tanh[ArcCosh[c*x]/2]])/(-(c^2*f^2) + g^2) + (2*g^2*(2*ArcCosh[c*x]*ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] - (2*I)*ArcCos[-((c*f)/g)]*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + (ArcCos[-((c*f)/g)] + 2*(ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]]))*Log[Sqrt[-(c^2*f^2) + g^2]/(Sqrt[2]*E^(ArcCosh[c*x]/2)*Sqrt[g]*Sqrt[c*f + c*g*x])] + (ArcCos[-((c*f)/g)] - 2*(ArcTan[((c*f + g)*Coth[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]] + ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]]))*Log[(E^(ArcCosh[c*x]/2)*Sqrt[-(c^2*f^2) + g^2])/(Sqrt[2]*Sqrt[g]*Sqrt[c*f + c*g*x])] - (ArcCos[-((c*f)/g)] + 2*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]])*Log[((c*f + g)*(c*f - g + I*Sqrt[-(c^2*f^2) + g^2])*(-1 + Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] - (ArcCos[-((c*f)/g)] - 2*ArcTan[((-(c*f) + g)*Tanh[ArcCosh[c*x]/2])/Sqrt[-(c^2*f^2) + g^2]])*Log[((c*f + g)*(-(c*f) + g + I*Sqrt[-(c^2*f^2) + g^2])*(1 + Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] + I*(PolyLog[2, ((c*f - I*Sqrt[-(c^2*f^2) + g^2])*(c*f + g - I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))] - PolyLog[2, ((c*f + I*Sqrt[-(c^2*f^2) + g^2])*(c*f + g - I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))/(g*(c*f + g + I*Sqrt[-(c^2*f^2) + g^2]*Tanh[ArcCosh[c*x]/2]))])))/((-(c*f) + g)*(c*f + g)*Sqrt[-(c^2*f^2) + g^2]) - (ArcCosh[c*x]*Tanh[ArcCosh[c*x]/2])/(c*f - g)))/(2*d*Sqrt[-(d*(-1 + c*x)*(1 + c*x))])","C",0
75,1,204,239,0.6611939,"\int \frac{(f+g x) \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{1-c^2 x^2}} \, dx","Integrate[((f + g*x)*(a + b*ArcCosh[c*x])^n)/Sqrt[1 - c^2*x^2],x]","\frac{e^{-\frac{a}{b}} \sqrt{\frac{c x-1}{c x+1}} (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^n \left(-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{b^2}\right)^{-n} \left(2 c f e^{a/b} \left(a+b \cosh ^{-1}(c x)\right) \left(-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{b^2}\right)^n+b g (n+1) \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)^n \Gamma \left(n+1,-\frac{a+b \cosh ^{-1}(c x)}{b}\right)-b g (n+1) e^{\frac{2 a}{b}} \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^n \Gamma \left(n+1,\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)}{2 b c^2 (n+1) \sqrt{1-c^2 x^2}}","\frac{f \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{b c (n+1) \sqrt{1-c^2 x^2}}+\frac{g e^{-\frac{a}{b}} \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^n \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \Gamma \left(n+1,-\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{1-c^2 x^2}}-\frac{g e^{a/b} \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^n \left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \Gamma \left(n+1,\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{1-c^2 x^2}}",1,"(Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcCosh[c*x])^n*(2*c*E^(a/b)*f*(a + b*ArcCosh[c*x])*(-((a + b*ArcCosh[c*x])^2/b^2))^n - b*E^((2*a)/b)*g*(1 + n)*(-((a + b*ArcCosh[c*x])/b))^n*Gamma[1 + n, a/b + ArcCosh[c*x]] + b*g*(1 + n)*(a/b + ArcCosh[c*x])^n*Gamma[1 + n, -((a + b*ArcCosh[c*x])/b)]))/(2*b*c^2*E^(a/b)*(1 + n)*Sqrt[1 - c^2*x^2]*(-((a + b*ArcCosh[c*x])^2/b^2))^n)","A",0
76,1,204,200,0.2570768,"\int \frac{(f+g x) \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{1-c x} \sqrt{1+c x}} \, dx","Integrate[((f + g*x)*(a + b*ArcCosh[c*x])^n)/(Sqrt[1 - c*x]*Sqrt[1 + c*x]),x]","\frac{e^{-\frac{a}{b}} \sqrt{\frac{c x-1}{c x+1}} (c x+1) \left(a+b \cosh ^{-1}(c x)\right)^n \left(-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{b^2}\right)^{-n} \left(2 c f e^{a/b} \left(a+b \cosh ^{-1}(c x)\right) \left(-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{b^2}\right)^n+b g (n+1) \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)^n \Gamma \left(n+1,-\frac{a+b \cosh ^{-1}(c x)}{b}\right)-b g (n+1) e^{\frac{2 a}{b}} \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^n \Gamma \left(n+1,\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)}{2 b c^2 (n+1) \sqrt{1-c^2 x^2}}","\frac{g e^{-\frac{a}{b}} \sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)^n \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \Gamma \left(n+1,-\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{1-c x}}-\frac{g e^{a/b} \sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)^n \left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \Gamma \left(n+1,\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{1-c x}}+\frac{f \sqrt{c x-1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{b c (n+1) \sqrt{1-c x}}",1,"(Sqrt[(-1 + c*x)/(1 + c*x)]*(1 + c*x)*(a + b*ArcCosh[c*x])^n*(2*c*E^(a/b)*f*(a + b*ArcCosh[c*x])*(-((a + b*ArcCosh[c*x])^2/b^2))^n - b*E^((2*a)/b)*g*(1 + n)*(-((a + b*ArcCosh[c*x])/b))^n*Gamma[1 + n, a/b + ArcCosh[c*x]] + b*g*(1 + n)*(a/b + ArcCosh[c*x])^n*Gamma[1 + n, -((a + b*ArcCosh[c*x])/b)]))/(2*b*c^2*E^(a/b)*(1 + n)*Sqrt[1 - c^2*x^2]*(-((a + b*ArcCosh[c*x])^2/b^2))^n)","A",0
77,1,219,260,2.1671873,"\int \frac{(f+g x) \left(a+b \cosh ^{-1}(c x)\right)^n}{\sqrt{\text{d1}+c \text{d1} x} \sqrt{\text{d2}-c \text{d2} x}} \, dx","Integrate[((f + g*x)*(a + b*ArcCosh[c*x])^n)/(Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]),x]","\frac{e^{-\frac{a}{b}} \sqrt{\frac{c x-1}{c x+1}} \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x} \left(a+b \cosh ^{-1}(c x)\right)^n \left(-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{b^2}\right)^{-n} \left(-2 c f e^{a/b} \left(a+b \cosh ^{-1}(c x)\right) \left(-\frac{\left(a+b \cosh ^{-1}(c x)\right)^2}{b^2}\right)^n-b g (n+1) \left(\frac{a}{b}+\cosh ^{-1}(c x)\right)^n \Gamma \left(n+1,-\frac{a+b \cosh ^{-1}(c x)}{b}\right)+b g (n+1) e^{\frac{2 a}{b}} \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^n \Gamma \left(n+1,\frac{a}{b}+\cosh ^{-1}(c x)\right)\right)}{2 b c^2 \text{d1} \text{d2} (n+1) (c x-1)}","\frac{g e^{-\frac{a}{b}} \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^n \left(-\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \Gamma \left(n+1,-\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}-\frac{g e^{a/b} \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^n \left(\frac{a+b \cosh ^{-1}(c x)}{b}\right)^{-n} \Gamma \left(n+1,\frac{a+b \cosh ^{-1}(c x)}{b}\right)}{2 c^2 \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}+\frac{f \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^{n+1}}{b c (n+1) \sqrt{c \text{d1} x+\text{d1}} \sqrt{\text{d2}-c \text{d2} x}}",1,"(Sqrt[(-1 + c*x)/(1 + c*x)]*Sqrt[d1 + c*d1*x]*Sqrt[d2 - c*d2*x]*(a + b*ArcCosh[c*x])^n*(-2*c*E^(a/b)*f*(a + b*ArcCosh[c*x])*(-((a + b*ArcCosh[c*x])^2/b^2))^n + b*E^((2*a)/b)*g*(1 + n)*(-((a + b*ArcCosh[c*x])/b))^n*Gamma[1 + n, a/b + ArcCosh[c*x]] - b*g*(1 + n)*(a/b + ArcCosh[c*x])^n*Gamma[1 + n, -((a + b*ArcCosh[c*x])/b)]))/(2*b*c^2*d1*d2*E^(a/b)*(1 + n)*(-1 + c*x)*(-((a + b*ArcCosh[c*x])^2/b^2))^n)","A",0
78,0,0,75,0.1819559,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Integrate[((a + b*ArcCosh[c*x])^n*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2],x]","\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^n \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","\frac{\sqrt{c x-1} \sqrt{c x+1} \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c x)\right)^n \log \left(h (f+g x)^m\right)}{\sqrt{c x-1} \sqrt{c x+1}},x\right)}{\sqrt{1-c^2 x^2}}",0,"Integrate[((a + b*ArcCosh[c*x])^n*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2], x]","A",-1
79,0,0,774,4.5000916,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Integrate[((a + b*ArcCosh[c*x])^2*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2],x]","\int \frac{\left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^4}{12 b^2 c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}+\frac{2 b m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \text{Li}_3\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}+\frac{2 b m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \text{Li}_3\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3 \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{3 b c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3 \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{3 b c \sqrt{1-c^2 x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3 \log \left(h (f+g x)^m\right)}{3 b c \sqrt{1-c^2 x^2}}-\frac{2 b^2 m \sqrt{c x-1} \sqrt{c x+1} \text{Li}_4\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}-\frac{2 b^2 m \sqrt{c x-1} \sqrt{c x+1} \text{Li}_4\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}",1,"Integrate[((a + b*ArcCosh[c*x])^2*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2], x]","F",-1
80,0,0,600,1.9399899,"\int \frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Integrate[((a + b*ArcCosh[c*x])*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2],x]","\int \frac{\left(a+b \cosh ^{-1}(c x)\right) \log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^3}{6 b^2 c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right) \text{Li}_2\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}+1\right)}{2 b c \sqrt{1-c^2 x^2}}-\frac{m \sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(\frac{g e^{\cosh ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}+1\right)}{2 b c \sqrt{1-c^2 x^2}}+\frac{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)^2 \log \left(h (f+g x)^m\right)}{2 b c \sqrt{1-c^2 x^2}}+\frac{b m \sqrt{c x-1} \sqrt{c x+1} \text{Li}_3\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}+\frac{b m \sqrt{c x-1} \sqrt{c x+1} \text{Li}_3\left(-\frac{e^{\cosh ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{c \sqrt{1-c^2 x^2}}",1,"Integrate[((a + b*ArcCosh[c*x])*Log[h*(f + g*x)^m])/Sqrt[1 - c^2*x^2], x]","F",-1
81,1,246,237,0.0212452,"\int \frac{\log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2}} \, dx","Integrate[Log[h*(f + g*x)^m]/Sqrt[1 - c^2*x^2],x]","\frac{i m \text{Li}_2\left(\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{i m \text{Li}_2\left(\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{m \sin ^{-1}(c x) \log \left(1-\frac{i c g e^{i \sin ^{-1}(c x)}}{c^2 f-c \sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{m \sin ^{-1}(c x) \log \left(1-\frac{i c g e^{i \sin ^{-1}(c x)}}{c \sqrt{c^2 f^2-g^2}+c^2 f}\right)}{c}+\frac{\sin ^{-1}(c x) \log \left(h (f+g x)^m\right)}{c}+\frac{i m \sin ^{-1}(c x)^2}{2 c}","\frac{i m \text{Li}_2\left(\frac{i e^{i \sin ^{-1}(c x)} g}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}+\frac{i m \text{Li}_2\left(\frac{i e^{i \sin ^{-1}(c x)} g}{c f+\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{m \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{c f-\sqrt{c^2 f^2-g^2}}\right)}{c}-\frac{m \sin ^{-1}(c x) \log \left(1-\frac{i g e^{i \sin ^{-1}(c x)}}{\sqrt{c^2 f^2-g^2}+c f}\right)}{c}+\frac{\sin ^{-1}(c x) \log \left(h (f+g x)^m\right)}{c}+\frac{i m \sin ^{-1}(c x)^2}{2 c}",1,"((I/2)*m*ArcSin[c*x]^2)/c - (m*ArcSin[c*x]*Log[1 - (I*c*E^(I*ArcSin[c*x])*g)/(c^2*f - c*Sqrt[c^2*f^2 - g^2])])/c - (m*ArcSin[c*x]*Log[1 - (I*c*E^(I*ArcSin[c*x])*g)/(c^2*f + c*Sqrt[c^2*f^2 - g^2])])/c + (ArcSin[c*x]*Log[h*(f + g*x)^m])/c + (I*m*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f - Sqrt[c^2*f^2 - g^2])])/c + (I*m*PolyLog[2, (I*E^(I*ArcSin[c*x])*g)/(c*f + Sqrt[c^2*f^2 - g^2])])/c","A",1
82,0,0,75,0.3157221,"\int \frac{\log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","Integrate[Log[h*(f + g*x)^m]/(Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])),x]","\int \frac{\log \left(h (f+g x)^m\right)}{\sqrt{1-c^2 x^2} \left(a+b \cosh ^{-1}(c x)\right)} \, dx","\frac{\sqrt{c x-1} \sqrt{c x+1} \text{Int}\left(\frac{\log \left(h (f+g x)^m\right)}{\sqrt{c x-1} \sqrt{c x+1} \left(a+b \cosh ^{-1}(c x)\right)},x\right)}{\sqrt{1-c^2 x^2}}",0,"Integrate[Log[h*(f + g*x)^m]/(Sqrt[1 - c^2*x^2]*(a + b*ArcCosh[c*x])), x]","A",-1
83,1,121,152,0.1904374,"\int x^3 \cosh ^{-1}(a+b x) \, dx","Integrate[x^3*ArcCosh[a + b*x],x]","\frac{-3 \left(8 a^4+24 a^2+3\right) \log \left(\sqrt{a+b x-1} \sqrt{a+b x+1}+a+b x\right)+\sqrt{a+b x-1} \sqrt{a+b x+1} \left(50 a^3-26 a^2 b x+14 a b^2 x^2+55 a-6 b^3 x^3-9 b x\right)+24 b^4 x^4 \cosh ^{-1}(a+b x)}{96 b^4}","\frac{\sqrt{a+b x-1} \sqrt{a+b x+1} \left(4 a \left(19 a^2+16\right)-\left(26 a^2+9\right) (a+b x)\right)}{96 b^4}-\frac{\left(8 a^4+24 a^2+3\right) \cosh ^{-1}(a+b x)}{32 b^4}+\frac{7 a x^2 \sqrt{a+b x-1} \sqrt{a+b x+1}}{48 b^2}+\frac{1}{4} x^4 \cosh ^{-1}(a+b x)-\frac{x^3 \sqrt{a+b x-1} \sqrt{a+b x+1}}{16 b}",1,"(Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]*(55*a + 50*a^3 - 9*b*x - 26*a^2*b*x + 14*a*b^2*x^2 - 6*b^3*x^3) + 24*b^4*x^4*ArcCosh[a + b*x] - 3*(3 + 24*a^2 + 8*a^4)*Log[a + b*x + Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]])/(96*b^4)","A",1
84,1,101,104,0.1274623,"\int x^2 \cosh ^{-1}(a+b x) \, dx","Integrate[x^2*ArcCosh[a + b*x],x]","\frac{\left(6 a^3+9 a\right) \log \left(\sqrt{a+b x-1} \sqrt{a+b x+1}+a+b x\right)-\sqrt{a+b x-1} \sqrt{a+b x+1} \left(11 a^2-5 a b x+2 b^2 x^2+4\right)+6 b^3 x^3 \cosh ^{-1}(a+b x)}{18 b^3}","-\frac{\sqrt{a+b x-1} \sqrt{a+b x+1} \left(11 a^2-5 a b x+4\right)}{18 b^3}+\frac{a \left(2 a^2+3\right) \cosh ^{-1}(a+b x)}{6 b^3}+\frac{1}{3} x^3 \cosh ^{-1}(a+b x)-\frac{x^2 \sqrt{a+b x-1} \sqrt{a+b x+1}}{9 b}",1,"(-(Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]*(4 + 11*a^2 - 5*a*b*x + 2*b^2*x^2)) + 6*b^3*x^3*ArcCosh[a + b*x] + (9*a + 6*a^3)*Log[a + b*x + Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]])/(18*b^3)","A",1
85,1,87,90,0.0755981,"\int x \cosh ^{-1}(a+b x) \, dx","Integrate[x*ArcCosh[a + b*x],x]","\frac{-\left(2 a^2+1\right) \log \left(\sqrt{a+b x-1} \sqrt{a+b x+1}+a+b x\right)+2 b^2 x^2 \cosh ^{-1}(a+b x)+(3 a-b x) \sqrt{a+b x-1} \sqrt{a+b x+1}}{4 b^2}","-\frac{\left(2 a^2+1\right) \cosh ^{-1}(a+b x)}{4 b^2}+\frac{3 a \sqrt{a+b x-1} \sqrt{a+b x+1}}{4 b^2}+\frac{1}{2} x^2 \cosh ^{-1}(a+b x)-\frac{x \sqrt{a+b x-1} \sqrt{a+b x+1}}{4 b}",1,"((3*a - b*x)*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x] + 2*b^2*x^2*ArcCosh[a + b*x] - (1 + 2*a^2)*Log[a + b*x + Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]])/(4*b^2)","A",1
86,1,56,41,0.0388307,"\int \cosh ^{-1}(a+b x) \, dx","Integrate[ArcCosh[a + b*x],x]","x \cosh ^{-1}(a+b x)-\frac{\sqrt{a+b x-1} \sqrt{a+b x+1}-2 a \sinh ^{-1}\left(\frac{\sqrt{a+b x-1}}{\sqrt{2}}\right)}{b}","\frac{(a+b x) \cosh ^{-1}(a+b x)}{b}-\frac{\sqrt{a+b x-1} \sqrt{a+b x+1}}{b}",1,"x*ArcCosh[a + b*x] - (Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x] - 2*a*ArcSinh[Sqrt[-1 + a + b*x]/Sqrt[2]])/b","A",1
87,1,153,131,0.0137325,"\int \frac{\cosh ^{-1}(a+b x)}{x} \, dx","Integrate[ArcCosh[a + b*x]/x,x]","\text{Li}_2\left(-\frac{e^{\cosh ^{-1}(a+b x)}}{\sqrt{a^2-1}-a}\right)+\text{Li}_2\left(\frac{e^{\cosh ^{-1}(a+b x)}}{a+\sqrt{a^2-1}}\right)+\cosh ^{-1}(a+b x) \log \left(\frac{e^{\cosh ^{-1}(a+b x)}}{b \left(-\frac{\sqrt{a^2-1}}{b}-\frac{a}{b}\right)}+1\right)+\cosh ^{-1}(a+b x) \log \left(\frac{e^{\cosh ^{-1}(a+b x)}}{b \left(\frac{\sqrt{a^2-1}}{b}-\frac{a}{b}\right)}+1\right)-\frac{1}{2} \cosh ^{-1}(a+b x)^2","\text{Li}_2\left(\frac{e^{\cosh ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)+\text{Li}_2\left(\frac{e^{\cosh ^{-1}(a+b x)}}{a+\sqrt{a^2-1}}\right)+\cosh ^{-1}(a+b x) \log \left(1-\frac{e^{\cosh ^{-1}(a+b x)}}{a-\sqrt{a^2-1}}\right)+\cosh ^{-1}(a+b x) \log \left(1-\frac{e^{\cosh ^{-1}(a+b x)}}{\sqrt{a^2-1}+a}\right)-\frac{1}{2} \cosh ^{-1}(a+b x)^2",1,"-1/2*ArcCosh[a + b*x]^2 + ArcCosh[a + b*x]*Log[1 + E^ArcCosh[a + b*x]/((-(a/b) - Sqrt[-1 + a^2]/b)*b)] + ArcCosh[a + b*x]*Log[1 + E^ArcCosh[a + b*x]/((-(a/b) + Sqrt[-1 + a^2]/b)*b)] + PolyLog[2, -(E^ArcCosh[a + b*x]/(-a + Sqrt[-1 + a^2]))] + PolyLog[2, E^ArcCosh[a + b*x]/(a + Sqrt[-1 + a^2])]","A",1
88,1,83,64,0.1162495,"\int \frac{\cosh ^{-1}(a+b x)}{x^2} \, dx","Integrate[ArcCosh[a + b*x]/x^2,x]","-\frac{\cosh ^{-1}(a+b x)}{x}-\frac{i b \log \left(\frac{2 \left(\sqrt{a+b x-1} \sqrt{a+b x+1}+\frac{i \left(a^2+a b x-1\right)}{\sqrt{1-a^2}}\right)}{b x}\right)}{\sqrt{1-a^2}}","-\frac{2 b \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{\sqrt{1-a^2}}-\frac{\cosh ^{-1}(a+b x)}{x}",1,"-(ArcCosh[a + b*x]/x) - (I*b*Log[(2*(Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x] + (I*(-1 + a^2 + a*b*x))/Sqrt[1 - a^2]))/(b*x)])/Sqrt[1 - a^2]","C",1
89,1,136,106,0.2855556,"\int \frac{\cosh ^{-1}(a+b x)}{x^3} \, dx","Integrate[ArcCosh[a + b*x]/x^3,x]","\frac{-\cosh ^{-1}(a+b x)+\frac{b x \left(-\sqrt{a+b x-1} \sqrt{a+b x+1}+\frac{i a b x \log \left(\frac{4 i \sqrt{1-a^2} \left(-i \sqrt{1-a^2} \sqrt{a+b x-1} \sqrt{a+b x+1}+a^2+a b x-1\right)}{a b^2 x}\right)}{\sqrt{1-a^2}}\right)}{a^2-1}}{2 x^2}","-\frac{a b^2 \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{\left(1-a^2\right)^{3/2}}+\frac{b \sqrt{a+b x-1} \sqrt{a+b x+1}}{2 \left(1-a^2\right) x}-\frac{\cosh ^{-1}(a+b x)}{2 x^2}",1,"(-ArcCosh[a + b*x] + (b*x*(-(Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]) + (I*a*b*x*Log[((4*I)*Sqrt[1 - a^2]*(-1 + a^2 + a*b*x - I*Sqrt[1 - a^2]*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]))/(a*b^2*x)])/Sqrt[1 - a^2]))/(-1 + a^2))/(2*x^2)","C",1
90,1,162,154,0.316181,"\int \frac{\cosh ^{-1}(a+b x)}{x^4} \, dx","Integrate[ArcCosh[a + b*x]/x^4,x]","\frac{1}{6} \left(-\frac{i \left(2 a^2+1\right) b^3 \log \left(\frac{12 \left(1-a^2\right)^{3/2} \left(\sqrt{1-a^2} \sqrt{a+b x-1} \sqrt{a+b x+1}+i a^2+i a b x-i\right)}{b^3 \left(2 a^2 x+x\right)}\right)}{\left(1-a^2\right)^{5/2}}+\frac{b \sqrt{a+b x-1} \sqrt{a+b x+1} \left(-a^2+3 a b x+1\right)}{\left(a^2-1\right)^2 x^2}-\frac{2 \cosh ^{-1}(a+b x)}{x^3}\right)","-\frac{\left(2 a^2+1\right) b^3 \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{3 \left(1-a^2\right)^{5/2}}+\frac{a b^2 \sqrt{a+b x-1} \sqrt{a+b x+1}}{2 \left(1-a^2\right)^2 x}+\frac{b \sqrt{a+b x-1} \sqrt{a+b x+1}}{6 \left(1-a^2\right) x^2}-\frac{\cosh ^{-1}(a+b x)}{3 x^3}",1,"((b*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]*(1 - a^2 + 3*a*b*x))/((-1 + a^2)^2*x^2) - (2*ArcCosh[a + b*x])/x^3 - (I*(1 + 2*a^2)*b^3*Log[(12*(1 - a^2)^(3/2)*(-I + I*a^2 + I*a*b*x + Sqrt[1 - a^2]*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]))/(b^3*(x + 2*a^2*x))])/(1 - a^2)^(5/2))/6","C",1
91,1,110,92,0.1685989,"\int \frac{1}{\sqrt{a+b \cosh ^{-1}(c+d x)}} \, dx","Integrate[1/Sqrt[a + b*ArcCosh[c + d*x]],x]","\frac{e^{-\frac{a}{b}} \left(e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)\right)}{2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}","\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}-\frac{\sqrt{\pi } e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}",1,"(E^((2*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, a/b + ArcCosh[c + d*x]] + Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)])/(2*d*E^(a/b)*Sqrt[a + b*ArcCosh[c + d*x]])","A",0
92,1,111,94,0.1069849,"\int \frac{1}{\sqrt{a-b \cosh ^{-1}(c+d x)}} \, dx","Integrate[1/Sqrt[a - b*ArcCosh[c + d*x]],x]","\frac{e^{-\frac{a}{b}} \left(e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}-\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{a}{b}-\cosh ^{-1}(c+d x)\right)+\sqrt{\cosh ^{-1}(c+d x)-\frac{a}{b}} \Gamma \left(\frac{1}{2},\cosh ^{-1}(c+d x)-\frac{a}{b}\right)\right)}{2 d \sqrt{a-b \cosh ^{-1}(c+d x)}}","\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a-b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}-\frac{\sqrt{\pi } e^{a/b} \text{erf}\left(\frac{\sqrt{a-b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}",1,"(E^((2*a)/b)*Sqrt[a/b - ArcCosh[c + d*x]]*Gamma[1/2, a/b - ArcCosh[c + d*x]] + Sqrt[-(a/b) + ArcCosh[c + d*x]]*Gamma[1/2, -(a/b) + ArcCosh[c + d*x]])/(2*d*E^(a/b)*Sqrt[a - b*ArcCosh[c + d*x]])","A",0
93,1,103,135,0.1260005,"\int (c e+d e x)^4 \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Integrate[(c*e + d*e*x)^4*(a + b*ArcCosh[c + d*x]),x]","\frac{e^4 \left((c+d x)^5 \left(a+b \cosh ^{-1}(c+d x)\right)-\frac{4}{15} b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(c^2+2 c d x+d^2 x^2+2\right)-\frac{1}{5} b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4\right)}{5 d}","\frac{e^4 (c+d x)^5 \left(a+b \cosh ^{-1}(c+d x)\right)}{5 d}-\frac{b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{25 d}-\frac{4 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{75 d}-\frac{8 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1}}{75 d}",1,"(e^4*(-1/5*(b*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x]) - (4*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(2 + c^2 + 2*c*d*x + d^2*x^2))/15 + (c + d*x)^5*(a + b*ArcCosh[c + d*x])))/(5*d)","A",1
94,1,115,119,0.1329256,"\int (c e+d e x)^3 \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Integrate[(c*e + d*e*x)^3*(a + b*ArcCosh[c + d*x]),x]","\frac{e^3 \left((c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)-\frac{1}{4} b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3-\frac{3}{8} b \left(\sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)+2 \tanh ^{-1}\left(\sqrt{\frac{c+d x-1}{c+d x+1}}\right)\right)\right)}{4 d}","\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)}{4 d}-\frac{b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{16 d}-\frac{3 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{32 d}-\frac{3 b e^3 \cosh ^{-1}(c+d x)}{32 d}",1,"(e^3*(-1/4*(b*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x]) + (c + d*x)^4*(a + b*ArcCosh[c + d*x]) - (3*b*(Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x] + 2*ArcTanh[Sqrt[(-1 + c + d*x)/(1 + c + d*x)]]))/8))/(4*d)","A",0
95,1,71,97,0.0760851,"\int (c e+d e x)^2 \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Integrate[(c*e + d*e*x)^2*(a + b*ArcCosh[c + d*x]),x]","\frac{e^2 \left(\frac{1}{3} (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)-\frac{1}{9} b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(c^2+2 c d x+d^2 x^2+2\right)\right)}{d}","\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d}-\frac{b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{9 d}-\frac{2 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{9 d}",1,"(e^2*(-1/9*(b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(2 + c^2 + 2*c*d*x + d^2*x^2)) + ((c + d*x)^3*(a + b*ArcCosh[c + d*x]))/3))/d","A",1
96,1,81,75,0.1643725,"\int (c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Integrate[(c*e + d*e*x)*(a + b*ArcCosh[c + d*x]),x]","\frac{e \left(\frac{1}{2} (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)-\frac{1}{4} b \left(\sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)+2 \tanh ^{-1}\left(\sqrt{\frac{c+d x-1}{c+d x+1}}\right)\right)\right)}{d}","\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{2 d}-\frac{b e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{4 d}-\frac{b e \cosh ^{-1}(c+d x)}{4 d}",1,"(e*(((c + d*x)^2*(a + b*ArcCosh[c + d*x]))/2 - (b*(Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x] + 2*ArcTanh[Sqrt[(-1 + c + d*x)/(1 + c + d*x)]]))/4))/d","A",0
97,1,61,46,0.0514653,"\int \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Integrate[a + b*ArcCosh[c + d*x],x]","a x-\frac{b \left(\sqrt{c+d x-1} \sqrt{c+d x+1}-2 c \sinh ^{-1}\left(\frac{\sqrt{c+d x-1}}{\sqrt{2}}\right)\right)}{d}+b x \cosh ^{-1}(c+d x)","a x-\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{d}+\frac{b (c+d x) \cosh ^{-1}(c+d x)}{d}",1,"a*x + b*x*ArcCosh[c + d*x] - (b*(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] - 2*c*ArcSinh[Sqrt[-1 + c + d*x]/Sqrt[2]]))/d","A",1
98,1,69,81,0.0686403,"\int \frac{a+b \cosh ^{-1}(c+d x)}{c e+d e x} \, dx","Integrate[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x),x]","\frac{2 a \log (c+d x)-b \text{Li}_2\left(-e^{-2 \cosh ^{-1}(c+d x)}\right)+b \cosh ^{-1}(c+d x)^2+2 b \cosh ^{-1}(c+d x) \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right)}{2 d e}","\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 b d e}+\frac{\log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e}-\frac{b \text{Li}_2\left(-e^{-2 \cosh ^{-1}(c+d x)}\right)}{2 d e}",1,"(b*ArcCosh[c + d*x]^2 + 2*b*ArcCosh[c + d*x]*Log[1 + E^(-2*ArcCosh[c + d*x])] + 2*a*Log[c + d*x] - b*PolyLog[2, -E^(-2*ArcCosh[c + d*x])])/(2*d*e)","A",0
99,1,78,56,0.1372178,"\int \frac{a+b \cosh ^{-1}(c+d x)}{(c e+d e x)^2} \, dx","Integrate[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x)^2,x]","\frac{\frac{-a-b \cosh ^{-1}(c+d x)}{c+d x}+\frac{b \sqrt{(c+d x)^2-1} \tan ^{-1}\left(\sqrt{(c+d x)^2-1}\right)}{\sqrt{c+d x-1} \sqrt{c+d x+1}}}{d e^2}","\frac{b \tan ^{-1}\left(\sqrt{c+d x-1} \sqrt{c+d x+1}\right)}{d e^2}-\frac{a+b \cosh ^{-1}(c+d x)}{d e^2 (c+d x)}",1,"((-a - b*ArcCosh[c + d*x])/(c + d*x) + (b*Sqrt[-1 + (c + d*x)^2]*ArcTan[Sqrt[-1 + (c + d*x)^2]])/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]))/(d*e^2)","A",1
100,1,55,66,0.0613746,"\int \frac{a+b \cosh ^{-1}(c+d x)}{(c e+d e x)^3} \, dx","Integrate[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x)^3,x]","-\frac{a-b \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1}+b \cosh ^{-1}(c+d x)}{2 d e^3 (c+d x)^2}","\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{2 d e^3 (c+d x)}-\frac{a+b \cosh ^{-1}(c+d x)}{2 d e^3 (c+d x)^2}",1,"-1/2*(a - b*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x] + b*ArcCosh[c + d*x])/(d*e^3*(c + d*x)^2)","A",1
101,1,101,99,0.2337972,"\int \frac{a+b \cosh ^{-1}(c+d x)}{(c e+d e x)^4} \, dx","Integrate[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x)^4,x]","\frac{\frac{b \left(\frac{(c+d x-1) (c+d x+1)}{(c+d x)^2}+\sqrt{(c+d x)^2-1} \tan ^{-1}\left(\sqrt{(c+d x)^2-1}\right)\right)}{\sqrt{c+d x-1} \sqrt{c+d x+1}}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{(c+d x)^3}}{6 d e^4}","-\frac{a+b \cosh ^{-1}(c+d x)}{3 d e^4 (c+d x)^3}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{6 d e^4 (c+d x)^2}+\frac{b \tan ^{-1}\left(\sqrt{c+d x-1} \sqrt{c+d x+1}\right)}{6 d e^4}",1,"((-2*(a + b*ArcCosh[c + d*x]))/(c + d*x)^3 + (b*(((-1 + c + d*x)*(1 + c + d*x))/(c + d*x)^2 + Sqrt[-1 + (c + d*x)^2]*ArcTan[Sqrt[-1 + (c + d*x)^2]]))/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]))/(6*d*e^4)","A",1
102,1,86,104,0.0811258,"\int \frac{a+b \cosh ^{-1}(c+d x)}{(c e+d e x)^5} \, dx","Integrate[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x)^5,x]","\frac{-3 a+b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(2 c^3+6 c^2 d x+6 c d^2 x^2+c+2 d^3 x^3+d x\right)-3 b \cosh ^{-1}(c+d x)}{12 d e^5 (c+d x)^4}","-\frac{a+b \cosh ^{-1}(c+d x)}{4 d e^5 (c+d x)^4}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{6 d e^5 (c+d x)}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{12 d e^5 (c+d x)^3}",1,"(-3*a + b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(c + 2*c^3 + d*x + 6*c^2*d*x + 6*c*d^2*x^2 + 2*d^3*x^3) - 3*b*ArcCosh[c + d*x])/(12*d*e^5*(c + d*x)^4)","A",1
103,1,136,137,0.23261,"\int \frac{a+b \cosh ^{-1}(c+d x)}{(c e+d e x)^6} \, dx","Integrate[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x)^6,x]","\frac{-\frac{a+b \cosh ^{-1}(c+d x)}{(c+d x)^5}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{4 (c+d x)^4}+\frac{3 b \left(\frac{(c+d x-1) (c+d x+1)}{(c+d x)^2}+\sqrt{(c+d x)^2-1} \tan ^{-1}\left(\sqrt{(c+d x)^2-1}\right)\right)}{8 \sqrt{c+d x-1} \sqrt{c+d x+1}}}{5 d e^6}","-\frac{a+b \cosh ^{-1}(c+d x)}{5 d e^6 (c+d x)^5}+\frac{3 b \sqrt{c+d x-1} \sqrt{c+d x+1}}{40 d e^6 (c+d x)^2}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{20 d e^6 (c+d x)^4}+\frac{3 b \tan ^{-1}\left(\sqrt{c+d x-1} \sqrt{c+d x+1}\right)}{40 d e^6}",1,"((b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(4*(c + d*x)^4) - (a + b*ArcCosh[c + d*x])/(c + d*x)^5 + (3*b*(((-1 + c + d*x)*(1 + c + d*x))/(c + d*x)^2 + Sqrt[-1 + (c + d*x)^2]*ArcTan[Sqrt[-1 + (c + d*x)^2]]))/(8*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]))/(5*d*e^6)","A",1
104,1,220,218,0.3351384,"\int (c e+d e x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Integrate[(c*e + d*e*x)^4*(a + b*ArcCosh[c + d*x])^2,x]","\frac{e^4 \left(9 \left(25 a^2+2 b^2\right) (c+d x)^5+30 a b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(-3 (c+d x)^4-4 (c+d x)^2-8\right)+30 b \cosh ^{-1}(c+d x) \left(15 a (c+d x)^5-3 b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4-4 b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2-8 b \sqrt{c+d x-1} \sqrt{c+d x+1}\right)+40 b^2 (c+d x)^3+240 b^2 (c+d x)+225 b^2 (c+d x)^5 \cosh ^{-1}(c+d x)^2\right)}{1125 d}","\frac{e^4 (c+d x)^5 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{5 d}-\frac{2 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)}{25 d}-\frac{8 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{75 d}-\frac{16 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{75 d}+\frac{2 b^2 e^4 (c+d x)^5}{125 d}+\frac{8 b^2 e^4 (c+d x)^3}{225 d}+\frac{16}{75} b^2 e^4 x",1,"(e^4*(240*b^2*(c + d*x) + 40*b^2*(c + d*x)^3 + 9*(25*a^2 + 2*b^2)*(c + d*x)^5 + 30*a*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(-8 - 4*(c + d*x)^2 - 3*(c + d*x)^4) + 30*b*(15*a*(c + d*x)^5 - 8*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] - 4*b*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x] - 3*b*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x])*ArcCosh[c + d*x] + 225*b^2*(c + d*x)^5*ArcCosh[c + d*x]^2))/(1125*d)","A",1
105,1,212,186,0.2738758,"\int (c e+d e x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Integrate[(c*e + d*e*x)^3*(a + b*ArcCosh[c + d*x])^2,x]","\frac{e^3 \left(\left(8 a^2+b^2\right) (c+d x)^4+2 a b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(-2 (c+d x)^2-3\right) (c+d x)-6 a b \log \left(\sqrt{c+d x-1} \sqrt{c+d x+1}+c+d x\right)+2 b (c+d x) \cosh ^{-1}(c+d x) \left(8 a (c+d x)^3-2 b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2-3 b \sqrt{c+d x-1} \sqrt{c+d x+1}\right)+3 b^2 (c+d x)^2+b^2 \left(8 (c+d x)^4-3\right) \cosh ^{-1}(c+d x)^2\right)}{32 d}","\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{4 d}-\frac{b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)}{8 d}-\frac{3 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)}{16 d}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{32 d}+\frac{b^2 e^3 (c+d x)^4}{32 d}+\frac{3 b^2 e^3 (c+d x)^2}{32 d}",1,"(e^3*(3*b^2*(c + d*x)^2 + (8*a^2 + b^2)*(c + d*x)^4 + 2*a*b*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*(-3 - 2*(c + d*x)^2) + 2*b*(c + d*x)*(8*a*(c + d*x)^3 - 3*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] - 2*b*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])*ArcCosh[c + d*x] + b^2*(-3 + 8*(c + d*x)^4)*ArcCosh[c + d*x]^2 - 6*a*b*Log[c + d*x + Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]]))/(32*d)","A",1
106,1,168,150,0.2370235,"\int (c e+d e x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Integrate[(c*e + d*e*x)^2*(a + b*ArcCosh[c + d*x])^2,x]","\frac{e^2 \left(\left(9 a^2+2 b^2\right) (c+d x)^3+6 a b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(-(c+d x)^2-2\right)+6 b \cosh ^{-1}(c+d x) \left(3 a (c+d x)^3-b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2-2 b \sqrt{c+d x-1} \sqrt{c+d x+1}\right)+12 b^2 (c+d x)+9 b^2 (c+d x)^3 \cosh ^{-1}(c+d x)^2\right)}{27 d}","\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d}-\frac{2 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{9 d}-\frac{4 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{9 d}+\frac{2 b^2 e^2 (c+d x)^3}{27 d}+\frac{4}{9} b^2 e^2 x",1,"(e^2*(12*b^2*(c + d*x) + (9*a^2 + 2*b^2)*(c + d*x)^3 + 6*a*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(-2 - (c + d*x)^2) + 6*b*(3*a*(c + d*x)^3 - 2*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] - b*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])*ArcCosh[c + d*x] + 9*b^2*(c + d*x)^3*ArcCosh[c + d*x]^2))/(27*d)","A",1
107,1,167,110,0.2286454,"\int (c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Integrate[(c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^2,x]","\frac{e \left((c+d x) \left(2 a^2 (c+d x)-2 a b \sqrt{c+d x-1} \sqrt{c+d x+1}+b^2 (c+d x)\right)-2 a b \log \left(\sqrt{c+d x-1} \sqrt{c+d x+1}+c+d x\right)-2 b (c+d x) \cosh ^{-1}(c+d x) \left(b \sqrt{c+d x-1} \sqrt{c+d x+1}-2 a (c+d x)\right)+b^2 \left(2 c^2+4 c d x+2 d^2 x^2-1\right) \cosh ^{-1}(c+d x)^2\right)}{4 d}","\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d}-\frac{b e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)}{2 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^2}{4 d}+\frac{b^2 e (c+d x)^2}{4 d}",1,"(e*((c + d*x)*(2*a^2*(c + d*x) + b^2*(c + d*x) - 2*a*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]) - 2*b*(c + d*x)*(-2*a*(c + d*x) + b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])*ArcCosh[c + d*x] + b^2*(-1 + 2*c^2 + 4*c*d*x + 2*d^2*x^2)*ArcCosh[c + d*x]^2 - 2*a*b*Log[c + d*x + Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]]))/(4*d)","A",1
108,1,105,64,0.0884917,"\int \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Integrate[(a + b*ArcCosh[c + d*x])^2,x]","\frac{a^2 (c+d x)-2 a b \sqrt{c+d x-1} \sqrt{c+d x+1}-2 b \cosh ^{-1}(c+d x) \left(b \sqrt{c+d x-1} \sqrt{c+d x+1}-a (c+d x)\right)+2 b^2 (c+d x)+b^2 (c+d x) \cosh ^{-1}(c+d x)^2}{d}","-\frac{2 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d}+2 b^2 x",1,"(a^2*(c + d*x) + 2*b^2*(c + d*x) - 2*a*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] - 2*b*(-(a*(c + d*x)) + b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])*ArcCosh[c + d*x] + b^2*(c + d*x)*ArcCosh[c + d*x]^2)/d","A",1
109,1,140,118,0.4222953,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{c e+d e x} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^2/(c*e + d*e*x),x]","\frac{a^2 \log (c+d x)-b \text{Li}_2\left(-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)+a b \cosh ^{-1}(c+d x)^2+2 a b \cosh ^{-1}(c+d x) \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right)-\frac{1}{2} b^2 \text{Li}_3\left(-e^{-2 \cosh ^{-1}(c+d x)}\right)+\frac{1}{3} b^2 \cosh ^{-1}(c+d x)^3+b^2 \cosh ^{-1}(c+d x)^2 \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right)}{d e}","-\frac{b \text{Li}_2\left(-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e}+\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 b d e}+\frac{\log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e}-\frac{b^2 \text{Li}_3\left(-e^{-2 \cosh ^{-1}(c+d x)}\right)}{2 d e}",1,"(a*b*ArcCosh[c + d*x]^2 + (b^2*ArcCosh[c + d*x]^3)/3 + 2*a*b*ArcCosh[c + d*x]*Log[1 + E^(-2*ArcCosh[c + d*x])] + b^2*ArcCosh[c + d*x]^2*Log[1 + E^(-2*ArcCosh[c + d*x])] + a^2*Log[c + d*x] - b*(a + b*ArcCosh[c + d*x])*PolyLog[2, -E^(-2*ArcCosh[c + d*x])] - (b^2*PolyLog[3, -E^(-2*ArcCosh[c + d*x])])/2)/(d*e)","A",0
110,1,161,110,0.7705841,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{(c e+d e x)^2} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^2/(c*e + d*e*x)^2,x]","\frac{-\frac{a^2}{c+d x}+2 a b \left(2 \tan ^{-1}\left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c+d x)\right)\right)-\frac{\cosh ^{-1}(c+d x)}{c+d x}\right)-i b^2 \left(2 \text{Li}_2\left(-i e^{-\cosh ^{-1}(c+d x)}\right)-2 \text{Li}_2\left(i e^{-\cosh ^{-1}(c+d x)}\right)+\cosh ^{-1}(c+d x) \left(-\frac{i \cosh ^{-1}(c+d x)}{c+d x}+2 \log \left(1-i e^{-\cosh ^{-1}(c+d x)}\right)-2 \log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right)\right)\right)}{d e^2}","-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^2 (c+d x)}+\frac{4 b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2}-\frac{2 i b^2 \text{Li}_2\left(-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}+\frac{2 i b^2 \text{Li}_2\left(i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}",1,"(-(a^2/(c + d*x)) + 2*a*b*(-(ArcCosh[c + d*x]/(c + d*x)) + 2*ArcTan[Tanh[ArcCosh[c + d*x]/2]]) - I*b^2*(ArcCosh[c + d*x]*(((-I)*ArcCosh[c + d*x])/(c + d*x) + 2*Log[1 - I/E^ArcCosh[c + d*x]] - 2*Log[1 + I/E^ArcCosh[c + d*x]]) + 2*PolyLog[2, (-I)/E^ArcCosh[c + d*x]] - 2*PolyLog[2, I/E^ArcCosh[c + d*x]]))/(d*e^2)","A",0
111,1,81,92,0.2070528,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{(c e+d e x)^3} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^2/(c*e + d*e*x)^3,x]","\frac{b \left(\frac{\sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{c+d x}-b \log (c+d x)\right)-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 (c+d x)^2}}{d e^3}","\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^3 (c+d x)}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)^2}-\frac{b^2 \log (c+d x)}{d e^3}",1,"(-1/2*(a + b*ArcCosh[c + d*x])^2/(c + d*x)^2 + b*((Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(a + b*ArcCosh[c + d*x]))/(c + d*x) - b*Log[c + d*x]))/(d*e^3)","A",1
112,1,251,186,1.0244932,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{(c e+d e x)^4} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^2/(c*e + d*e*x)^4,x]","\frac{-\frac{a^2}{(c+d x)^3}+a b \left(\frac{\sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1)}{(c+d x)^2}-\frac{2 \cosh ^{-1}(c+d x)}{(c+d x)^3}+2 \tan ^{-1}\left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c+d x)\right)\right)\right)+b^2 \left(-i \text{Li}_2\left(-i e^{-\cosh ^{-1}(c+d x)}\right)+i \text{Li}_2\left(i e^{-\cosh ^{-1}(c+d x)}\right)+\frac{1}{c+d x}-\frac{\cosh ^{-1}(c+d x)^2}{(c+d x)^3}+\frac{\sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \cosh ^{-1}(c+d x)}{(c+d x)^2}-i \cosh ^{-1}(c+d x) \log \left(1-i e^{-\cosh ^{-1}(c+d x)}\right)+i \cosh ^{-1}(c+d x) \log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right)\right)}{3 d e^4}","\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d e^4 (c+d x)^3}+\frac{2 b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e^4}-\frac{i b^2 \text{Li}_2\left(-i e^{\cosh ^{-1}(c+d x)}\right)}{3 d e^4}+\frac{i b^2 \text{Li}_2\left(i e^{\cosh ^{-1}(c+d x)}\right)}{3 d e^4}+\frac{b^2}{3 d e^4 (c+d x)}",1,"(-(a^2/(c + d*x)^3) + a*b*((Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x))/(c + d*x)^2 - (2*ArcCosh[c + d*x])/(c + d*x)^3 + 2*ArcTan[Tanh[ArcCosh[c + d*x]/2]]) + b^2*((c + d*x)^(-1) + (Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*ArcCosh[c + d*x])/(c + d*x)^2 - ArcCosh[c + d*x]^2/(c + d*x)^3 - I*ArcCosh[c + d*x]*Log[1 - I/E^ArcCosh[c + d*x]] + I*ArcCosh[c + d*x]*Log[1 + I/E^ArcCosh[c + d*x]] - I*PolyLog[2, (-I)/E^ArcCosh[c + d*x]] + I*PolyLog[2, I/E^ArcCosh[c + d*x]]))/(3*d*e^4)","A",0
113,1,404,382,0.6109162,"\int (c e+d e x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","Integrate[(c*e + d*e*x)^4*(a + b*ArcCosh[c + d*x])^3,x]","\frac{e^4 \left(3 a \left(25 a^2+6 b^2\right) (c+d x)^5+\frac{1}{15} b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(-27 \left(25 a^2+2 b^2\right) (c+d x)^4-4 \left(225 a^2+68 b^2\right) (c+d x)^2-8 \left(225 a^2+518 b^2\right)\right)-b \cosh ^{-1}(c+d x) \left(-225 a^2 (c+d x)^5+90 a b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4+120 a b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2+240 a b \sqrt{c+d x-1} \sqrt{c+d x+1}-18 b^2 (c+d x)^5-40 b^2 (c+d x)^3-240 b^2 (c+d x)\right)+40 a b^2 (c+d x)^3+240 a b^2 (c+d x)-15 b^2 \cosh ^{-1}(c+d x)^2 \left(-15 a (c+d x)^5+3 b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4+4 b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2+8 b \sqrt{c+d x-1} \sqrt{c+d x+1}\right)+75 b^3 (c+d x)^5 \cosh ^{-1}(c+d x)^3\right)}{375 d}","\frac{6 b^2 e^4 (c+d x)^5 \left(a+b \cosh ^{-1}(c+d x)\right)}{125 d}+\frac{8 b^2 e^4 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)}{75 d}+\frac{16}{25} a b^2 e^4 x+\frac{e^4 (c+d x)^5 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{5 d}-\frac{3 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{25 d}-\frac{4 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{25 d}-\frac{8 b e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{25 d}-\frac{6 b^3 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{625 d}-\frac{272 b^3 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{5625 d}-\frac{4144 b^3 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1}}{5625 d}+\frac{16 b^3 e^4 (c+d x) \cosh ^{-1}(c+d x)}{25 d}",1,"(e^4*(240*a*b^2*(c + d*x) + 40*a*b^2*(c + d*x)^3 + 3*a*(25*a^2 + 6*b^2)*(c + d*x)^5 + (b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(-8*(225*a^2 + 518*b^2) - 4*(225*a^2 + 68*b^2)*(c + d*x)^2 - 27*(25*a^2 + 2*b^2)*(c + d*x)^4))/15 - b*(-240*b^2*(c + d*x) - 40*b^2*(c + d*x)^3 - 225*a^2*(c + d*x)^5 - 18*b^2*(c + d*x)^5 + 240*a*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] + 120*a*b*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x] + 90*a*b*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x])*ArcCosh[c + d*x] - 15*b^2*(-15*a*(c + d*x)^5 + 8*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] + 4*b*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x] + 3*b*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x])*ArcCosh[c + d*x]^2 + 75*b^3*(c + d*x)^5*ArcCosh[c + d*x]^3))/(375*d)","A",1
114,1,359,307,0.5601743,"\int (c e+d e x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","Integrate[(c*e + d*e*x)^3*(a + b*ArcCosh[c + d*x])^3,x]","\frac{e^3 \left(8 a \left(8 a^2+3 b^2\right) (c+d x)^4+3 b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \left(-2 \left(8 a^2+b^2\right) (c+d x)^2-3 \left(8 a^2+5 b^2\right)\right)-9 b \left(8 a^2+5 b^2\right) \log \left(\sqrt{c+d x-1} \sqrt{c+d x+1}+c+d x\right)-24 b (c+d x) \cosh ^{-1}(c+d x) \left(-8 a^2 (c+d x)^3+4 a b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2+6 a b \sqrt{c+d x-1} \sqrt{c+d x+1}-b^2 (c+d x)^3-3 b^2 (c+d x)\right)+72 a b^2 (c+d x)^2+24 b^2 \cosh ^{-1}(c+d x)^2 \left(8 a (c+d x)^4-3 a-2 b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3-3 b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)\right)+8 b^3 \left(8 (c+d x)^4-3\right) \cosh ^{-1}(c+d x)^3\right)}{256 d}","\frac{3 b^2 e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)}{32 d}+\frac{9 b^2 e^3 (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{32 d}+\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{4 d}-\frac{3 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{16 d}-\frac{9 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{32 d}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{32 d}-\frac{3 b^3 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{128 d}-\frac{45 b^3 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{256 d}-\frac{45 b^3 e^3 \cosh ^{-1}(c+d x)}{256 d}",1,"(e^3*(72*a*b^2*(c + d*x)^2 + 8*a*(8*a^2 + 3*b^2)*(c + d*x)^4 + 3*b*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*(-3*(8*a^2 + 5*b^2) - 2*(8*a^2 + b^2)*(c + d*x)^2) - 24*b*(c + d*x)*(-3*b^2*(c + d*x) - 8*a^2*(c + d*x)^3 - b^2*(c + d*x)^3 + 6*a*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] + 4*a*b*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])*ArcCosh[c + d*x] + 24*b^2*(-3*a + 8*a*(c + d*x)^4 - 3*b*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x] - 2*b*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x])*ArcCosh[c + d*x]^2 + 8*b^3*(-3 + 8*(c + d*x)^4)*ArcCosh[c + d*x]^3 - 9*b*(8*a^2 + 5*b^2)*Log[c + d*x + Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]]))/(256*d)","A",1
115,1,296,262,0.4263382,"\int (c e+d e x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","Integrate[(c*e + d*e*x)^2*(a + b*ArcCosh[c + d*x])^3,x]","\frac{e^2 \left(a \left(3 a^2+2 b^2\right) (c+d x)^3+\frac{1}{3} b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(-\left(\left(9 a^2+2 b^2\right) (c+d x)^2\right)-2 \left(9 a^2+20 b^2\right)\right)-b \cosh ^{-1}(c+d x) \left(-9 a^2 (c+d x)^3+6 a b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2+12 a b \sqrt{c+d x-1} \sqrt{c+d x+1}-2 b^2 (c+d x)^3-12 b^2 (c+d x)\right)+12 a b^2 (c+d x)-3 b^2 \cosh ^{-1}(c+d x)^2 \left(-3 a (c+d x)^3+b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2+2 b \sqrt{c+d x-1} \sqrt{c+d x+1}\right)+3 b^3 (c+d x)^3 \cosh ^{-1}(c+d x)^3\right)}{9 d}","\frac{2 b^2 e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)}{9 d}+\frac{4}{3} a b^2 e^2 x-\frac{b e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d}-\frac{2 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d}+\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 d}-\frac{2 b^3 e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1}}{27 d}-\frac{40 b^3 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{27 d}+\frac{4 b^3 e^2 (c+d x) \cosh ^{-1}(c+d x)}{3 d}",1,"(e^2*(12*a*b^2*(c + d*x) + a*(3*a^2 + 2*b^2)*(c + d*x)^3 + (b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(-2*(9*a^2 + 20*b^2) - (9*a^2 + 2*b^2)*(c + d*x)^2))/3 - b*(-12*b^2*(c + d*x) - 9*a^2*(c + d*x)^3 - 2*b^2*(c + d*x)^3 + 12*a*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] + 6*a*b*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])*ArcCosh[c + d*x] - 3*b^2*(-3*a*(c + d*x)^3 + 2*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] + b*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])*ArcCosh[c + d*x]^2 + 3*b^3*(c + d*x)^3*ArcCosh[c + d*x]^3))/(9*d)","A",1
116,1,244,175,0.3193868,"\int (c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","Integrate[(c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^3,x]","\frac{e \left(2 a \left(2 a^2+3 b^2\right) (c+d x)^2-3 b \left(2 a^2+b^2\right) \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1}-3 b \left(2 a^2+b^2\right) \log \left(\sqrt{c+d x-1} \sqrt{c+d x+1}+c+d x\right)-6 b (c+d x) \cosh ^{-1}(c+d x) \left(-2 a^2 (c+d x)+2 a b \sqrt{c+d x-1} \sqrt{c+d x+1}-b^2 (c+d x)\right)+6 b^2 \cosh ^{-1}(c+d x)^2 \left(2 a (c+d x)^2-a-b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)\right)+2 b^3 \left(2 (c+d x)^2-1\right) \cosh ^{-1}(c+d x)^3\right)}{8 d}","\frac{3 b^2 e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{4 d}-\frac{3 b e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{4 d}+\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{2 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^3}{4 d}-\frac{3 b^3 e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1}}{8 d}-\frac{3 b^3 e \cosh ^{-1}(c+d x)}{8 d}",1,"(e*(2*a*(2*a^2 + 3*b^2)*(c + d*x)^2 - 3*b*(2*a^2 + b^2)*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x] - 6*b*(c + d*x)*(-2*a^2*(c + d*x) - b^2*(c + d*x) + 2*a*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])*ArcCosh[c + d*x] + 6*b^2*(-a + 2*a*(c + d*x)^2 - b*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])*ArcCosh[c + d*x]^2 + 2*b^3*(-1 + 2*(c + d*x)^2)*ArcCosh[c + d*x]^3 - 3*b*(2*a^2 + b^2)*Log[c + d*x + Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]]))/(8*d)","A",1
117,1,168,114,0.1863456,"\int \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","Integrate[(a + b*ArcCosh[c + d*x])^3,x]","\frac{a \left(a^2+6 b^2\right) (c+d x)-3 b \left(a^2+2 b^2\right) \sqrt{c+d x-1} \sqrt{c+d x+1}-3 b \cosh ^{-1}(c+d x) \left(-\left(a^2 (c+d x)\right)+2 a b \sqrt{c+d x-1} \sqrt{c+d x+1}-2 b^2 (c+d x)\right)-3 b^2 \cosh ^{-1}(c+d x)^2 \left(b \sqrt{c+d x-1} \sqrt{c+d x+1}-a (c+d x)\right)+b^3 (c+d x) \cosh ^{-1}(c+d x)^3}{d}","6 a b^2 x-\frac{3 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d}-\frac{6 b^3 \sqrt{c+d x-1} \sqrt{c+d x+1}}{d}+\frac{6 b^3 (c+d x) \cosh ^{-1}(c+d x)}{d}",1,"(a*(a^2 + 6*b^2)*(c + d*x) - 3*b*(a^2 + 2*b^2)*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] - 3*b*(-(a^2*(c + d*x)) - 2*b^2*(c + d*x) + 2*a*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])*ArcCosh[c + d*x] - 3*b^2*(-(a*(c + d*x)) + b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])*ArcCosh[c + d*x]^2 + b^3*(c + d*x)*ArcCosh[c + d*x]^3)/d","A",1
118,1,217,159,0.5715067,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{c e+d e x} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x),x]","\frac{4 a^3 \log (c+d x)+6 a^2 b \cosh ^{-1}(c+d x)^2+12 a^2 b \cosh ^{-1}(c+d x) \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right)-6 b^2 \text{Li}_3\left(-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)+4 a b^2 \cosh ^{-1}(c+d x)^3+12 a b^2 \cosh ^{-1}(c+d x)^2 \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right)-6 b \text{Li}_2\left(-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2-3 b^3 \text{Li}_4\left(-e^{-2 \cosh ^{-1}(c+d x)}\right)+b^3 \cosh ^{-1}(c+d x)^4+4 b^3 \cosh ^{-1}(c+d x)^3 \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right)}{4 d e}","-\frac{3 b^2 \text{Li}_3\left(-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{2 d e}-\frac{3 b \text{Li}_2\left(-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d e}+\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{4 b d e}+\frac{\log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e}-\frac{3 b^3 \text{Li}_4\left(-e^{-2 \cosh ^{-1}(c+d x)}\right)}{4 d e}",1,"(6*a^2*b*ArcCosh[c + d*x]^2 + 4*a*b^2*ArcCosh[c + d*x]^3 + b^3*ArcCosh[c + d*x]^4 + 12*a^2*b*ArcCosh[c + d*x]*Log[1 + E^(-2*ArcCosh[c + d*x])] + 12*a*b^2*ArcCosh[c + d*x]^2*Log[1 + E^(-2*ArcCosh[c + d*x])] + 4*b^3*ArcCosh[c + d*x]^3*Log[1 + E^(-2*ArcCosh[c + d*x])] + 4*a^3*Log[c + d*x] - 6*b*(a + b*ArcCosh[c + d*x])^2*PolyLog[2, -E^(-2*ArcCosh[c + d*x])] - 6*b^2*(a + b*ArcCosh[c + d*x])*PolyLog[3, -E^(-2*ArcCosh[c + d*x])] - 3*b^3*PolyLog[4, -E^(-2*ArcCosh[c + d*x])])/(4*d*e)","A",0
119,1,327,186,1.1837842,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^2} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x)^2,x]","-\frac{\frac{a^3}{c+d x}+3 a^2 b \tan ^{-1}\left(\frac{1}{\sqrt{c+d x-1} \sqrt{c+d x+1}}\right)+\frac{3 a^2 b \cosh ^{-1}(c+d x)}{c+d x}+3 i a b^2 \left(2 \text{Li}_2\left(-i e^{-\cosh ^{-1}(c+d x)}\right)-2 \text{Li}_2\left(i e^{-\cosh ^{-1}(c+d x)}\right)+\cosh ^{-1}(c+d x) \left(-\frac{i \cosh ^{-1}(c+d x)}{c+d x}+2 \log \left(1-i e^{-\cosh ^{-1}(c+d x)}\right)-2 \log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right)\right)\right)+b^3 \left(\frac{\cosh ^{-1}(c+d x)^3}{c+d x}-3 i \left(-2 \cosh ^{-1}(c+d x) \left(\text{Li}_2\left(-i e^{-\cosh ^{-1}(c+d x)}\right)-\text{Li}_2\left(i e^{-\cosh ^{-1}(c+d x)}\right)\right)-2 \text{Li}_3\left(-i e^{-\cosh ^{-1}(c+d x)}\right)+2 \text{Li}_3\left(i e^{-\cosh ^{-1}(c+d x)}\right)-\left(\cosh ^{-1}(c+d x)^2 \left(\log \left(1-i e^{-\cosh ^{-1}(c+d x)}\right)-\log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right)\right)\right)\right)\right)}{d e^2}","-\frac{6 i b^2 \text{Li}_2\left(-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2}+\frac{6 i b^2 \text{Li}_2\left(i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e^2 (c+d x)}+\frac{6 b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^2}+\frac{6 i b^3 \text{Li}_3\left(-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}-\frac{6 i b^3 \text{Li}_3\left(i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}",1,"-((a^3/(c + d*x) + (3*a^2*b*ArcCosh[c + d*x])/(c + d*x) + 3*a^2*b*ArcTan[1/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])] + (3*I)*a*b^2*(ArcCosh[c + d*x]*(((-I)*ArcCosh[c + d*x])/(c + d*x) + 2*Log[1 - I/E^ArcCosh[c + d*x]] - 2*Log[1 + I/E^ArcCosh[c + d*x]]) + 2*PolyLog[2, (-I)/E^ArcCosh[c + d*x]] - 2*PolyLog[2, I/E^ArcCosh[c + d*x]]) + b^3*(ArcCosh[c + d*x]^3/(c + d*x) - (3*I)*(-(ArcCosh[c + d*x]^2*(Log[1 - I/E^ArcCosh[c + d*x]] - Log[1 + I/E^ArcCosh[c + d*x]])) - 2*ArcCosh[c + d*x]*(PolyLog[2, (-I)/E^ArcCosh[c + d*x]] - PolyLog[2, I/E^ArcCosh[c + d*x]]) - 2*PolyLog[3, (-I)/E^ArcCosh[c + d*x]] + 2*PolyLog[3, I/E^ArcCosh[c + d*x]])))/(d*e^2))","A",0
120,1,266,164,1.1130442,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^3} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x)^3,x]","\frac{-\frac{a^3}{(c+d x)^2}+\frac{3 a^2 b \left(\sqrt{\frac{c+d x-1}{c+d x+1}} \left(c^2+2 c d x+c+d x (d x+1)\right)-\cosh ^{-1}(c+d x)\right)}{(c+d x)^2}+6 a b^2 \left(-\log (c+d x)-\frac{\cosh ^{-1}(c+d x)^2}{2 (c+d x)^2}+\frac{\sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \cosh ^{-1}(c+d x)}{c+d x}\right)+3 b^3 \left(\text{Li}_2\left(-e^{-2 \cosh ^{-1}(c+d x)}\right)+\cosh ^{-1}(c+d x) \left(\frac{\sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \cosh ^{-1}(c+d x)}{c+d x}-\cosh ^{-1}(c+d x)-2 \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right)\right)\right)-\frac{b^3 \cosh ^{-1}(c+d x)^3}{(c+d x)^2}}{2 d e^3}","-\frac{3 b^2 \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^3}+\frac{3 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d e^3 (c+d x)}-\frac{3 b \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d e^3}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{2 d e^3 (c+d x)^2}+\frac{3 b^3 \text{Li}_2\left(-e^{-2 \cosh ^{-1}(c+d x)}\right)}{2 d e^3}",1,"(-(a^3/(c + d*x)^2) + (3*a^2*b*(Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(c + c^2 + 2*c*d*x + d*x*(1 + d*x)) - ArcCosh[c + d*x]))/(c + d*x)^2 - (b^3*ArcCosh[c + d*x]^3)/(c + d*x)^2 + 6*a*b^2*((Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*ArcCosh[c + d*x])/(c + d*x) - ArcCosh[c + d*x]^2/(2*(c + d*x)^2) - Log[c + d*x]) + 3*b^3*(ArcCosh[c + d*x]*(-ArcCosh[c + d*x] + (Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*ArcCosh[c + d*x])/(c + d*x) - 2*Log[1 + E^(-2*ArcCosh[c + d*x])]) + PolyLog[2, -E^(-2*ArcCosh[c + d*x])]))/(2*d*e^3)","A",0
121,1,504,297,2.3842522,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^4} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x)^4,x]","\frac{-\frac{2 a^3}{(c+d x)^3}+\frac{3 a^2 b \sqrt{c+d x-1} \sqrt{c+d x+1}}{(c+d x)^2}-3 a^2 b \tan ^{-1}\left(\frac{1}{\sqrt{c+d x-1} \sqrt{c+d x+1}}\right)-\frac{6 a^2 b \cosh ^{-1}(c+d x)}{(c+d x)^3}+6 a b^2 \left(-i \text{Li}_2\left(-i e^{-\cosh ^{-1}(c+d x)}\right)+i \text{Li}_2\left(i e^{-\cosh ^{-1}(c+d x)}\right)+\frac{1}{c+d x}-\frac{\cosh ^{-1}(c+d x)^2}{(c+d x)^3}+\frac{\sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \cosh ^{-1}(c+d x)}{(c+d x)^2}-i \cosh ^{-1}(c+d x) \log \left(1-i e^{-\cosh ^{-1}(c+d x)}\right)+i \cosh ^{-1}(c+d x) \log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right)\right)+b^3 \left(-3 i \left(2 \cosh ^{-1}(c+d x) \text{Li}_2\left(-i e^{-\cosh ^{-1}(c+d x)}\right)-2 \cosh ^{-1}(c+d x) \text{Li}_2\left(i e^{-\cosh ^{-1}(c+d x)}\right)+2 \text{Li}_3\left(-i e^{-\cosh ^{-1}(c+d x)}\right)-2 \text{Li}_3\left(i e^{-\cosh ^{-1}(c+d x)}\right)+\cosh ^{-1}(c+d x)^2 \log \left(1-i e^{-\cosh ^{-1}(c+d x)}\right)-\cosh ^{-1}(c+d x)^2 \log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right)-4 i \tan ^{-1}\left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c+d x)\right)\right)\right)-\frac{2 \cosh ^{-1}(c+d x)^3}{(c+d x)^3}+\frac{3 \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \cosh ^{-1}(c+d x)^2}{(c+d x)^2}+\frac{6 \cosh ^{-1}(c+d x)}{c+d x}\right)}{6 d e^4}","-\frac{i b^2 \text{Li}_2\left(-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4}+\frac{i b^2 \text{Li}_2\left(i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4}+\frac{b^2 \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4 (c+d x)}+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d e^4 (c+d x)^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^3}+\frac{b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^4}+\frac{i b^3 \text{Li}_3\left(-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}-\frac{i b^3 \text{Li}_3\left(i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}-\frac{b^3 \tan ^{-1}\left(\sqrt{c+d x-1} \sqrt{c+d x+1}\right)}{d e^4}",1,"((-2*a^3)/(c + d*x)^3 + (3*a^2*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(c + d*x)^2 - (6*a^2*b*ArcCosh[c + d*x])/(c + d*x)^3 - 3*a^2*b*ArcTan[1/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])] + 6*a*b^2*((c + d*x)^(-1) + (Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*ArcCosh[c + d*x])/(c + d*x)^2 - ArcCosh[c + d*x]^2/(c + d*x)^3 - I*ArcCosh[c + d*x]*Log[1 - I/E^ArcCosh[c + d*x]] + I*ArcCosh[c + d*x]*Log[1 + I/E^ArcCosh[c + d*x]] - I*PolyLog[2, (-I)/E^ArcCosh[c + d*x]] + I*PolyLog[2, I/E^ArcCosh[c + d*x]]) + b^3*((6*ArcCosh[c + d*x])/(c + d*x) + (3*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*ArcCosh[c + d*x]^2)/(c + d*x)^2 - (2*ArcCosh[c + d*x]^3)/(c + d*x)^3 - (3*I)*((-4*I)*ArcTan[Tanh[ArcCosh[c + d*x]/2]] + ArcCosh[c + d*x]^2*Log[1 - I/E^ArcCosh[c + d*x]] - ArcCosh[c + d*x]^2*Log[1 + I/E^ArcCosh[c + d*x]] + 2*ArcCosh[c + d*x]*PolyLog[2, (-I)/E^ArcCosh[c + d*x]] - 2*ArcCosh[c + d*x]*PolyLog[2, I/E^ArcCosh[c + d*x]] + 2*PolyLog[3, (-I)/E^ArcCosh[c + d*x]] - 2*PolyLog[3, I/E^ArcCosh[c + d*x]])))/(6*d*e^4)","A",0
122,1,562,377,0.8879182,"\int (c e+d e x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","Integrate[(c*e + d*e*x)^3*(a + b*ArcCosh[c + d*x])^4,x]","\frac{e^3 \left(9 b^2 \left(8 a^2+5 b^2\right) (c+d x)^2+2 a b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \left(-2 \left(8 a^2+3 b^2\right) (c+d x)^2-3 \left(8 a^2+15 b^2\right)\right)-6 a b \left(8 a^2+15 b^2\right) \log \left(\sqrt{c+d x-1} \sqrt{c+d x+1}+c+d x\right)+3 b^2 \cosh ^{-1}(c+d x)^2 \left(64 a^2 (c+d x)^4-24 a^2-32 a b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3-48 a b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)+8 b^2 (c+d x)^4+24 b^2 (c+d x)^2-15 b^2\right)+\left(32 a^4+24 a^2 b^2+3 b^4\right) (c+d x)^4+2 b (c+d x) \cosh ^{-1}(c+d x) \left(64 a^3 (c+d x)^3-48 a^2 b \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1}-72 a^2 b \sqrt{c+d x-1} \sqrt{c+d x+1}+24 a b^2 (c+d x)^3+72 a b^2 (c+d x)-6 b^3 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1}-45 b^3 \sqrt{c+d x-1} \sqrt{c+d x+1}\right)+16 b^3 \cosh ^{-1}(c+d x)^3 \left(8 a (c+d x)^4-3 a-2 b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3-3 b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)\right)+4 b^4 \left(8 (c+d x)^4-3\right) \cosh ^{-1}(c+d x)^4\right)}{128 d}","-\frac{3 b^3 e^3 \sqrt{c+d x-1} (c+d x)^3 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{32 d}-\frac{45 b^3 e^3 \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{64 d}+\frac{3 b^2 e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{16 d}-\frac{45 b^2 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{128 d}+\frac{9 b^2 e^3 (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{16 d}-\frac{b e^3 \sqrt{c+d x-1} (c+d x)^3 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{4 d}-\frac{3 b e^3 \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{8 d}+\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{4 d}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{32 d}+\frac{3 b^4 e^3 (c+d x)^4}{128 d}+\frac{45 b^4 e^3 (c+d x)^2}{128 d}",1,"(e^3*(9*b^2*(8*a^2 + 5*b^2)*(c + d*x)^2 + (32*a^4 + 24*a^2*b^2 + 3*b^4)*(c + d*x)^4 + 2*a*b*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x]*(-3*(8*a^2 + 15*b^2) - 2*(8*a^2 + 3*b^2)*(c + d*x)^2) + 2*b*(c + d*x)*(72*a*b^2*(c + d*x) + 64*a^3*(c + d*x)^3 + 24*a*b^2*(c + d*x)^3 - 72*a^2*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] - 45*b^3*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] - 48*a^2*b*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x] - 6*b^3*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])*ArcCosh[c + d*x] + 3*b^2*(-24*a^2 - 15*b^2 + 24*b^2*(c + d*x)^2 + 64*a^2*(c + d*x)^4 + 8*b^2*(c + d*x)^4 - 48*a*b*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x] - 32*a*b*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x])*ArcCosh[c + d*x]^2 + 16*b^3*(-3*a + 8*a*(c + d*x)^4 - 3*b*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x] - 2*b*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x])*ArcCosh[c + d*x]^3 + 4*b^4*(-3 + 8*(c + d*x)^4)*ArcCosh[c + d*x]^4 - 6*a*b*(8*a^2 + 15*b^2)*Log[c + d*x + Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]]))/(128*d)","A",1
123,1,475,309,0.637474,"\int (c e+d e x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","Integrate[(c*e + d*e*x)^2*(a + b*ArcCosh[c + d*x])^4,x]","\frac{e^2 \left(24 b^2 \left(9 a^2+20 b^2\right) (c+d x)+12 a b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(-\left(3 a^2+2 b^2\right) (c+d x)^2-6 a^2-40 b^2\right)+18 b^2 \cosh ^{-1}(c+d x)^2 \left(9 a^2 (c+d x)^3-6 a b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2-12 a b \sqrt{c+d x-1} \sqrt{c+d x+1}+2 b^2 (c+d x)^3+12 b^2 (c+d x)\right)+\left(27 a^4+36 a^2 b^2+8 b^4\right) (c+d x)^3+12 b \cosh ^{-1}(c+d x) \left(9 a^3 (c+d x)^3-9 a^2 b \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1}-18 a^2 b \sqrt{c+d x-1} \sqrt{c+d x+1}+6 a b^2 (c+d x)^3+36 a b^2 (c+d x)-2 b^3 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1}-40 b^3 \sqrt{c+d x-1} \sqrt{c+d x+1}\right)-36 b^3 \cosh ^{-1}(c+d x)^3 \left(-3 a (c+d x)^3+b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2+2 b \sqrt{c+d x-1} \sqrt{c+d x+1}\right)+27 b^4 (c+d x)^3 \cosh ^{-1}(c+d x)^4\right)}{81 d}","-\frac{8 b^3 e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{27 d}-\frac{160 b^3 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{27 d}+\frac{4 b^2 e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{9 d}+\frac{8 b^2 e^2 (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d}-\frac{4 b e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{9 d}-\frac{8 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{9 d}+\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{3 d}+\frac{8 b^4 e^2 (c+d x)^3}{81 d}+\frac{160}{27} b^4 e^2 x",1,"(e^2*(24*b^2*(9*a^2 + 20*b^2)*(c + d*x) + (27*a^4 + 36*a^2*b^2 + 8*b^4)*(c + d*x)^3 + 12*a*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(-6*a^2 - 40*b^2 - (3*a^2 + 2*b^2)*(c + d*x)^2) + 12*b*(36*a*b^2*(c + d*x) + 9*a^3*(c + d*x)^3 + 6*a*b^2*(c + d*x)^3 - 18*a^2*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] - 40*b^3*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] - 9*a^2*b*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x] - 2*b^3*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])*ArcCosh[c + d*x] + 18*b^2*(12*b^2*(c + d*x) + 9*a^2*(c + d*x)^3 + 2*b^2*(c + d*x)^3 - 12*a*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] - 6*a*b*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])*ArcCosh[c + d*x]^2 - 36*b^3*(-3*a*(c + d*x)^3 + 2*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] + b*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])*ArcCosh[c + d*x]^3 + 27*b^4*(c + d*x)^3*ArcCosh[c + d*x]^4))/(81*d)","A",1
124,1,360,209,0.4919223,"\int (c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","Integrate[(c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^4,x]","\frac{e \left(-2 a b \left(2 a^2+3 b^2\right) \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1}-2 a b \left(2 a^2+3 b^2\right) \log \left(\sqrt{c+d x-1} \sqrt{c+d x+1}+c+d x\right)+3 b^2 \cosh ^{-1}(c+d x)^2 \left(4 a^2 (c+d x)^2-2 a^2-4 a b \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1}+2 b^2 (c+d x)^2-b^2\right)+\left(2 a^4+6 a^2 b^2+3 b^4\right) (c+d x)^2-2 b (c+d x) \cosh ^{-1}(c+d x) \left(-4 a^3 (c+d x)+6 a^2 b \sqrt{c+d x-1} \sqrt{c+d x+1}-6 a b^2 (c+d x)+3 b^3 \sqrt{c+d x-1} \sqrt{c+d x+1}\right)+4 b^3 \cosh ^{-1}(c+d x)^3 \left(2 a (c+d x)^2-a-b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)\right)+b^4 \left(2 (c+d x)^2-1\right) \cosh ^{-1}(c+d x)^4\right)}{4 d}","-\frac{3 b^3 e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{2 d}+\frac{3 b^2 e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{2 d}-\frac{3 b^2 e \left(a+b \cosh ^{-1}(c+d x)\right)^2}{4 d}-\frac{b e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d}+\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{2 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^4}{4 d}+\frac{3 b^4 e (c+d x)^2}{4 d}",1,"(e*((2*a^4 + 6*a^2*b^2 + 3*b^4)*(c + d*x)^2 - 2*a*b*(2*a^2 + 3*b^2)*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x] - 2*b*(c + d*x)*(-4*a^3*(c + d*x) - 6*a*b^2*(c + d*x) + 6*a^2*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] + 3*b^3*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])*ArcCosh[c + d*x] + 3*b^2*(-2*a^2 - b^2 + 4*a^2*(c + d*x)^2 + 2*b^2*(c + d*x)^2 - 4*a*b*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])*ArcCosh[c + d*x]^2 + 4*b^3*(-a + 2*a*(c + d*x)^2 - b*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])*ArcCosh[c + d*x]^3 + b^4*(-1 + 2*(c + d*x)^2)*ArcCosh[c + d*x]^4 - 2*a*b*(2*a^2 + 3*b^2)*Log[c + d*x + Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]]))/(4*d)","A",1
125,1,261,129,0.2718419,"\int \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","Integrate[(a + b*ArcCosh[c + d*x])^4,x]","\frac{-4 a b \left(a^2+6 b^2\right) \sqrt{c+d x-1} \sqrt{c+d x+1}+6 b^2 \cosh ^{-1}(c+d x)^2 \left(a^2 (c+d x)-2 a b \sqrt{c+d x-1} \sqrt{c+d x+1}+2 b^2 (c+d x)\right)+\left(a^4+12 a^2 b^2+24 b^4\right) (c+d x)-4 b \cosh ^{-1}(c+d x) \left(-\left(a^3 (c+d x)\right)+3 a^2 b \sqrt{c+d x-1} \sqrt{c+d x+1}-6 a b^2 (c+d x)+6 b^3 \sqrt{c+d x-1} \sqrt{c+d x+1}\right)-4 b^3 \cosh ^{-1}(c+d x)^3 \left(b \sqrt{c+d x-1} \sqrt{c+d x+1}-a (c+d x)\right)+b^4 (c+d x) \cosh ^{-1}(c+d x)^4}{d}","-\frac{24 b^3 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{d}+\frac{12 b^2 (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d}-\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^4}{d}+24 b^4 x",1,"((a^4 + 12*a^2*b^2 + 24*b^4)*(c + d*x) - 4*a*b*(a^2 + 6*b^2)*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] - 4*b*(-(a^3*(c + d*x)) - 6*a*b^2*(c + d*x) + 3*a^2*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] + 6*b^3*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])*ArcCosh[c + d*x] + 6*b^2*(a^2*(c + d*x) + 2*b^2*(c + d*x) - 2*a*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])*ArcCosh[c + d*x]^2 - 4*b^3*(-(a*(c + d*x)) + b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])*ArcCosh[c + d*x]^3 + b^4*(c + d*x)*ArcCosh[c + d*x]^4)/d","B",1
126,1,308,192,0.7997723,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{c e+d e x} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x),x]","\frac{a^4 \log (c+d x)+2 a^3 b \cosh ^{-1}(c+d x)^2+4 a^3 b \cosh ^{-1}(c+d x) \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right)+2 a^2 b^2 \cosh ^{-1}(c+d x)^3+6 a^2 b^2 \cosh ^{-1}(c+d x)^2 \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right)-3 a b^3 \text{Li}_4\left(-e^{-2 \cosh ^{-1}(c+d x)}\right)+a b^3 \cosh ^{-1}(c+d x)^4+4 a b^3 \cosh ^{-1}(c+d x)^3 \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right)-3 b^2 \text{Li}_3\left(-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2-2 b \text{Li}_2\left(-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^3-3 b^4 \cosh ^{-1}(c+d x) \text{Li}_4\left(-e^{-2 \cosh ^{-1}(c+d x)}\right)-\frac{3}{2} b^4 \text{Li}_5\left(-e^{-2 \cosh ^{-1}(c+d x)}\right)+\frac{1}{5} b^4 \cosh ^{-1}(c+d x)^5+b^4 \cosh ^{-1}(c+d x)^4 \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right)}{d e}","-\frac{3 b^3 \text{Li}_4\left(-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e}-\frac{3 b^2 \text{Li}_3\left(-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e}-\frac{2 b \text{Li}_2\left(-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e}+\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^5}{5 b d e}+\frac{\log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)^4}{d e}-\frac{3 b^4 \text{Li}_5\left(-e^{-2 \cosh ^{-1}(c+d x)}\right)}{2 d e}",1,"(2*a^3*b*ArcCosh[c + d*x]^2 + 2*a^2*b^2*ArcCosh[c + d*x]^3 + a*b^3*ArcCosh[c + d*x]^4 + (b^4*ArcCosh[c + d*x]^5)/5 + 4*a^3*b*ArcCosh[c + d*x]*Log[1 + E^(-2*ArcCosh[c + d*x])] + 6*a^2*b^2*ArcCosh[c + d*x]^2*Log[1 + E^(-2*ArcCosh[c + d*x])] + 4*a*b^3*ArcCosh[c + d*x]^3*Log[1 + E^(-2*ArcCosh[c + d*x])] + b^4*ArcCosh[c + d*x]^4*Log[1 + E^(-2*ArcCosh[c + d*x])] + a^4*Log[c + d*x] - 2*b*(a + b*ArcCosh[c + d*x])^3*PolyLog[2, -E^(-2*ArcCosh[c + d*x])] - 3*b^2*(a + b*ArcCosh[c + d*x])^2*PolyLog[3, -E^(-2*ArcCosh[c + d*x])] - 3*a*b^3*PolyLog[4, -E^(-2*ArcCosh[c + d*x])] - 3*b^4*ArcCosh[c + d*x]*PolyLog[4, -E^(-2*ArcCosh[c + d*x])] - (3*b^4*PolyLog[5, -E^(-2*ArcCosh[c + d*x])])/2)/(d*e)","A",0
127,1,872,264,2.5216251,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^2} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x)^2,x]","\frac{-\frac{a^4}{c+d x}+4 b \left(2 \tan ^{-1}\left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c+d x)\right)\right)-\frac{\cosh ^{-1}(c+d x)}{c+d x}\right) a^3-6 i b^2 \left(\cosh ^{-1}(c+d x) \left(-\frac{i \cosh ^{-1}(c+d x)}{c+d x}+2 \log \left(1-i e^{-\cosh ^{-1}(c+d x)}\right)-2 \log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right)\right)+2 \text{Li}_2\left(-i e^{-\cosh ^{-1}(c+d x)}\right)-2 \text{Li}_2\left(i e^{-\cosh ^{-1}(c+d x)}\right)\right) a^2+4 b^3 \left(3 i \left(-\left(\left(\log \left(1-i e^{-\cosh ^{-1}(c+d x)}\right)-\log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right)\right) \cosh ^{-1}(c+d x)^2\right)-2 \left(\text{Li}_2\left(-i e^{-\cosh ^{-1}(c+d x)}\right)-\text{Li}_2\left(i e^{-\cosh ^{-1}(c+d x)}\right)\right) \cosh ^{-1}(c+d x)-2 \text{Li}_3\left(-i e^{-\cosh ^{-1}(c+d x)}\right)+2 \text{Li}_3\left(i e^{-\cosh ^{-1}(c+d x)}\right)\right)-\frac{\cosh ^{-1}(c+d x)^3}{c+d x}\right) a+b^4 \left(-\frac{\cosh ^{-1}(c+d x)^4}{c+d x}+i \cosh ^{-1}(c+d x)^4+4 i \log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)^3-4 i \log \left(1+i e^{\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)^3-2 \pi  \cosh ^{-1}(c+d x)^3-6 \pi  \log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)^2+6 \pi  \log \left(1-i e^{\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)^2-12 i \text{Li}_2\left(-i e^{\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)^2-\frac{3}{2} i \pi ^2 \cosh ^{-1}(c+d x)^2-3 i \pi ^2 \log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)+3 i \pi ^2 \log \left(1-i e^{\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)+12 \pi  \text{Li}_2\left(i e^{\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)-24 i \text{Li}_3\left(-i e^{-\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)+24 i \text{Li}_3\left(-i e^{\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)+\frac{1}{2} \pi ^3 \cosh ^{-1}(c+d x)+\frac{1}{2} \pi ^3 \log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right)-\frac{1}{2} \pi ^3 \log \left(1+i e^{\cosh ^{-1}(c+d x)}\right)+\frac{1}{2} \pi ^3 \log \left(\tan \left(\frac{1}{4} \left(2 i \cosh ^{-1}(c+d x)+\pi \right)\right)\right)+3 i \left(\pi -2 i \cosh ^{-1}(c+d x)\right)^2 \text{Li}_2\left(-i e^{-\cosh ^{-1}(c+d x)}\right)+3 i \pi ^2 \text{Li}_2\left(i e^{\cosh ^{-1}(c+d x)}\right)+12 \pi  \text{Li}_3\left(-i e^{-\cosh ^{-1}(c+d x)}\right)-12 \pi  \text{Li}_3\left(i e^{\cosh ^{-1}(c+d x)}\right)-24 i \text{Li}_4\left(-i e^{-\cosh ^{-1}(c+d x)}\right)-24 i \text{Li}_4\left(-i e^{\cosh ^{-1}(c+d x)}\right)-\frac{7 i \pi ^4}{16}\right)}{d e^2}","\frac{24 i b^3 \text{Li}_3\left(-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2}-\frac{24 i b^3 \text{Li}_3\left(i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2}-\frac{12 i b^2 \text{Li}_2\left(-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^2}+\frac{12 i b^2 \text{Li}_2\left(i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{d e^2 (c+d x)}+\frac{8 b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e^2}-\frac{24 i b^4 \text{Li}_4\left(-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}+\frac{24 i b^4 \text{Li}_4\left(i e^{\cosh ^{-1}(c+d x)}\right)}{d e^2}",1,"(-(a^4/(c + d*x)) + 4*a^3*b*(-(ArcCosh[c + d*x]/(c + d*x)) + 2*ArcTan[Tanh[ArcCosh[c + d*x]/2]]) - (6*I)*a^2*b^2*(ArcCosh[c + d*x]*(((-I)*ArcCosh[c + d*x])/(c + d*x) + 2*Log[1 - I/E^ArcCosh[c + d*x]] - 2*Log[1 + I/E^ArcCosh[c + d*x]]) + 2*PolyLog[2, (-I)/E^ArcCosh[c + d*x]] - 2*PolyLog[2, I/E^ArcCosh[c + d*x]]) + 4*a*b^3*(-(ArcCosh[c + d*x]^3/(c + d*x)) + (3*I)*(-(ArcCosh[c + d*x]^2*(Log[1 - I/E^ArcCosh[c + d*x]] - Log[1 + I/E^ArcCosh[c + d*x]])) - 2*ArcCosh[c + d*x]*(PolyLog[2, (-I)/E^ArcCosh[c + d*x]] - PolyLog[2, I/E^ArcCosh[c + d*x]]) - 2*PolyLog[3, (-I)/E^ArcCosh[c + d*x]] + 2*PolyLog[3, I/E^ArcCosh[c + d*x]])) + b^4*(((-7*I)/16)*Pi^4 + (Pi^3*ArcCosh[c + d*x])/2 - ((3*I)/2)*Pi^2*ArcCosh[c + d*x]^2 - 2*Pi*ArcCosh[c + d*x]^3 + I*ArcCosh[c + d*x]^4 - ArcCosh[c + d*x]^4/(c + d*x) + (Pi^3*Log[1 + I/E^ArcCosh[c + d*x]])/2 - (3*I)*Pi^2*ArcCosh[c + d*x]*Log[1 + I/E^ArcCosh[c + d*x]] - 6*Pi*ArcCosh[c + d*x]^2*Log[1 + I/E^ArcCosh[c + d*x]] + (4*I)*ArcCosh[c + d*x]^3*Log[1 + I/E^ArcCosh[c + d*x]] + (3*I)*Pi^2*ArcCosh[c + d*x]*Log[1 - I*E^ArcCosh[c + d*x]] + 6*Pi*ArcCosh[c + d*x]^2*Log[1 - I*E^ArcCosh[c + d*x]] - (Pi^3*Log[1 + I*E^ArcCosh[c + d*x]])/2 - (4*I)*ArcCosh[c + d*x]^3*Log[1 + I*E^ArcCosh[c + d*x]] + (Pi^3*Log[Tan[(Pi + (2*I)*ArcCosh[c + d*x])/4]])/2 + (3*I)*(Pi - (2*I)*ArcCosh[c + d*x])^2*PolyLog[2, (-I)/E^ArcCosh[c + d*x]] - (12*I)*ArcCosh[c + d*x]^2*PolyLog[2, (-I)*E^ArcCosh[c + d*x]] + (3*I)*Pi^2*PolyLog[2, I*E^ArcCosh[c + d*x]] + 12*Pi*ArcCosh[c + d*x]*PolyLog[2, I*E^ArcCosh[c + d*x]] + 12*Pi*PolyLog[3, (-I)/E^ArcCosh[c + d*x]] - (24*I)*ArcCosh[c + d*x]*PolyLog[3, (-I)/E^ArcCosh[c + d*x]] + (24*I)*ArcCosh[c + d*x]*PolyLog[3, (-I)*E^ArcCosh[c + d*x]] - 12*Pi*PolyLog[3, I*E^ArcCosh[c + d*x]] - (24*I)*PolyLog[4, (-I)/E^ArcCosh[c + d*x]] - (24*I)*PolyLog[4, (-I)*E^ArcCosh[c + d*x]]))/(d*e^2)","B",0
128,1,398,195,2.3079355,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^3} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x)^3,x]","\frac{-\frac{a^4}{(c+d x)^2}+\frac{4 a^3 b \sqrt{c+d x-1} \sqrt{c+d x+1}}{c+d x}-\frac{4 a^3 b \cosh ^{-1}(c+d x)}{(c+d x)^2}+12 a^2 b^2 \left(-\log (c+d x)-\frac{\cosh ^{-1}(c+d x)^2}{2 (c+d x)^2}+\frac{\sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \cosh ^{-1}(c+d x)}{c+d x}\right)+4 a b^3 \left(3 \text{Li}_2\left(-e^{-2 \cosh ^{-1}(c+d x)}\right)-\cosh ^{-1}(c+d x) \left(\frac{\cosh ^{-1}(c+d x)^2}{(c+d x)^2}-\frac{3 \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \cosh ^{-1}(c+d x)}{c+d x}+3 \cosh ^{-1}(c+d x)+6 \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right)\right)\right)+2 b^4 \left(6 \cosh ^{-1}(c+d x) \text{Li}_2\left(-e^{-2 \cosh ^{-1}(c+d x)}\right)+3 \text{Li}_3\left(-e^{-2 \cosh ^{-1}(c+d x)}\right)+2 \cosh ^{-1}(c+d x)^2 \left(\frac{\sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \cosh ^{-1}(c+d x)}{c+d x}-\cosh ^{-1}(c+d x)-3 \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right)\right)\right)-\frac{b^4 \cosh ^{-1}(c+d x)^4}{(c+d x)^2}}{2 d e^3}","\frac{6 b^3 \text{Li}_2\left(-e^{-2 \cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^3}-\frac{6 b^2 \log \left(e^{-2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^3}+\frac{2 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e^3 (c+d x)}-\frac{2 b \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e^3}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{2 d e^3 (c+d x)^2}+\frac{3 b^4 \text{Li}_3\left(-e^{-2 \cosh ^{-1}(c+d x)}\right)}{d e^3}",1,"(-(a^4/(c + d*x)^2) + (4*a^3*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(c + d*x) - (4*a^3*b*ArcCosh[c + d*x])/(c + d*x)^2 - (b^4*ArcCosh[c + d*x]^4)/(c + d*x)^2 + 12*a^2*b^2*((Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*ArcCosh[c + d*x])/(c + d*x) - ArcCosh[c + d*x]^2/(2*(c + d*x)^2) - Log[c + d*x]) + 4*a*b^3*(-(ArcCosh[c + d*x]*(3*ArcCosh[c + d*x] - (3*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*ArcCosh[c + d*x])/(c + d*x) + ArcCosh[c + d*x]^2/(c + d*x)^2 + 6*Log[1 + E^(-2*ArcCosh[c + d*x])])) + 3*PolyLog[2, -E^(-2*ArcCosh[c + d*x])]) + 2*b^4*(2*ArcCosh[c + d*x]^2*(-ArcCosh[c + d*x] + (Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*ArcCosh[c + d*x])/(c + d*x) - 3*Log[1 + E^(-2*ArcCosh[c + d*x])]) + 6*ArcCosh[c + d*x]*PolyLog[2, -E^(-2*ArcCosh[c + d*x])] + 3*PolyLog[3, -E^(-2*ArcCosh[c + d*x])]))/(2*d*e^3)","B",0
129,1,1374,432,9.3564969,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^4} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x)^4,x]","-\frac{a^4}{3 d e^4 (c+d x)^3}+\frac{4 b \sqrt{c+d x-1} \left(\frac{\sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1)}{6 (c+d x)^2}-\frac{\cosh ^{-1}(c+d x)}{3 (c+d x)^3}+\frac{1}{3} \tan ^{-1}\left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c+d x)\right)\right)\right) a^3}{d e^4 \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{c+d x+1}}+\frac{2 b^2 \sqrt{c+d x-1} \left(-\frac{\cosh ^{-1}(c+d x)^2}{(c+d x)^3}+\frac{\sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \cosh ^{-1}(c+d x)}{(c+d x)^2}-i \log \left(1-i e^{-\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)+i \log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)-i \text{Li}_2\left(-i e^{-\cosh ^{-1}(c+d x)}\right)+i \text{Li}_2\left(i e^{-\cosh ^{-1}(c+d x)}\right)+\frac{1}{c+d x}\right) a^2}{d e^4 \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{c+d x+1}}+\frac{4 b^3 \sqrt{c+d x-1} \left(-\frac{\cosh ^{-1}(c+d x)^3}{3 (c+d x)^3}+\frac{\sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \cosh ^{-1}(c+d x)^2}{2 (c+d x)^2}+\frac{\cosh ^{-1}(c+d x)}{c+d x}-\frac{1}{2} i \left(\log \left(1-i e^{-\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)^2-\log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)^2+2 \text{Li}_2\left(-i e^{-\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)-2 \text{Li}_2\left(i e^{-\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)-4 i \tan ^{-1}\left(\tanh \left(\frac{1}{2} \cosh ^{-1}(c+d x)\right)\right)+2 \text{Li}_3\left(-i e^{-\cosh ^{-1}(c+d x)}\right)-2 \text{Li}_3\left(i e^{-\cosh ^{-1}(c+d x)}\right)\right)\right) a}{d e^4 \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{c+d x+1}}+\frac{b^4 \sqrt{c+d x-1} \left(\frac{1}{2} i \left(-4 \cosh ^{-1}(c+d x)^2-4 i \pi  \cosh ^{-1}(c+d x)+\pi ^2+8\right) \text{Li}_2\left(-i e^{-\cosh ^{-1}(c+d x)}\right)-\frac{1}{96} i \left(-\frac{32 i \cosh ^{-1}(c+d x)^4}{(c+d x)^3}-16 \cosh ^{-1}(c+d x)^4+\frac{64 i \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \cosh ^{-1}(c+d x)^3}{(c+d x)^2}-64 \log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)^3+64 \log \left(1+i e^{\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)^3-32 i \pi  \cosh ^{-1}(c+d x)^3-96 i \pi  \log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)^2+96 i \pi  \log \left(1-i e^{\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)^2+192 \text{Li}_2\left(-i e^{\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)^2+\frac{192 i \cosh ^{-1}(c+d x)^2}{c+d x}+24 \pi ^2 \cosh ^{-1}(c+d x)^2-384 \log \left(1-i e^{-\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)+48 \pi ^2 \log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)+384 \log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)-48 \pi ^2 \log \left(1-i e^{\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)+192 i \pi  \text{Li}_2\left(i e^{\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)+384 \text{Li}_3\left(-i e^{-\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)-384 \text{Li}_3\left(-i e^{\cosh ^{-1}(c+d x)}\right) \cosh ^{-1}(c+d x)+8 i \pi ^3 \cosh ^{-1}(c+d x)+8 i \pi ^3 \log \left(1+i e^{-\cosh ^{-1}(c+d x)}\right)-8 i \pi ^3 \log \left(1+i e^{\cosh ^{-1}(c+d x)}\right)+8 i \pi ^3 \log \left(\tan \left(\frac{1}{4} \left(2 i \cosh ^{-1}(c+d x)+\pi \right)\right)\right)+384 \text{Li}_2\left(i e^{-\cosh ^{-1}(c+d x)}\right)-48 \pi ^2 \text{Li}_2\left(i e^{\cosh ^{-1}(c+d x)}\right)+192 i \pi  \text{Li}_3\left(-i e^{-\cosh ^{-1}(c+d x)}\right)-192 i \pi  \text{Li}_3\left(i e^{\cosh ^{-1}(c+d x)}\right)+384 \text{Li}_4\left(-i e^{-\cosh ^{-1}(c+d x)}\right)+384 \text{Li}_4\left(-i e^{\cosh ^{-1}(c+d x)}\right)+7 \pi ^4\right)\right)}{d e^4 \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{c+d x+1}}","\frac{4 i b^3 \text{Li}_3\left(-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4}-\frac{4 i b^3 \text{Li}_3\left(i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4}-\frac{8 b^3 \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^4}-\frac{2 i b^2 \text{Li}_2\left(-i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^4}+\frac{2 i b^2 \text{Li}_2\left(i e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^4}+\frac{2 b^2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e^4 (c+d x)}+\frac{2 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 d e^4 (c+d x)^2}-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{3 d e^4 (c+d x)^3}+\frac{4 b \tan ^{-1}\left(e^{\cosh ^{-1}(c+d x)}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 d e^4}+\frac{4 i b^4 \text{Li}_2\left(-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}-\frac{4 i b^4 \text{Li}_2\left(i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}-\frac{4 i b^4 \text{Li}_4\left(-i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}+\frac{4 i b^4 \text{Li}_4\left(i e^{\cosh ^{-1}(c+d x)}\right)}{d e^4}",1,"-1/3*a^4/(d*e^4*(c + d*x)^3) + (4*a^3*b*Sqrt[-1 + c + d*x]*((Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x))/(6*(c + d*x)^2) - ArcCosh[c + d*x]/(3*(c + d*x)^3) + ArcTan[Tanh[ArcCosh[c + d*x]/2]]/3))/(d*e^4*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*Sqrt[1 + c + d*x]) + (2*a^2*b^2*Sqrt[-1 + c + d*x]*((c + d*x)^(-1) + (Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*ArcCosh[c + d*x])/(c + d*x)^2 - ArcCosh[c + d*x]^2/(c + d*x)^3 - I*ArcCosh[c + d*x]*Log[1 - I/E^ArcCosh[c + d*x]] + I*ArcCosh[c + d*x]*Log[1 + I/E^ArcCosh[c + d*x]] - I*PolyLog[2, (-I)/E^ArcCosh[c + d*x]] + I*PolyLog[2, I/E^ArcCosh[c + d*x]]))/(d*e^4*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*Sqrt[1 + c + d*x]) + (4*a*b^3*Sqrt[-1 + c + d*x]*(ArcCosh[c + d*x]/(c + d*x) + (Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*ArcCosh[c + d*x]^2)/(2*(c + d*x)^2) - ArcCosh[c + d*x]^3/(3*(c + d*x)^3) - (I/2)*((-4*I)*ArcTan[Tanh[ArcCosh[c + d*x]/2]] + ArcCosh[c + d*x]^2*Log[1 - I/E^ArcCosh[c + d*x]] - ArcCosh[c + d*x]^2*Log[1 + I/E^ArcCosh[c + d*x]] + 2*ArcCosh[c + d*x]*PolyLog[2, (-I)/E^ArcCosh[c + d*x]] - 2*ArcCosh[c + d*x]*PolyLog[2, I/E^ArcCosh[c + d*x]] + 2*PolyLog[3, (-I)/E^ArcCosh[c + d*x]] - 2*PolyLog[3, I/E^ArcCosh[c + d*x]])))/(d*e^4*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*Sqrt[1 + c + d*x]) + (b^4*Sqrt[-1 + c + d*x]*((I/2)*(8 + Pi^2 - (4*I)*Pi*ArcCosh[c + d*x] - 4*ArcCosh[c + d*x]^2)*PolyLog[2, (-I)/E^ArcCosh[c + d*x]] - (I/96)*(7*Pi^4 + (8*I)*Pi^3*ArcCosh[c + d*x] + 24*Pi^2*ArcCosh[c + d*x]^2 + ((192*I)*ArcCosh[c + d*x]^2)/(c + d*x) - (32*I)*Pi*ArcCosh[c + d*x]^3 + ((64*I)*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*ArcCosh[c + d*x]^3)/(c + d*x)^2 - 16*ArcCosh[c + d*x]^4 - ((32*I)*ArcCosh[c + d*x]^4)/(c + d*x)^3 - 384*ArcCosh[c + d*x]*Log[1 - I/E^ArcCosh[c + d*x]] + (8*I)*Pi^3*Log[1 + I/E^ArcCosh[c + d*x]] + 384*ArcCosh[c + d*x]*Log[1 + I/E^ArcCosh[c + d*x]] + 48*Pi^2*ArcCosh[c + d*x]*Log[1 + I/E^ArcCosh[c + d*x]] - (96*I)*Pi*ArcCosh[c + d*x]^2*Log[1 + I/E^ArcCosh[c + d*x]] - 64*ArcCosh[c + d*x]^3*Log[1 + I/E^ArcCosh[c + d*x]] - 48*Pi^2*ArcCosh[c + d*x]*Log[1 - I*E^ArcCosh[c + d*x]] + (96*I)*Pi*ArcCosh[c + d*x]^2*Log[1 - I*E^ArcCosh[c + d*x]] - (8*I)*Pi^3*Log[1 + I*E^ArcCosh[c + d*x]] + 64*ArcCosh[c + d*x]^3*Log[1 + I*E^ArcCosh[c + d*x]] + (8*I)*Pi^3*Log[Tan[(Pi + (2*I)*ArcCosh[c + d*x])/4]] + 384*PolyLog[2, I/E^ArcCosh[c + d*x]] + 192*ArcCosh[c + d*x]^2*PolyLog[2, (-I)*E^ArcCosh[c + d*x]] - 48*Pi^2*PolyLog[2, I*E^ArcCosh[c + d*x]] + (192*I)*Pi*ArcCosh[c + d*x]*PolyLog[2, I*E^ArcCosh[c + d*x]] + (192*I)*Pi*PolyLog[3, (-I)/E^ArcCosh[c + d*x]] + 384*ArcCosh[c + d*x]*PolyLog[3, (-I)/E^ArcCosh[c + d*x]] - 384*ArcCosh[c + d*x]*PolyLog[3, (-I)*E^ArcCosh[c + d*x]] - (192*I)*Pi*PolyLog[3, I*E^ArcCosh[c + d*x]] + 384*PolyLog[4, (-I)/E^ArcCosh[c + d*x]] + 384*PolyLog[4, (-I)*E^ArcCosh[c + d*x]])))/(d*e^4*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*Sqrt[1 + c + d*x])","B",0
130,1,151,213,0.2484054,"\int \frac{(c e+d e x)^4}{a+b \cosh ^{-1}(c+d x)} \, dx","Integrate[(c*e + d*e*x)^4/(a + b*ArcCosh[c + d*x]),x]","\frac{e^4 \left(-2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-3 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(5 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+3 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+\cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(5 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)\right)}{16 b d}","-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{8 b d}-\frac{3 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{16 b d}-\frac{e^4 \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{16 b d}+\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{8 b d}+\frac{3 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{16 b d}+\frac{e^4 \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{16 b d}",1,"(e^4*(-2*CoshIntegral[a/b + ArcCosh[c + d*x]]*Sinh[a/b] - 3*CoshIntegral[3*(a/b + ArcCosh[c + d*x])]*Sinh[(3*a)/b] - CoshIntegral[5*(a/b + ArcCosh[c + d*x])]*Sinh[(5*a)/b] + 2*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]] + 3*Cosh[(3*a)/b]*SinhIntegral[3*(a/b + ArcCosh[c + d*x])] + Cosh[(5*a)/b]*SinhIntegral[5*(a/b + ArcCosh[c + d*x])]))/(16*b*d)","A",1
131,1,109,145,0.1839572,"\int \frac{(c e+d e x)^3}{a+b \cosh ^{-1}(c+d x)} \, dx","Integrate[(c*e + d*e*x)^3/(a + b*ArcCosh[c + d*x]),x]","\frac{e^3 \left(-2 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(4 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+2 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+\cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(4 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)\right)}{8 b d}","-\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{4 b d}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{8 b d}+\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{4 b d}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{8 b d}",1,"(e^3*(-2*CoshIntegral[2*(a/b + ArcCosh[c + d*x])]*Sinh[(2*a)/b] - CoshIntegral[4*(a/b + ArcCosh[c + d*x])]*Sinh[(4*a)/b] + 2*Cosh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c + d*x])] + Cosh[(4*a)/b]*SinhIntegral[4*(a/b + ArcCosh[c + d*x])]))/(8*b*d)","A",1
132,1,102,141,0.1571689,"\int \frac{(c e+d e x)^2}{a+b \cosh ^{-1}(c+d x)} \, dx","Integrate[(c*e + d*e*x)^2/(a + b*ArcCosh[c + d*x]),x]","\frac{e^2 \left(\sinh \left(\frac{a}{b}\right) \left(-\text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)\right)}{4 b d}","-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{4 b d}-\frac{e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{4 b d}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{4 b d}+\frac{e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{4 b d}",1,"(e^2*(-(CoshIntegral[a/b + ArcCosh[c + d*x]]*Sinh[a/b]) - CoshIntegral[3*(a/b + ArcCosh[c + d*x])]*Sinh[(3*a)/b] + Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]] + Cosh[(3*a)/b]*SinhIntegral[3*(a/b + ArcCosh[c + d*x])]))/(4*b*d)","A",1
133,1,61,69,0.0829419,"\int \frac{c e+d e x}{a+b \cosh ^{-1}(c+d x)} \, dx","Integrate[(c*e + d*e*x)/(a + b*ArcCosh[c + d*x]),x]","-\frac{e \left(\sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)-\cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 a}{b}+2 \cosh ^{-1}(c+d x)\right)\right)}{2 b d}","\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{2 b d}-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{2 b d}",1,"-1/2*(e*(CoshIntegral[(2*a)/b + 2*ArcCosh[c + d*x]]*Sinh[(2*a)/b] - Cosh[(2*a)/b]*SinhIntegral[(2*a)/b + 2*ArcCosh[c + d*x]]))/(b*d)","A",1
134,1,49,58,0.1154908,"\int \frac{1}{a+b \cosh ^{-1}(c+d x)} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^(-1),x]","\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{b d}","\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{b d}-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{b d}",1,"(-(CoshIntegral[a/b + ArcCosh[c + d*x]]*Sinh[a/b]) + Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]])/(b*d)","A",1
135,0,0,27,0.8777759,"\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)} \, dx","Integrate[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])),x]","\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)},x\right)}{e}",0,"Integrate[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])), x]","A",-1
136,1,293,263,1.9720864,"\int \frac{(c e+d e x)^4}{\left(a+b \cosh ^{-1}(c+d x)\right)^2} \, dx","Integrate[(c*e + d*e*x)^4/(a + b*ArcCosh[c + d*x])^2,x]","\frac{e^4 \left(-16 \left(3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-\sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)\right)+5 \left(10 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+5 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+\cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(5 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-10 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-5 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(5 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)\right)-\frac{16 b \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) (c+d x)^4}{a+b \cosh ^{-1}(c+d x)}\right)}{16 b^2 d}","\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{8 b^2 d}+\frac{9 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{16 b^2 d}+\frac{5 e^4 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{16 b^2 d}-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{8 b^2 d}-\frac{9 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{16 b^2 d}-\frac{5 e^4 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{16 b^2 d}-\frac{e^4 \sqrt{c+d x-1} (c+d x)^4 \sqrt{c+d x+1}}{b d \left(a+b \cosh ^{-1}(c+d x)\right)}",1,"(e^4*((-16*b*(c + d*x)^4*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x))/(a + b*ArcCosh[c + d*x]) - 16*(3*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c + d*x]] + Cosh[(3*a)/b]*CoshIntegral[3*(a/b + ArcCosh[c + d*x])] - 3*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]] - Sinh[(3*a)/b]*SinhIntegral[3*(a/b + ArcCosh[c + d*x])]) + 5*(10*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c + d*x]] + 5*Cosh[(3*a)/b]*CoshIntegral[3*(a/b + ArcCosh[c + d*x])] + Cosh[(5*a)/b]*CoshIntegral[5*(a/b + ArcCosh[c + d*x])] - 10*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]] - 5*Sinh[(3*a)/b]*SinhIntegral[3*(a/b + ArcCosh[c + d*x])] - Sinh[(5*a)/b]*SinhIntegral[5*(a/b + ArcCosh[c + d*x])])))/(16*b^2*d)","A",0
137,1,230,195,2.5800786,"\int \frac{(c e+d e x)^3}{\left(a+b \cosh ^{-1}(c+d x)\right)^2} \, dx","Integrate[(c*e + d*e*x)^3/(a + b*ArcCosh[c + d*x])^2,x]","\frac{e^3 \left(-3 \left(\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+\log \left(a+b \cosh ^{-1}(c+d x)\right)\right)+4 \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+\cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(4 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-4 \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(4 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\frac{2 b \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) (c+d x)^3}{a+b \cosh ^{-1}(c+d x)}+3 \log \left(a+b \cosh ^{-1}(c+d x)\right)\right)}{2 b^2 d}","\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{2 b^2 d}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{2 b^2 d}-\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{2 b^2 d}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{2 b^2 d}-\frac{e^3 \sqrt{c+d x-1} (c+d x)^3 \sqrt{c+d x+1}}{b d \left(a+b \cosh ^{-1}(c+d x)\right)}",1,"(e^3*((-2*b*(c + d*x)^3*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x))/(a + b*ArcCosh[c + d*x]) + 4*Cosh[(2*a)/b]*CoshIntegral[2*(a/b + ArcCosh[c + d*x])] + Cosh[(4*a)/b]*CoshIntegral[4*(a/b + ArcCosh[c + d*x])] + 3*Log[a + b*ArcCosh[c + d*x]] - 4*Sinh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c + d*x])] - 3*(Cosh[(2*a)/b]*CoshIntegral[2*(a/b + ArcCosh[c + d*x])] + Log[a + b*ArcCosh[c + d*x]] - Sinh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c + d*x])]) - Sinh[(4*a)/b]*SinhIntegral[4*(a/b + ArcCosh[c + d*x])]))/(2*b^2*d)","A",0
138,1,150,191,1.9565285,"\int \frac{(c e+d e x)^2}{\left(a+b \cosh ^{-1}(c+d x)\right)^2} \, dx","Integrate[(c*e + d*e*x)^2/(a + b*ArcCosh[c + d*x])^2,x]","\frac{e^2 \left(\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+3 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-3 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\frac{4 b \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) (c+d x)^2}{a+b \cosh ^{-1}(c+d x)}\right)}{4 b^2 d}","\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{4 b^2 d}+\frac{3 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{4 b^2 d}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{4 b^2 d}-\frac{3 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{4 b^2 d}-\frac{e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1}}{b d \left(a+b \cosh ^{-1}(c+d x)\right)}",1,"(e^2*((-4*b*(c + d*x)^2*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x))/(a + b*ArcCosh[c + d*x]) + Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c + d*x]] + 3*Cosh[(3*a)/b]*CoshIntegral[3*(a/b + ArcCosh[c + d*x])] - Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]] - 3*Sinh[(3*a)/b]*SinhIntegral[3*(a/b + ArcCosh[c + d*x])]))/(4*b^2*d)","A",0
139,1,108,110,0.4887165,"\int \frac{c e+d e x}{\left(a+b \cosh ^{-1}(c+d x)\right)^2} \, dx","Integrate[(c*e + d*e*x)/(a + b*ArcCosh[c + d*x])^2,x]","\frac{e \left(-\frac{b \sqrt{\frac{c+d x-1}{c+d x+1}} \left(c^2+2 c d x+c+d x (d x+1)\right)}{a+b \cosh ^{-1}(c+d x)}+\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)\right)}{b^2 d}","\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{b^2 d}-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{b^2 d}-\frac{e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{b d \left(a+b \cosh ^{-1}(c+d x)\right)}",1,"(e*(-((b*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(c + c^2 + 2*c*d*x + d*x*(1 + d*x)))/(a + b*ArcCosh[c + d*x])) + Cosh[(2*a)/b]*CoshIntegral[2*(a/b + ArcCosh[c + d*x])] - Sinh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c + d*x])]))/(b^2*d)","A",0
140,1,143,98,1.0293148,"\int \frac{1}{\left(a+b \cosh ^{-1}(c+d x)\right)^2} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^(-2),x]","\frac{\sqrt{\frac{c+d x-1}{c+d x+1}} \coth \left(\frac{1}{2} \cosh ^{-1}(c+d x)\right) \left(\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-\log \left(a+b \cosh ^{-1}(c+d x)\right)\right)-\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{a+b \cosh ^{-1}(c+d x)}+\log \left(\frac{b \cosh ^{-1}(c+d x)}{a}+1\right)}{b^2 d}","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{b^2 d}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{b^2 d}-\frac{\sqrt{c+d x-1} \sqrt{c+d x+1}}{b d \left(a+b \cosh ^{-1}(c+d x)\right)}",1,"(-((b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(a + b*ArcCosh[c + d*x])) + Log[1 + (b*ArcCosh[c + d*x])/a] + Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*Coth[ArcCosh[c + d*x]/2]*(Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c + d*x]] - Log[a + b*ArcCosh[c + d*x]] - Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]]))/(b^2*d)","A",0
141,0,0,27,7.7663857,"\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^2} \, dx","Integrate[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^2),x]","\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^2} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^2},x\right)}{e}",0,"Integrate[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^2), x]","A",-1
142,1,323,327,1.2805527,"\int \frac{(c e+d e x)^4}{\left(a+b \cosh ^{-1}(c+d x)\right)^3} \, dx","Integrate[(c*e + d*e*x)^4/(a + b*ArcCosh[c + d*x])^3,x]","\frac{e^4 \left(-\frac{16 b^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{\left(a+b \cosh ^{-1}(c+d x)\right)^2}+48 \left(\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-\cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)\right)+25 \left(-2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-3 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(5 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+3 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+\cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(5 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)\right)+\frac{16 b \left(4 (c+d x)^3-5 (c+d x)^5\right)}{a+b \cosh ^{-1}(c+d x)}\right)}{32 b^3 d}","-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{16 b^3 d}-\frac{27 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{32 b^3 d}-\frac{25 e^4 \sinh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{32 b^3 d}+\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{16 b^3 d}+\frac{27 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{32 b^3 d}+\frac{25 e^4 \cosh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{32 b^3 d}-\frac{5 e^4 (c+d x)^5}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{2 e^4 (c+d x)^3}{b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{2 b d \left(a+b \cosh ^{-1}(c+d x)\right)^2}",1,"(e^4*((-16*b^2*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x])/(a + b*ArcCosh[c + d*x])^2 + (16*b*(4*(c + d*x)^3 - 5*(c + d*x)^5))/(a + b*ArcCosh[c + d*x]) + 48*(CoshIntegral[a/b + ArcCosh[c + d*x]]*Sinh[a/b] + CoshIntegral[3*(a/b + ArcCosh[c + d*x])]*Sinh[(3*a)/b] - Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]] - Cosh[(3*a)/b]*SinhIntegral[3*(a/b + ArcCosh[c + d*x])]) + 25*(-2*CoshIntegral[a/b + ArcCosh[c + d*x]]*Sinh[a/b] - 3*CoshIntegral[3*(a/b + ArcCosh[c + d*x])]*Sinh[(3*a)/b] - CoshIntegral[5*(a/b + ArcCosh[c + d*x])]*Sinh[(5*a)/b] + 2*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]] + 3*Cosh[(3*a)/b]*SinhIntegral[3*(a/b + ArcCosh[c + d*x])] + Cosh[(5*a)/b]*SinhIntegral[5*(a/b + ArcCosh[c + d*x])])))/(32*b^3*d)","A",1
143,1,186,254,0.5585146,"\int \frac{(c e+d e x)^3}{\left(a+b \cosh ^{-1}(c+d x)\right)^3} \, dx","Integrate[(c*e + d*e*x)^3/(a + b*ArcCosh[c + d*x])^3,x]","\frac{e^3 \left(-\frac{b^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{\left(a+b \cosh ^{-1}(c+d x)\right)^2}-\sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-2 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(4 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+\cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+2 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(4 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+\frac{b \left(3 (c+d x)^2-4 (c+d x)^4\right)}{a+b \cosh ^{-1}(c+d x)}\right)}{2 b^3 d}","-\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{2 b^3 d}-\frac{e^3 \sinh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{b^3 d}+\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{2 b^3 d}+\frac{e^3 \cosh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{b^3 d}-\frac{2 e^3 (c+d x)^4}{b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{3 e^3 (c+d x)^2}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{2 b d \left(a+b \cosh ^{-1}(c+d x)\right)^2}",1,"(e^3*(-((b^2*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x])/(a + b*ArcCosh[c + d*x])^2) + (b*(3*(c + d*x)^2 - 4*(c + d*x)^4))/(a + b*ArcCosh[c + d*x]) - CoshIntegral[2*(a/b + ArcCosh[c + d*x])]*Sinh[(2*a)/b] - 2*CoshIntegral[4*(a/b + ArcCosh[c + d*x])]*Sinh[(4*a)/b] + Cosh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c + d*x])] + 2*Cosh[(4*a)/b]*SinhIntegral[4*(a/b + ArcCosh[c + d*x])]))/(2*b^3*d)","A",1
144,1,223,252,0.6915338,"\int \frac{(c e+d e x)^2}{\left(a+b \cosh ^{-1}(c+d x)\right)^3} \, dx","Integrate[(c*e + d*e*x)^2/(a + b*ArcCosh[c + d*x])^3,x]","\frac{e^2 \left(-\frac{4 b^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{\left(a+b \cosh ^{-1}(c+d x)\right)^2}+9 \left(\sinh \left(\frac{a}{b}\right) \left(-\text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)\right)+8 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-8 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\frac{4 b \left(2 (c+d x)-3 (c+d x)^3\right)}{a+b \cosh ^{-1}(c+d x)}\right)}{8 b^3 d}","-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{8 b^3 d}-\frac{9 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{8 b^3 d}+\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{8 b^3 d}+\frac{9 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{8 b^3 d}-\frac{3 e^2 (c+d x)^3}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{e^2 (c+d x)}{b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{2 b d \left(a+b \cosh ^{-1}(c+d x)\right)^2}",1,"(e^2*((-4*b^2*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])/(a + b*ArcCosh[c + d*x])^2 + (4*b*(2*(c + d*x) - 3*(c + d*x)^3))/(a + b*ArcCosh[c + d*x]) + 8*CoshIntegral[a/b + ArcCosh[c + d*x]]*Sinh[a/b] - 8*Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]] + 9*(-(CoshIntegral[a/b + ArcCosh[c + d*x]]*Sinh[a/b]) - CoshIntegral[3*(a/b + ArcCosh[c + d*x])]*Sinh[(3*a)/b] + Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]] + Cosh[(3*a)/b]*SinhIntegral[3*(a/b + ArcCosh[c + d*x])])))/(8*b^3*d)","A",1
145,1,127,163,0.3260799,"\int \frac{c e+d e x}{\left(a+b \cosh ^{-1}(c+d x)\right)^3} \, dx","Integrate[(c*e + d*e*x)/(a + b*ArcCosh[c + d*x])^3,x]","\frac{e \left(-\frac{b^2 \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1}}{\left(a+b \cosh ^{-1}(c+d x)\right)^2}-2 \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+2 \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+\frac{b \left(1-2 (c+d x)^2\right)}{a+b \cosh ^{-1}(c+d x)}\right)}{2 b^3 d}","-\frac{e \sinh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{b^3 d}+\frac{e \cosh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{b^3 d}-\frac{e (c+d x)^2}{b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{e}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{2 b d \left(a+b \cosh ^{-1}(c+d x)\right)^2}",1,"(e*(-((b^2*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(a + b*ArcCosh[c + d*x])^2) + (b*(1 - 2*(c + d*x)^2))/(a + b*ArcCosh[c + d*x]) - 2*CoshIntegral[2*(a/b + ArcCosh[c + d*x])]*Sinh[(2*a)/b] + 2*Cosh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c + d*x])]))/(2*b^3*d)","A",1
146,1,109,132,0.4199967,"\int \frac{1}{\left(a+b \cosh ^{-1}(c+d x)\right)^3} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^(-3),x]","-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\frac{b \left(a c+a d x+b \sqrt{c+d x-1} \sqrt{c+d x+1}+b (c+d x) \cosh ^{-1}(c+d x)\right)}{\left(a+b \cosh ^{-1}(c+d x)\right)^2}}{2 b^3 d}","-\frac{\sinh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{2 b^3 d}+\frac{\cosh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{2 b^3 d}-\frac{c+d x}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{\sqrt{c+d x-1} \sqrt{c+d x+1}}{2 b d \left(a+b \cosh ^{-1}(c+d x)\right)^2}",1,"-1/2*((b*(a*c + a*d*x + b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x] + b*(c + d*x)*ArcCosh[c + d*x]))/(a + b*ArcCosh[c + d*x])^2 + CoshIntegral[a/b + ArcCosh[c + d*x]]*Sinh[a/b] - Cosh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]])/(b^3*d)","A",1
147,0,0,27,1.7440521,"\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^3} \, dx","Integrate[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^3),x]","\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^3} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^3},x\right)}{e}",0,"Integrate[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^3), x]","A",-1
148,1,424,431,2.0132505,"\int \frac{(c e+d e x)^4}{\left(a+b \cosh ^{-1}(c+d x)\right)^4} \, dx","Integrate[(c*e + d*e*x)^4/(a + b*ArcCosh[c + d*x])^4,x]","\frac{e^4 \left(-\frac{32 b^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{\left(a+b \cosh ^{-1}(c+d x)\right)^3}+\frac{16 b^2 \left(4 (c+d x)^3-5 (c+d x)^5\right)}{\left(a+b \cosh ^{-1}(c+d x)\right)^2}+384 \left(\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-544 \left(3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-\sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)\right)+125 \left(10 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+5 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+\cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(5 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-10 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-5 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(5 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)\right)-\frac{16 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(25 (c+d x)^4-12 (c+d x)^2\right)}{a+b \cosh ^{-1}(c+d x)}\right)}{96 b^4 d}","\frac{e^4 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{48 b^4 d}+\frac{27 e^4 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{32 b^4 d}+\frac{125 e^4 \cosh \left(\frac{5 a}{b}\right) \text{Chi}\left(\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{96 b^4 d}-\frac{e^4 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{48 b^4 d}-\frac{27 e^4 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{32 b^4 d}-\frac{125 e^4 \sinh \left(\frac{5 a}{b}\right) \text{Shi}\left(\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{96 b^4 d}-\frac{25 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{6 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{2 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{5 e^4 (c+d x)^5}{6 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}+\frac{2 e^4 (c+d x)^3}{3 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^3}",1,"(e^4*((-32*b^3*Sqrt[-1 + c + d*x]*(c + d*x)^4*Sqrt[1 + c + d*x])/(a + b*ArcCosh[c + d*x])^3 + (16*b^2*(4*(c + d*x)^3 - 5*(c + d*x)^5))/(a + b*ArcCosh[c + d*x])^2 - (16*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(-12*(c + d*x)^2 + 25*(c + d*x)^4))/(a + b*ArcCosh[c + d*x]) + 384*(Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c + d*x]] - Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]]) - 544*(3*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c + d*x]] + Cosh[(3*a)/b]*CoshIntegral[3*(a/b + ArcCosh[c + d*x])] - 3*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]] - Sinh[(3*a)/b]*SinhIntegral[3*(a/b + ArcCosh[c + d*x])]) + 125*(10*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c + d*x]] + 5*Cosh[(3*a)/b]*CoshIntegral[3*(a/b + ArcCosh[c + d*x])] + Cosh[(5*a)/b]*CoshIntegral[5*(a/b + ArcCosh[c + d*x])] - 10*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]] - 5*Sinh[(3*a)/b]*SinhIntegral[3*(a/b + ArcCosh[c + d*x])] - Sinh[(5*a)/b]*SinhIntegral[5*(a/b + ArcCosh[c + d*x])])))/(96*b^4*d)","A",1
149,1,330,360,1.3040727,"\int \frac{(c e+d e x)^3}{\left(a+b \cosh ^{-1}(c+d x)\right)^4} \, dx","Integrate[(c*e + d*e*x)^3/(a + b*ArcCosh[c + d*x])^4,x]","\frac{e^3 \left(-\frac{2 b^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{\left(a+b \cosh ^{-1}(c+d x)\right)^3}+\frac{b^2 \left(3 (c+d x)^2-4 (c+d x)^4\right)}{\left(a+b \cosh ^{-1}(c+d x)\right)^2}-30 \left(\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+\log \left(a+b \cosh ^{-1}(c+d x)\right)\right)+8 \left(4 \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+\cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(4 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-4 \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(4 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+3 \log \left(a+b \cosh ^{-1}(c+d x)\right)\right)-\frac{2 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(8 (c+d x)^3-3 (c+d x)\right)}{a+b \cosh ^{-1}(c+d x)}+6 \log \left(a+b \cosh ^{-1}(c+d x)\right)\right)}{6 b^4 d}","\frac{e^3 \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}+\frac{4 e^3 \cosh \left(\frac{4 a}{b}\right) \text{Chi}\left(\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}-\frac{e^3 \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}-\frac{4 e^3 \sinh \left(\frac{4 a}{b}\right) \text{Shi}\left(\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}-\frac{8 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{3 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{2 e^3 (c+d x)^4}{3 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}+\frac{e^3 (c+d x)^2}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^3}",1,"(e^3*((-2*b^3*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x])/(a + b*ArcCosh[c + d*x])^3 + (b^2*(3*(c + d*x)^2 - 4*(c + d*x)^4))/(a + b*ArcCosh[c + d*x])^2 - (2*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(-3*(c + d*x) + 8*(c + d*x)^3))/(a + b*ArcCosh[c + d*x]) + 6*Log[a + b*ArcCosh[c + d*x]] - 30*(Cosh[(2*a)/b]*CoshIntegral[2*(a/b + ArcCosh[c + d*x])] + Log[a + b*ArcCosh[c + d*x]] - Sinh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c + d*x])]) + 8*(4*Cosh[(2*a)/b]*CoshIntegral[2*(a/b + ArcCosh[c + d*x])] + Cosh[(4*a)/b]*CoshIntegral[4*(a/b + ArcCosh[c + d*x])] + 3*Log[a + b*ArcCosh[c + d*x]] - 4*Sinh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c + d*x])] - Sinh[(4*a)/b]*SinhIntegral[4*(a/b + ArcCosh[c + d*x])])))/(6*b^4*d)","A",1
150,1,272,352,1.3256106,"\int \frac{(c e+d e x)^2}{\left(a+b \cosh ^{-1}(c+d x)\right)^4} \, dx","Integrate[(c*e + d*e*x)^2/(a + b*ArcCosh[c + d*x])^4,x]","\frac{e^2 \left(-\frac{8 b^3 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1}}{\left(a+b \cosh ^{-1}(c+d x)\right)^3}+\frac{4 b^2 \left(2 (c+d x)-3 (c+d x)^3\right)}{\left(a+b \cosh ^{-1}(c+d x)\right)^2}+27 \left(3 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-3 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-\sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)\right)-80 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+80 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(9 (c+d x)^2-2\right)}{a+b \cosh ^{-1}(c+d x)}\right)}{24 b^4 d}","\frac{e^2 \cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{24 b^4 d}+\frac{9 e^2 \cosh \left(\frac{3 a}{b}\right) \text{Chi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{8 b^4 d}-\frac{e^2 \sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{24 b^4 d}-\frac{9 e^2 \sinh \left(\frac{3 a}{b}\right) \text{Shi}\left(\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{8 b^4 d}-\frac{3 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{2 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}+\frac{e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{3 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e^2 (c+d x)^3}{2 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}+\frac{e^2 (c+d x)}{3 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^3}",1,"(e^2*((-8*b^3*Sqrt[-1 + c + d*x]*(c + d*x)^2*Sqrt[1 + c + d*x])/(a + b*ArcCosh[c + d*x])^3 + (4*b^2*(2*(c + d*x) - 3*(c + d*x)^3))/(a + b*ArcCosh[c + d*x])^2 - (4*b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]*(-2 + 9*(c + d*x)^2))/(a + b*ArcCosh[c + d*x]) - 80*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c + d*x]] + 80*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]] + 27*(3*Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c + d*x]] + Cosh[(3*a)/b]*CoshIntegral[3*(a/b + ArcCosh[c + d*x])] - 3*Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]] - Sinh[(3*a)/b]*SinhIntegral[3*(a/b + ArcCosh[c + d*x])])))/(24*b^4*d)","A",1
151,1,195,218,1.0324389,"\int \frac{c e+d e x}{\left(a+b \cosh ^{-1}(c+d x)\right)^4} \, dx","Integrate[(c*e + d*e*x)/(a + b*ArcCosh[c + d*x])^4,x]","\frac{e \left(-\frac{2 b^3 \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1}}{\left(a+b \cosh ^{-1}(c+d x)\right)^3}+\frac{b^2 \left(1-2 (c+d x)^2\right)}{\left(a+b \cosh ^{-1}(c+d x)\right)^2}+4 \left(\cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)-\sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(2 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right)+\log \left(a+b \cosh ^{-1}(c+d x)\right)\right)-\frac{4 b \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1}}{a+b \cosh ^{-1}(c+d x)}-4 \log \left(a+b \cosh ^{-1}(c+d x)\right)\right)}{6 b^4 d}","\frac{2 e \cosh \left(\frac{2 a}{b}\right) \text{Chi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}-\frac{2 e \sinh \left(\frac{2 a}{b}\right) \text{Shi}\left(\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)}{3 b^4 d}-\frac{2 e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{3 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{e (c+d x)^2}{3 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}+\frac{e}{6 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^3}",1,"(e*((-2*b^3*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(a + b*ArcCosh[c + d*x])^3 + (b^2*(1 - 2*(c + d*x)^2))/(a + b*ArcCosh[c + d*x])^2 - (4*b*Sqrt[-1 + c + d*x]*(c + d*x)*Sqrt[1 + c + d*x])/(a + b*ArcCosh[c + d*x]) - 4*Log[a + b*ArcCosh[c + d*x]] + 4*(Cosh[(2*a)/b]*CoshIntegral[2*(a/b + ArcCosh[c + d*x])] + Log[a + b*ArcCosh[c + d*x]] - Sinh[(2*a)/b]*SinhIntegral[2*(a/b + ArcCosh[c + d*x])])))/(6*b^4*d)","A",1
152,1,144,174,0.6728808,"\int \frac{1}{\left(a+b \cosh ^{-1}(c+d x)\right)^4} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^(-4),x]","-\frac{\frac{2 b^3 \sqrt{c+d x-1} \sqrt{c+d x+1}}{\left(a+b \cosh ^{-1}(c+d x)\right)^3}+\frac{b^2 (c+d x)}{\left(a+b \cosh ^{-1}(c+d x)\right)^2}-\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\frac{b \sqrt{c+d x-1} \sqrt{c+d x+1}}{a+b \cosh ^{-1}(c+d x)}}{6 b^4 d}","\frac{\cosh \left(\frac{a}{b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{6 b^4 d}-\frac{\sinh \left(\frac{a}{b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{6 b^4 d}-\frac{\sqrt{c+d x-1} \sqrt{c+d x+1}}{6 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)}-\frac{c+d x}{6 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^2}-\frac{\sqrt{c+d x-1} \sqrt{c+d x+1}}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^3}",1,"-1/6*((2*b^3*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(a + b*ArcCosh[c + d*x])^3 + (b^2*(c + d*x))/(a + b*ArcCosh[c + d*x])^2 + (b*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])/(a + b*ArcCosh[c + d*x]) - Cosh[a/b]*CoshIntegral[a/b + ArcCosh[c + d*x]] + Sinh[a/b]*SinhIntegral[a/b + ArcCosh[c + d*x]])/(b^4*d)","A",1
153,0,0,27,14.5540406,"\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^4} \, dx","Integrate[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^4),x]","\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^4} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^4},x\right)}{e}",0,"Integrate[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^4), x]","A",-1
154,1,342,361,0.7403129,"\int (c e+d e x)^4 \sqrt{a+b \cosh ^{-1}(c+d x)} \, dx","Integrate[(c*e + d*e*x)^4*Sqrt[a + b*ArcCosh[c + d*x]],x]","\frac{e^4 e^{-\frac{5 a}{b}} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(150 e^{\frac{6 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+3 \sqrt{5} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+25 \sqrt{3} e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+150 e^{\frac{4 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)+25 \sqrt{3} e^{\frac{8 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{3}{2},\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+3 \sqrt{5} e^{\frac{10 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{3}{2},\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)\right)}{2400 d \sqrt{-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{b^2}}}","-\frac{\sqrt{\pi } \sqrt{b} e^4 e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^4 e^{\frac{3 a}{b}} \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{\sqrt{\frac{\pi }{5}} \sqrt{b} e^4 e^{\frac{5 a}{b}} \text{erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{320 d}-\frac{\sqrt{\pi } \sqrt{b} e^4 e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^4 e^{-\frac{3 a}{b}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{\sqrt{\frac{\pi }{5}} \sqrt{b} e^4 e^{-\frac{5 a}{b}} \text{erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{320 d}+\frac{e^4 (c+d x)^5 \sqrt{a+b \cosh ^{-1}(c+d x)}}{5 d}",1,"(e^4*Sqrt[a + b*ArcCosh[c + d*x]]*(150*E^((6*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[3/2, a/b + ArcCosh[c + d*x]] + 3*Sqrt[5]*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, (-5*(a + b*ArcCosh[c + d*x]))/b] + 25*Sqrt[3]*E^((2*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, (-3*(a + b*ArcCosh[c + d*x]))/b] + 150*E^((4*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, -((a + b*ArcCosh[c + d*x])/b)] + 25*Sqrt[3]*E^((8*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[3/2, (3*(a + b*ArcCosh[c + d*x]))/b] + 3*Sqrt[5]*E^((10*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[3/2, (5*(a + b*ArcCosh[c + d*x]))/b]))/(2400*d*E^((5*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])^2/b^2)])","A",0
155,1,223,272,0.5359525,"\int (c e+d e x)^3 \sqrt{a+b \cosh ^{-1}(c+d x)} \, dx","Integrate[(c*e + d*e*x)^3*Sqrt[a + b*ArcCosh[c + d*x]],x]","\frac{e^3 e^{-\frac{4 a}{b}} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(\sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+4 \sqrt{2} e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+e^{\frac{6 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \left(4 \sqrt{2} \Gamma \left(\frac{3}{2},\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+e^{\frac{2 a}{b}} \Gamma \left(\frac{3}{2},\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)\right)\right)}{128 d \sqrt{-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{b^2}}}","-\frac{\sqrt{\pi } \sqrt{b} e^3 e^{\frac{4 a}{b}} \text{erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^3 e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{\sqrt{\pi } \sqrt{b} e^3 e^{-\frac{4 a}{b}} \text{erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^3 e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{e^3 (c+d x)^4 \sqrt{a+b \cosh ^{-1}(c+d x)}}{4 d}-\frac{3 e^3 \sqrt{a+b \cosh ^{-1}(c+d x)}}{32 d}",1,"(e^3*Sqrt[a + b*ArcCosh[c + d*x]]*(Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, (-4*(a + b*ArcCosh[c + d*x]))/b] + 4*Sqrt[2]*E^((2*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, (-2*(a + b*ArcCosh[c + d*x]))/b] + E^((6*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*(4*Sqrt[2]*Gamma[3/2, (2*(a + b*ArcCosh[c + d*x]))/b] + E^((2*a)/b)*Gamma[3/2, (4*(a + b*ArcCosh[c + d*x]))/b])))/(128*d*E^((4*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])^2/b^2)])","A",0
156,1,237,245,0.5109144,"\int (c e+d e x)^2 \sqrt{a+b \cosh ^{-1}(c+d x)} \, dx","Integrate[(c*e + d*e*x)^2*Sqrt[a + b*ArcCosh[c + d*x]],x]","\frac{e^2 e^{-\frac{3 a}{b}} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(9 e^{\frac{4 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\sqrt{3} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+9 e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)+\sqrt{3} e^{\frac{6 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{3}{2},\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)\right)}{72 d \sqrt{-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{b^2}}}","-\frac{\sqrt{\pi } \sqrt{b} e^2 e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^2 e^{\frac{3 a}{b}} \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{48 d}-\frac{\sqrt{\pi } \sqrt{b} e^2 e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{b} e^2 e^{-\frac{3 a}{b}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{48 d}+\frac{e^2 (c+d x)^3 \sqrt{a+b \cosh ^{-1}(c+d x)}}{3 d}",1,"(e^2*Sqrt[a + b*ArcCosh[c + d*x]]*(9*E^((4*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[3/2, a/b + ArcCosh[c + d*x]] + Sqrt[3]*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, (-3*(a + b*ArcCosh[c + d*x]))/b] + 9*E^((2*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, -((a + b*ArcCosh[c + d*x])/b)] + Sqrt[3]*E^((6*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[3/2, (3*(a + b*ArcCosh[c + d*x]))/b]))/(72*d*E^((3*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])^2/b^2)])","A",0
157,1,437,164,2.5165762,"\int (c e+d e x) \sqrt{a+b \cosh ^{-1}(c+d x)} \, dx","Integrate[(c*e + d*e*x)*Sqrt[a + b*ArcCosh[c + d*x]],x]","\frac{e \left(8 \sqrt{\pi } \sqrt{b} c \left(\sinh \left(\frac{a}{b}\right)+\cosh \left(\frac{a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-\sqrt{2 \pi } \sqrt{b} \left(\sinh \left(\frac{2 a}{b}\right)+\cosh \left(\frac{2 a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+8 \sqrt{\pi } \sqrt{b} c \cosh \left(\frac{a}{b}\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-\sqrt{2 \pi } \sqrt{b} \cosh \left(\frac{2 a}{b}\right) \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-8 \sqrt{\pi } \sqrt{b} c \sinh \left(\frac{a}{b}\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+\sqrt{2 \pi } \sqrt{b} \sinh \left(\frac{2 a}{b}\right) \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-32 c (c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}+8 \cosh \left(2 \cosh ^{-1}(c+d x)\right) \sqrt{a+b \cosh ^{-1}(c+d x)}+16 c e^{-\frac{a}{b}} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(\frac{e^{\frac{2 a}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{\sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)}}+\frac{\Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{\sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}}}\right)\right)}{32 d}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}+\frac{e (c+d x)^2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{2 d}-\frac{e \sqrt{a+b \cosh ^{-1}(c+d x)}}{4 d}",1,"(e*(-32*c*(c + d*x)*Sqrt[a + b*ArcCosh[c + d*x]] + 8*Sqrt[a + b*ArcCosh[c + d*x]]*Cosh[2*ArcCosh[c + d*x]] + 8*Sqrt[b]*c*Sqrt[Pi]*Cosh[a/b]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]] - Sqrt[b]*Sqrt[2*Pi]*Cosh[(2*a)/b]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]] + (16*c*Sqrt[a + b*ArcCosh[c + d*x]]*((E^((2*a)/b)*Gamma[3/2, a/b + ArcCosh[c + d*x]])/Sqrt[a/b + ArcCosh[c + d*x]] + Gamma[3/2, -((a + b*ArcCosh[c + d*x])/b)]/Sqrt[-((a + b*ArcCosh[c + d*x])/b)]))/E^(a/b) - 8*Sqrt[b]*c*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*Sinh[a/b] + 8*Sqrt[b]*c*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b]) + Sqrt[b]*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*Sinh[(2*a)/b] - Sqrt[b]*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b])))/(32*d)","B",0
158,1,110,115,0.2254874,"\int \sqrt{a+b \cosh ^{-1}(c+d x)} \, dx","Integrate[Sqrt[a + b*ArcCosh[c + d*x]],x]","\frac{e^{-\frac{a}{b}} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(\frac{e^{\frac{2 a}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{\sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)}}+\frac{\Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{\sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}}}\right)}{2 d}","-\frac{\sqrt{\pi } \sqrt{b} e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}-\frac{\sqrt{\pi } \sqrt{b} e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 d}+\frac{(c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}}{d}",1,"(Sqrt[a + b*ArcCosh[c + d*x]]*((E^((2*a)/b)*Gamma[3/2, a/b + ArcCosh[c + d*x]])/Sqrt[a/b + ArcCosh[c + d*x]] + Gamma[3/2, -((a + b*ArcCosh[c + d*x])/b)]/Sqrt[-((a + b*ArcCosh[c + d*x])/b)]))/(2*d*E^(a/b))","A",0
159,0,0,29,2.2677784,"\int \frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{c e+d e x} \, dx","Integrate[Sqrt[a + b*ArcCosh[c + d*x]]/(c*e + d*e*x),x]","\int \frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{c e+d e x} \, dx","\frac{\text{Int}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{c+d x},x\right)}{e}",0,"Integrate[Sqrt[a + b*ArcCosh[c + d*x]]/(c*e + d*e*x), x]","A",-1
160,1,558,374,3.9532544,"\int (c e+d e x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2} \, dx","Integrate[(c*e + d*e*x)^3*(a + b*ArcCosh[c + d*x])^(3/2),x]","e^3 \left(\frac{a e^{-\frac{4 a}{b}} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(\sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+4 \sqrt{2} e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+e^{\frac{6 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \left(4 \sqrt{2} \Gamma \left(\frac{3}{2},\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+e^{\frac{2 a}{b}} \Gamma \left(\frac{3}{2},\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)\right)\right)}{128 d \sqrt{-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{b^2}}}+\frac{\sqrt{b} \left(8 \left(\sqrt{2 \pi } (4 a-3 b) \left(\sinh \left(\frac{2 a}{b}\right)+\cosh \left(\frac{2 a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+\sqrt{2 \pi } (4 a+3 b) \left(\cosh \left(\frac{2 a}{b}\right)-\sinh \left(\frac{2 a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+8 \sqrt{b} \left(4 \cosh ^{-1}(c+d x) \cosh \left(2 \cosh ^{-1}(c+d x)\right)-3 \sinh \left(2 \cosh ^{-1}(c+d x)\right)\right) \sqrt{a+b \cosh ^{-1}(c+d x)}\right)+\sqrt{\pi } (8 a-3 b) \left(\sinh \left(\frac{4 a}{b}\right)+\cosh \left(\frac{4 a}{b}\right)\right) \text{erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+\sqrt{\pi } (8 a+3 b) \left(\cosh \left(\frac{4 a}{b}\right)-\sinh \left(\frac{4 a}{b}\right)\right) \text{erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+8 \sqrt{b} \left(8 \cosh ^{-1}(c+d x) \cosh \left(4 \cosh ^{-1}(c+d x)\right)-3 \sinh \left(4 \cosh ^{-1}(c+d x)\right)\right) \sqrt{a+b \cosh ^{-1}(c+d x)}\right)}{2048 d}\right)","-\frac{3 \sqrt{\pi } b^{3/2} e^3 e^{\frac{4 a}{b}} \text{erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2048 d}-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^3 e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{3 \sqrt{\pi } b^{3/2} e^3 e^{-\frac{4 a}{b}} \text{erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2048 d}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e^3 e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{4 d}-\frac{3 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3 \sqrt{a+b \cosh ^{-1}(c+d x)}}{32 d}-\frac{9 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}}{64 d}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{32 d}",1,"e^3*((a*Sqrt[a + b*ArcCosh[c + d*x]]*(Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, (-4*(a + b*ArcCosh[c + d*x]))/b] + 4*Sqrt[2]*E^((2*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, (-2*(a + b*ArcCosh[c + d*x]))/b] + E^((6*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*(4*Sqrt[2]*Gamma[3/2, (2*(a + b*ArcCosh[c + d*x]))/b] + E^((2*a)/b)*Gamma[3/2, (4*(a + b*ArcCosh[c + d*x]))/b])))/(128*d*E^((4*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])^2/b^2)]) + (Sqrt[b]*((8*a + 3*b)*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(4*a)/b] - Sinh[(4*a)/b]) + (8*a - 3*b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(4*a)/b] + Sinh[(4*a)/b]) + 8*((4*a + 3*b)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] - Sinh[(2*a)/b]) + (4*a - 3*b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b]) + 8*Sqrt[b]*Sqrt[a + b*ArcCosh[c + d*x]]*(4*ArcCosh[c + d*x]*Cosh[2*ArcCosh[c + d*x]] - 3*Sinh[2*ArcCosh[c + d*x]])) + 8*Sqrt[b]*Sqrt[a + b*ArcCosh[c + d*x]]*(8*ArcCosh[c + d*x]*Cosh[4*ArcCosh[c + d*x]] - 3*Sinh[4*ArcCosh[c + d*x]])))/(2048*d))","A",0
161,1,592,342,2.5090778,"\int (c e+d e x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2} \, dx","Integrate[(c*e + d*e*x)^2*(a + b*ArcCosh[c + d*x])^(3/2),x]","e^2 \left(\frac{a e^{-\frac{3 a}{b}} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(9 e^{\frac{4 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\sqrt{3} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+9 e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)+\sqrt{3} e^{\frac{6 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{3}{2},\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)\right)}{72 d \sqrt{-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{b^2}}}+\frac{\sqrt{b} \left(9 \left(\sqrt{\pi } (2 a-3 b) \left(\sinh \left(\frac{a}{b}\right)+\cosh \left(\frac{a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+\sqrt{\pi } (2 a+3 b) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-12 \sqrt{b} \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \sqrt{a+b \cosh ^{-1}(c+d x)}+8 \sqrt{b} (c+d x) \cosh ^{-1}(c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}\right)+\sqrt{3 \pi } (2 a-b) \left(\sinh \left(\frac{3 a}{b}\right)+\cosh \left(\frac{3 a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+\sqrt{3 \pi } (2 a+b) \left(\cosh \left(\frac{3 a}{b}\right)-\sinh \left(\frac{3 a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+12 \sqrt{b} \left(2 \cosh ^{-1}(c+d x) \cosh \left(3 \cosh ^{-1}(c+d x)\right)-\sinh \left(3 \cosh ^{-1}(c+d x)\right)\right) \sqrt{a+b \cosh ^{-1}(c+d x)}\right)}{288 d}\right)","-\frac{3 \sqrt{\pi } b^{3/2} e^2 e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^2 e^{\frac{3 a}{b}} \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{96 d}+\frac{3 \sqrt{\pi } b^{3/2} e^2 e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{\sqrt{\frac{\pi }{3}} b^{3/2} e^2 e^{-\frac{3 a}{b}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{96 d}+\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{3 d}-\frac{b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{6 d}-\frac{b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{3 d}",1,"e^2*((a*Sqrt[a + b*ArcCosh[c + d*x]]*(9*E^((4*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[3/2, a/b + ArcCosh[c + d*x]] + Sqrt[3]*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, (-3*(a + b*ArcCosh[c + d*x]))/b] + 9*E^((2*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, -((a + b*ArcCosh[c + d*x])/b)] + Sqrt[3]*E^((6*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[3/2, (3*(a + b*ArcCosh[c + d*x]))/b]))/(72*d*E^((3*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])^2/b^2)]) + (Sqrt[b]*(9*(-12*Sqrt[b]*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*Sqrt[a + b*ArcCosh[c + d*x]] + 8*Sqrt[b]*(c + d*x)*ArcCosh[c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]] + (2*a + 3*b)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) + (2*a - 3*b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b])) + (2*a + b)*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(3*a)/b] - Sinh[(3*a)/b]) + (2*a - b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(3*a)/b] + Sinh[(3*a)/b]) + 12*Sqrt[b]*Sqrt[a + b*ArcCosh[c + d*x]]*(2*ArcCosh[c + d*x]*Cosh[3*ArcCosh[c + d*x]] - Sinh[3*ArcCosh[c + d*x]])))/(288*d))","A",0
162,1,1144,212,7.9401854,"\int (c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2} \, dx","Integrate[(c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^(3/2),x]","e \left(\frac{a c e^{-\frac{a}{b}} \sqrt{c+d x-1} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(\frac{e^{\frac{2 a}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{\sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)}}+\frac{\Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{\sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}}}\right)}{2 d \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{c+d x+1}}+\frac{b c \sqrt{c+d x-1} \left(-12 \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{a+b \cosh ^{-1}(c+d x)} (c+d x+1)+\frac{(2 a+3 b) \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right)}{\sqrt{b}}+\frac{(2 a-3 b) \sqrt{\pi } \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)+\sinh \left(\frac{a}{b}\right)\right)}{\sqrt{b}}+8 (c+d x) \cosh ^{-1}(c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}\right)}{8 d \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{c+d x+1}}+\frac{a \sqrt{c+d x-1} \left(-32 c \sqrt{a+b \cosh ^{-1}(c+d x)} (c+d x)+8 \sqrt{a+b \cosh ^{-1}(c+d x)} \cosh \left(2 \cosh ^{-1}(c+d x)\right)+8 \sqrt{b} c \sqrt{\pi } \cosh \left(\frac{a}{b}\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-\sqrt{b} \sqrt{2 \pi } \cosh \left(\frac{2 a}{b}\right) \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-8 \sqrt{b} c \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \sinh \left(\frac{a}{b}\right)+8 \sqrt{b} c \sqrt{\pi } \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)+\sinh \left(\frac{a}{b}\right)\right)+\sqrt{b} \sqrt{2 \pi } \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \sinh \left(\frac{2 a}{b}\right)-\sqrt{b} \sqrt{2 \pi } \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{2 a}{b}\right)+\sinh \left(\frac{2 a}{b}\right)\right)\right)}{32 d \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{c+d x+1}}+\frac{\sqrt{c+d x-1} \left(-16 c \left(-12 b \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{a+b \cosh ^{-1}(c+d x)} (c+d x+1)+\sqrt{b} (2 a+3 b) \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right)+(2 a-3 b) \sqrt{b} \sqrt{\pi } \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)+\sinh \left(\frac{a}{b}\right)\right)+8 b (c+d x) \cosh ^{-1}(c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}\right)+\sqrt{b} (4 a+3 b) \sqrt{2 \pi } \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{2 a}{b}\right)-\sinh \left(\frac{2 a}{b}\right)\right)+(4 a-3 b) \sqrt{b} \sqrt{2 \pi } \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{2 a}{b}\right)+\sinh \left(\frac{2 a}{b}\right)\right)+8 b \sqrt{a+b \cosh ^{-1}(c+d x)} \left(4 \cosh ^{-1}(c+d x) \cosh \left(2 \cosh ^{-1}(c+d x)\right)-3 \sinh \left(2 \cosh ^{-1}(c+d x)\right)\right)\right)}{128 d \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{c+d x+1}}\right)","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} e e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}+\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{2 d}-\frac{3 b e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}}{8 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{4 d}",1,"e*((a*c*Sqrt[-1 + c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]]*((E^((2*a)/b)*Gamma[3/2, a/b + ArcCosh[c + d*x]])/Sqrt[a/b + ArcCosh[c + d*x]] + Gamma[3/2, -((a + b*ArcCosh[c + d*x])/b)]/Sqrt[-((a + b*ArcCosh[c + d*x])/b)]))/(2*d*E^(a/b)*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*Sqrt[1 + c + d*x]) + (b*c*Sqrt[-1 + c + d*x]*(-12*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*Sqrt[a + b*ArcCosh[c + d*x]] + 8*(c + d*x)*ArcCosh[c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]] + ((2*a + 3*b)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]))/Sqrt[b] + ((2*a - 3*b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b]))/Sqrt[b]))/(8*d*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*Sqrt[1 + c + d*x]) + (a*Sqrt[-1 + c + d*x]*(-32*c*(c + d*x)*Sqrt[a + b*ArcCosh[c + d*x]] + 8*Sqrt[a + b*ArcCosh[c + d*x]]*Cosh[2*ArcCosh[c + d*x]] + 8*Sqrt[b]*c*Sqrt[Pi]*Cosh[a/b]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]] - Sqrt[b]*Sqrt[2*Pi]*Cosh[(2*a)/b]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]] - 8*Sqrt[b]*c*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*Sinh[a/b] + 8*Sqrt[b]*c*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b]) + Sqrt[b]*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*Sinh[(2*a)/b] - Sqrt[b]*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b])))/(32*d*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*Sqrt[1 + c + d*x]) + (Sqrt[-1 + c + d*x]*(-16*c*(-12*b*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*Sqrt[a + b*ArcCosh[c + d*x]] + 8*b*(c + d*x)*ArcCosh[c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]] + Sqrt[b]*(2*a + 3*b)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) + (2*a - 3*b)*Sqrt[b]*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b])) + Sqrt[b]*(4*a + 3*b)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] - Sinh[(2*a)/b]) + (4*a - 3*b)*Sqrt[b]*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b]) + 8*b*Sqrt[a + b*ArcCosh[c + d*x]]*(4*ArcCosh[c + d*x]*Cosh[2*ArcCosh[c + d*x]] - 3*Sinh[2*ArcCosh[c + d*x]])))/(128*d*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*Sqrt[1 + c + d*x]))","B",0
163,1,290,157,0.7597189,"\int \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^(3/2),x]","\frac{\sqrt{\pi } \sqrt{b} (2 a-3 b) \left(\sinh \left(\frac{a}{b}\right)+\cosh \left(\frac{a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+\sqrt{\pi } \sqrt{b} (2 a+3 b) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-12 b \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \sqrt{a+b \cosh ^{-1}(c+d x)}+8 b (c+d x) \cosh ^{-1}(c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}+4 a e^{-\frac{a}{b}} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(\frac{e^{\frac{2 a}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{\sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)}}+\frac{\Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{\sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}}}\right)}{8 d}","-\frac{3 \sqrt{\pi } b^{3/2} e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}+\frac{3 \sqrt{\pi } b^{3/2} e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 d}-\frac{3 b \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{2 d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{d}",1,"(-12*b*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*Sqrt[a + b*ArcCosh[c + d*x]] + 8*b*(c + d*x)*ArcCosh[c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]] + (4*a*Sqrt[a + b*ArcCosh[c + d*x]]*((E^((2*a)/b)*Gamma[3/2, a/b + ArcCosh[c + d*x]])/Sqrt[a/b + ArcCosh[c + d*x]] + Gamma[3/2, -((a + b*ArcCosh[c + d*x])/b)]/Sqrt[-((a + b*ArcCosh[c + d*x])/b)]))/E^(a/b) + Sqrt[b]*(2*a + 3*b)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) + (2*a - 3*b)*Sqrt[b]*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b]))/(8*d)","A",0
164,0,0,29,1.553429,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{c e+d e x} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^(3/2)/(c*e + d*e*x),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{c e+d e x} \, dx","\frac{\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{c+d x},x\right)}{e}",0,"Integrate[(a + b*ArcCosh[c + d*x])^(3/2)/(c*e + d*e*x), x]","A",-1
165,1,968,469,11.2186515,"\int (c e+d e x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2} \, dx","Integrate[(c*e + d*e*x)^3*(a + b*ArcCosh[c + d*x])^(5/2),x]","e^3 \left(\frac{e^{-\frac{4 a}{b}} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(\sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+4 \sqrt{2} e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+e^{\frac{6 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \left(4 \sqrt{2} \Gamma \left(\frac{3}{2},\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+e^{\frac{2 a}{b}} \Gamma \left(\frac{3}{2},\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)\right)\right) a^2}{128 d \sqrt{-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{b^2}}}+\frac{\sqrt{b} \left((8 a+3 b) \sqrt{\pi } \text{erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{4 a}{b}\right)-\sinh \left(\frac{4 a}{b}\right)\right)+(8 a-3 b) \sqrt{\pi } \text{erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{4 a}{b}\right)+\sinh \left(\frac{4 a}{b}\right)\right)+8 \left((4 a+3 b) \sqrt{2 \pi } \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{2 a}{b}\right)-\sinh \left(\frac{2 a}{b}\right)\right)+(4 a-3 b) \sqrt{2 \pi } \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{2 a}{b}\right)+\sinh \left(\frac{2 a}{b}\right)\right)+8 \sqrt{b} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(4 \cosh ^{-1}(c+d x) \cosh \left(2 \cosh ^{-1}(c+d x)\right)-3 \sinh \left(2 \cosh ^{-1}(c+d x)\right)\right)\right)+8 \sqrt{b} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(8 \cosh ^{-1}(c+d x) \cosh \left(4 \cosh ^{-1}(c+d x)\right)-3 \sinh \left(4 \cosh ^{-1}(c+d x)\right)\right)\right) a}{1024 d}+\frac{-\sqrt{b} \left(64 a^2+48 b a+15 b^2\right) \sqrt{\pi } \text{erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{4 a}{b}\right)-\sinh \left(\frac{4 a}{b}\right)\right)-\sqrt{b} \left(64 a^2-48 b a+15 b^2\right) \sqrt{\pi } \text{erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{4 a}{b}\right)+\sinh \left(\frac{4 a}{b}\right)\right)-16 \left(\sqrt{b} \left(16 a^2+24 b a+15 b^2\right) \sqrt{2 \pi } \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{2 a}{b}\right)-\sinh \left(\frac{2 a}{b}\right)\right)+\sqrt{b} \left(16 a^2-24 b a+15 b^2\right) \sqrt{2 \pi } \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{2 a}{b}\right)+\sinh \left(\frac{2 a}{b}\right)\right)-8 b \sqrt{a+b \cosh ^{-1}(c+d x)} \left(b \left(16 \cosh ^{-1}(c+d x)^2+15\right) \cosh \left(2 \cosh ^{-1}(c+d x)\right)+4 \left(a-5 b \cosh ^{-1}(c+d x)\right) \sinh \left(2 \cosh ^{-1}(c+d x)\right)\right)\right)+8 b \sqrt{a+b \cosh ^{-1}(c+d x)} \left(b \left(64 \cosh ^{-1}(c+d x)^2+15\right) \cosh \left(4 \cosh ^{-1}(c+d x)\right)+8 \left(a-5 b \cosh ^{-1}(c+d x)\right) \sinh \left(4 \cosh ^{-1}(c+d x)\right)\right)}{16384 d}\right)","-\frac{15 \sqrt{\pi } b^{5/2} e^3 e^{\frac{4 a}{b}} \text{erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16384 d}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^3 e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{512 d}-\frac{15 \sqrt{\pi } b^{5/2} e^3 e^{-\frac{4 a}{b}} \text{erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16384 d}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e^3 e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{512 d}+\frac{15 b^2 e^3 (c+d x)^4 \sqrt{a+b \cosh ^{-1}(c+d x)}}{256 d}+\frac{45 b^2 e^3 (c+d x)^2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{256 d}-\frac{225 b^2 e^3 \sqrt{a+b \cosh ^{-1}(c+d x)}}{2048 d}+\frac{e^3 (c+d x)^4 \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{4 d}-\frac{5 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{32 d}-\frac{15 b e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{64 d}-\frac{3 e^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{32 d}",1,"e^3*((a^2*Sqrt[a + b*ArcCosh[c + d*x]]*(Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, (-4*(a + b*ArcCosh[c + d*x]))/b] + 4*Sqrt[2]*E^((2*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, (-2*(a + b*ArcCosh[c + d*x]))/b] + E^((6*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*(4*Sqrt[2]*Gamma[3/2, (2*(a + b*ArcCosh[c + d*x]))/b] + E^((2*a)/b)*Gamma[3/2, (4*(a + b*ArcCosh[c + d*x]))/b])))/(128*d*E^((4*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])^2/b^2)]) + (a*Sqrt[b]*((8*a + 3*b)*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(4*a)/b] - Sinh[(4*a)/b]) + (8*a - 3*b)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(4*a)/b] + Sinh[(4*a)/b]) + 8*((4*a + 3*b)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] - Sinh[(2*a)/b]) + (4*a - 3*b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b]) + 8*Sqrt[b]*Sqrt[a + b*ArcCosh[c + d*x]]*(4*ArcCosh[c + d*x]*Cosh[2*ArcCosh[c + d*x]] - 3*Sinh[2*ArcCosh[c + d*x]])) + 8*Sqrt[b]*Sqrt[a + b*ArcCosh[c + d*x]]*(8*ArcCosh[c + d*x]*Cosh[4*ArcCosh[c + d*x]] - 3*Sinh[4*ArcCosh[c + d*x]])))/(1024*d) + (-(Sqrt[b]*(64*a^2 + 48*a*b + 15*b^2)*Sqrt[Pi]*Erfi[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(4*a)/b] - Sinh[(4*a)/b])) - Sqrt[b]*(64*a^2 - 48*a*b + 15*b^2)*Sqrt[Pi]*Erf[(2*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(4*a)/b] + Sinh[(4*a)/b]) - 16*(Sqrt[b]*(16*a^2 + 24*a*b + 15*b^2)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] - Sinh[(2*a)/b]) + Sqrt[b]*(16*a^2 - 24*a*b + 15*b^2)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b]) - 8*b*Sqrt[a + b*ArcCosh[c + d*x]]*(b*(15 + 16*ArcCosh[c + d*x]^2)*Cosh[2*ArcCosh[c + d*x]] + 4*(a - 5*b*ArcCosh[c + d*x])*Sinh[2*ArcCosh[c + d*x]])) + 8*b*Sqrt[a + b*ArcCosh[c + d*x]]*(b*(15 + 64*ArcCosh[c + d*x]^2)*Cosh[4*ArcCosh[c + d*x]] + 8*(a - 5*b*ArcCosh[c + d*x])*Sinh[4*ArcCosh[c + d*x]]))/(16384*d))","B",0
166,1,1008,408,9.3065174,"\int (c e+d e x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2} \, dx","Integrate[(c*e + d*e*x)^2*(a + b*ArcCosh[c + d*x])^(5/2),x]","e^2 \left(\frac{e^{-\frac{3 a}{b}} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(9 e^{\frac{4 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\sqrt{3} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+9 e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)+\sqrt{3} e^{\frac{6 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{3}{2},\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)\right) a^2}{72 d \sqrt{-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{b^2}}}+\frac{\sqrt{b} \left(9 \left(-12 \sqrt{b} \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{a+b \cosh ^{-1}(c+d x)} (c+d x+1)+(2 a+3 b) \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right)+(2 a-3 b) \sqrt{\pi } \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)+\sinh \left(\frac{a}{b}\right)\right)+8 \sqrt{b} (c+d x) \cosh ^{-1}(c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}\right)+(2 a+b) \sqrt{3 \pi } \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{3 a}{b}\right)-\sinh \left(\frac{3 a}{b}\right)\right)+(2 a-b) \sqrt{3 \pi } \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{3 a}{b}\right)+\sinh \left(\frac{3 a}{b}\right)\right)+12 \sqrt{b} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(2 \cosh ^{-1}(c+d x) \cosh \left(3 \cosh ^{-1}(c+d x)\right)-\sinh \left(3 \cosh ^{-1}(c+d x)\right)\right)\right) a}{144 d}+\frac{-27 \left(-4 b \sqrt{a+b \cosh ^{-1}(c+d x)} \left(2 \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \left(a-5 b \cosh ^{-1}(c+d x)\right)+b (c+d x) \left(4 \cosh ^{-1}(c+d x)^2+15\right)\right)+\sqrt{b} \left(4 a^2+12 b a+15 b^2\right) \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right)+\sqrt{b} \left(4 a^2-12 b a+15 b^2\right) \sqrt{\pi } \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)+\sinh \left(\frac{a}{b}\right)\right)\right)-\sqrt{b} \left(12 a^2+12 b a+5 b^2\right) \sqrt{3 \pi } \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{3 a}{b}\right)-\sinh \left(\frac{3 a}{b}\right)\right)-\sqrt{b} \left(12 a^2-12 b a+5 b^2\right) \sqrt{3 \pi } \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{3 a}{b}\right)+\sinh \left(\frac{3 a}{b}\right)\right)+12 b \sqrt{a+b \cosh ^{-1}(c+d x)} \left(b \left(12 \cosh ^{-1}(c+d x)^2+5\right) \cosh \left(3 \cosh ^{-1}(c+d x)\right)+2 \left(a-5 b \cosh ^{-1}(c+d x)\right) \sinh \left(3 \cosh ^{-1}(c+d x)\right)\right)}{1728 d}\right)","-\frac{15 \sqrt{\pi } b^{5/2} e^2 e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{5 \sqrt{\frac{\pi }{3}} b^{5/2} e^2 e^{\frac{3 a}{b}} \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{576 d}-\frac{15 \sqrt{\pi } b^{5/2} e^2 e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{64 d}-\frac{5 \sqrt{\frac{\pi }{3}} b^{5/2} e^2 e^{-\frac{3 a}{b}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{576 d}+\frac{5 b^2 e^2 (c+d x)^3 \sqrt{a+b \cosh ^{-1}(c+d x)}}{36 d}+\frac{5 b^2 e^2 (c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}}{6 d}+\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{3 d}-\frac{5 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{18 d}-\frac{5 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{9 d}",1,"e^2*((a^2*Sqrt[a + b*ArcCosh[c + d*x]]*(9*E^((4*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[3/2, a/b + ArcCosh[c + d*x]] + Sqrt[3]*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, (-3*(a + b*ArcCosh[c + d*x]))/b] + 9*E^((2*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, -((a + b*ArcCosh[c + d*x])/b)] + Sqrt[3]*E^((6*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[3/2, (3*(a + b*ArcCosh[c + d*x]))/b]))/(72*d*E^((3*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])^2/b^2)]) + (a*Sqrt[b]*(9*(-12*Sqrt[b]*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*Sqrt[a + b*ArcCosh[c + d*x]] + 8*Sqrt[b]*(c + d*x)*ArcCosh[c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]] + (2*a + 3*b)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) + (2*a - 3*b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b])) + (2*a + b)*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(3*a)/b] - Sinh[(3*a)/b]) + (2*a - b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(3*a)/b] + Sinh[(3*a)/b]) + 12*Sqrt[b]*Sqrt[a + b*ArcCosh[c + d*x]]*(2*ArcCosh[c + d*x]*Cosh[3*ArcCosh[c + d*x]] - Sinh[3*ArcCosh[c + d*x]])))/(144*d) + (-27*(-4*b*Sqrt[a + b*ArcCosh[c + d*x]]*(2*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*(a - 5*b*ArcCosh[c + d*x]) + b*(c + d*x)*(15 + 4*ArcCosh[c + d*x]^2)) + Sqrt[b]*(4*a^2 + 12*a*b + 15*b^2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) + Sqrt[b]*(4*a^2 - 12*a*b + 15*b^2)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b])) - Sqrt[b]*(12*a^2 + 12*a*b + 5*b^2)*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(3*a)/b] - Sinh[(3*a)/b]) - Sqrt[b]*(12*a^2 - 12*a*b + 5*b^2)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(3*a)/b] + Sinh[(3*a)/b]) + 12*b*Sqrt[a + b*ArcCosh[c + d*x]]*(b*(5 + 12*ArcCosh[c + d*x]^2)*Cosh[3*ArcCosh[c + d*x]] + 2*(a - 5*b*ArcCosh[c + d*x])*Sinh[3*ArcCosh[c + d*x]]))/(1728*d))","B",0
167,1,1846,269,9.2634424,"\int (c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2} \, dx","Integrate[(c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^(5/2),x]","e \left(\frac{c e^{-\frac{a}{b}} \sqrt{c+d x-1} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(\frac{e^{\frac{2 a}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{\sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)}}+\frac{\Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{\sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}}}\right) a^2}{2 d \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{c+d x+1}}+\frac{\sqrt{c+d x-1} \left(-32 c \sqrt{a+b \cosh ^{-1}(c+d x)} (c+d x)+8 \sqrt{a+b \cosh ^{-1}(c+d x)} \cosh \left(2 \cosh ^{-1}(c+d x)\right)+8 \sqrt{b} c \sqrt{\pi } \cosh \left(\frac{a}{b}\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-\sqrt{b} \sqrt{2 \pi } \cosh \left(\frac{2 a}{b}\right) \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-8 \sqrt{b} c \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \sinh \left(\frac{a}{b}\right)+8 \sqrt{b} c \sqrt{\pi } \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)+\sinh \left(\frac{a}{b}\right)\right)+\sqrt{b} \sqrt{2 \pi } \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \sinh \left(\frac{2 a}{b}\right)-\sqrt{b} \sqrt{2 \pi } \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{2 a}{b}\right)+\sinh \left(\frac{2 a}{b}\right)\right)\right) a^2}{32 d \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{c+d x+1}}+\frac{b c \sqrt{c+d x-1} \left(-12 \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{a+b \cosh ^{-1}(c+d x)} (c+d x+1)+\frac{(2 a+3 b) \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right)}{\sqrt{b}}+\frac{(2 a-3 b) \sqrt{\pi } \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)+\sinh \left(\frac{a}{b}\right)\right)}{\sqrt{b}}+8 (c+d x) \cosh ^{-1}(c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}\right) a}{4 d \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{c+d x+1}}+\frac{\sqrt{c+d x-1} \left(-16 c \left(-12 b \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{a+b \cosh ^{-1}(c+d x)} (c+d x+1)+\sqrt{b} (2 a+3 b) \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right)+(2 a-3 b) \sqrt{b} \sqrt{\pi } \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)+\sinh \left(\frac{a}{b}\right)\right)+8 b (c+d x) \cosh ^{-1}(c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}\right)+\sqrt{b} (4 a+3 b) \sqrt{2 \pi } \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{2 a}{b}\right)-\sinh \left(\frac{2 a}{b}\right)\right)+(4 a-3 b) \sqrt{b} \sqrt{2 \pi } \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{2 a}{b}\right)+\sinh \left(\frac{2 a}{b}\right)\right)+8 b \sqrt{a+b \cosh ^{-1}(c+d x)} \left(4 \cosh ^{-1}(c+d x) \cosh \left(2 \cosh ^{-1}(c+d x)\right)-3 \sinh \left(2 \cosh ^{-1}(c+d x)\right)\right)\right) a}{64 d \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{c+d x+1}}-\frac{c \sqrt{c+d x-1} \left(-4 b \sqrt{a+b \cosh ^{-1}(c+d x)} \left(2 \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \left(a-5 b \cosh ^{-1}(c+d x)\right)+b (c+d x) \left(4 \cosh ^{-1}(c+d x)^2+15\right)\right)+\sqrt{b} \left(4 a^2+12 b a+15 b^2\right) \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right)+\sqrt{b} \left(4 a^2-12 b a+15 b^2\right) \sqrt{\pi } \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)+\sinh \left(\frac{a}{b}\right)\right)\right)}{16 d \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{c+d x+1}}-\frac{\sqrt{c+d x-1} \left(-32 c \left(-4 b \sqrt{a+b \cosh ^{-1}(c+d x)} \left(2 \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \left(a-5 b \cosh ^{-1}(c+d x)\right)+b (c+d x) \left(4 \cosh ^{-1}(c+d x)^2+15\right)\right)+\sqrt{b} \left(4 a^2+12 b a+15 b^2\right) \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right)+\sqrt{b} \left(4 a^2-12 b a+15 b^2\right) \sqrt{\pi } \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)+\sinh \left(\frac{a}{b}\right)\right)\right)+\sqrt{b} \left(16 a^2+24 b a+15 b^2\right) \sqrt{2 \pi } \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{2 a}{b}\right)-\sinh \left(\frac{2 a}{b}\right)\right)+\sqrt{b} \left(16 a^2-24 b a+15 b^2\right) \sqrt{2 \pi } \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{2 a}{b}\right)+\sinh \left(\frac{2 a}{b}\right)\right)-8 b \sqrt{a+b \cosh ^{-1}(c+d x)} \left(b \left(16 \cosh ^{-1}(c+d x)^2+15\right) \cosh \left(2 \cosh ^{-1}(c+d x)\right)+4 \left(a-5 b \cosh ^{-1}(c+d x)\right) \sinh \left(2 \cosh ^{-1}(c+d x)\right)\right)\right)}{512 d \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{c+d x+1}}\right)","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} e e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{256 d}+\frac{15 b^2 e (c+d x)^2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{32 d}-\frac{15 b^2 e \sqrt{a+b \cosh ^{-1}(c+d x)}}{64 d}-\frac{5 b e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{8 d}+\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{2 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{4 d}",1,"e*((a^2*c*Sqrt[-1 + c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]]*((E^((2*a)/b)*Gamma[3/2, a/b + ArcCosh[c + d*x]])/Sqrt[a/b + ArcCosh[c + d*x]] + Gamma[3/2, -((a + b*ArcCosh[c + d*x])/b)]/Sqrt[-((a + b*ArcCosh[c + d*x])/b)]))/(2*d*E^(a/b)*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*Sqrt[1 + c + d*x]) + (a*b*c*Sqrt[-1 + c + d*x]*(-12*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*Sqrt[a + b*ArcCosh[c + d*x]] + 8*(c + d*x)*ArcCosh[c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]] + ((2*a + 3*b)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]))/Sqrt[b] + ((2*a - 3*b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b]))/Sqrt[b]))/(4*d*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*Sqrt[1 + c + d*x]) - (c*Sqrt[-1 + c + d*x]*(-4*b*Sqrt[a + b*ArcCosh[c + d*x]]*(2*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*(a - 5*b*ArcCosh[c + d*x]) + b*(c + d*x)*(15 + 4*ArcCosh[c + d*x]^2)) + Sqrt[b]*(4*a^2 + 12*a*b + 15*b^2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) + Sqrt[b]*(4*a^2 - 12*a*b + 15*b^2)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b])))/(16*d*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*Sqrt[1 + c + d*x]) + (a^2*Sqrt[-1 + c + d*x]*(-32*c*(c + d*x)*Sqrt[a + b*ArcCosh[c + d*x]] + 8*Sqrt[a + b*ArcCosh[c + d*x]]*Cosh[2*ArcCosh[c + d*x]] + 8*Sqrt[b]*c*Sqrt[Pi]*Cosh[a/b]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]] - Sqrt[b]*Sqrt[2*Pi]*Cosh[(2*a)/b]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]] - 8*Sqrt[b]*c*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*Sinh[a/b] + 8*Sqrt[b]*c*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b]) + Sqrt[b]*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*Sinh[(2*a)/b] - Sqrt[b]*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b])))/(32*d*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*Sqrt[1 + c + d*x]) + (a*Sqrt[-1 + c + d*x]*(-16*c*(-12*b*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*Sqrt[a + b*ArcCosh[c + d*x]] + 8*b*(c + d*x)*ArcCosh[c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]] + Sqrt[b]*(2*a + 3*b)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) + (2*a - 3*b)*Sqrt[b]*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b])) + Sqrt[b]*(4*a + 3*b)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] - Sinh[(2*a)/b]) + (4*a - 3*b)*Sqrt[b]*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b]) + 8*b*Sqrt[a + b*ArcCosh[c + d*x]]*(4*ArcCosh[c + d*x]*Cosh[2*ArcCosh[c + d*x]] - 3*Sinh[2*ArcCosh[c + d*x]])))/(64*d*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*Sqrt[1 + c + d*x]) - (Sqrt[-1 + c + d*x]*(-32*c*(-4*b*Sqrt[a + b*ArcCosh[c + d*x]]*(2*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*(a - 5*b*ArcCosh[c + d*x]) + b*(c + d*x)*(15 + 4*ArcCosh[c + d*x]^2)) + Sqrt[b]*(4*a^2 + 12*a*b + 15*b^2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) + Sqrt[b]*(4*a^2 - 12*a*b + 15*b^2)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b])) + Sqrt[b]*(16*a^2 + 24*a*b + 15*b^2)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] - Sinh[(2*a)/b]) + Sqrt[b]*(16*a^2 - 24*a*b + 15*b^2)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b]) - 8*b*Sqrt[a + b*ArcCosh[c + d*x]]*(b*(15 + 16*ArcCosh[c + d*x]^2)*Cosh[2*ArcCosh[c + d*x]] + 4*(a - 5*b*ArcCosh[c + d*x])*Sinh[2*ArcCosh[c + d*x]])))/(512*d*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*Sqrt[1 + c + d*x]))","B",0
168,1,494,186,3.5568363,"\int \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^(5/2),x]","\frac{-\sqrt{\pi } \sqrt{b} \left(4 a^2-12 a b+15 b^2\right) \left(\sinh \left(\frac{a}{b}\right)+\cosh \left(\frac{a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-\sqrt{\pi } \sqrt{b} \left(4 a^2+12 a b+15 b^2\right) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+8 a^2 e^{-\frac{a}{b}} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(\frac{e^{\frac{2 a}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{\sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)}}+\frac{\Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{\sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}}}\right)+4 a b \left(\frac{\sqrt{\pi } (2 a-3 b) \left(\sinh \left(\frac{a}{b}\right)+\cosh \left(\frac{a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b}}+\frac{\sqrt{\pi } (2 a+3 b) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b}}-12 \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \sqrt{a+b \cosh ^{-1}(c+d x)}+8 (c+d x) \cosh ^{-1}(c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}\right)+4 b \sqrt{a+b \cosh ^{-1}(c+d x)} \left(2 \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \left(a-5 b \cosh ^{-1}(c+d x)\right)+b (c+d x) \left(4 \cosh ^{-1}(c+d x)^2+15\right)\right)}{16 d}","-\frac{15 \sqrt{\pi } b^{5/2} e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}-\frac{15 \sqrt{\pi } b^{5/2} e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 d}+\frac{15 b^2 (c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}}{4 d}-\frac{5 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{2 d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{d}",1,"(4*b*Sqrt[a + b*ArcCosh[c + d*x]]*(2*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*(a - 5*b*ArcCosh[c + d*x]) + b*(c + d*x)*(15 + 4*ArcCosh[c + d*x]^2)) + (8*a^2*Sqrt[a + b*ArcCosh[c + d*x]]*((E^((2*a)/b)*Gamma[3/2, a/b + ArcCosh[c + d*x]])/Sqrt[a/b + ArcCosh[c + d*x]] + Gamma[3/2, -((a + b*ArcCosh[c + d*x])/b)]/Sqrt[-((a + b*ArcCosh[c + d*x])/b)]))/E^(a/b) - Sqrt[b]*(4*a^2 + 12*a*b + 15*b^2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) - Sqrt[b]*(4*a^2 - 12*a*b + 15*b^2)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b]) + 4*a*b*(-12*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*Sqrt[a + b*ArcCosh[c + d*x]] + 8*(c + d*x)*ArcCosh[c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]] + ((2*a + 3*b)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]))/Sqrt[b] + ((2*a - 3*b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b]))/Sqrt[b]))/(16*d)","B",0
169,0,0,29,1.1390963,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{c e+d e x} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^(5/2)/(c*e + d*e*x),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{c e+d e x} \, dx","\frac{\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{c+d x},x\right)}{e}",0,"Integrate[(a + b*ArcCosh[c + d*x])^(5/2)/(c*e + d*e*x), x]","A",-1
170,1,1523,509,14.0650991,"\int (c e+d e x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2} \, dx","Integrate[(c*e + d*e*x)^2*(a + b*ArcCosh[c + d*x])^(7/2),x]","e^2 \left(\frac{e^{-\frac{3 a}{b}} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(9 e^{\frac{4 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\sqrt{3} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+9 e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)+\sqrt{3} e^{\frac{6 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{3}{2},\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)\right) a^3}{72 d \sqrt{-\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{b^2}}}+\frac{\sqrt{b} \left(9 \left(-12 \sqrt{b} \sqrt{\frac{c+d x-1}{c+d x+1}} \sqrt{a+b \cosh ^{-1}(c+d x)} (c+d x+1)+(2 a+3 b) \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right)+(2 a-3 b) \sqrt{\pi } \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)+\sinh \left(\frac{a}{b}\right)\right)+8 \sqrt{b} (c+d x) \cosh ^{-1}(c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}\right)+(2 a+b) \sqrt{3 \pi } \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{3 a}{b}\right)-\sinh \left(\frac{3 a}{b}\right)\right)+(2 a-b) \sqrt{3 \pi } \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{3 a}{b}\right)+\sinh \left(\frac{3 a}{b}\right)\right)+12 \sqrt{b} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(2 \cosh ^{-1}(c+d x) \cosh \left(3 \cosh ^{-1}(c+d x)\right)-\sinh \left(3 \cosh ^{-1}(c+d x)\right)\right)\right) a^2}{96 d}+\frac{\left(-27 \left(-4 b \sqrt{a+b \cosh ^{-1}(c+d x)} \left(2 \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \left(a-5 b \cosh ^{-1}(c+d x)\right)+b (c+d x) \left(4 \cosh ^{-1}(c+d x)^2+15\right)\right)+\sqrt{b} \left(4 a^2+12 b a+15 b^2\right) \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right)+\sqrt{b} \left(4 a^2-12 b a+15 b^2\right) \sqrt{\pi } \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)+\sinh \left(\frac{a}{b}\right)\right)\right)-\sqrt{b} \left(12 a^2+12 b a+5 b^2\right) \sqrt{3 \pi } \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{3 a}{b}\right)-\sinh \left(\frac{3 a}{b}\right)\right)-\sqrt{b} \left(12 a^2-12 b a+5 b^2\right) \sqrt{3 \pi } \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{3 a}{b}\right)+\sinh \left(\frac{3 a}{b}\right)\right)+12 b \sqrt{a+b \cosh ^{-1}(c+d x)} \left(b \left(12 \cosh ^{-1}(c+d x)^2+5\right) \cosh \left(3 \cosh ^{-1}(c+d x)\right)+2 \left(a-5 b \cosh ^{-1}(c+d x)\right) \sinh \left(3 \cosh ^{-1}(c+d x)\right)\right)\right) a}{576 d}+\frac{-81 \left(4 b \sqrt{a+b \cosh ^{-1}(c+d x)} \left(\sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \left(4 a^2-4 b \cosh ^{-1}(c+d x) a+7 b^2 \left(4 \cosh ^{-1}(c+d x)^2+15\right)\right)-2 b (c+d x) \left(b \cosh ^{-1}(c+d x) \left(4 \cosh ^{-1}(c+d x)^2+35\right)-10 a\right)\right)+\sqrt{b} \left(8 a^3+36 b a^2+90 b^2 a+105 b^3\right) \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\sinh \left(\frac{a}{b}\right)-\cosh \left(\frac{a}{b}\right)\right)+\sqrt{b} \left(-8 a^3+36 b a^2-90 b^2 a+105 b^3\right) \sqrt{\pi } \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{a}{b}\right)+\sinh \left(\frac{a}{b}\right)\right)\right)+\sqrt{b} \left(72 a^3+108 b a^2+90 b^2 a+35 b^3\right) \sqrt{3 \pi } \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{3 a}{b}\right)-\sinh \left(\frac{3 a}{b}\right)\right)-\sqrt{b} \left(-72 a^3+108 b a^2-90 b^2 a+35 b^3\right) \sqrt{3 \pi } \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \left(\cosh \left(\frac{3 a}{b}\right)+\sinh \left(\frac{3 a}{b}\right)\right)-12 b \sqrt{a+b \cosh ^{-1}(c+d x)} \left(\left(12 a^2-12 b \cosh ^{-1}(c+d x) a+7 b^2 \left(12 \cosh ^{-1}(c+d x)^2+5\right)\right) \sinh \left(3 \cosh ^{-1}(c+d x)\right)-2 b \left(b \cosh ^{-1}(c+d x) \left(36 \cosh ^{-1}(c+d x)^2+35\right)-10 a\right) \cosh \left(3 \cosh ^{-1}(c+d x)\right)\right)}{10368 d}\right)","-\frac{105 \sqrt{\pi } b^{7/2} e^2 e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}-\frac{35 \sqrt{\frac{\pi }{3}} b^{7/2} e^2 e^{\frac{3 a}{b}} \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3456 d}+\frac{105 \sqrt{\pi } b^{7/2} e^2 e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{128 d}+\frac{35 \sqrt{\frac{\pi }{3}} b^{7/2} e^2 e^{-\frac{3 a}{b}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3456 d}-\frac{35 b^3 e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{216 d}-\frac{175 b^3 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{54 d}+\frac{35 b^2 e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{108 d}+\frac{35 b^2 e^2 (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{18 d}-\frac{7 b e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{18 d}-\frac{7 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{9 d}+\frac{e^2 (c+d x)^3 \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{3 d}",1,"e^2*((a^3*Sqrt[a + b*ArcCosh[c + d*x]]*(9*E^((4*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[3/2, a/b + ArcCosh[c + d*x]] + Sqrt[3]*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, (-3*(a + b*ArcCosh[c + d*x]))/b] + 9*E^((2*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[3/2, -((a + b*ArcCosh[c + d*x])/b)] + Sqrt[3]*E^((6*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[3/2, (3*(a + b*ArcCosh[c + d*x]))/b]))/(72*d*E^((3*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])^2/b^2)]) + (a^2*Sqrt[b]*(9*(-12*Sqrt[b]*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*Sqrt[a + b*ArcCosh[c + d*x]] + 8*Sqrt[b]*(c + d*x)*ArcCosh[c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]] + (2*a + 3*b)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) + (2*a - 3*b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b])) + (2*a + b)*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(3*a)/b] - Sinh[(3*a)/b]) + (2*a - b)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(3*a)/b] + Sinh[(3*a)/b]) + 12*Sqrt[b]*Sqrt[a + b*ArcCosh[c + d*x]]*(2*ArcCosh[c + d*x]*Cosh[3*ArcCosh[c + d*x]] - Sinh[3*ArcCosh[c + d*x]])))/(96*d) + (a*(-27*(-4*b*Sqrt[a + b*ArcCosh[c + d*x]]*(2*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*(a - 5*b*ArcCosh[c + d*x]) + b*(c + d*x)*(15 + 4*ArcCosh[c + d*x]^2)) + Sqrt[b]*(4*a^2 + 12*a*b + 15*b^2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) + Sqrt[b]*(4*a^2 - 12*a*b + 15*b^2)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b])) - Sqrt[b]*(12*a^2 + 12*a*b + 5*b^2)*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(3*a)/b] - Sinh[(3*a)/b]) - Sqrt[b]*(12*a^2 - 12*a*b + 5*b^2)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(3*a)/b] + Sinh[(3*a)/b]) + 12*b*Sqrt[a + b*ArcCosh[c + d*x]]*(b*(5 + 12*ArcCosh[c + d*x]^2)*Cosh[3*ArcCosh[c + d*x]] + 2*(a - 5*b*ArcCosh[c + d*x])*Sinh[3*ArcCosh[c + d*x]])))/(576*d) + (-81*(4*b*Sqrt[a + b*ArcCosh[c + d*x]]*(Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*(4*a^2 - 4*a*b*ArcCosh[c + d*x] + 7*b^2*(15 + 4*ArcCosh[c + d*x]^2)) - 2*b*(c + d*x)*(-10*a + b*ArcCosh[c + d*x]*(35 + 4*ArcCosh[c + d*x]^2))) + Sqrt[b]*(8*a^3 + 36*a^2*b + 90*a*b^2 + 105*b^3)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(-Cosh[a/b] + Sinh[a/b]) + Sqrt[b]*(-8*a^3 + 36*a^2*b - 90*a*b^2 + 105*b^3)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b])) + Sqrt[b]*(72*a^3 + 108*a^2*b + 90*a*b^2 + 35*b^3)*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(3*a)/b] - Sinh[(3*a)/b]) - Sqrt[b]*(-72*a^3 + 108*a^2*b - 90*a*b^2 + 35*b^3)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(3*a)/b] + Sinh[(3*a)/b]) - 12*b*Sqrt[a + b*ArcCosh[c + d*x]]*(-2*b*(-10*a + b*ArcCosh[c + d*x]*(35 + 36*ArcCosh[c + d*x]^2))*Cosh[3*ArcCosh[c + d*x]] + (12*a^2 - 12*a*b*ArcCosh[c + d*x] + 7*b^2*(5 + 12*ArcCosh[c + d*x]^2))*Sinh[3*ArcCosh[c + d*x]]))/(10368*d))","B",0
171,1,288,319,5.7497983,"\int (c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2} \, dx","Integrate[(c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^(7/2),x]","\frac{e \left(8 \sqrt{a+b \cosh ^{-1}(c+d x)} \left(4 a \left(16 a^2+35 b^2\right) \cosh \left(2 \cosh ^{-1}(c+d x)\right)+4 b \cosh ^{-1}(c+d x) \left(\left(48 a^2+35 b^2\right) \cosh \left(2 \cosh ^{-1}(c+d x)\right)-56 a b \sinh \left(2 \cosh ^{-1}(c+d x)\right)\right)-7 b \left(16 a^2+15 b^2\right) \sinh \left(2 \cosh ^{-1}(c+d x)\right)+16 b^2 \cosh ^{-1}(c+d x)^2 \left(12 a \cosh \left(2 \cosh ^{-1}(c+d x)\right)-7 b \sinh \left(2 \cosh ^{-1}(c+d x)\right)\right)+64 b^3 \cosh \left(2 \cosh ^{-1}(c+d x)\right) \cosh ^{-1}(c+d x)^3\right)-105 \sqrt{2 \pi } b^{7/2} \left(\sinh \left(\frac{2 a}{b}\right)+\cosh \left(\frac{2 a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+105 \sqrt{2 \pi } b^{7/2} \left(\cosh \left(\frac{2 a}{b}\right)-\sinh \left(\frac{2 a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)\right)}{2048 d}","-\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{1024 d}+\frac{105 \sqrt{\frac{\pi }{2}} b^{7/2} e e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{1024 d}-\frac{105 b^3 e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{128 d}+\frac{35 b^2 e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{32 d}-\frac{35 b^2 e \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{64 d}-\frac{7 b e \sqrt{c+d x-1} (c+d x) \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{8 d}+\frac{e (c+d x)^2 \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{2 d}-\frac{e \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{4 d}",1,"(e*(105*b^(7/2)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] - Sinh[(2*a)/b]) - 105*b^(7/2)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b]) + 8*Sqrt[a + b*ArcCosh[c + d*x]]*(4*a*(16*a^2 + 35*b^2)*Cosh[2*ArcCosh[c + d*x]] + 64*b^3*ArcCosh[c + d*x]^3*Cosh[2*ArcCosh[c + d*x]] - 7*b*(16*a^2 + 15*b^2)*Sinh[2*ArcCosh[c + d*x]] + 16*b^2*ArcCosh[c + d*x]^2*(12*a*Cosh[2*ArcCosh[c + d*x]] - 7*b*Sinh[2*ArcCosh[c + d*x]]) + 4*b*ArcCosh[c + d*x]*((48*a^2 + 35*b^2)*Cosh[2*ArcCosh[c + d*x]] - 56*a*b*Sinh[2*ArcCosh[c + d*x]]))))/(2048*d)","A",0
172,1,765,230,7.5075359,"\int \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^(7/2),x]","\frac{a^3 e^{-\frac{a}{b}} \sqrt{a+b \cosh ^{-1}(c+d x)} \left(\frac{e^{\frac{2 a}{b}} \Gamma \left(\frac{3}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{\sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)}}+\frac{\Gamma \left(\frac{3}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{\sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}}}\right)}{2 d}+\frac{3 a \left(-\sqrt{\pi } \sqrt{b} \left(4 a^2-12 a b+15 b^2\right) \left(\sinh \left(\frac{a}{b}\right)+\cosh \left(\frac{a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-\sqrt{\pi } \sqrt{b} \left(4 a^2+12 a b+15 b^2\right) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+4 b \sqrt{a+b \cosh ^{-1}(c+d x)} \left(2 \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \left(a-5 b \cosh ^{-1}(c+d x)\right)+b (c+d x) \left(4 \cosh ^{-1}(c+d x)^2+15\right)\right)\right)}{16 d}+\frac{3 a^2 b \left(\frac{\sqrt{\pi } (2 a-3 b) \left(\sinh \left(\frac{a}{b}\right)+\cosh \left(\frac{a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b}}+\frac{\sqrt{\pi } (2 a+3 b) \left(\cosh \left(\frac{a}{b}\right)-\sinh \left(\frac{a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b}}-12 \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \sqrt{a+b \cosh ^{-1}(c+d x)}+8 (c+d x) \cosh ^{-1}(c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}\right)}{8 d}+\frac{-4 b \sqrt{a+b \cosh ^{-1}(c+d x)} \left(\sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \left(4 a^2-4 a b \cosh ^{-1}(c+d x)+7 b^2 \left(4 \cosh ^{-1}(c+d x)^2+15\right)\right)-2 b (c+d x) \left(b \cosh ^{-1}(c+d x) \left(4 \cosh ^{-1}(c+d x)^2+35\right)-10 a\right)\right)-\sqrt{\pi } \sqrt{b} \left(-8 a^3+36 a^2 b-90 a b^2+105 b^3\right) \left(\sinh \left(\frac{a}{b}\right)+\cosh \left(\frac{a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-\sqrt{\pi } \sqrt{b} \left(8 a^3+36 a^2 b+90 a b^2+105 b^3\right) \left(\sinh \left(\frac{a}{b}\right)-\cosh \left(\frac{a}{b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}","-\frac{105 \sqrt{\pi } b^{7/2} e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}+\frac{105 \sqrt{\pi } b^{7/2} e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 d}-\frac{105 b^3 \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{a+b \cosh ^{-1}(c+d x)}}{8 d}+\frac{35 b^2 (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}{4 d}-\frac{7 b \sqrt{c+d x-1} \sqrt{c+d x+1} \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}{2 d}+\frac{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{d}",1,"(a^3*Sqrt[a + b*ArcCosh[c + d*x]]*((E^((2*a)/b)*Gamma[3/2, a/b + ArcCosh[c + d*x]])/Sqrt[a/b + ArcCosh[c + d*x]] + Gamma[3/2, -((a + b*ArcCosh[c + d*x])/b)]/Sqrt[-((a + b*ArcCosh[c + d*x])/b)]))/(2*d*E^(a/b)) + (3*a^2*b*(-12*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*Sqrt[a + b*ArcCosh[c + d*x]] + 8*(c + d*x)*ArcCosh[c + d*x]*Sqrt[a + b*ArcCosh[c + d*x]] + ((2*a + 3*b)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]))/Sqrt[b] + ((2*a - 3*b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b]))/Sqrt[b]))/(8*d) + (3*a*(4*b*Sqrt[a + b*ArcCosh[c + d*x]]*(2*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*(a - 5*b*ArcCosh[c + d*x]) + b*(c + d*x)*(15 + 4*ArcCosh[c + d*x]^2)) - Sqrt[b]*(4*a^2 + 12*a*b + 15*b^2)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] - Sinh[a/b]) - Sqrt[b]*(4*a^2 - 12*a*b + 15*b^2)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b])))/(16*d) + (-4*b*Sqrt[a + b*ArcCosh[c + d*x]]*(Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*(4*a^2 - 4*a*b*ArcCosh[c + d*x] + 7*b^2*(15 + 4*ArcCosh[c + d*x]^2)) - 2*b*(c + d*x)*(-10*a + b*ArcCosh[c + d*x]*(35 + 4*ArcCosh[c + d*x]^2))) - Sqrt[b]*(8*a^3 + 36*a^2*b + 90*a*b^2 + 105*b^3)*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(-Cosh[a/b] + Sinh[a/b]) - Sqrt[b]*(-8*a^3 + 36*a^2*b - 90*a*b^2 + 105*b^3)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b]))/(32*d)","B",0
173,0,0,29,1.2088368,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{c e+d e x} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^(7/2)/(c*e + d*e*x),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{c e+d e x} \, dx","\frac{\text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}}{c+d x},x\right)}{e}",0,"Integrate[(a + b*ArcCosh[c + d*x])^(7/2)/(c*e + d*e*x), x]","A",-1
174,1,319,326,0.640244,"\int \frac{(c e+d e x)^4}{\sqrt{a+b \cosh ^{-1}(c+d x)}} \, dx","Integrate[(c*e + d*e*x)^4/Sqrt[a + b*ArcCosh[c + d*x]],x]","\frac{e^4 e^{-\frac{5 a}{b}} \left(10 e^{\frac{6 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\sqrt{5} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+5 \sqrt{3} e^{\frac{2 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+10 e^{\frac{4 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)+5 \sqrt{3} e^{\frac{8 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+\sqrt{5} e^{\frac{10 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)\right)}{160 d \sqrt{a+b \cosh ^{-1}(c+d x)}}","-\frac{\sqrt{\pi } e^4 e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 \sqrt{b} d}-\frac{\sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{5}} e^4 e^{\frac{5 a}{b}} \text{erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 \sqrt{b} d}+\frac{\sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{5}} e^4 e^{-\frac{5 a}{b}} \text{erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}",1,"(e^4*(10*E^((6*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, a/b + ArcCosh[c + d*x]] + Sqrt[5]*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, (-5*(a + b*ArcCosh[c + d*x]))/b] + 5*Sqrt[3]*E^((2*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, (-3*(a + b*ArcCosh[c + d*x]))/b] + 10*E^((4*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)] + 5*Sqrt[3]*E^((8*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, (3*(a + b*ArcCosh[c + d*x]))/b] + Sqrt[5]*E^((10*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, (5*(a + b*ArcCosh[c + d*x]))/b]))/(160*d*E^((5*a)/b)*Sqrt[a + b*ArcCosh[c + d*x]])","A",0
175,1,205,217,0.4117888,"\int \frac{(c e+d e x)^3}{\sqrt{a+b \cosh ^{-1}(c+d x)}} \, dx","Integrate[(c*e + d*e*x)^3/Sqrt[a + b*ArcCosh[c + d*x]],x]","\frac{e^3 e^{-\frac{4 a}{b}} \left(\sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+2 \sqrt{2} e^{\frac{2 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+e^{\frac{6 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(2 \sqrt{2} \Gamma \left(\frac{1}{2},\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+e^{\frac{2 a}{b}} \Gamma \left(\frac{1}{2},\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)\right)\right)}{32 d \sqrt{a+b \cosh ^{-1}(c+d x)}}","-\frac{\sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{2}} e^3 e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{32 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{2}} e^3 e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}",1,"(e^3*(Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, (-4*(a + b*ArcCosh[c + d*x]))/b] + 2*Sqrt[2]*E^((2*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, (-2*(a + b*ArcCosh[c + d*x]))/b] + E^((6*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*(2*Sqrt[2]*Gamma[1/2, (2*(a + b*ArcCosh[c + d*x]))/b] + E^((2*a)/b)*Gamma[1/2, (4*(a + b*ArcCosh[c + d*x]))/b])))/(32*d*E^((4*a)/b)*Sqrt[a + b*ArcCosh[c + d*x]])","A",0
176,1,216,214,0.3801767,"\int \frac{(c e+d e x)^2}{\sqrt{a+b \cosh ^{-1}(c+d x)}} \, dx","Integrate[(c*e + d*e*x)^2/Sqrt[a + b*ArcCosh[c + d*x]],x]","\frac{e^2 e^{-\frac{3 a}{b}} \left(3 e^{\frac{4 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\sqrt{3} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+3 e^{\frac{2 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)+\sqrt{3} e^{\frac{6 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)\right)}{24 d \sqrt{a+b \cosh ^{-1}(c+d x)}}","-\frac{\sqrt{\pi } e^2 e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{3}} e^2 e^{\frac{3 a}{b}} \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}+\frac{\sqrt{\frac{\pi }{3}} e^2 e^{-\frac{3 a}{b}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 \sqrt{b} d}",1,"(e^2*(3*E^((4*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, a/b + ArcCosh[c + d*x]] + Sqrt[3]*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, (-3*(a + b*ArcCosh[c + d*x]))/b] + 3*E^((2*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)] + Sqrt[3]*E^((6*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, (3*(a + b*ArcCosh[c + d*x]))/b]))/(24*d*E^((3*a)/b)*Sqrt[a + b*ArcCosh[c + d*x]])","A",0
177,1,306,113,1.4288299,"\int \frac{c e+d e x}{\sqrt{a+b \cosh ^{-1}(c+d x)}} \, dx","Integrate[(c*e + d*e*x)/Sqrt[a + b*ArcCosh[c + d*x]],x]","\frac{e \left(\frac{4 \sqrt{\pi } c e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b}}-\frac{\sqrt{2 \pi } e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b}}-\frac{4 \sqrt{\pi } c e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b}}+\frac{\sqrt{2 \pi } e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{\sqrt{b}}+\frac{4 c e^{a/b} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)}{\sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{4 c e^{-\frac{a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)}{\sqrt{a+b \cosh ^{-1}(c+d x)}}\right)}{8 d}","\frac{\sqrt{\frac{\pi }{2}} e e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d}-\frac{\sqrt{\frac{\pi }{2}} e e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 \sqrt{b} d}",1,"(e*((4*c*E^(a/b)*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/Sqrt[b] - (E^((2*a)/b)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/Sqrt[b] - (4*c*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/(Sqrt[b]*E^(a/b)) + (Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/(Sqrt[b]*E^((2*a)/b)) + (4*c*E^(a/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, a/b + ArcCosh[c + d*x]])/Sqrt[a + b*ArcCosh[c + d*x]] + (4*c*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)])/(E^(a/b)*Sqrt[a + b*ArcCosh[c + d*x]])))/(8*d)","B",0
178,1,110,92,0.1095499,"\int \frac{1}{\sqrt{a+b \cosh ^{-1}(c+d x)}} \, dx","Integrate[1/Sqrt[a + b*ArcCosh[c + d*x]],x]","\frac{e^{-\frac{a}{b}} \left(e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)\right)}{2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}","\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}-\frac{\sqrt{\pi } e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 \sqrt{b} d}",1,"(E^((2*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, a/b + ArcCosh[c + d*x]] + Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)])/(2*d*E^(a/b)*Sqrt[a + b*ArcCosh[c + d*x]])","A",0
179,0,0,29,0.0808086,"\int \frac{1}{(c e+d e x) \sqrt{a+b \cosh ^{-1}(c+d x)}} \, dx","Integrate[1/((c*e + d*e*x)*Sqrt[a + b*ArcCosh[c + d*x]]),x]","\int \frac{1}{(c e+d e x) \sqrt{a+b \cosh ^{-1}(c+d x)}} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \sqrt{a+b \cosh ^{-1}(c+d x)}},x\right)}{e}",0,"Integrate[1/((c*e + d*e*x)*Sqrt[a + b*ArcCosh[c + d*x]]), x]","A",-1
180,1,396,374,1.5363686,"\int \frac{(c e+d e x)^4}{\left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}} \, dx","Integrate[(c*e + d*e*x)^4/(a + b*ArcCosh[c + d*x])^(3/2),x]","\frac{e^4 e^{-\frac{5 a}{b}} \left(-4 e^{\frac{5 a}{b}} \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1)-6 e^{\frac{5 a}{b}} \sinh \left(3 \cosh ^{-1}(c+d x)\right)-2 e^{\frac{5 a}{b}} \sinh \left(5 \cosh ^{-1}(c+d x)\right)-2 e^{\frac{6 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\sqrt{5} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+3 \sqrt{3} e^{\frac{2 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+2 e^{\frac{4 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)-3 \sqrt{3} e^{\frac{8 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)-\sqrt{5} e^{\frac{10 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)\right)}{16 b d \sqrt{a+b \cosh ^{-1}(c+d x)}}","\frac{\sqrt{\pi } e^4 e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{3/2} d}+\frac{3 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}+\frac{\sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{3/2} d}+\frac{3 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}+\frac{\sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{16 b^{3/2} d}-\frac{2 e^4 \sqrt{c+d x-1} (c+d x)^4 \sqrt{c+d x+1}}{b d \sqrt{a+b \cosh ^{-1}(c+d x)}}",1,"(e^4*(-4*E^((5*a)/b)*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x) - 2*E^((6*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, a/b + ArcCosh[c + d*x]] + Sqrt[5]*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, (-5*(a + b*ArcCosh[c + d*x]))/b] + 3*Sqrt[3]*E^((2*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, (-3*(a + b*ArcCosh[c + d*x]))/b] + 2*E^((4*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)] - 3*Sqrt[3]*E^((8*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, (3*(a + b*ArcCosh[c + d*x]))/b] - Sqrt[5]*E^((10*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, (5*(a + b*ArcCosh[c + d*x]))/b] - 6*E^((5*a)/b)*Sinh[3*ArcCosh[c + d*x]] - 2*E^((5*a)/b)*Sinh[5*ArcCosh[c + d*x]]))/(16*b*d*E^((5*a)/b)*Sqrt[a + b*ArcCosh[c + d*x]])","A",0
181,1,265,269,1.0151037,"\int \frac{(c e+d e x)^3}{\left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}} \, dx","Integrate[(c*e + d*e*x)^3/(a + b*ArcCosh[c + d*x])^(3/2),x]","\frac{e^3 e^{-\frac{4 a}{b}} \left(\sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+\sqrt{2} e^{\frac{2 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)-e^{\frac{4 a}{b}} \left(\sqrt{2} e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+e^{\frac{4 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+8 \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) (c+d x)^3\right)\right)}{4 b d \sqrt{a+b \cosh ^{-1}(c+d x)}}","\frac{\sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{\frac{\pi }{2}} e^3 e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{3/2} d}+\frac{\sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{\frac{\pi }{2}} e^3 e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{3/2} d}-\frac{2 e^3 \sqrt{c+d x-1} (c+d x)^3 \sqrt{c+d x+1}}{b d \sqrt{a+b \cosh ^{-1}(c+d x)}}",1,"(e^3*(Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, (-4*(a + b*ArcCosh[c + d*x]))/b] + Sqrt[2]*E^((2*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, (-2*(a + b*ArcCosh[c + d*x]))/b] - E^((4*a)/b)*(8*(c + d*x)^3*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x) + Sqrt[2]*E^((2*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, (2*(a + b*ArcCosh[c + d*x]))/b] + E^((4*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, (4*(a + b*ArcCosh[c + d*x]))/b])))/(4*b*d*E^((4*a)/b)*Sqrt[a + b*ArcCosh[c + d*x]])","A",0
182,1,265,262,1.6277512,"\int \frac{(c e+d e x)^2}{\left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}} \, dx","Integrate[(c*e + d*e*x)^2/(a + b*ArcCosh[c + d*x])^(3/2),x]","\frac{e^2 e^{-\frac{3 a}{b}} \left(-2 e^{\frac{3 a}{b}} \left(\sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1)+\sinh \left(3 \cosh ^{-1}(c+d x)\right)\right)-e^{\frac{4 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\sqrt{3} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+e^{\frac{2 a}{b}} \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)-\sqrt{3} e^{\frac{6 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)\right)}{4 b d \sqrt{a+b \cosh ^{-1}(c+d x)}}","\frac{\sqrt{\pi } e^2 e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}+\frac{\sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{4 b^{3/2} d}-\frac{2 e^2 \sqrt{c+d x-1} (c+d x)^2 \sqrt{c+d x+1}}{b d \sqrt{a+b \cosh ^{-1}(c+d x)}}",1,"(e^2*(-(E^((4*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, a/b + ArcCosh[c + d*x]]) + Sqrt[3]*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, (-3*(a + b*ArcCosh[c + d*x]))/b] + E^((2*a)/b)*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)] - Sqrt[3]*E^((6*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, (3*(a + b*ArcCosh[c + d*x]))/b] - 2*E^((3*a)/b)*(Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x) + Sinh[3*ArcCosh[c + d*x]])))/(4*b*d*E^((3*a)/b)*Sqrt[a + b*ArcCosh[c + d*x]])","A",0
183,1,314,155,6.7124457,"\int \frac{c e+d e x}{\left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}} \, dx","Integrate[(c*e + d*e*x)/(a + b*ArcCosh[c + d*x])^(3/2),x]","\frac{e \left(-2 \sqrt{\pi } c \left(\sinh \left(\frac{a}{b}\right)+\cosh \left(\frac{a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+\sqrt{2 \pi } \left(\sinh \left(\frac{2 a}{b}\right)+\cosh \left(\frac{2 a}{b}\right)\right) \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-2 \sqrt{\pi } c e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+\sqrt{2 \pi } e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-\frac{2 \sqrt{b} e^{-\frac{a}{b}} \left(e^{a/b} \sinh \left(2 \cosh ^{-1}(c+d x)\right)+c e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-c \sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)\right)}{\sqrt{a+b \cosh ^{-1}(c+d x)}}\right)}{2 b^{3/2} d}","\frac{\sqrt{\frac{\pi }{2}} e e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\frac{\pi }{2}} e e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{b d \sqrt{a+b \cosh ^{-1}(c+d x)}}",1,"(e*((-2*c*Sqrt[Pi]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]])/E^(a/b) + (Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]])/E^((2*a)/b) - 2*c*Sqrt[Pi]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*(Cosh[a/b] + Sinh[a/b]) + Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*(Cosh[(2*a)/b] + Sinh[(2*a)/b]) - (2*Sqrt[b]*(c*E^((2*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, a/b + ArcCosh[c + d*x]] - c*Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)] + E^(a/b)*Sinh[2*ArcCosh[c + d*x]]))/(E^(a/b)*Sqrt[a + b*ArcCosh[c + d*x]])))/(2*b^(3/2)*d)","B",0
184,1,145,128,0.1821944,"\int \frac{1}{\left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^(-3/2),x]","\frac{e^{-\frac{a}{b}} \left(-2 e^{a/b} \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1)-e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+\sqrt{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)\right)}{b d \sqrt{a+b \cosh ^{-1}(c+d x)}}","\frac{\sqrt{\pi } e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}+\frac{\sqrt{\pi } e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{b^{3/2} d}-\frac{2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{b d \sqrt{a+b \cosh ^{-1}(c+d x)}}",1,"(-2*E^(a/b)*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x) - E^((2*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*Gamma[1/2, a/b + ArcCosh[c + d*x]] + Sqrt[-((a + b*ArcCosh[c + d*x])/b)]*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)])/(b*d*E^(a/b)*Sqrt[a + b*ArcCosh[c + d*x]])","A",0
185,0,0,29,0.0902197,"\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}} \, dx","Integrate[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^(3/2)),x]","\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}},x\right)}{e}",0,"Integrate[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^(3/2)), x]","A",-1
186,1,615,444,3.6561932,"\int \frac{(c e+d e x)^4}{\left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}} \, dx","Integrate[(c*e + d*e*x)^4/(a + b*ArcCosh[c + d*x])^(5/2),x]","\frac{e^4 e^{-5 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)} \left(-10 \sqrt{5} b e^{5 \cosh ^{-1}(c+d x)} \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)-18 \sqrt{3} b e^{\frac{2 a}{b}+5 \cosh ^{-1}(c+d x)} \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+2 e^{4 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)} \left(2 e^{\frac{2 a}{b}+\cosh ^{-1}(c+d x)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-2 \left(e^{a/b} \left(\left(e^{2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)+b \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) e^{\cosh ^{-1}(c+d x)}\right)+b e^{\cosh ^{-1}(c+d x)} \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)\right)\right)+3 e^{\frac{5 a}{b}+2 \cosh ^{-1}(c+d x)} \left(6 \sqrt{3} e^{3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)-6 a \left(e^{6 \cosh ^{-1}(c+d x)}+1\right)-6 b \cosh ^{-1}(c+d x)-b e^{6 \cosh ^{-1}(c+d x)} \left(6 \cosh ^{-1}(c+d x)+1\right)+b\right)+2 e^{\frac{5 a}{b}} \left(-5 \left(e^{10 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)+5 \sqrt{5} e^{5 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)-\frac{1}{2} b \left(e^{10 \cosh ^{-1}(c+d x)}-1\right)\right)\right)}{48 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}","-\frac{\sqrt{\pi } e^4 e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{5/2} d}-\frac{3 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{5/2} d}-\frac{5 \sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{24 b^{5/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{5/2} d}+\frac{3 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{8 b^{5/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{24 b^{5/2} d}-\frac{20 e^4 (c+d x)^5}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{16 e^4 (c+d x)^3}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}",1,"(e^4*(-10*Sqrt[5]*b*E^(5*ArcCosh[c + d*x])*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, (-5*(a + b*ArcCosh[c + d*x]))/b] - 18*Sqrt[3]*b*E^((2*a)/b + 5*ArcCosh[c + d*x])*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, (-3*(a + b*ArcCosh[c + d*x]))/b] + 2*E^(4*(a/b + ArcCosh[c + d*x]))*(2*E^((2*a)/b + ArcCosh[c + d*x])*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, a/b + ArcCosh[c + d*x]] - 2*(E^(a/b)*(b*E^ArcCosh[c + d*x]*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x) + (1 + E^(2*ArcCosh[c + d*x]))*(a + b*ArcCosh[c + d*x])) + b*E^ArcCosh[c + d*x]*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)])) + 3*E^((5*a)/b + 2*ArcCosh[c + d*x])*(b - 6*a*(1 + E^(6*ArcCosh[c + d*x])) - 6*b*ArcCosh[c + d*x] - b*E^(6*ArcCosh[c + d*x])*(1 + 6*ArcCosh[c + d*x]) + 6*Sqrt[3]*E^(3*(a/b + ArcCosh[c + d*x]))*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, (3*(a + b*ArcCosh[c + d*x]))/b]) + 2*E^((5*a)/b)*(-1/2*(b*(-1 + E^(10*ArcCosh[c + d*x]))) - 5*(1 + E^(10*ArcCosh[c + d*x]))*(a + b*ArcCosh[c + d*x]) + 5*Sqrt[5]*E^(5*(a/b + ArcCosh[c + d*x]))*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, (5*(a + b*ArcCosh[c + d*x]))/b])))/(48*b^2*d*E^(5*(a/b + ArcCosh[c + d*x]))*(a + b*ArcCosh[c + d*x])^(3/2))","A",0
187,1,391,333,2.4653988,"\int \frac{(c e+d e x)^3}{\left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}} \, dx","Integrate[(c*e + d*e*x)^3/(a + b*ArcCosh[c + d*x])^(5/2),x]","\frac{e^3 e^{-4 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)} \left(-16 b e^{4 \cosh ^{-1}(c+d x)} \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)-8 \sqrt{2} b e^{\frac{2 a}{b}+4 \cosh ^{-1}(c+d x)} \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+e^{\frac{4 a}{b}} \left(-\left(\left(e^{2 \cosh ^{-1}(c+d x)}+1\right)^2 \left(8 a \left(-e^{2 \cosh ^{-1}(c+d x)}+e^{4 \cosh ^{-1}(c+d x)}+1\right)+b \left(e^{4 \cosh ^{-1}(c+d x)}-1\right)+8 b \left(-e^{2 \cosh ^{-1}(c+d x)}+e^{4 \cosh ^{-1}(c+d x)}+1\right) \cosh ^{-1}(c+d x)\right)\right)+8 \sqrt{2} e^{\frac{2 a}{b}+4 \cosh ^{-1}(c+d x)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+16 e^{4 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)\right)\right)}{24 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}","-\frac{2 \sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{\sqrt{2 \pi } e^3 e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{\sqrt{2 \pi } e^3 e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{16 e^3 (c+d x)^4}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{4 e^3 (c+d x)^2}{b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}",1,"(e^3*(-16*b*E^(4*ArcCosh[c + d*x])*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, (-4*(a + b*ArcCosh[c + d*x]))/b] - 8*Sqrt[2]*b*E^((2*a)/b + 4*ArcCosh[c + d*x])*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, (-2*(a + b*ArcCosh[c + d*x]))/b] + E^((4*a)/b)*(-((1 + E^(2*ArcCosh[c + d*x]))^2*(b*(-1 + E^(4*ArcCosh[c + d*x])) + 8*a*(1 - E^(2*ArcCosh[c + d*x]) + E^(4*ArcCosh[c + d*x])) + 8*b*(1 - E^(2*ArcCosh[c + d*x]) + E^(4*ArcCosh[c + d*x]))*ArcCosh[c + d*x])) + 8*Sqrt[2]*E^((2*a)/b + 4*ArcCosh[c + d*x])*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, (2*(a + b*ArcCosh[c + d*x]))/b] + 16*E^(4*(a/b + ArcCosh[c + d*x]))*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, (4*(a + b*ArcCosh[c + d*x]))/b])))/(24*b^2*d*E^(4*(a/b + ArcCosh[c + d*x]))*(a + b*ArcCosh[c + d*x])^(3/2))","A",0
188,1,391,328,3.0386747,"\int \frac{(c e+d e x)^2}{\left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}} \, dx","Integrate[(c*e + d*e*x)^2/(a + b*ArcCosh[c + d*x])^(5/2),x]","\frac{e^2 e^{-3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)} \left(-6 \sqrt{3} b e^{3 \cosh ^{-1}(c+d x)} \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)-2 b e^{\frac{2 a}{b}+3 \cosh ^{-1}(c+d x)} \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)+2 e^{\frac{4 a}{b}+3 \cosh ^{-1}(c+d x)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+e^{\frac{3 a}{b}} \left(6 \sqrt{3} e^{3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)-\left(e^{2 \cosh ^{-1}(c+d x)}+1\right) \left(a \left(-4 e^{2 \cosh ^{-1}(c+d x)}+6 e^{4 \cosh ^{-1}(c+d x)}+6\right)+b \left(-4 e^{2 \cosh ^{-1}(c+d x)} \cosh ^{-1}(c+d x)+6 \cosh ^{-1}(c+d x)+e^{4 \cosh ^{-1}(c+d x)} \left(6 \cosh ^{-1}(c+d x)+1\right)-1\right)\right)\right)\right)}{12 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}","-\frac{\sqrt{\pi } e^2 e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{6 b^{5/2} d}-\frac{\sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{5/2} d}+\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{6 b^{5/2} d}+\frac{\sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{2 b^{5/2} d}-\frac{4 e^2 (c+d x)^3}{b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{8 e^2 (c+d x)}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}",1,"(e^2*(2*E^((4*a)/b + 3*ArcCosh[c + d*x])*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, a/b + ArcCosh[c + d*x]] - 6*Sqrt[3]*b*E^(3*ArcCosh[c + d*x])*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, (-3*(a + b*ArcCosh[c + d*x]))/b] - 2*b*E^((2*a)/b + 3*ArcCosh[c + d*x])*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)] + E^((3*a)/b)*(-((1 + E^(2*ArcCosh[c + d*x]))*(a*(6 - 4*E^(2*ArcCosh[c + d*x]) + 6*E^(4*ArcCosh[c + d*x])) + b*(-1 + 6*ArcCosh[c + d*x] - 4*E^(2*ArcCosh[c + d*x])*ArcCosh[c + d*x] + E^(4*ArcCosh[c + d*x])*(1 + 6*ArcCosh[c + d*x])))) + 6*Sqrt[3]*E^(3*(a/b + ArcCosh[c + d*x]))*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, (3*(a + b*ArcCosh[c + d*x]))/b])))/(12*b^2*d*E^(3*(a/b + ArcCosh[c + d*x]))*(a + b*ArcCosh[c + d*x])^(3/2))","A",0
189,1,687,216,5.483799,"\int \frac{c e+d e x}{\left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}} \, dx","Integrate[(c*e + d*e*x)/(a + b*ArcCosh[c + d*x])^(5/2),x]","\frac{e \left(-2 b^{3/2} c e^{-\frac{a}{b}} \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)+2 \sqrt{\pi } c \cosh \left(\frac{a}{b}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-2 \sqrt{2 \pi } \cosh \left(\frac{2 a}{b}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+2 \sqrt{\pi } c \sinh \left(\frac{a}{b}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-2 \sqrt{2 \pi } \sinh \left(\frac{2 a}{b}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-2 \sqrt{\pi } c \cosh \left(\frac{a}{b}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+2 \sqrt{2 \pi } \cosh \left(\frac{2 a}{b}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+2 \sqrt{\pi } c \sinh \left(\frac{a}{b}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-2 \sqrt{2 \pi } \sinh \left(\frac{2 a}{b}\right) \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+4 a \sqrt{b} c (c+d x)-2 \sqrt{b} c e^{-\cosh ^{-1}(c+d x)} \left(e^{2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)-4 a \sqrt{b} \cosh \left(2 \cosh ^{-1}(c+d x)\right)+2 \sqrt{b} c e^{a/b} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)+4 b^{3/2} c (c+d x) \cosh ^{-1}(c+d x)-4 b^{3/2} \cosh ^{-1}(c+d x) \cosh \left(2 \cosh ^{-1}(c+d x)\right)-b^{3/2} \sinh \left(2 \cosh ^{-1}(c+d x)\right)\right)}{3 b^{5/2} d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}","-\frac{2 \sqrt{2 \pi } e e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{2 \pi } e e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{8 e (c+d x)^2}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{4 e}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}",1,"(e*(4*a*Sqrt[b]*c*(c + d*x) + 4*b^(3/2)*c*(c + d*x)*ArcCosh[c + d*x] - (2*Sqrt[b]*c*(1 + E^(2*ArcCosh[c + d*x]))*(a + b*ArcCosh[c + d*x]))/E^ArcCosh[c + d*x] - 4*a*Sqrt[b]*Cosh[2*ArcCosh[c + d*x]] - 4*b^(3/2)*ArcCosh[c + d*x]*Cosh[2*ArcCosh[c + d*x]] + 2*c*Sqrt[Pi]*(a + b*ArcCosh[c + d*x])^(3/2)*Cosh[a/b]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]] - 2*Sqrt[2*Pi]*(a + b*ArcCosh[c + d*x])^(3/2)*Cosh[(2*a)/b]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]] - 2*c*Sqrt[Pi]*(a + b*ArcCosh[c + d*x])^(3/2)*Cosh[a/b]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]] + 2*Sqrt[2*Pi]*(a + b*ArcCosh[c + d*x])^(3/2)*Cosh[(2*a)/b]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]] + 2*Sqrt[b]*c*E^(a/b)*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, a/b + ArcCosh[c + d*x]] - (2*b^(3/2)*c*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)])/E^(a/b) + 2*c*Sqrt[Pi]*(a + b*ArcCosh[c + d*x])^(3/2)*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*Sinh[a/b] + 2*c*Sqrt[Pi]*(a + b*ArcCosh[c + d*x])^(3/2)*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*Sinh[a/b] - 2*Sqrt[2*Pi]*(a + b*ArcCosh[c + d*x])^(3/2)*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*Sinh[(2*a)/b] - 2*Sqrt[2*Pi]*(a + b*ArcCosh[c + d*x])^(3/2)*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*Sinh[(2*a)/b] - b^(3/2)*Sinh[2*ArcCosh[c + d*x]]))/(3*b^(5/2)*d*(a + b*ArcCosh[c + d*x])^(3/2))","B",0
190,1,219,165,1.2064645,"\int \frac{1}{\left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^(-5/2),x]","\frac{e^{-\frac{a+b \cosh ^{-1}(c+d x)}{b}} \left(2 e^{\frac{2 a}{b}+\cosh ^{-1}(c+d x)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-2 \left(e^{a/b} \left(\left(e^{2 \cosh ^{-1}(c+d x)}+1\right) \left(a+b \cosh ^{-1}(c+d x)\right)+b \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) e^{\cosh ^{-1}(c+d x)}\right)+b e^{\cosh ^{-1}(c+d x)} \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)\right)\right)}{3 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}","-\frac{2 \sqrt{\pi } e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}+\frac{2 \sqrt{\pi } e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{3 b^{5/2} d}-\frac{4 (c+d x)}{3 b^2 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{3 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}",1,"(2*E^((2*a)/b + ArcCosh[c + d*x])*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, a/b + ArcCosh[c + d*x]] - 2*(E^(a/b)*(b*E^ArcCosh[c + d*x]*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x) + (1 + E^(2*ArcCosh[c + d*x]))*(a + b*ArcCosh[c + d*x])) + b*E^ArcCosh[c + d*x]*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)]))/(3*b^2*d*E^((a + b*ArcCosh[c + d*x])/b)*(a + b*ArcCosh[c + d*x])^(3/2))","A",0
191,0,0,29,0.0996997,"\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}} \, dx","Integrate[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^(5/2)),x]","\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}},x\right)}{e}",0,"Integrate[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^(5/2)), x]","A",-1
192,1,654,552,5.0733432,"\int \frac{(c e+d e x)^4}{\left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}} \, dx","Integrate[(c*e + d*e*x)^4/(a + b*ArcCosh[c + d*x])^(7/2),x]","\frac{e^4 \left(-4 \left(e^{-\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \left(2 e^{\frac{a}{b}+\cosh ^{-1}(c+d x)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-2 a-2 b \cosh ^{-1}(c+d x)+b\right)+e^{-\frac{a}{b}} \left(a+b \cosh ^{-1}(c+d x)\right) \left(e^{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(2 a+2 b \cosh ^{-1}(c+d x)+b\right)+2 b \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)\right)+3 b^2 \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1)\right)-9 \left(a+b \cosh ^{-1}(c+d x)\right) \left(12 \sqrt{3} b e^{-\frac{3 a}{b}} \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+2 e^{-3 \cosh ^{-1}(c+d x)} \left(6 \sqrt{3} e^{3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+6 a \left(e^{6 \cosh ^{-1}(c+d x)}-1\right)-6 b \cosh ^{-1}(c+d x)+b e^{6 \cosh ^{-1}(c+d x)} \left(6 \cosh ^{-1}(c+d x)+1\right)+b\right)\right)-5 \left(a+b \cosh ^{-1}(c+d x)\right) \left(2 e^{-5 \cosh ^{-1}(c+d x)} \left(10 a \left(e^{10 \cosh ^{-1}(c+d x)}-1\right)-10 b \cosh ^{-1}(c+d x)+b e^{10 \cosh ^{-1}(c+d x)} \left(10 \cosh ^{-1}(c+d x)+1\right)+b\right)+20 \sqrt{5} b e^{-\frac{5 a}{b}} \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+20 \sqrt{5} e^{\frac{5 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{5 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)\right)-18 b^2 \sinh \left(3 \cosh ^{-1}(c+d x)\right)-6 b^2 \sinh \left(5 \cosh ^{-1}(c+d x)\right)\right)}{240 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}","\frac{\sqrt{\pi } e^4 e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{30 b^{7/2} d}+\frac{9 \sqrt{3 \pi } e^4 e^{\frac{3 a}{b}} \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{20 b^{7/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{\frac{5 a}{b}} \text{erf}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{7/2} d}+\frac{\sqrt{\pi } e^4 e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{30 b^{7/2} d}+\frac{9 \sqrt{3 \pi } e^4 e^{-\frac{3 a}{b}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{20 b^{7/2} d}+\frac{5 \sqrt{5 \pi } e^4 e^{-\frac{5 a}{b}} \text{erfi}\left(\frac{\sqrt{5} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{12 b^{7/2} d}-\frac{40 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{3 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{32 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{5 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{4 e^4 (c+d x)^5}{3 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}+\frac{16 e^4 (c+d x)^3}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{2 e^4 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^4}{5 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}",1,"(e^4*(-4*(3*b^2*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x) + ((a + b*ArcCosh[c + d*x])*(-2*a + b - 2*b*ArcCosh[c + d*x] + 2*E^(a/b + ArcCosh[c + d*x])*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, a/b + ArcCosh[c + d*x]]))/E^ArcCosh[c + d*x] + ((a + b*ArcCosh[c + d*x])*(E^(a/b + ArcCosh[c + d*x])*(2*a + b + 2*b*ArcCosh[c + d*x]) + 2*b*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)]))/E^(a/b)) - 9*(a + b*ArcCosh[c + d*x])*((12*Sqrt[3]*b*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, (-3*(a + b*ArcCosh[c + d*x]))/b])/E^((3*a)/b) + (2*(b + 6*a*(-1 + E^(6*ArcCosh[c + d*x])) - 6*b*ArcCosh[c + d*x] + b*E^(6*ArcCosh[c + d*x])*(1 + 6*ArcCosh[c + d*x]) + 6*Sqrt[3]*E^(3*(a/b + ArcCosh[c + d*x]))*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, (3*(a + b*ArcCosh[c + d*x]))/b]))/E^(3*ArcCosh[c + d*x])) - 5*(a + b*ArcCosh[c + d*x])*((2*(b + 10*a*(-1 + E^(10*ArcCosh[c + d*x])) - 10*b*ArcCosh[c + d*x] + b*E^(10*ArcCosh[c + d*x])*(1 + 10*ArcCosh[c + d*x])))/E^(5*ArcCosh[c + d*x]) + (20*Sqrt[5]*b*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, (-5*(a + b*ArcCosh[c + d*x]))/b])/E^((5*a)/b) + 20*Sqrt[5]*E^((5*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, (5*(a + b*ArcCosh[c + d*x]))/b]) - 18*b^2*Sinh[3*ArcCosh[c + d*x]] - 6*b^2*Sinh[5*ArcCosh[c + d*x]]))/(240*b^3*d*(a + b*ArcCosh[c + d*x])^(5/2))","A",0
193,1,445,441,3.1037235,"\int \frac{(c e+d e x)^3}{\left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}} \, dx","Integrate[(c*e + d*e*x)^3/(a + b*ArcCosh[c + d*x])^(7/2),x]","\frac{e^3 \left(-2 \left(\left(a+b \cosh ^{-1}(c+d x)\right) \left(2 e^{-2 \cosh ^{-1}(c+d x)} \left(4 a \left(e^{4 \cosh ^{-1}(c+d x)}-1\right)-4 b \cosh ^{-1}(c+d x)+b e^{4 \cosh ^{-1}(c+d x)} \left(4 \cosh ^{-1}(c+d x)+1\right)+b\right)+8 \sqrt{2} b e^{-\frac{2 a}{b}} \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+8 \sqrt{2} e^{\frac{2 a}{b}} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)\right)+3 b^2 \sinh \left(2 \cosh ^{-1}(c+d x)\right)\right)-4 e^{-4 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)} \left(a+b \cosh ^{-1}(c+d x)\right) \left(16 b e^{4 \cosh ^{-1}(c+d x)} \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+e^{\frac{4 a}{b}} \left(16 e^{4 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{4 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+8 a \left(e^{8 \cosh ^{-1}(c+d x)}-1\right)-8 b \cosh ^{-1}(c+d x)+b e^{8 \cosh ^{-1}(c+d x)} \left(8 \cosh ^{-1}(c+d x)+1\right)+b\right)\right)-3 b^2 \sinh \left(4 \cosh ^{-1}(c+d x)\right)\right)}{60 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}","\frac{16 \sqrt{\pi } e^3 e^{\frac{4 a}{b}} \text{erf}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 \sqrt{2 \pi } e^3 e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{16 \sqrt{\pi } e^3 e^{-\frac{4 a}{b}} \text{erfi}\left(\frac{2 \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 \sqrt{2 \pi } e^3 e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{128 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{15 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{16 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{5 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{16 e^3 (c+d x)^4}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}+\frac{4 e^3 (c+d x)^2}{5 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{2 e^3 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3}{5 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}",1,"(e^3*((-4*(a + b*ArcCosh[c + d*x])*(16*b*E^(4*ArcCosh[c + d*x])*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, (-4*(a + b*ArcCosh[c + d*x]))/b] + E^((4*a)/b)*(b + 8*a*(-1 + E^(8*ArcCosh[c + d*x])) - 8*b*ArcCosh[c + d*x] + b*E^(8*ArcCosh[c + d*x])*(1 + 8*ArcCosh[c + d*x]) + 16*E^(4*(a/b + ArcCosh[c + d*x]))*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, (4*(a + b*ArcCosh[c + d*x]))/b])))/E^(4*(a/b + ArcCosh[c + d*x])) - 2*((a + b*ArcCosh[c + d*x])*((2*(b + 4*a*(-1 + E^(4*ArcCosh[c + d*x])) - 4*b*ArcCosh[c + d*x] + b*E^(4*ArcCosh[c + d*x])*(1 + 4*ArcCosh[c + d*x])))/E^(2*ArcCosh[c + d*x]) + (8*Sqrt[2]*b*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, (-2*(a + b*ArcCosh[c + d*x]))/b])/E^((2*a)/b) + 8*Sqrt[2]*E^((2*a)/b)*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, (2*(a + b*ArcCosh[c + d*x]))/b]) + 3*b^2*Sinh[2*ArcCosh[c + d*x]]) - 3*b^2*Sinh[4*ArcCosh[c + d*x]]))/(60*b^3*d*(a + b*ArcCosh[c + d*x])^(5/2))","A",0
194,1,452,431,2.920428,"\int \frac{(c e+d e x)^2}{\left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}} \, dx","Integrate[(c*e + d*e*x)^2/(a + b*ArcCosh[c + d*x])^(7/2),x]","\frac{e^2 \left(-2 e^{-\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \left(2 e^{\frac{a}{b}+\cosh ^{-1}(c+d x)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-2 a-2 b \cosh ^{-1}(c+d x)+b\right)-2 e^{-\frac{a}{b}} \left(a+b \cosh ^{-1}(c+d x)\right) \left(e^{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(2 a+2 b \cosh ^{-1}(c+d x)+b\right)+2 b \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)\right)-3 \left(a+b \cosh ^{-1}(c+d x)\right) \left(12 \sqrt{3} b e^{-\frac{3 a}{b}} \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+2 e^{-3 \cosh ^{-1}(c+d x)} \left(6 \sqrt{3} e^{3 \left(\frac{a}{b}+\cosh ^{-1}(c+d x)\right)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{3 \left(a+b \cosh ^{-1}(c+d x)\right)}{b}\right)+6 a \left(e^{6 \cosh ^{-1}(c+d x)}-1\right)-6 b \cosh ^{-1}(c+d x)+b e^{6 \cosh ^{-1}(c+d x)} \left(6 \cosh ^{-1}(c+d x)+1\right)+b\right)\right)-6 b^2 \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1)-6 b^2 \sinh \left(3 \cosh ^{-1}(c+d x)\right)\right)}{60 b^3 d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}","\frac{\sqrt{\pi } e^2 e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{3 \sqrt{3 \pi } e^2 e^{\frac{3 a}{b}} \text{erf}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{5 b^{7/2} d}+\frac{\sqrt{\pi } e^2 e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{3 \sqrt{3 \pi } e^2 e^{-\frac{3 a}{b}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{5 b^{7/2} d}-\frac{24 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{5 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}+\frac{16 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{15 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{4 e^2 (c+d x)^3}{5 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}+\frac{8 e^2 (c+d x)}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{2 e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^2}{5 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}",1,"(e^2*(-6*b^2*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x) - (2*(a + b*ArcCosh[c + d*x])*(-2*a + b - 2*b*ArcCosh[c + d*x] + 2*E^(a/b + ArcCosh[c + d*x])*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, a/b + ArcCosh[c + d*x]]))/E^ArcCosh[c + d*x] - (2*(a + b*ArcCosh[c + d*x])*(E^(a/b + ArcCosh[c + d*x])*(2*a + b + 2*b*ArcCosh[c + d*x]) + 2*b*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)]))/E^(a/b) - 3*(a + b*ArcCosh[c + d*x])*((12*Sqrt[3]*b*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, (-3*(a + b*ArcCosh[c + d*x]))/b])/E^((3*a)/b) + (2*(b + 6*a*(-1 + E^(6*ArcCosh[c + d*x])) - 6*b*ArcCosh[c + d*x] + b*E^(6*ArcCosh[c + d*x])*(1 + 6*ArcCosh[c + d*x]) + 6*Sqrt[3]*E^(3*(a/b + ArcCosh[c + d*x]))*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, (3*(a + b*ArcCosh[c + d*x]))/b]))/E^(3*ArcCosh[c + d*x])) - 6*b^2*Sinh[3*ArcCosh[c + d*x]]))/(60*b^3*d*(a + b*ArcCosh[c + d*x])^(5/2))","A",0
195,1,916,266,4.7686718,"\int \frac{c e+d e x}{\left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}} \, dx","Integrate[(c*e + d*e*x)/(a + b*ArcCosh[c + d*x])^(7/2),x]","\frac{e \left(8 c \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \cosh ^{-1}(c+d x)^2 b^{5/2}+4 c (c+d x) \cosh ^{-1}(c+d x) b^{5/2}-4 \cosh ^{-1}(c+d x) \cosh \left(2 \cosh ^{-1}(c+d x)\right) b^{5/2}-16 \cosh ^{-1}(c+d x)^2 \sinh \left(2 \cosh ^{-1}(c+d x)\right) b^{5/2}-3 \sinh \left(2 \cosh ^{-1}(c+d x)\right) b^{5/2}+4 a c (c+d x) b^{3/2}+16 a c \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \cosh ^{-1}(c+d x) b^{3/2}-4 a \cosh \left(2 \cosh ^{-1}(c+d x)\right) b^{3/2}-32 a \cosh ^{-1}(c+d x) \sinh \left(2 \cosh ^{-1}(c+d x)\right) b^{3/2}+8 a^2 c \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1) \sqrt{b}-2 c e^{-\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \left(-2 a+b-2 b \cosh ^{-1}(c+d x)+2 e^{\frac{a}{b}+\cosh ^{-1}(c+d x)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)\right) \sqrt{b}-2 c e^{-\frac{a}{b}} \left(a+b \cosh ^{-1}(c+d x)\right) \left(2 b \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right) \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2}+e^{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(2 a+b+2 b \cosh ^{-1}(c+d x)\right)\right) \sqrt{b}-16 a^2 \sinh \left(2 \cosh ^{-1}(c+d x)\right) \sqrt{b}-4 c \sqrt{\pi } \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2} \cosh \left(\frac{a}{b}\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+8 \sqrt{2 \pi } \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2} \cosh \left(\frac{2 a}{b}\right) \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-4 c \sqrt{\pi } \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2} \cosh \left(\frac{a}{b}\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)+8 \sqrt{2 \pi } \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2} \cosh \left(\frac{2 a}{b}\right) \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)-4 c \sqrt{\pi } \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \sinh \left(\frac{a}{b}\right)+4 c \sqrt{\pi } \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \sinh \left(\frac{a}{b}\right)+8 \sqrt{2 \pi } \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \sinh \left(\frac{2 a}{b}\right)-8 \sqrt{2 \pi } \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right) \sinh \left(\frac{2 a}{b}\right)\right)}{15 b^{7/2} d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}","\frac{8 \sqrt{2 \pi } e e^{\frac{2 a}{b}} \text{erf}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{8 \sqrt{2 \pi } e e^{-\frac{2 a}{b}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{32 e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{15 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{8 e (c+d x)^2}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}+\frac{4 e}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{2 e \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)}{5 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}",1,"(e*(4*a*b^(3/2)*c*(c + d*x) + 8*a^2*Sqrt[b]*c*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x) + 4*b^(5/2)*c*(c + d*x)*ArcCosh[c + d*x] + 16*a*b^(3/2)*c*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*ArcCosh[c + d*x] + 8*b^(5/2)*c*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x)*ArcCosh[c + d*x]^2 - 4*a*b^(3/2)*Cosh[2*ArcCosh[c + d*x]] - 4*b^(5/2)*ArcCosh[c + d*x]*Cosh[2*ArcCosh[c + d*x]] - 4*c*Sqrt[Pi]*(a + b*ArcCosh[c + d*x])^(5/2)*Cosh[a/b]*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]] + 8*Sqrt[2*Pi]*(a + b*ArcCosh[c + d*x])^(5/2)*Cosh[(2*a)/b]*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]] - 4*c*Sqrt[Pi]*(a + b*ArcCosh[c + d*x])^(5/2)*Cosh[a/b]*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]] + 8*Sqrt[2*Pi]*(a + b*ArcCosh[c + d*x])^(5/2)*Cosh[(2*a)/b]*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]] - (2*Sqrt[b]*c*(a + b*ArcCosh[c + d*x])*(-2*a + b - 2*b*ArcCosh[c + d*x] + 2*E^(a/b + ArcCosh[c + d*x])*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, a/b + ArcCosh[c + d*x]]))/E^ArcCosh[c + d*x] - (2*Sqrt[b]*c*(a + b*ArcCosh[c + d*x])*(E^(a/b + ArcCosh[c + d*x])*(2*a + b + 2*b*ArcCosh[c + d*x]) + 2*b*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)]))/E^(a/b) - 4*c*Sqrt[Pi]*(a + b*ArcCosh[c + d*x])^(5/2)*Erf[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*Sinh[a/b] + 4*c*Sqrt[Pi]*(a + b*ArcCosh[c + d*x])^(5/2)*Erfi[Sqrt[a + b*ArcCosh[c + d*x]]/Sqrt[b]]*Sinh[a/b] + 8*Sqrt[2*Pi]*(a + b*ArcCosh[c + d*x])^(5/2)*Erf[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*Sinh[(2*a)/b] - 8*Sqrt[2*Pi]*(a + b*ArcCosh[c + d*x])^(5/2)*Erfi[(Sqrt[2]*Sqrt[a + b*ArcCosh[c + d*x]])/Sqrt[b]]*Sinh[(2*a)/b] - 16*a^2*Sqrt[b]*Sinh[2*ArcCosh[c + d*x]] - 3*b^(5/2)*Sinh[2*ArcCosh[c + d*x]] - 32*a*b^(3/2)*ArcCosh[c + d*x]*Sinh[2*ArcCosh[c + d*x]] - 16*b^(5/2)*ArcCosh[c + d*x]^2*Sinh[2*ArcCosh[c + d*x]]))/(15*b^(7/2)*d*(a + b*ArcCosh[c + d*x])^(5/2))","B",0
196,1,243,209,0.807004,"\int \frac{1}{\left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^(-7/2),x]","\frac{-\frac{2 e^{-\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \left(2 e^{\frac{a}{b}+\cosh ^{-1}(c+d x)} \sqrt{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right) \Gamma \left(\frac{1}{2},\frac{a}{b}+\cosh ^{-1}(c+d x)\right)-2 a-2 b \cosh ^{-1}(c+d x)+b\right)}{b^2}-\frac{2 e^{-\frac{a}{b}} \left(a+b \cosh ^{-1}(c+d x)\right) \left(e^{\frac{a}{b}+\cosh ^{-1}(c+d x)} \left(2 a+2 b \cosh ^{-1}(c+d x)+b\right)+2 b \left(-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{a+b \cosh ^{-1}(c+d x)}{b}\right)\right)}{b^2}-6 \sqrt{\frac{c+d x-1}{c+d x+1}} (c+d x+1)}{15 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}","\frac{4 \sqrt{\pi } e^{a/b} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}+\frac{4 \sqrt{\pi } e^{-\frac{a}{b}} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}(c+d x)}}{\sqrt{b}}\right)}{15 b^{7/2} d}-\frac{8 \sqrt{c+d x-1} \sqrt{c+d x+1}}{15 b^3 d \sqrt{a+b \cosh ^{-1}(c+d x)}}-\frac{4 (c+d x)}{15 b^2 d \left(a+b \cosh ^{-1}(c+d x)\right)^{3/2}}-\frac{2 \sqrt{c+d x-1} \sqrt{c+d x+1}}{5 b d \left(a+b \cosh ^{-1}(c+d x)\right)^{5/2}}",1,"(-6*Sqrt[(-1 + c + d*x)/(1 + c + d*x)]*(1 + c + d*x) - (2*(a + b*ArcCosh[c + d*x])*(-2*a + b - 2*b*ArcCosh[c + d*x] + 2*E^(a/b + ArcCosh[c + d*x])*Sqrt[a/b + ArcCosh[c + d*x]]*(a + b*ArcCosh[c + d*x])*Gamma[1/2, a/b + ArcCosh[c + d*x]]))/(b^2*E^ArcCosh[c + d*x]) - (2*(a + b*ArcCosh[c + d*x])*(E^(a/b + ArcCosh[c + d*x])*(2*a + b + 2*b*ArcCosh[c + d*x]) + 2*b*(-((a + b*ArcCosh[c + d*x])/b))^(3/2)*Gamma[1/2, -((a + b*ArcCosh[c + d*x])/b)]))/(b^2*E^(a/b)))/(15*b*d*(a + b*ArcCosh[c + d*x])^(5/2))","A",0
197,0,0,29,0.0988055,"\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}} \, dx","Integrate[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^(7/2)),x]","\int \frac{1}{(c e+d e x) \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}} \, dx","\frac{\text{Int}\left(\frac{1}{(c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)^{7/2}},x\right)}{e}",0,"Integrate[1/((c*e + d*e*x)*(a + b*ArcCosh[c + d*x])^(7/2)), x]","A",-1
198,1,150,189,0.3711324,"\int (c e+d e x)^{7/2} \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Integrate[(c*e + d*e*x)^(7/2)*(a + b*ArcCosh[c + d*x]),x]","\frac{2 (e (c+d x))^{7/2} \left((c+d x)^{9/2} \left(a+b \cosh ^{-1}(c+d x)\right)+\frac{2 b (c+d x)^{3/2} \left(-7 \sqrt{1-(c+d x)^2} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};(c+d x)^2\right)+5 \left(1-(c+d x)^2\right) (c+d x)^2+7 \left(1-(c+d x)^2\right)\right)}{45 \sqrt{c+d x-1} \sqrt{c+d x+1}}\right)}{9 d (c+d x)^{7/2}}","\frac{2 (e (c+d x))^{9/2} \left(a+b \cosh ^{-1}(c+d x)\right)}{9 d e}-\frac{28 b e^3 \sqrt{-c-d x+1} \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c+d x+1}}{\sqrt{2}}\right)\right|2\right)}{135 d \sqrt{-c-d x} \sqrt{c+d x-1}}-\frac{28 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{3/2}}{405 d}-\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{7/2}}{81 d}",1,"(2*(e*(c + d*x))^(7/2)*((c + d*x)^(9/2)*(a + b*ArcCosh[c + d*x]) + (2*b*(c + d*x)^(3/2)*(7*(1 - (c + d*x)^2) + 5*(c + d*x)^2*(1 - (c + d*x)^2) - 7*Sqrt[1 - (c + d*x)^2]*Hypergeometric2F1[1/2, 3/4, 7/4, (c + d*x)^2]))/(45*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])))/(9*d*(c + d*x)^(7/2))","C",1
199,1,180,169,0.2761061,"\int (c e+d e x)^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Integrate[(c*e + d*e*x)^(5/2)*(a + b*ArcCosh[c + d*x]),x]","\frac{2 (e (c+d x))^{5/2} \left(21 a \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3-10 b \sqrt{1-(c+d x)^2} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};(c+d x)^2\right)-6 b (c+d x)^4-4 b (c+d x)^2+21 b \sqrt{c+d x-1} \sqrt{c+d x+1} (c+d x)^3 \cosh ^{-1}(c+d x)+10 b\right)}{147 d \sqrt{\frac{c+d x-1}{c+d x}} (c+d x)^{5/2} \sqrt{c+d x+1}}","\frac{2 (e (c+d x))^{7/2} \left(a+b \cosh ^{-1}(c+d x)\right)}{7 d e}-\frac{20 b e^{5/2} \sqrt{-c-d x+1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{147 d \sqrt{c+d x-1}}-\frac{20 b e^2 \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{e (c+d x)}}{147 d}-\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{5/2}}{49 d}",1,"(2*(e*(c + d*x))^(5/2)*(10*b - 4*b*(c + d*x)^2 - 6*b*(c + d*x)^4 + 21*a*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x] + 21*b*Sqrt[-1 + c + d*x]*(c + d*x)^3*Sqrt[1 + c + d*x]*ArcCosh[c + d*x] - 10*b*Sqrt[1 - (c + d*x)^2]*Hypergeometric2F1[1/4, 1/2, 5/4, (c + d*x)^2]))/(147*d*Sqrt[(-1 + c + d*x)/(c + d*x)]*(c + d*x)^(5/2)*Sqrt[1 + c + d*x])","C",1
200,1,109,145,0.4870701,"\int (c e+d e x)^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Integrate[(c*e + d*e*x)^(3/2)*(a + b*ArcCosh[c + d*x]),x]","\frac{2 (e (c+d x))^{3/2} \left(5 (c+d x) \left(a+b \cosh ^{-1}(c+d x)\right)-\frac{2 b \left(c^2+\sqrt{1-(c+d x)^2} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};(c+d x)^2\right)+2 c d x+d^2 x^2-1\right)}{\sqrt{c+d x-1} \sqrt{c+d x+1}}\right)}{25 d}","\frac{2 (e (c+d x))^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right)}{5 d e}-\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{3/2}}{25 d}-\frac{12 b e \sqrt{-c-d x+1} \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c+d x+1}}{\sqrt{2}}\right)\right|2\right)}{25 d \sqrt{-c-d x} \sqrt{c+d x-1}}",1,"(2*(e*(c + d*x))^(3/2)*(5*(c + d*x)*(a + b*ArcCosh[c + d*x]) - (2*b*(-1 + c^2 + 2*c*d*x + d^2*x^2 + Sqrt[1 - (c + d*x)^2]*Hypergeometric2F1[1/2, 3/4, 7/4, (c + d*x)^2]))/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])))/(25*d)","C",1
201,1,131,127,0.4617447,"\int \sqrt{c e+d e x} \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Integrate[Sqrt[c*e + d*e*x]*(a + b*ArcCosh[c + d*x]),x]","\frac{\sqrt{e (c+d x)} \left(\frac{2}{3} (c+d x)^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)-\frac{4 b \left(c^2+\sqrt{1-(c+d x)^2} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};(c+d x)^2\right)+2 c d x+d^2 x^2-1\right)}{9 \sqrt{\frac{c+d x-1}{c+d x}} \sqrt{c+d x+1}}\right)}{d \sqrt{c+d x}}","\frac{2 (e (c+d x))^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e}-\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{e (c+d x)}}{9 d}-\frac{4 b \sqrt{e} \sqrt{-c-d x+1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{9 d \sqrt{c+d x-1}}",1,"(Sqrt[e*(c + d*x)]*((2*(c + d*x)^(3/2)*(a + b*ArcCosh[c + d*x]))/3 - (4*b*(-1 + c^2 + 2*c*d*x + d^2*x^2 + Sqrt[1 - (c + d*x)^2]*Hypergeometric2F1[1/4, 1/2, 5/4, (c + d*x)^2]))/(9*Sqrt[(-1 + c + d*x)/(c + d*x)]*Sqrt[1 + c + d*x])))/(d*Sqrt[c + d*x])","C",1
202,1,94,104,0.1905187,"\int \frac{a+b \cosh ^{-1}(c+d x)}{\sqrt{c e+d e x}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])/Sqrt[c*e + d*e*x],x]","\frac{2 \sqrt{e (c+d x)} \left(3 \left(a+b \cosh ^{-1}(c+d x)\right)-\frac{2 b (c+d x) \sqrt{1-(c+d x)^2} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};(c+d x)^2\right)}{\sqrt{c+d x-1} \sqrt{c+d x+1}}\right)}{3 d e}","\frac{2 \sqrt{e (c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right)}{d e}-\frac{4 b \sqrt{-c-d x+1} \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c+d x+1}}{\sqrt{2}}\right)\right|2\right)}{d e \sqrt{-c-d x} \sqrt{c+d x-1}}",1,"(2*Sqrt[e*(c + d*x)]*(3*(a + b*ArcCosh[c + d*x]) - (2*b*(c + d*x)*Sqrt[1 - (c + d*x)^2]*Hypergeometric2F1[1/2, 3/4, 7/4, (c + d*x)^2])/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])))/(3*d*e)","C",1
203,1,92,84,0.1653036,"\int \frac{a+b \cosh ^{-1}(c+d x)}{(c e+d e x)^{3/2}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x)^(3/2),x]","\frac{2 \left(-a+\frac{2 b (c+d x) \sqrt{1-(c+d x)^2} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};(c+d x)^2\right)}{\sqrt{c+d x-1} \sqrt{c+d x+1}}-b \cosh ^{-1}(c+d x)\right)}{d e \sqrt{e (c+d x)}}","\frac{4 b \sqrt{-c-d x+1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{d e^{3/2} \sqrt{c+d x-1}}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{d e \sqrt{e (c+d x)}}",1,"(2*(-a - b*ArcCosh[c + d*x] + (2*b*(c + d*x)*Sqrt[1 - (c + d*x)^2]*Hypergeometric2F1[1/4, 1/2, 5/4, (c + d*x)^2])/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])))/(d*e*Sqrt[e*(c + d*x)])","C",1
204,1,94,150,0.1459155,"\int \frac{a+b \cosh ^{-1}(c+d x)}{(c e+d e x)^{5/2}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x)^(5/2),x]","\frac{2 \left(-a-\frac{2 b (c+d x) \sqrt{1-(c+d x)^2} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};(c+d x)^2\right)}{\sqrt{c+d x-1} \sqrt{c+d x+1}}-b \cosh ^{-1}(c+d x)\right)}{3 d e (e (c+d x))^{3/2}}","-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e (e (c+d x))^{3/2}}-\frac{4 b \sqrt{-c-d x+1} \sqrt{e (c+d x)} E\left(\left.\sin ^{-1}\left(\frac{\sqrt{c+d x+1}}{\sqrt{2}}\right)\right|2\right)}{3 d e^3 \sqrt{-c-d x} \sqrt{c+d x-1}}+\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1}}{3 d e^2 \sqrt{e (c+d x)}}",1,"(2*(-a - b*ArcCosh[c + d*x] - (2*b*(c + d*x)*Sqrt[1 - (c + d*x)^2]*Hypergeometric2F1[-1/4, 1/2, 3/4, (c + d*x)^2])/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])))/(3*d*e*(e*(c + d*x))^(3/2))","C",1
205,1,94,130,0.1586855,"\int \frac{a+b \cosh ^{-1}(c+d x)}{(c e+d e x)^{7/2}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])/(c*e + d*e*x)^(7/2),x]","\frac{2 \left(-3 \left(a+b \cosh ^{-1}(c+d x)\right)-\frac{2 b (c+d x) \sqrt{1-(c+d x)^2} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};(c+d x)^2\right)}{\sqrt{c+d x-1} \sqrt{c+d x+1}}\right)}{15 d e (e (c+d x))^{5/2}}","-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)}{5 d e (e (c+d x))^{5/2}}+\frac{4 b \sqrt{-c-d x+1} F\left(\left.\sin ^{-1}\left(\frac{\sqrt{e (c+d x)}}{\sqrt{e}}\right)\right|-1\right)}{15 d e^{7/2} \sqrt{c+d x-1}}+\frac{4 b \sqrt{c+d x-1} \sqrt{c+d x+1}}{15 d e^2 (e (c+d x))^{3/2}}",1,"(2*(-3*(a + b*ArcCosh[c + d*x]) - (2*b*(c + d*x)*Sqrt[1 - (c + d*x)^2]*Hypergeometric2F1[-3/4, 1/2, 1/4, (c + d*x)^2])/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])))/(15*d*e*(e*(c + d*x))^(5/2))","C",1
206,1,140,153,0.5422164,"\int (c e+d e x)^{7/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Integrate[(c*e + d*e*x)^(7/2)*(a + b*ArcCosh[c + d*x])^2,x]","\frac{2 (e (c+d x))^{9/2} \left(143 \left(a+b \cosh ^{-1}(c+d x)\right)^2-4 b (c+d x) \left(2 b (c+d x) \, _3F_2\left(1,\frac{13}{4},\frac{13}{4};\frac{15}{4},\frac{17}{4};(c+d x)^2\right)+\frac{13 \sqrt{1-(c+d x)^2} \, _2F_1\left(\frac{1}{2},\frac{11}{4};\frac{15}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{\sqrt{c+d x-1} \sqrt{c+d x+1}}\right)\right)}{1287 d e}","-\frac{16 b^2 (e (c+d x))^{13/2} \, _3F_2\left(1,\frac{13}{4},\frac{13}{4};\frac{15}{4},\frac{17}{4};(c+d x)^2\right)}{1287 d e^3}-\frac{8 b \sqrt{-c-d x+1} (e (c+d x))^{11/2} \, _2F_1\left(\frac{1}{2},\frac{11}{4};\frac{15}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{99 d e^2 \sqrt{c+d x-1}}+\frac{2 (e (c+d x))^{9/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{9 d e}",1,"(2*(e*(c + d*x))^(9/2)*(143*(a + b*ArcCosh[c + d*x])^2 - 4*b*(c + d*x)*((13*Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[1/2, 11/4, 15/4, (c + d*x)^2])/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]) + 2*b*(c + d*x)*HypergeometricPFQ[{1, 13/4, 13/4}, {15/4, 17/4}, (c + d*x)^2])))/(1287*d*e)","A",1
207,1,140,153,0.4820023,"\int (c e+d e x)^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Integrate[(c*e + d*e*x)^(5/2)*(a + b*ArcCosh[c + d*x])^2,x]","\frac{2 (e (c+d x))^{7/2} \left(99 \left(a+b \cosh ^{-1}(c+d x)\right)^2-4 b (c+d x) \left(2 b (c+d x) \, _3F_2\left(1,\frac{11}{4},\frac{11}{4};\frac{13}{4},\frac{15}{4};(c+d x)^2\right)+\frac{11 \sqrt{1-(c+d x)^2} \, _2F_1\left(\frac{1}{2},\frac{9}{4};\frac{13}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{\sqrt{c+d x-1} \sqrt{c+d x+1}}\right)\right)}{693 d e}","-\frac{16 b^2 (e (c+d x))^{11/2} \, _3F_2\left(1,\frac{11}{4},\frac{11}{4};\frac{13}{4},\frac{15}{4};(c+d x)^2\right)}{693 d e^3}-\frac{8 b \sqrt{-c-d x+1} (e (c+d x))^{9/2} \, _2F_1\left(\frac{1}{2},\frac{9}{4};\frac{13}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{63 d e^2 \sqrt{c+d x-1}}+\frac{2 (e (c+d x))^{7/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{7 d e}",1,"(2*(e*(c + d*x))^(7/2)*(99*(a + b*ArcCosh[c + d*x])^2 - 4*b*(c + d*x)*((11*Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[1/2, 9/4, 13/4, (c + d*x)^2])/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]) + 2*b*(c + d*x)*HypergeometricPFQ[{1, 11/4, 11/4}, {13/4, 15/4}, (c + d*x)^2])))/(693*d*e)","A",1
208,1,140,153,0.4891616,"\int (c e+d e x)^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Integrate[(c*e + d*e*x)^(3/2)*(a + b*ArcCosh[c + d*x])^2,x]","\frac{2 (e (c+d x))^{5/2} \left(63 \left(a+b \cosh ^{-1}(c+d x)\right)^2-4 b (c+d x) \left(2 b (c+d x) \, _3F_2\left(1,\frac{9}{4},\frac{9}{4};\frac{11}{4},\frac{13}{4};(c+d x)^2\right)+\frac{9 \sqrt{1-(c+d x)^2} \, _2F_1\left(\frac{1}{2},\frac{7}{4};\frac{11}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{\sqrt{c+d x-1} \sqrt{c+d x+1}}\right)\right)}{315 d e}","-\frac{16 b^2 (e (c+d x))^{9/2} \, _3F_2\left(1,\frac{9}{4},\frac{9}{4};\frac{11}{4},\frac{13}{4};(c+d x)^2\right)}{315 d e^3}-\frac{8 b \sqrt{-c-d x+1} (e (c+d x))^{7/2} \, _2F_1\left(\frac{1}{2},\frac{7}{4};\frac{11}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{35 d e^2 \sqrt{c+d x-1}}+\frac{2 (e (c+d x))^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{5 d e}",1,"(2*(e*(c + d*x))^(5/2)*(63*(a + b*ArcCosh[c + d*x])^2 - 4*b*(c + d*x)*((9*Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[1/2, 7/4, 11/4, (c + d*x)^2])/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]) + 2*b*(c + d*x)*HypergeometricPFQ[{1, 9/4, 9/4}, {11/4, 13/4}, (c + d*x)^2])))/(315*d*e)","A",1
209,1,140,153,0.4335045,"\int \sqrt{c e+d e x} \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Integrate[Sqrt[c*e + d*e*x]*(a + b*ArcCosh[c + d*x])^2,x]","\frac{2 (e (c+d x))^{3/2} \left(35 \left(a+b \cosh ^{-1}(c+d x)\right)^2-4 b (c+d x) \left(2 b (c+d x) \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};(c+d x)^2\right)+\frac{7 \sqrt{1-(c+d x)^2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{\sqrt{c+d x-1} \sqrt{c+d x+1}}\right)\right)}{105 d e}","-\frac{16 b^2 (e (c+d x))^{7/2} \, _3F_2\left(1,\frac{7}{4},\frac{7}{4};\frac{9}{4},\frac{11}{4};(c+d x)^2\right)}{105 d e^3}-\frac{8 b \sqrt{-c-d x+1} (e (c+d x))^{5/2} \, _2F_1\left(\frac{1}{2},\frac{5}{4};\frac{9}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{15 d e^2 \sqrt{c+d x-1}}+\frac{2 (e (c+d x))^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d e}",1,"(2*(e*(c + d*x))^(3/2)*(35*(a + b*ArcCosh[c + d*x])^2 - 4*b*(c + d*x)*((7*Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[1/2, 5/4, 9/4, (c + d*x)^2])/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]) + 2*b*(c + d*x)*HypergeometricPFQ[{1, 7/4, 7/4}, {9/4, 11/4}, (c + d*x)^2])))/(105*d*e)","A",1
210,1,140,151,0.2999827,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{\sqrt{c e+d e x}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^2/Sqrt[c*e + d*e*x],x]","\frac{2 \sqrt{e (c+d x)} \left(15 \left(a+b \cosh ^{-1}(c+d x)\right)^2-4 b (c+d x) \left(2 b (c+d x) \, _3F_2\left(1,\frac{5}{4},\frac{5}{4};\frac{7}{4},\frac{9}{4};(c+d x)^2\right)+\frac{5 \sqrt{1-(c+d x)^2} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{\sqrt{c+d x-1} \sqrt{c+d x+1}}\right)\right)}{15 d e}","-\frac{16 b^2 (e (c+d x))^{5/2} \, _3F_2\left(1,\frac{5}{4},\frac{5}{4};\frac{7}{4},\frac{9}{4};(c+d x)^2\right)}{15 d e^3}-\frac{8 b \sqrt{-c-d x+1} (e (c+d x))^{3/2} \, _2F_1\left(\frac{1}{2},\frac{3}{4};\frac{7}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e^2 \sqrt{c+d x-1}}+\frac{2 \sqrt{e (c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e}",1,"(2*Sqrt[e*(c + d*x)]*(15*(a + b*ArcCosh[c + d*x])^2 - 4*b*(c + d*x)*((5*Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[1/2, 3/4, 7/4, (c + d*x)^2])/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]) + 2*b*(c + d*x)*HypergeometricPFQ[{1, 5/4, 5/4}, {7/4, 9/4}, (c + d*x)^2])))/(15*d*e)","A",1
211,1,140,149,0.3020606,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{(c e+d e x)^{3/2}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^2/(c*e + d*e*x)^(3/2),x]","\frac{2 \left(4 b (c+d x) \left(2 b (c+d x) \, _3F_2\left(\frac{3}{4},\frac{3}{4},1;\frac{5}{4},\frac{7}{4};(c+d x)^2\right)+\frac{3 \sqrt{1-(c+d x)^2} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{\sqrt{c+d x-1} \sqrt{c+d x+1}}\right)-3 \left(a+b \cosh ^{-1}(c+d x)\right)^2\right)}{3 d e \sqrt{e (c+d x)}}","\frac{16 b^2 (e (c+d x))^{3/2} \, _3F_2\left(\frac{3}{4},\frac{3}{4},1;\frac{5}{4},\frac{7}{4};(c+d x)^2\right)}{3 d e^3}+\frac{8 b \sqrt{-c-d x+1} \sqrt{e (c+d x)} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2 \sqrt{c+d x-1}}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e \sqrt{e (c+d x)}}",1,"(2*(-3*(a + b*ArcCosh[c + d*x])^2 + 4*b*(c + d*x)*((3*Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[1/4, 1/2, 5/4, (c + d*x)^2])/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]) + 2*b*(c + d*x)*HypergeometricPFQ[{3/4, 3/4, 1}, {5/4, 7/4}, (c + d*x)^2])))/(3*d*e*Sqrt[e*(c + d*x)])","A",1
212,1,140,153,0.343481,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{(c e+d e x)^{5/2}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^2/(c*e + d*e*x)^(5/2),x]","\frac{2 \left(4 b (c+d x) \left(-2 b (c+d x) \, _3F_2\left(\frac{1}{4},\frac{1}{4},1;\frac{3}{4},\frac{5}{4};(c+d x)^2\right)-\frac{\sqrt{1-(c+d x)^2} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{\sqrt{c+d x-1} \sqrt{c+d x+1}}\right)-\left(a+b \cosh ^{-1}(c+d x)\right)^2\right)}{3 d e (e (c+d x))^{3/2}}","-\frac{16 b^2 \sqrt{e (c+d x)} \, _3F_2\left(\frac{1}{4},\frac{1}{4},1;\frac{3}{4},\frac{5}{4};(c+d x)^2\right)}{3 d e^3}-\frac{8 b \sqrt{-c-d x+1} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{3 d e^2 \sqrt{c+d x-1} \sqrt{e (c+d x)}}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{3 d e (e (c+d x))^{3/2}}",1,"(2*(-(a + b*ArcCosh[c + d*x])^2 + 4*b*(c + d*x)*(-((Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[-1/4, 1/2, 3/4, (c + d*x)^2])/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])) - 2*b*(c + d*x)*HypergeometricPFQ[{1/4, 1/4, 1}, {3/4, 5/4}, (c + d*x)^2])))/(3*d*e*(e*(c + d*x))^(3/2))","A",1
213,1,140,153,0.3643994,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{(c e+d e x)^{7/2}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^2/(c*e + d*e*x)^(7/2),x]","\frac{2 \left(4 b (c+d x) \left(2 b (c+d x) \, _3F_2\left(-\frac{1}{4},-\frac{1}{4},1;\frac{1}{4},\frac{3}{4};(c+d x)^2\right)-\frac{\sqrt{1-(c+d x)^2} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{\sqrt{c+d x-1} \sqrt{c+d x+1}}\right)-3 \left(a+b \cosh ^{-1}(c+d x)\right)^2\right)}{15 d e (e (c+d x))^{5/2}}","\frac{16 b^2 \, _3F_2\left(-\frac{1}{4},-\frac{1}{4},1;\frac{1}{4},\frac{3}{4};(c+d x)^2\right)}{15 d e^3 \sqrt{e (c+d x)}}-\frac{8 b \sqrt{-c-d x+1} \, _2F_1\left(-\frac{3}{4},\frac{1}{2};\frac{1}{4};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{15 d e^2 \sqrt{c+d x-1} (e (c+d x))^{3/2}}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^2}{5 d e (e (c+d x))^{5/2}}",1,"(2*(-3*(a + b*ArcCosh[c + d*x])^2 + 4*b*(c + d*x)*(-((Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[-3/4, 1/2, 1/4, (c + d*x)^2])/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])) + 2*b*(c + d*x)*HypergeometricPFQ[{-1/4, -1/4, 1}, {1/4, 3/4}, (c + d*x)^2])))/(15*d*e*(e*(c + d*x))^(5/2))","A",1
214,0,0,89,107.3353059,"\int (c e+d e x)^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","Integrate[(c*e + d*e*x)^(3/2)*(a + b*ArcCosh[c + d*x])^3,x]","\int (c e+d e x)^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","\frac{2 (e (c+d x))^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{5 d e}-\frac{6 b \text{Int}\left(\frac{(e (c+d x))^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{\sqrt{c+d x-1} \sqrt{c+d x+1}},x\right)}{5 e}",0,"Integrate[(c*e + d*e*x)^(3/2)*(a + b*ArcCosh[c + d*x])^3, x]","A",-1
215,-1,0,87,180.0011629,"\int \sqrt{c e+d e x} \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","Integrate[Sqrt[c*e + d*e*x]*(a + b*ArcCosh[c + d*x])^3,x]","\text{\$Aborted}","\frac{2 (e (c+d x))^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 d e}-\frac{2 b \text{Int}\left(\frac{(e (c+d x))^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{\sqrt{c+d x-1} \sqrt{c+d x+1}},x\right)}{e}",0,"$Aborted","F",-1
216,0,0,85,24.0462103,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c e+d e x}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^3/Sqrt[c*e + d*e*x],x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c e+d e x}} \, dx","\frac{2 \sqrt{e (c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e}-\frac{6 b \text{Int}\left(\frac{\sqrt{e (c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{\sqrt{c+d x-1} \sqrt{c+d x+1}},x\right)}{e}",0,"Integrate[(a + b*ArcCosh[c + d*x])^3/Sqrt[c*e + d*e*x], x]","A",-1
217,0,0,85,32.2129577,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{3/2}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x)^(3/2),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{3/2}} \, dx","\frac{6 b \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{\sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{e (c+d x)}},x\right)}{e}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e \sqrt{e (c+d x)}}",0,"Integrate[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x)^(3/2), x]","A",-1
218,0,0,87,36.8835449,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{5/2}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x)^(5/2),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{5/2}} \, dx","\frac{2 b \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{\sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{3/2}},x\right)}{e}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{3 d e (e (c+d x))^{3/2}}",0,"Integrate[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x)^(5/2), x]","A",-1
219,0,0,89,123.3203966,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{7/2}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x)^(7/2),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{(c e+d e x)^{7/2}} \, dx","\frac{6 b \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^2}{\sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{5/2}},x\right)}{5 e}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^3}{5 d e (e (c+d x))^{5/2}}",0,"Integrate[(a + b*ArcCosh[c + d*x])^3/(c*e + d*e*x)^(7/2), x]","A",-1
220,0,0,89,75.4510302,"\int (c e+d e x)^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","Integrate[(c*e + d*e*x)^(3/2)*(a + b*ArcCosh[c + d*x])^4,x]","\int (c e+d e x)^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","\frac{2 (e (c+d x))^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right)^4}{5 d e}-\frac{8 b \text{Int}\left(\frac{(e (c+d x))^{5/2} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c+d x-1} \sqrt{c+d x+1}},x\right)}{5 e}",0,"Integrate[(c*e + d*e*x)^(3/2)*(a + b*ArcCosh[c + d*x])^4, x]","A",-1
221,-1,0,89,180.0004046,"\int \sqrt{c e+d e x} \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","Integrate[Sqrt[c*e + d*e*x]*(a + b*ArcCosh[c + d*x])^4,x]","\text{\$Aborted}","\frac{2 (e (c+d x))^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^4}{3 d e}-\frac{8 b \text{Int}\left(\frac{(e (c+d x))^{3/2} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c+d x-1} \sqrt{c+d x+1}},x\right)}{3 e}",0,"$Aborted","F",-1
222,0,0,85,15.1926685,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{\sqrt{c e+d e x}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^4/Sqrt[c*e + d*e*x],x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{\sqrt{c e+d e x}} \, dx","\frac{2 \sqrt{e (c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right)^4}{d e}-\frac{8 b \text{Int}\left(\frac{\sqrt{e (c+d x)} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c+d x-1} \sqrt{c+d x+1}},x\right)}{e}",0,"Integrate[(a + b*ArcCosh[c + d*x])^4/Sqrt[c*e + d*e*x], x]","A",-1
223,0,0,85,39.1259489,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{3/2}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x)^(3/2),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{3/2}} \, dx","\frac{8 b \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c+d x-1} \sqrt{c+d x+1} \sqrt{e (c+d x)}},x\right)}{e}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{d e \sqrt{e (c+d x)}}",0,"Integrate[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x)^(3/2), x]","A",-1
224,0,0,89,39.123372,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{5/2}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x)^(5/2),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{5/2}} \, dx","\frac{8 b \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{3/2}},x\right)}{3 e}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{3 d e (e (c+d x))^{3/2}}",0,"Integrate[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x)^(5/2), x]","A",-1
225,0,0,89,175.7032902,"\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{7/2}} \, dx","Integrate[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x)^(7/2),x]","\int \frac{\left(a+b \cosh ^{-1}(c+d x)\right)^4}{(c e+d e x)^{7/2}} \, dx","\frac{8 b \text{Int}\left(\frac{\left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c+d x-1} \sqrt{c+d x+1} (e (c+d x))^{5/2}},x\right)}{5 e}-\frac{2 \left(a+b \cosh ^{-1}(c+d x)\right)^4}{5 d e (e (c+d x))^{5/2}}",0,"Integrate[(a + b*ArcCosh[c + d*x])^4/(c*e + d*e*x)^(7/2), x]","A",-1
226,0,0,94,4.1162446,"\int (c e+d e x)^m \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","Integrate[(c*e + d*e*x)^m*(a + b*ArcCosh[c + d*x])^4,x]","\int (c e+d e x)^m \left(a+b \cosh ^{-1}(c+d x)\right)^4 \, dx","\frac{(e (c+d x))^{m+1} \left(a+b \cosh ^{-1}(c+d x)\right)^4}{d e (m+1)}-\frac{4 b \text{Int}\left(\frac{(e (c+d x))^{m+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{\sqrt{c+d x-1} \sqrt{c+d x+1}},x\right)}{e (m+1)}",0,"Integrate[(c*e + d*e*x)^m*(a + b*ArcCosh[c + d*x])^4, x]","A",-1
227,0,0,94,1.9844361,"\int (c e+d e x)^m \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","Integrate[(c*e + d*e*x)^m*(a + b*ArcCosh[c + d*x])^3,x]","\int (c e+d e x)^m \left(a+b \cosh ^{-1}(c+d x)\right)^3 \, dx","\frac{(e (c+d x))^{m+1} \left(a+b \cosh ^{-1}(c+d x)\right)^3}{d e (m+1)}-\frac{3 b \text{Int}\left(\frac{(e (c+d x))^{m+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{\sqrt{c+d x-1} \sqrt{c+d x+1}},x\right)}{e (m+1)}",0,"Integrate[(c*e + d*e*x)^m*(a + b*ArcCosh[c + d*x])^3, x]","A",-1
228,1,178,206,0.4269242,"\int (c e+d e x)^m \left(a+b \cosh ^{-1}(c+d x)\right)^2 \, dx","Integrate[(c*e + d*e*x)^m*(a + b*ArcCosh[c + d*x])^2,x]","\frac{(c+d x) (e (c+d x))^m \left(\left(a+b \cosh ^{-1}(c+d x)\right)^2-\frac{2 b (c+d x) \left(\frac{b (c+d x) \, _3F_2\left(1,\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};\frac{m}{2}+2,\frac{m}{2}+\frac{5}{2};(c+d x)^2\right)}{m+3}+\frac{\sqrt{1-(c+d x)^2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{\sqrt{c+d x-1} \sqrt{c+d x+1}}\right)}{m+2}\right)}{d (m+1)}","-\frac{2 b^2 (e (c+d x))^{m+3} \, _3F_2\left(1,\frac{m}{2}+\frac{3}{2},\frac{m}{2}+\frac{3}{2};\frac{m}{2}+2,\frac{m}{2}+\frac{5}{2};(c+d x)^2\right)}{d e^3 (m+1) (m+2) (m+3)}-\frac{2 b \sqrt{-c-d x+1} (e (c+d x))^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};(c+d x)^2\right) \left(a+b \cosh ^{-1}(c+d x)\right)}{d e^2 (m+1) (m+2) \sqrt{c+d x-1}}+\frac{(e (c+d x))^{m+1} \left(a+b \cosh ^{-1}(c+d x)\right)^2}{d e (m+1)}",1,"((c + d*x)*(e*(c + d*x))^m*((a + b*ArcCosh[c + d*x])^2 - (2*b*(c + d*x)*((Sqrt[1 - (c + d*x)^2]*(a + b*ArcCosh[c + d*x])*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, (c + d*x)^2])/(Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x]) + (b*(c + d*x)*HypergeometricPFQ[{1, 3/2 + m/2, 3/2 + m/2}, {2 + m/2, 5/2 + m/2}, (c + d*x)^2])/(3 + m)))/(2 + m)))/(d*(1 + m))","A",1
229,1,106,118,0.2021772,"\int (c e+d e x)^m \left(a+b \cosh ^{-1}(c+d x)\right) \, dx","Integrate[(c*e + d*e*x)^m*(a + b*ArcCosh[c + d*x]),x]","\frac{(c+d x) (e (c+d x))^m \left(a-\frac{b (c+d x) \sqrt{1-(c+d x)^2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};(c+d x)^2\right)}{(m+2) \sqrt{c+d x-1} \sqrt{c+d x+1}}+b \cosh ^{-1}(c+d x)\right)}{d (m+1)}","\frac{(e (c+d x))^{m+1} \left(a+b \cosh ^{-1}(c+d x)\right)}{d e (m+1)}-\frac{b \left(1-(c+d x)^2\right) (e (c+d x))^{m+2} \, _2F_1\left(1,\frac{m+3}{2};\frac{m+4}{2};(c+d x)^2\right)}{d e^2 (m+1) (m+2) \sqrt{c+d x-1} \sqrt{c+d x+1}}",1,"((c + d*x)*(e*(c + d*x))^m*(a + b*ArcCosh[c + d*x] - (b*(c + d*x)*Sqrt[1 - (c + d*x)^2]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, (c + d*x)^2])/((2 + m)*Sqrt[-1 + c + d*x]*Sqrt[1 + c + d*x])))/(d*(1 + m))","A",1
230,0,0,25,1.2521057,"\int \frac{(c e+d e x)^m}{a+b \cosh ^{-1}(c+d x)} \, dx","Integrate[(c*e + d*e*x)^m/(a + b*ArcCosh[c + d*x]),x]","\int \frac{(c e+d e x)^m}{a+b \cosh ^{-1}(c+d x)} \, dx","\text{Int}\left(\frac{(e (c+d x))^m}{a+b \cosh ^{-1}(c+d x)},x\right)",0,"Integrate[(c*e + d*e*x)^m/(a + b*ArcCosh[c + d*x]), x]","A",-1
231,1,50,54,0.0470323,"\int \frac{\cosh ^{-1}\left(a x^5\right)}{x} \, dx","Integrate[ArcCosh[a*x^5]/x,x]","\frac{1}{10} \left(\cosh ^{-1}\left(a x^5\right) \left(\cosh ^{-1}\left(a x^5\right)+2 \log \left(e^{-2 \cosh ^{-1}\left(a x^5\right)}+1\right)\right)-\text{Li}_2\left(-e^{-2 \cosh ^{-1}\left(a x^5\right)}\right)\right)","\frac{1}{10} \text{Li}_2\left(-e^{2 \cosh ^{-1}\left(a x^5\right)}\right)-\frac{1}{10} \cosh ^{-1}\left(a x^5\right)^2+\frac{1}{5} \cosh ^{-1}\left(a x^5\right) \log \left(e^{2 \cosh ^{-1}\left(a x^5\right)}+1\right)",1,"(ArcCosh[a*x^5]*(ArcCosh[a*x^5] + 2*Log[1 + E^(-2*ArcCosh[a*x^5])]) - PolyLog[2, -E^(-2*ArcCosh[a*x^5])])/10","A",0
232,1,79,117,0.0583551,"\int x^2 \cosh ^{-1}\left(\sqrt{x}\right) \, dx","Integrate[x^2*ArcCosh[Sqrt[x]],x]","\frac{1}{144} \left(48 x^3 \cosh ^{-1}\left(\sqrt{x}\right)-\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \left(8 x^2+10 x+15\right) \sqrt{x}-30 \tanh ^{-1}\left(\sqrt{\frac{\sqrt{x}-1}{\sqrt{x}+1}}\right)\right)","-\frac{1}{18} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{5/2}-\frac{5}{72} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{3/2}+\frac{1}{3} x^3 \cosh ^{-1}\left(\sqrt{x}\right)-\frac{5}{48} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}-\frac{5}{48} \cosh ^{-1}\left(\sqrt{x}\right)",1,"(-(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x]*(15 + 10*x + 8*x^2)) + 48*x^3*ArcCosh[Sqrt[x]] - 30*ArcTanh[Sqrt[(-1 + Sqrt[x])/(1 + Sqrt[x])]])/144","A",0
233,1,74,86,0.0415195,"\int x \cosh ^{-1}\left(\sqrt{x}\right) \, dx","Integrate[x*ArcCosh[Sqrt[x]],x]","\frac{1}{16} \left(8 x^2 \cosh ^{-1}\left(\sqrt{x}\right)-\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} (2 x+3) \sqrt{x}-6 \tanh ^{-1}\left(\sqrt{\frac{\sqrt{x}-1}{\sqrt{x}+1}}\right)\right)","-\frac{1}{8} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{3/2}+\frac{1}{2} x^2 \cosh ^{-1}\left(\sqrt{x}\right)-\frac{3}{16} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}-\frac{3}{16} \cosh ^{-1}\left(\sqrt{x}\right)",1,"(-(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x]*(3 + 2*x)) + 8*x^2*ArcCosh[Sqrt[x]] - 6*ArcTanh[Sqrt[(-1 + Sqrt[x])/(1 + Sqrt[x])]])/16","A",0
234,1,64,50,0.0247914,"\int \cosh ^{-1}\left(\sqrt{x}\right) \, dx","Integrate[ArcCosh[Sqrt[x]],x]","-\frac{1}{2} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}+x \cosh ^{-1}\left(\sqrt{x}\right)-\tanh ^{-1}\left(\sqrt{\frac{\sqrt{x}-1}{\sqrt{x}+1}}\right)","-\frac{1}{2} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}+x \cosh ^{-1}\left(\sqrt{x}\right)-\frac{1}{2} \cosh ^{-1}\left(\sqrt{x}\right)",1,"-1/2*(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x]) + x*ArcCosh[Sqrt[x]] - ArcTanh[Sqrt[(-1 + Sqrt[x])/(1 + Sqrt[x])]]","A",0
235,1,46,46,0.0380964,"\int \frac{\cosh ^{-1}\left(\sqrt{x}\right)}{x} \, dx","Integrate[ArcCosh[Sqrt[x]]/x,x]","\cosh ^{-1}\left(\sqrt{x}\right) \left(\cosh ^{-1}\left(\sqrt{x}\right)+2 \log \left(e^{-2 \cosh ^{-1}\left(\sqrt{x}\right)}+1\right)\right)-\text{Li}_2\left(-e^{-2 \cosh ^{-1}\left(\sqrt{x}\right)}\right)","\text{Li}_2\left(-e^{2 \cosh ^{-1}\left(\sqrt{x}\right)}\right)-\cosh ^{-1}\left(\sqrt{x}\right)^2+2 \cosh ^{-1}\left(\sqrt{x}\right) \log \left(e^{2 \cosh ^{-1}\left(\sqrt{x}\right)}+1\right)",1,"ArcCosh[Sqrt[x]]*(ArcCosh[Sqrt[x]] + 2*Log[1 + E^(-2*ArcCosh[Sqrt[x]])]) - PolyLog[2, -E^(-2*ArcCosh[Sqrt[x]])]","A",0
236,1,40,40,0.0156695,"\int \frac{\cosh ^{-1}\left(\sqrt{x}\right)}{x^2} \, dx","Integrate[ArcCosh[Sqrt[x]]/x^2,x]","\frac{\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{\sqrt{x}}-\frac{\cosh ^{-1}\left(\sqrt{x}\right)}{x}","\frac{\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{\sqrt{x}}-\frac{\cosh ^{-1}\left(\sqrt{x}\right)}{x}",1,"(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/Sqrt[x] - ArcCosh[Sqrt[x]]/x","A",1
237,1,49,76,0.0291143,"\int \frac{\cosh ^{-1}\left(\sqrt{x}\right)}{x^3} \, dx","Integrate[ArcCosh[Sqrt[x]]/x^3,x]","\frac{\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x} (2 x+1)-3 \cosh ^{-1}\left(\sqrt{x}\right)}{6 x^2}","\frac{\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{6 x^{3/2}}-\frac{\cosh ^{-1}\left(\sqrt{x}\right)}{2 x^2}+\frac{\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{3 \sqrt{x}}",1,"(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x]*(1 + 2*x) - 3*ArcCosh[Sqrt[x]])/(6*x^2)","A",1
238,1,46,24,0.0485274,"\int \cosh ^{-1}\left(\frac{1}{x}\right) \, dx","Integrate[ArcCosh[x^(-1)],x]","x \cosh ^{-1}\left(\frac{1}{x}\right)-\frac{\sqrt{\frac{1}{x^2}-1} \tan ^{-1}\left(\sqrt{\frac{1}{x^2}-1}\right)}{\sqrt{\frac{1}{x}-1} \sqrt{\frac{1}{x}+1}}","\sqrt{\frac{1}{x+1}} \sqrt{x+1} \sin ^{-1}(x)+x \text{sech}^{-1}(x)",1,"x*ArcCosh[x^(-1)] - (Sqrt[-1 + x^(-2)]*ArcTan[Sqrt[-1 + x^(-2)]])/(Sqrt[-1 + x^(-1)]*Sqrt[1 + x^(-1)])","A",1
239,1,179,60,0.5110254,"\int \frac{\cosh ^{-1}\left(a x^n\right)}{x} \, dx","Integrate[ArcCosh[a*x^n]/x,x]","\frac{a \sqrt{1-a^2 x^{2 n}} \left(-\text{Li}_2\left(e^{-2 \sinh ^{-1}\left(\sqrt{-a^2} x^n\right)}\right)+\sinh ^{-1}\left(\sqrt{-a^2} x^n\right)^2+2 \sinh ^{-1}\left(\sqrt{-a^2} x^n\right) \log \left(1-e^{-2 \sinh ^{-1}\left(\sqrt{-a^2} x^n\right)}\right)-2 n \log (x) \log \left(\sqrt{1-a^2 x^{2 n}}+\sqrt{-a^2} x^n\right)\right)}{2 \sqrt{-a^2} n \sqrt{a x^n-1} \sqrt{a x^n+1}}+\log (x) \cosh ^{-1}\left(a x^n\right)","\frac{\text{Li}_2\left(-e^{2 \cosh ^{-1}\left(a x^n\right)}\right)}{2 n}-\frac{\cosh ^{-1}\left(a x^n\right)^2}{2 n}+\frac{\cosh ^{-1}\left(a x^n\right) \log \left(e^{2 \cosh ^{-1}\left(a x^n\right)}+1\right)}{n}",1,"ArcCosh[a*x^n]*Log[x] + (a*Sqrt[1 - a^2*x^(2*n)]*(ArcSinh[Sqrt[-a^2]*x^n]^2 + 2*ArcSinh[Sqrt[-a^2]*x^n]*Log[1 - E^(-2*ArcSinh[Sqrt[-a^2]*x^n])] - 2*n*Log[x]*Log[Sqrt[-a^2]*x^n + Sqrt[1 - a^2*x^(2*n)]] - PolyLog[2, E^(-2*ArcSinh[Sqrt[-a^2]*x^n])]))/(2*Sqrt[-a^2]*n*Sqrt[-1 + a*x^n]*Sqrt[1 + a*x^n])","B",0
240,1,264,145,0.2327107,"\int \left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^4 \, dx","Integrate[(a + b*ArcCosh[1 + d*x^2])^4,x]","\frac{-8 a b \left(a^2+24 b^2\right) \sqrt{d x^2} \sqrt{d x^2+2}+6 b^2 \cosh ^{-1}\left(d x^2+1\right)^2 \left(a^2 d x^2-4 a b \sqrt{d x^2} \sqrt{d x^2+2}+8 b^2 d x^2\right)+d x^2 \left(a^4+48 a^2 b^2+384 b^4\right)+4 b \cosh ^{-1}\left(d x^2+1\right) \left(a^3 d x^2-6 a^2 b \sqrt{d x^2} \sqrt{d x^2+2}+24 a b^2 d x^2-48 b^3 \sqrt{d x^2} \sqrt{d x^2+2}\right)+4 b^3 \cosh ^{-1}\left(d x^2+1\right)^3 \left(a d x^2-2 b \sqrt{d x^2} \sqrt{d x^2+2}\right)+b^4 d x^2 \cosh ^{-1}\left(d x^2+1\right)^4}{d x}","-\frac{192 b^3 \left(d x^4+2 x^2\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)}{x \sqrt{d x^2} \sqrt{d x^2+2}}+48 b^2 x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^2+x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^4-\frac{8 b \left(d x^4+2 x^2\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^3}{x \sqrt{d x^2} \sqrt{d x^2+2}}+384 b^4 x",1,"((a^4 + 48*a^2*b^2 + 384*b^4)*d*x^2 - 8*a*b*(a^2 + 24*b^2)*Sqrt[d*x^2]*Sqrt[2 + d*x^2] + 4*b*(a^3*d*x^2 + 24*a*b^2*d*x^2 - 6*a^2*b*Sqrt[d*x^2]*Sqrt[2 + d*x^2] - 48*b^3*Sqrt[d*x^2]*Sqrt[2 + d*x^2])*ArcCosh[1 + d*x^2] + 6*b^2*(a^2*d*x^2 + 8*b^2*d*x^2 - 4*a*b*Sqrt[d*x^2]*Sqrt[2 + d*x^2])*ArcCosh[1 + d*x^2]^2 + 4*b^3*(a*d*x^2 - 2*b*Sqrt[d*x^2]*Sqrt[2 + d*x^2])*ArcCosh[1 + d*x^2]^3 + b^4*d*x^2*ArcCosh[1 + d*x^2]^4)/(d*x)","A",1
241,1,171,125,0.1279489,"\int \left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^3 \, dx","Integrate[(a + b*ArcCosh[1 + d*x^2])^3,x]","\frac{a d x^2 \left(a^2+24 b^2\right)-6 b \left(a^2+8 b^2\right) \sqrt{d x^2} \sqrt{d x^2+2}+3 b \cosh ^{-1}\left(d x^2+1\right) \left(a^2 d x^2-4 a b \sqrt{d x^2} \sqrt{d x^2+2}+8 b^2 d x^2\right)+3 b^2 \cosh ^{-1}\left(d x^2+1\right)^2 \left(a d x^2-2 b \sqrt{d x^2} \sqrt{d x^2+2}\right)+b^3 d x^2 \cosh ^{-1}\left(d x^2+1\right)^3}{d x}","24 a b^2 x+x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^3-\frac{6 b \left(d x^4+2 x^2\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^2}{x \sqrt{d x^2} \sqrt{d x^2+2}}-\frac{48 b^3 \sqrt{\frac{d x^2}{d x^2+2}} \left(d x^2+2\right)}{d x}+24 b^3 x \cosh ^{-1}\left(d x^2+1\right)",1,"(a*(a^2 + 24*b^2)*d*x^2 - 6*b*(a^2 + 8*b^2)*Sqrt[d*x^2]*Sqrt[2 + d*x^2] + 3*b*(a^2*d*x^2 + 8*b^2*d*x^2 - 4*a*b*Sqrt[d*x^2]*Sqrt[2 + d*x^2])*ArcCosh[1 + d*x^2] + 3*b^2*(a*d*x^2 - 2*b*Sqrt[d*x^2]*Sqrt[2 + d*x^2])*ArcCosh[1 + d*x^2]^2 + b^3*d*x^2*ArcCosh[1 + d*x^2]^3)/(d*x)","A",1
242,1,104,72,0.0665459,"\int \left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^2 \, dx","Integrate[(a + b*ArcCosh[1 + d*x^2])^2,x]","x \left(a^2+8 b^2\right)-\frac{4 a b \sqrt{d x^2} \sqrt{d x^2+2}}{d x}+\frac{2 b \cosh ^{-1}\left(d x^2+1\right) \left(a d x^2-2 b \sqrt{d x^2} \sqrt{d x^2+2}\right)}{d x}+b^2 x \cosh ^{-1}\left(d x^2+1\right)^2","x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^2-\frac{4 b \left(d x^4+2 x^2\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)}{x \sqrt{d x^2} \sqrt{d x^2+2}}+8 b^2 x",1,"(a^2 + 8*b^2)*x - (4*a*b*Sqrt[d*x^2]*Sqrt[2 + d*x^2])/(d*x) + (2*b*(a*d*x^2 - 2*b*Sqrt[d*x^2]*Sqrt[2 + d*x^2])*ArcCosh[1 + d*x^2])/(d*x) + b^2*x*ArcCosh[1 + d*x^2]^2","A",1
243,1,37,49,0.0662351,"\int \left(a+b \cosh ^{-1}\left(1+d x^2\right)\right) \, dx","Integrate[a + b*ArcCosh[1 + d*x^2],x]","a x-\frac{2 b x}{\sqrt{\frac{d x^2}{d x^2+2}}}+b x \cosh ^{-1}\left(d x^2+1\right)","a x-\frac{2 b \sqrt{\frac{d x^2}{d x^2+2}} \left(d x^2+2\right)}{d x}+b x \cosh ^{-1}\left(d x^2+1\right)",1,"a*x - (2*b*x)/Sqrt[(d*x^2)/(2 + d*x^2)] + b*x*ArcCosh[1 + d*x^2]","A",1
244,1,118,98,0.1391183,"\int \frac{1}{a+b \cosh ^{-1}\left(1+d x^2\right)} \, dx","Integrate[(a + b*ArcCosh[1 + d*x^2])^(-1),x]","\frac{x \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)\right)}{b \sqrt{d x^2} \sqrt{\frac{d x^2}{d x^2+2}} \sqrt{d x^2+2}}","\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{d x^2}}-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{d x^2}}",1,"(x*Sinh[ArcCosh[1 + d*x^2]/2]*(Cosh[a/(2*b)]*CoshIntegral[(a + b*ArcCosh[1 + d*x^2])/(2*b)] - Sinh[a/(2*b)]*SinhIntegral[(a + b*ArcCosh[1 + d*x^2])/(2*b)]))/(b*Sqrt[d*x^2]*Sqrt[(d*x^2)/(2 + d*x^2)]*Sqrt[2 + d*x^2])","A",0
245,1,130,150,0.9282881,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^2} \, dx","Integrate[(a + b*ArcCosh[1 + d*x^2])^(-2),x]","-\frac{x^2 \text{csch}\left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)-\cosh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)\right)+\frac{2 b \sqrt{d x^2} \sqrt{d x^2+2}}{a d+b d \cosh ^{-1}\left(d x^2+1\right)}}{4 b^2 x}","-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{d x^2}}+\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{d x^2}}-\frac{\sqrt{d x^2} \sqrt{d x^2+2}}{2 b d x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)}",1,"-1/4*((2*b*Sqrt[d*x^2]*Sqrt[2 + d*x^2])/(a*d + b*d*ArcCosh[1 + d*x^2]) + x^2*Csch[ArcCosh[1 + d*x^2]/2]*(CoshIntegral[(a + b*ArcCosh[1 + d*x^2])/(2*b)]*Sinh[a/(2*b)] - Cosh[a/(2*b)]*SinhIntegral[(a + b*ArcCosh[1 + d*x^2])/(2*b)]))/(b^2*x)","A",0
246,1,152,180,0.4770574,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^3} \, dx","Integrate[(a + b*ArcCosh[1 + d*x^2])^(-3),x]","\frac{-\frac{2 b^2 \sqrt{d x^2} \sqrt{d x^2+2}}{d \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^2}+\frac{\sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)\right)}{d}-\frac{b x^2}{a+b \cosh ^{-1}\left(d x^2+1\right)}}{8 b^3 x}","\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{d x^2}}-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2+1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{d x^2}}-\frac{x}{8 b^2 \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)}-\frac{d x^4+2 x^2}{4 b x \sqrt{d x^2} \sqrt{d x^2+2} \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^2}",1,"((-2*b^2*Sqrt[d*x^2]*Sqrt[2 + d*x^2])/(d*(a + b*ArcCosh[1 + d*x^2])^2) - (b*x^2)/(a + b*ArcCosh[1 + d*x^2]) + (Sinh[ArcCosh[1 + d*x^2]/2]*(Cosh[a/(2*b)]*CoshIntegral[(a + b*ArcCosh[1 + d*x^2])/(2*b)] - Sinh[a/(2*b)]*SinhIntegral[(a + b*ArcCosh[1 + d*x^2])/(2*b)]))/d)/(8*b^3*x)","A",1
247,1,264,147,0.239688,"\int \left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^4 \, dx","Integrate[(a + b*ArcCosh[-1 + d*x^2])^4,x]","\frac{-8 a b \left(a^2+24 b^2\right) \sqrt{d x^2} \sqrt{d x^2-2}+6 b^2 \cosh ^{-1}\left(d x^2-1\right)^2 \left(a^2 d x^2-4 a b \sqrt{d x^2} \sqrt{d x^2-2}+8 b^2 d x^2\right)+d x^2 \left(a^4+48 a^2 b^2+384 b^4\right)+4 b \cosh ^{-1}\left(d x^2-1\right) \left(a^3 d x^2-6 a^2 b \sqrt{d x^2} \sqrt{d x^2-2}+24 a b^2 d x^2-48 b^3 \sqrt{d x^2} \sqrt{d x^2-2}\right)+4 b^3 \cosh ^{-1}\left(d x^2-1\right)^3 \left(a d x^2-2 b \sqrt{d x^2} \sqrt{d x^2-2}\right)+b^4 d x^2 \cosh ^{-1}\left(d x^2-1\right)^4}{d x}","\frac{192 b^3 \left(2 x^2-d x^4\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)}{x \sqrt{d x^2} \sqrt{d x^2-2}}+48 b^2 x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^2+x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^4+\frac{8 b \left(2 x^2-d x^4\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^3}{x \sqrt{d x^2} \sqrt{d x^2-2}}+384 b^4 x",1,"((a^4 + 48*a^2*b^2 + 384*b^4)*d*x^2 - 8*a*b*(a^2 + 24*b^2)*Sqrt[d*x^2]*Sqrt[-2 + d*x^2] + 4*b*(a^3*d*x^2 + 24*a*b^2*d*x^2 - 6*a^2*b*Sqrt[d*x^2]*Sqrt[-2 + d*x^2] - 48*b^3*Sqrt[d*x^2]*Sqrt[-2 + d*x^2])*ArcCosh[-1 + d*x^2] + 6*b^2*(a^2*d*x^2 + 8*b^2*d*x^2 - 4*a*b*Sqrt[d*x^2]*Sqrt[-2 + d*x^2])*ArcCosh[-1 + d*x^2]^2 + 4*b^3*(a*d*x^2 - 2*b*Sqrt[d*x^2]*Sqrt[-2 + d*x^2])*ArcCosh[-1 + d*x^2]^3 + b^4*d*x^2*ArcCosh[-1 + d*x^2]^4)/(d*x)","A",1
248,1,171,110,0.1306713,"\int \left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^3 \, dx","Integrate[(a + b*ArcCosh[-1 + d*x^2])^3,x]","\frac{a d x^2 \left(a^2+24 b^2\right)-6 b \left(a^2+8 b^2\right) \sqrt{d x^2} \sqrt{d x^2-2}+3 b \cosh ^{-1}\left(d x^2-1\right) \left(a^2 d x^2-4 a b \sqrt{d x^2} \sqrt{d x^2-2}+8 b^2 d x^2\right)+3 b^2 \cosh ^{-1}\left(d x^2-1\right)^2 \left(a d x^2-2 b \sqrt{d x^2} \sqrt{d x^2-2}\right)+b^3 d x^2 \cosh ^{-1}\left(d x^2-1\right)^3}{d x}","24 a b^2 x+x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^3+\frac{6 b \left(2 x^2-d x^4\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^2}{x \sqrt{d x^2} \sqrt{d x^2-2}}-48 b^3 x \sqrt{1-\frac{2}{d x^2}}+24 b^3 x \cosh ^{-1}\left(d x^2-1\right)",1,"(a*(a^2 + 24*b^2)*d*x^2 - 6*b*(a^2 + 8*b^2)*Sqrt[d*x^2]*Sqrt[-2 + d*x^2] + 3*b*(a^2*d*x^2 + 8*b^2*d*x^2 - 4*a*b*Sqrt[d*x^2]*Sqrt[-2 + d*x^2])*ArcCosh[-1 + d*x^2] + 3*b^2*(a*d*x^2 - 2*b*Sqrt[d*x^2]*Sqrt[-2 + d*x^2])*ArcCosh[-1 + d*x^2]^2 + b^3*d*x^2*ArcCosh[-1 + d*x^2]^3)/(d*x)","A",1
249,1,104,73,0.0658425,"\int \left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^2 \, dx","Integrate[(a + b*ArcCosh[-1 + d*x^2])^2,x]","x \left(a^2+8 b^2\right)-\frac{4 a b \sqrt{d x^2} \sqrt{d x^2-2}}{d x}+\frac{2 b \cosh ^{-1}\left(d x^2-1\right) \left(a d x^2-2 b \sqrt{d x^2} \sqrt{d x^2-2}\right)}{d x}+b^2 x \cosh ^{-1}\left(d x^2-1\right)^2","x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^2+\frac{4 b \left(2 x^2-d x^4\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)}{x \sqrt{d x^2} \sqrt{d x^2-2}}+8 b^2 x",1,"(a^2 + 8*b^2)*x - (4*a*b*Sqrt[d*x^2]*Sqrt[-2 + d*x^2])/(d*x) + (2*b*(a*d*x^2 - 2*b*Sqrt[d*x^2]*Sqrt[-2 + d*x^2])*ArcCosh[-1 + d*x^2])/(d*x) + b^2*x*ArcCosh[-1 + d*x^2]^2","A",1
250,1,33,33,0.0266987,"\int \left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right) \, dx","Integrate[a + b*ArcCosh[-1 + d*x^2],x]","a x-2 b x \sqrt{1-\frac{2}{d x^2}}+b x \cosh ^{-1}\left(d x^2-1\right)","a x-2 b x \sqrt{1-\frac{2}{d x^2}}+b x \cosh ^{-1}\left(d x^2-1\right)",1,"a*x - 2*b*Sqrt[1 - 2/(d*x^2)]*x + b*x*ArcCosh[-1 + d*x^2]","A",1
251,1,86,98,0.1425923,"\int \frac{1}{a+b \cosh ^{-1}\left(-1+d x^2\right)} \, dx","Integrate[(a + b*ArcCosh[-1 + d*x^2])^(-1),x]","-\frac{\cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)-\cosh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)\right)}{b d x}","\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{d x^2}}-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{\sqrt{2} b \sqrt{d x^2}}",1,"-((Cosh[ArcCosh[-1 + d*x^2]/2]*(CoshIntegral[(a + b*ArcCosh[-1 + d*x^2])/(2*b)]*Sinh[a/(2*b)] - Cosh[a/(2*b)]*SinhIntegral[(a + b*ArcCosh[-1 + d*x^2])/(2*b)]))/(b*d*x))","A",0
252,1,141,150,0.7463934,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^2} \, dx","Integrate[(a + b*ArcCosh[-1 + d*x^2])^(-2),x]","\frac{\frac{\sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)\right)}{\sqrt{1-\frac{2}{d x^2}}}-\frac{b \sqrt{d x^2} \sqrt{d x^2-2}}{a+b \cosh ^{-1}\left(d x^2-1\right)}}{2 b^2 d x}","\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{d x^2}}-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{2 \sqrt{2} b^2 \sqrt{d x^2}}-\frac{\sqrt{d x^2} \sqrt{d x^2-2}}{2 b d x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)}",1,"(-((b*Sqrt[d*x^2]*Sqrt[-2 + d*x^2])/(a + b*ArcCosh[-1 + d*x^2])) + (Sinh[ArcCosh[-1 + d*x^2]/2]*(Cosh[a/(2*b)]*CoshIntegral[(a + b*ArcCosh[-1 + d*x^2])/(2*b)] - Sinh[a/(2*b)]*SinhIntegral[(a + b*ArcCosh[-1 + d*x^2])/(2*b)]))/Sqrt[1 - 2/(d*x^2)])/(2*b^2*d*x)","A",0
253,1,168,181,0.6877521,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^3} \, dx","Integrate[(a + b*ArcCosh[-1 + d*x^2])^(-3),x]","-\frac{\frac{2 b^2 \sqrt{d x^2} \sqrt{d x^2-2}}{d \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^2}+\frac{1}{2} x^2 \sqrt{1-\frac{2}{d x^2}} \text{csch}\left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)-\cosh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)\right)+\frac{b x^2}{a+b \cosh ^{-1}\left(d x^2-1\right)}}{8 b^3 x}","-\frac{x \sinh \left(\frac{a}{2 b}\right) \text{Chi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{d x^2}}+\frac{x \cosh \left(\frac{a}{2 b}\right) \text{Shi}\left(\frac{a+b \cosh ^{-1}\left(d x^2-1\right)}{2 b}\right)}{8 \sqrt{2} b^3 \sqrt{d x^2}}-\frac{x}{8 b^2 \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)}+\frac{2 x^2-d x^4}{4 b x \sqrt{d x^2} \sqrt{d x^2-2} \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^2}",1,"-1/8*((2*b^2*Sqrt[d*x^2]*Sqrt[-2 + d*x^2])/(d*(a + b*ArcCosh[-1 + d*x^2])^2) + (b*x^2)/(a + b*ArcCosh[-1 + d*x^2]) + (Sqrt[1 - 2/(d*x^2)]*x^2*Csch[ArcCosh[-1 + d*x^2]/2]*(CoshIntegral[(a + b*ArcCosh[-1 + d*x^2])/(2*b)]*Sinh[a/(2*b)] - Cosh[a/(2*b)]*SinhIntegral[(a + b*ArcCosh[-1 + d*x^2])/(2*b)]))/2)/(b^3*x)","A",0
254,1,311,280,3.6073144,"\int \left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^{5/2} \, dx","Integrate[(a + b*ArcCosh[1 + d*x^2])^(5/2),x]","\frac{x \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \left(4 \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)} \left(\left(a^2+15 b^2\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right)-5 a b \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right)-b \cosh ^{-1}\left(d x^2+1\right) \left(5 b \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right)-2 a \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right)\right)+b^2 \cosh ^{-1}\left(d x^2+1\right)^2 \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right)\right)+15 \sqrt{2 \pi } b^{5/2} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)-15 \sqrt{2 \pi } b^{5/2} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)\right)}{2 \sqrt{d x^2} \sqrt{\frac{d x^2}{d x^2+2}} \sqrt{d x^2+2}}","\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{30 b^2 \sinh ^2\left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{d x}+x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{5/2}-\frac{5 b \left(d x^4+2 x^2\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{3/2}}{x \sqrt{d x^2} \sqrt{d x^2+2}}",1,"(x*Sinh[ArcCosh[1 + d*x^2]/2]*(-15*b^(5/2)*Sqrt[2*Pi]*Erfi[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)]) + 15*b^(5/2)*Sqrt[2*Pi]*Erf[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]) + 4*Sqrt[a + b*ArcCosh[1 + d*x^2]]*(-5*a*b*Cosh[ArcCosh[1 + d*x^2]/2] + (a^2 + 15*b^2)*Sinh[ArcCosh[1 + d*x^2]/2] + b^2*ArcCosh[1 + d*x^2]^2*Sinh[ArcCosh[1 + d*x^2]/2] - b*ArcCosh[1 + d*x^2]*(5*b*Cosh[ArcCosh[1 + d*x^2]/2] - 2*a*Sinh[ArcCosh[1 + d*x^2]/2]))))/(2*Sqrt[d*x^2]*Sqrt[(d*x^2)/(2 + d*x^2)]*Sqrt[2 + d*x^2])","A",1
255,1,254,238,0.7228503,"\int \left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^{3/2} \, dx","Integrate[(a + b*ArcCosh[1 + d*x^2])^(3/2),x]","\frac{x \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \left(3 \sqrt{2 \pi } b^{3/2} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)+3 \sqrt{2 \pi } b^{3/2} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)+4 \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)} \left(a \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right)-3 b \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right)+b \cosh ^{-1}\left(d x^2+1\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right)\right)\right)}{2 \sqrt{d x^2} \sqrt{\frac{d x^2}{d x^2+2}} \sqrt{d x^2+2}}","\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+x \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{3/2}-\frac{3 b \left(d x^4+2 x^2\right) \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{x \sqrt{d x^2} \sqrt{d x^2+2}}",1,"(x*Sinh[ArcCosh[1 + d*x^2]/2]*(3*b^(3/2)*Sqrt[2*Pi]*Erfi[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)]) + 3*b^(3/2)*Sqrt[2*Pi]*Erf[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]) + 4*Sqrt[a + b*ArcCosh[1 + d*x^2]]*(-3*b*Cosh[ArcCosh[1 + d*x^2]/2] + a*Sinh[ArcCosh[1 + d*x^2]/2] + b*ArcCosh[1 + d*x^2]*Sinh[ArcCosh[1 + d*x^2]/2])))/(2*Sqrt[d*x^2]*Sqrt[(d*x^2)/(2 + d*x^2)]*Sqrt[2 + d*x^2])","A",1
256,1,210,205,0.3069187,"\int \sqrt{a+b \cosh ^{-1}\left(1+d x^2\right)} \, dx","Integrate[Sqrt[a + b*ArcCosh[1 + d*x^2]],x]","\frac{x \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \left(\sqrt{2 \pi } \sqrt{b} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)+\sqrt{2 \pi } \sqrt{b} \left(\sinh \left(\frac{a}{2 b}\right)-\cosh \left(\frac{a}{2 b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)+4 \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}\right)}{2 \sqrt{d x^2} \sqrt{\frac{d x^2}{d x^2+2}} \sqrt{d x^2+2}}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{2 \sinh ^2\left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{d x}",1,"(x*Sinh[ArcCosh[1 + d*x^2]/2]*(Sqrt[b]*Sqrt[2*Pi]*Erfi[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(-Cosh[a/(2*b)] + Sinh[a/(2*b)]) + Sqrt[b]*Sqrt[2*Pi]*Erf[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]) + 4*Sqrt[a + b*ArcCosh[1 + d*x^2]]*Sinh[ArcCosh[1 + d*x^2]/2]))/(2*Sqrt[d*x^2]*Sqrt[(d*x^2)/(2 + d*x^2)]*Sqrt[2 + d*x^2])","A",0
257,1,166,165,0.31442,"\int \frac{1}{\sqrt{a+b \cosh ^{-1}\left(1+d x^2\right)}} \, dx","Integrate[1/Sqrt[a + b*ArcCosh[1 + d*x^2]],x]","\frac{\sqrt{\frac{\pi }{2}} x \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \left(\left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)+\left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)\right)}{\sqrt{b} \sqrt{d x^2} \sqrt{\frac{d x^2}{d x^2+2}} \sqrt{d x^2+2}}","\frac{\sqrt{\frac{\pi }{2}} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{b} d x}+\frac{\sqrt{\frac{\pi }{2}} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{b} d x}",1,"(Sqrt[Pi/2]*x*(Erfi[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)]) + Erf[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]))*Sinh[ArcCosh[1 + d*x^2]/2])/(Sqrt[b]*Sqrt[d*x^2]*Sqrt[(d*x^2)/(2 + d*x^2)]*Sqrt[2 + d*x^2])","A",0
258,1,242,213,1.1102378,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^{3/2}} \, dx","Integrate[(a + b*ArcCosh[1 + d*x^2])^(-3/2),x]","-\frac{x \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \left(\sqrt{2 \pi } \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)+\sqrt{2 \pi } \left(\sinh \left(\frac{a}{2 b}\right)-\cosh \left(\frac{a}{2 b}\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)+4 \sqrt{b} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right)\right)}{2 b^{3/2} \sqrt{d x^2} \sqrt{\frac{d x^2}{d x^2+2}} \sqrt{d x^2+2} \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}","-\frac{\sqrt{\frac{\pi }{2}} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{b^{3/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{b^{3/2} d x}-\frac{\sqrt{d x^2} \sqrt{d x^2+2}}{b d x \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}",1,"-1/2*(x*(4*Sqrt[b]*Cosh[ArcCosh[1 + d*x^2]/2] + Sqrt[2*Pi]*Sqrt[a + b*ArcCosh[1 + d*x^2]]*Erfi[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(-Cosh[a/(2*b)] + Sinh[a/(2*b)]) + Sqrt[2*Pi]*Sqrt[a + b*ArcCosh[1 + d*x^2]]*Erf[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]))*Sinh[ArcCosh[1 + d*x^2]/2])/(b^(3/2)*Sqrt[d*x^2]*Sqrt[(d*x^2)/(2 + d*x^2)]*Sqrt[2 + d*x^2]*Sqrt[a + b*ArcCosh[1 + d*x^2]])","A",0
259,1,273,252,1.0422782,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^{5/2}} \, dx","Integrate[(a + b*ArcCosh[1 + d*x^2])^(-5/2),x]","\frac{x \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \left(\sqrt{2 \pi } \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{3/2} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)+\sqrt{2 \pi } \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{3/2} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)+4 \sqrt{b} \left(-\sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)-b \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right)\right)\right)}{6 b^{5/2} \sqrt{d x^2} \sqrt{\frac{d x^2}{d x^2+2}} \sqrt{d x^2+2} \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{3/2}}","\frac{\sqrt{\frac{\pi }{2}} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{3 b^{5/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{3 b^{5/2} d x}-\frac{x}{3 b^2 \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}-\frac{d x^4+2 x^2}{3 b x \sqrt{d x^2} \sqrt{d x^2+2} \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{3/2}}",1,"(x*Sinh[ArcCosh[1 + d*x^2]/2]*(Sqrt[2*Pi]*(a + b*ArcCosh[1 + d*x^2])^(3/2)*Erfi[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)]) + Sqrt[2*Pi]*(a + b*ArcCosh[1 + d*x^2])^(3/2)*Erf[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]) + 4*Sqrt[b]*(-(b*Cosh[ArcCosh[1 + d*x^2]/2]) - (a + b*ArcCosh[1 + d*x^2])*Sinh[ArcCosh[1 + d*x^2]/2])))/(6*b^(5/2)*Sqrt[d*x^2]*Sqrt[(d*x^2)/(2 + d*x^2)]*Sqrt[2 + d*x^2]*(a + b*ArcCosh[1 + d*x^2])^(3/2))","A",1
260,1,291,301,1.3390182,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(1+d x^2\right)\right)^{7/2}} \, dx","Integrate[(a + b*ArcCosh[1 + d*x^2])^(-7/2),x]","-\frac{x \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \left(4 \sqrt{b} \left(\cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \left(\left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^2+3 b^2\right)+b \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)\right)+\sqrt{2 \pi } \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{5/2} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)+\sqrt{2 \pi } \left(\sinh \left(\frac{a}{2 b}\right)-\cosh \left(\frac{a}{2 b}\right)\right) \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{5/2} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)\right)}{30 b^{7/2} \sqrt{d x^2} \sqrt{\frac{d x^2}{d x^2+2}} \sqrt{d x^2+2} \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{5/2}}","-\frac{\sqrt{\frac{\pi }{2}} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{15 b^{7/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2+1\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}{\sqrt{2} \sqrt{b}}\right)}{15 b^{7/2} d x}-\frac{\sqrt{d x^2} \sqrt{d x^2+2}}{15 b^3 d x \sqrt{a+b \cosh ^{-1}\left(d x^2+1\right)}}-\frac{x}{15 b^2 \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{3/2}}-\frac{d x^4+2 x^2}{5 b x \sqrt{d x^2} \sqrt{d x^2+2} \left(a+b \cosh ^{-1}\left(d x^2+1\right)\right)^{5/2}}",1,"-1/30*(x*Sinh[ArcCosh[1 + d*x^2]/2]*(Sqrt[2*Pi]*(a + b*ArcCosh[1 + d*x^2])^(5/2)*Erfi[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(-Cosh[a/(2*b)] + Sinh[a/(2*b)]) + Sqrt[2*Pi]*(a + b*ArcCosh[1 + d*x^2])^(5/2)*Erf[Sqrt[a + b*ArcCosh[1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]) + 4*Sqrt[b]*((3*b^2 + (a + b*ArcCosh[1 + d*x^2])^2)*Cosh[ArcCosh[1 + d*x^2]/2] + b*(a + b*ArcCosh[1 + d*x^2])*Sinh[ArcCosh[1 + d*x^2]/2])))/(b^(7/2)*Sqrt[d*x^2]*Sqrt[(d*x^2)/(2 + d*x^2)]*Sqrt[2 + d*x^2]*(a + b*ArcCosh[1 + d*x^2])^(5/2))","A",0
261,1,277,281,1.6763844,"\int \left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^{5/2} \, dx","Integrate[(a + b*ArcCosh[-1 + d*x^2])^(5/2),x]","\frac{\cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(4 \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)} \left(\left(a^2+15 b^2\right) \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right)+b \cosh ^{-1}\left(d x^2-1\right) \left(2 a \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right)-5 b \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right)\right)-5 a b \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right)+b^2 \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \cosh ^{-1}\left(d x^2-1\right)^2\right)-15 \sqrt{2 \pi } b^{5/2} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)-15 \sqrt{2 \pi } b^{5/2} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)\right)}{2 d x}","-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}-\frac{15 \sqrt{\frac{\pi }{2}} b^{5/2} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{30 b^2 \cosh ^2\left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{d x}+x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{5/2}+\frac{5 b \left(2 x^2-d x^4\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{3/2}}{x \sqrt{d x^2} \sqrt{d x^2-2}}",1,"(Cosh[ArcCosh[-1 + d*x^2]/2]*(-15*b^(5/2)*Sqrt[2*Pi]*Erfi[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)]) - 15*b^(5/2)*Sqrt[2*Pi]*Erf[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]) + 4*Sqrt[a + b*ArcCosh[-1 + d*x^2]]*((a^2 + 15*b^2)*Cosh[ArcCosh[-1 + d*x^2]/2] + b^2*ArcCosh[-1 + d*x^2]^2*Cosh[ArcCosh[-1 + d*x^2]/2] - 5*a*b*Sinh[ArcCosh[-1 + d*x^2]/2] + b*ArcCosh[-1 + d*x^2]*(2*a*Cosh[ArcCosh[-1 + d*x^2]/2] - 5*b*Sinh[ArcCosh[-1 + d*x^2]/2]))))/(2*d*x)","A",0
262,1,221,239,0.6519562,"\int \left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^{3/2} \, dx","Integrate[(a + b*ArcCosh[-1 + d*x^2])^(3/2),x]","\frac{\cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(-3 \sqrt{2 \pi } b^{3/2} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)+3 \sqrt{2 \pi } b^{3/2} \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)+4 \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)} \left(a \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right)+b \cosh ^{-1}\left(d x^2-1\right) \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right)-3 b \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right)\right)\right)}{2 d x}","-\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{3 \sqrt{\frac{\pi }{2}} b^{3/2} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{3/2}+\frac{3 b \left(2 x^2-d x^4\right) \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{x \sqrt{d x^2} \sqrt{d x^2-2}}",1,"(Cosh[ArcCosh[-1 + d*x^2]/2]*(3*b^(3/2)*Sqrt[2*Pi]*Erfi[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)]) - 3*b^(3/2)*Sqrt[2*Pi]*Erf[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]) + 4*Sqrt[a + b*ArcCosh[-1 + d*x^2]]*(a*Cosh[ArcCosh[-1 + d*x^2]/2] + b*ArcCosh[-1 + d*x^2]*Cosh[ArcCosh[-1 + d*x^2]/2] - 3*b*Sinh[ArcCosh[-1 + d*x^2]/2])))/(2*d*x)","A",0
263,1,178,206,0.3077546,"\int \sqrt{a+b \cosh ^{-1}\left(-1+d x^2\right)} \, dx","Integrate[Sqrt[a + b*ArcCosh[-1 + d*x^2]],x]","\frac{\cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(-\sqrt{2 \pi } \sqrt{b} \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)+\sqrt{2 \pi } \sqrt{b} \left(\sinh \left(\frac{a}{2 b}\right)-\cosh \left(\frac{a}{2 b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)+4 \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}\right)}{2 d x}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{d x}+\frac{2 \cosh ^2\left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{d x}",1,"(Cosh[ArcCosh[-1 + d*x^2]/2]*(4*Sqrt[a + b*ArcCosh[-1 + d*x^2]]*Cosh[ArcCosh[-1 + d*x^2]/2] + Sqrt[b]*Sqrt[2*Pi]*Erfi[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(-Cosh[a/(2*b)] + Sinh[a/(2*b)]) - Sqrt[b]*Sqrt[2*Pi]*Erf[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)])))/(2*d*x)","A",1
264,1,134,166,0.2803001,"\int \frac{1}{\sqrt{a+b \cosh ^{-1}\left(-1+d x^2\right)}} \, dx","Integrate[1/Sqrt[a + b*ArcCosh[-1 + d*x^2]],x]","-\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)+\left(\sinh \left(\frac{a}{2 b}\right)-\cosh \left(\frac{a}{2 b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)\right)}{\sqrt{b} d x}","\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{b} d x}-\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{\sqrt{b} d x}",1,"-((Sqrt[Pi/2]*Cosh[ArcCosh[-1 + d*x^2]/2]*(Erfi[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(-Cosh[a/(2*b)] + Sinh[a/(2*b)]) + Erf[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)])))/(Sqrt[b]*d*x))","A",1
265,1,209,212,1.0533109,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^{3/2}} \, dx","Integrate[(a + b*ArcCosh[-1 + d*x^2])^(-3/2),x]","\frac{\cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sqrt{2 \pi } \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)+\sqrt{2 \pi } \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)-4 \sqrt{b} \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right)\right)}{2 b^{3/2} d x \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}","\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{b^{3/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{b^{3/2} d x}-\frac{\sqrt{d x^2} \sqrt{d x^2-2}}{b d x \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}",1,"(Cosh[ArcCosh[-1 + d*x^2]/2]*(Sqrt[2*Pi]*Sqrt[a + b*ArcCosh[-1 + d*x^2]]*Erfi[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)]) + Sqrt[2*Pi]*Sqrt[a + b*ArcCosh[-1 + d*x^2]]*Erf[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]) - 4*Sqrt[b]*Sinh[ArcCosh[-1 + d*x^2]/2]))/(2*b^(3/2)*d*x*Sqrt[a + b*ArcCosh[-1 + d*x^2]])","A",0
266,1,238,253,0.9047947,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^{5/2}} \, dx","Integrate[(a + b*ArcCosh[-1 + d*x^2])^(-5/2),x]","-\frac{\cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sqrt{2 \pi } \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{3/2} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)+\sqrt{2 \pi } \left(\sinh \left(\frac{a}{2 b}\right)-\cosh \left(\frac{a}{2 b}\right)\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{3/2} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)+4 \sqrt{b} \left(\cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)+b \sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right)\right)\right)}{6 b^{5/2} d x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{3/2}}","-\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{3 b^{5/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{3 b^{5/2} d x}-\frac{x}{3 b^2 \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}+\frac{2 x^2-d x^4}{3 b x \sqrt{d x^2} \sqrt{d x^2-2} \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{3/2}}",1,"-1/6*(Cosh[ArcCosh[-1 + d*x^2]/2]*(Sqrt[2*Pi]*(a + b*ArcCosh[-1 + d*x^2])^(3/2)*Erfi[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(-Cosh[a/(2*b)] + Sinh[a/(2*b)]) + Sqrt[2*Pi]*(a + b*ArcCosh[-1 + d*x^2])^(3/2)*Erf[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]) + 4*Sqrt[b]*((a + b*ArcCosh[-1 + d*x^2])*Cosh[ArcCosh[-1 + d*x^2]/2] + b*Sinh[ArcCosh[-1 + d*x^2]/2])))/(b^(5/2)*d*x*(a + b*ArcCosh[-1 + d*x^2])^(3/2))","A",0
267,1,260,302,1.0835583,"\int \frac{1}{\left(a+b \cosh ^{-1}\left(-1+d x^2\right)\right)^{7/2}} \, dx","Integrate[(a + b*ArcCosh[-1 + d*x^2])^(-7/2),x]","\frac{\cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(4 \sqrt{b} \left(-\sinh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^2+3 b^2\right)-b \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)\right)+\sqrt{2 \pi } \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{5/2} \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)+\sqrt{2 \pi } \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{5/2} \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)\right)}{30 b^{7/2} d x \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{5/2}}","\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\sinh \left(\frac{a}{2 b}\right)+\cosh \left(\frac{a}{2 b}\right)\right) \text{erf}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{15 b^{7/2} d x}+\frac{\sqrt{\frac{\pi }{2}} \cosh \left(\frac{1}{2} \cosh ^{-1}\left(d x^2-1\right)\right) \left(\cosh \left(\frac{a}{2 b}\right)-\sinh \left(\frac{a}{2 b}\right)\right) \text{erfi}\left(\frac{\sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}{\sqrt{2} \sqrt{b}}\right)}{15 b^{7/2} d x}-\frac{\sqrt{d x^2} \sqrt{d x^2-2}}{15 b^3 d x \sqrt{a+b \cosh ^{-1}\left(d x^2-1\right)}}-\frac{x}{15 b^2 \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{3/2}}+\frac{2 x^2-d x^4}{5 b x \sqrt{d x^2} \sqrt{d x^2-2} \left(a+b \cosh ^{-1}\left(d x^2-1\right)\right)^{5/2}}",1,"(Cosh[ArcCosh[-1 + d*x^2]/2]*(Sqrt[2*Pi]*(a + b*ArcCosh[-1 + d*x^2])^(5/2)*Erfi[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] - Sinh[a/(2*b)]) + Sqrt[2*Pi]*(a + b*ArcCosh[-1 + d*x^2])^(5/2)*Erf[Sqrt[a + b*ArcCosh[-1 + d*x^2]]/(Sqrt[2]*Sqrt[b])]*(Cosh[a/(2*b)] + Sinh[a/(2*b)]) + 4*Sqrt[b]*(-(b*(a + b*ArcCosh[-1 + d*x^2])*Cosh[ArcCosh[-1 + d*x^2]/2]) - (3*b^2 + (a + b*ArcCosh[-1 + d*x^2])^2)*Sinh[ArcCosh[-1 + d*x^2]/2])))/(30*b^(7/2)*d*x*(a + b*ArcCosh[-1 + d*x^2])^(5/2))","A",0
268,0,0,43,0.1446849,"\int \frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^n}{1-c^2 x^2} \, dx","Integrate[(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2),x]","\int \frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^n}{1-c^2 x^2} \, dx","\text{Int}\left(\frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^n}{1-c^2 x^2},x\right)",0,"Integrate[(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^n/(1 - c^2*x^2), x]","A",-1
269,0,0,265,0.3957463,"\int \frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^3}{1-c^2 x^2} \, dx","Integrate[(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3/(1 - c^2*x^2),x]","\int \frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^3}{1-c^2 x^2} \, dx","\frac{3 b^2 \text{Li}_3\left(-e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{2 c}+\frac{3 b \text{Li}_2\left(-e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 c}-\frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^4}{4 b c}-\frac{\log \left(e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}+1\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{c}+\frac{3 b^3 \text{Li}_4\left(-e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{4 c}",1,"Integrate[(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^3/(1 - c^2*x^2), x]","F",-1
270,0,0,196,1.0654852,"\int \frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2}{1-c^2 x^2} \, dx","Integrate[(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2/(1 - c^2*x^2),x]","\int \frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2}{1-c^2 x^2} \, dx","\frac{b \text{Li}_2\left(-e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}-\frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^3}{3 b c}-\frac{\log \left(e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}+1\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{c}+\frac{b^2 \text{Li}_3\left(-e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}",1,"Integrate[(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2/(1 - c^2*x^2), x]","F",-1
271,0,0,133,3.1631835,"\int \frac{a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)}{1-c^2 x^2} \, dx","Integrate[(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])/(1 - c^2*x^2),x]","\int \frac{a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)}{1-c^2 x^2} \, dx","-\frac{\left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2}{2 b c}-\frac{\log \left(e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}+1\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)}{c}+\frac{b \text{Li}_2\left(-e^{-2 \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)}\right)}{2 c}",1,"Integrate[(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])/(1 - c^2*x^2), x]","F",-1
272,0,0,43,0.1387432,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)} \, dx","Integrate[1/((1 - c^2*x^2)*(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])),x]","\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)} \, dx","\text{Int}\left(\frac{1}{\left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)},x\right)",0,"Integrate[1/((1 - c^2*x^2)*(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])), x]","A",-1
273,0,0,43,5.3353137,"\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2} \, dx","Integrate[1/((1 - c^2*x^2)*(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2),x]","\int \frac{1}{\left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{1+c x}}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(1-c^2 x^2\right) \left(a+b \cosh ^{-1}\left(\frac{\sqrt{1-c x}}{\sqrt{c x+1}}\right)\right)^2},x\right)",0,"Integrate[1/((1 - c^2*x^2)*(a + b*ArcCosh[Sqrt[1 - c*x]/Sqrt[1 + c*x]])^2), x]","A",-1
274,0,0,76,0.7196174,"\int \cosh ^{-1}\left(c e^{a+b x}\right) \, dx","Integrate[ArcCosh[c*E^(a + b*x)],x]","\int \cosh ^{-1}\left(c e^{a+b x}\right) \, dx","\frac{\text{Li}_2\left(-e^{2 \cosh ^{-1}\left(c e^{a+b x}\right)}\right)}{2 b}-\frac{\cosh ^{-1}\left(c e^{a+b x}\right)^2}{2 b}+\frac{\cosh ^{-1}\left(c e^{a+b x}\right) \log \left(e^{2 \cosh ^{-1}\left(c e^{a+b x}\right)}+1\right)}{b}",1,"Integrate[ArcCosh[c*E^(a + b*x)], x]","F",-1
275,1,138,165,0.0994078,"\int e^{\cosh ^{-1}(a+b x)} x^3 \, dx","Integrate[E^ArcCosh[a + b*x]*x^3,x]","\frac{15 a \left(4 a^2+3\right) \log \left(\sqrt{a+b x-1} \sqrt{a+b x+1}+a+b x\right)+\sqrt{a+b x-1} \sqrt{a+b x+1} \left(-6 a^4-2 \left(3 a^2+4\right) b^2 x^2+\left(6 a^2+29\right) a b x-83 a^2+6 a b^3 x^3+24 b^4 x^4-16\right)+30 a b^4 x^4+24 b^5 x^5}{120 b^4}","-\frac{\left(4 a^2+3\right) a e^{2 \cosh ^{-1}(a+b x)}}{16 b^4}+\frac{\left(4 a^2+3\right) a \cosh ^{-1}(a+b x)}{8 b^4}+\frac{\left(6 a^2+1\right) e^{-\cosh ^{-1}(a+b x)}}{8 b^4}+\frac{\left(6 a^2+1\right) e^{3 \cosh ^{-1}(a+b x)}}{24 b^4}-\frac{3 a e^{-2 \cosh ^{-1}(a+b x)}}{16 b^4}-\frac{3 a e^{4 \cosh ^{-1}(a+b x)}}{32 b^4}+\frac{e^{-3 \cosh ^{-1}(a+b x)}}{48 b^4}+\frac{e^{5 \cosh ^{-1}(a+b x)}}{80 b^4}",1,"(30*a*b^4*x^4 + 24*b^5*x^5 + Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]*(-16 - 83*a^2 - 6*a^4 + a*(29 + 6*a^2)*b*x - 2*(4 + 3*a^2)*b^2*x^2 + 6*a*b^3*x^3 + 24*b^4*x^4) + 15*a*(3 + 4*a^2)*Log[a + b*x + Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]])/(120*b^4)","A",0
276,1,119,115,0.1388063,"\int e^{\cosh ^{-1}(a+b x)} x^2 \, dx","Integrate[E^ArcCosh[a + b*x]*x^2,x]","\frac{-3 \left(4 a^2+1\right) \log \left(\sqrt{a+b x-1} \sqrt{a+b x+1}+a+b x\right)+\sqrt{a+b x-1} \sqrt{a+b x+1} \left(2 a^3-2 a^2 b x+a \left(2 b^2 x^2+13\right)+6 b^3 x^3-3 b x\right)+8 a b^3 x^3+6 b^4 x^4}{24 b^3}","\frac{\left(4 a^2+1\right) e^{2 \cosh ^{-1}(a+b x)}}{16 b^3}-\frac{\left(4 a^2+1\right) \cosh ^{-1}(a+b x)}{8 b^3}-\frac{a e^{-\cosh ^{-1}(a+b x)}}{2 b^3}-\frac{a e^{3 \cosh ^{-1}(a+b x)}}{6 b^3}+\frac{e^{-2 \cosh ^{-1}(a+b x)}}{16 b^3}+\frac{e^{4 \cosh ^{-1}(a+b x)}}{32 b^3}",1,"(8*a*b^3*x^3 + 6*b^4*x^4 + Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]*(2*a^3 - 3*b*x - 2*a^2*b*x + 6*b^3*x^3 + a*(13 + 2*b^2*x^2)) - 3*(1 + 4*a^2)*Log[a + b*x + Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]])/(24*b^3)","A",0
277,1,93,67,0.16812,"\int e^{\cosh ^{-1}(a+b x)} x \, dx","Integrate[E^ArcCosh[a + b*x]*x,x]","\frac{1}{6} \left(\frac{\sqrt{a+b x-1} \sqrt{a+b x+1} \left(-a^2+a b x+2 b^2 x^2-2\right)}{b^2}+\frac{3 a \log \left(\sqrt{a+b x-1} \sqrt{a+b x+1}+a+b x\right)}{b^2}+3 a x^2+2 b x^3\right)","-\frac{a e^{2 \cosh ^{-1}(a+b x)}}{4 b^2}+\frac{a \cosh ^{-1}(a+b x)}{2 b^2}+\frac{e^{-\cosh ^{-1}(a+b x)}}{4 b^2}+\frac{e^{3 \cosh ^{-1}(a+b x)}}{12 b^2}",1,"(3*a*x^2 + 2*b*x^3 + (Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]*(-2 - a^2 + a*b*x + 2*b^2*x^2))/b^2 + (3*a*Log[a + b*x + Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]])/b^2)/6","A",0
278,1,69,31,0.0314648,"\int e^{\cosh ^{-1}(a+b x)} \, dx","Integrate[E^ArcCosh[a + b*x],x]","\frac{(a+b x) \left(\sqrt{a+b x-1} \sqrt{a+b x+1}+a+b x\right)-\log \left(\sqrt{a+b x-1} \sqrt{a+b x+1}+a+b x\right)}{2 b}","\frac{e^{2 \cosh ^{-1}(a+b x)}}{4 b}-\frac{\cosh ^{-1}(a+b x)}{2 b}",1,"((a + b*x)*(a + b*x + Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]) - Log[a + b*x + Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]])/(2*b)","B",0
279,1,141,100,0.1023332,"\int \frac{e^{\cosh ^{-1}(a+b x)}}{x} \, dx","Integrate[E^ArcCosh[a + b*x]/x,x]","i \sqrt{1-a^2} \log \left(\frac{2 \sqrt{a+b x-1} \sqrt{a+b x+1}}{\left(a^2-1\right) x}+\frac{2 i \left(a^2+a b x-1\right)}{\sqrt{1-a^2} \left(a^2-1\right) x}\right)+\sqrt{a+b x-1} \sqrt{a+b x+1}+a \log \left(\sqrt{a+b x-1} \sqrt{a+b x+1}+a+b x\right)+a \log (x)+b x","2 \sqrt{1-a^2} \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)+\sqrt{a+b x-1} \sqrt{a+b x+1}+2 a \sinh ^{-1}\left(\frac{\sqrt{a+b x-1}}{\sqrt{2}}\right)+a \log (x)+b x",1,"b*x + Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x] + a*Log[x] + a*Log[a + b*x + Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]] + I*Sqrt[1 - a^2]*Log[(2*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/((-1 + a^2)*x) + ((2*I)*(-1 + a^2 + a*b*x))/(Sqrt[1 - a^2]*(-1 + a^2)*x)]","C",0
280,1,140,109,0.1672419,"\int \frac{e^{\cosh ^{-1}(a+b x)}}{x^2} \, dx","Integrate[E^ArcCosh[a + b*x]/x^2,x]","-\frac{i a b \log \left(\frac{2 \left(\sqrt{a+b x-1} \sqrt{a+b x+1}+\frac{i \left(a^2+a b x-1\right)}{\sqrt{1-a^2}}\right)}{a b x}\right)}{\sqrt{1-a^2}}-\frac{\sqrt{a+b x-1} \sqrt{a+b x+1}}{x}+b \log \left(\sqrt{a+b x-1} \sqrt{a+b x+1}+a+b x\right)-\frac{a}{x}+b \log (x)","-\frac{2 a b \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{\sqrt{1-a^2}}-\frac{\sqrt{a+b x-1} \sqrt{a+b x+1}}{x}+2 b \sinh ^{-1}\left(\frac{\sqrt{a+b x-1}}{\sqrt{2}}\right)-\frac{a}{x}+b \log (x)",1,"-(a/x) - (Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x])/x + b*Log[x] + b*Log[a + b*x + Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]] - (I*a*b*Log[(2*(Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x] + (I*(-1 + a^2 + a*b*x))/Sqrt[1 - a^2]))/(a*b*x)])/Sqrt[1 - a^2]","C",0
281,1,142,138,0.2664315,"\int \frac{e^{\cosh ^{-1}(a+b x)}}{x^3} \, dx","Integrate[E^ArcCosh[a + b*x]/x^3,x]","\frac{1}{2} \left(-\frac{i b^2 \log \left(\frac{4 i \sqrt{1-a^2} \left(-i \sqrt{1-a^2} \sqrt{a+b x-1} \sqrt{a+b x+1}+a^2+a b x-1\right)}{b^2 x}\right)}{\left(1-a^2\right)^{3/2}}-\frac{\sqrt{a+b x-1} \sqrt{a+b x+1} \left(a^2+a b x-1\right)}{\left(a^2-1\right) x^2}-\frac{a}{x^2}-\frac{2 b}{x}\right)","-\frac{b^2 \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{\left(1-a^2\right)^{3/2}}+\frac{b \sqrt{a+b x-1} \sqrt{a+b x+1}}{2 \left(1-a^2\right) x}-\frac{\sqrt{a+b x-1} (a+b x+1)^{3/2}}{2 (a+1) x^2}-\frac{a}{2 x^2}-\frac{b}{x}",1,"(-(a/x^2) - (2*b)/x - (Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]*(-1 + a^2 + a*b*x))/((-1 + a^2)*x^2) - (I*b^2*Log[((4*I)*Sqrt[1 - a^2]*(-1 + a^2 + a*b*x - I*Sqrt[1 - a^2]*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]))/(b^2*x)])/(1 - a^2)^(3/2))/2","C",0
282,1,179,189,0.1680408,"\int \frac{e^{\cosh ^{-1}(a+b x)}}{x^4} \, dx","Integrate[E^ArcCosh[a + b*x]/x^4,x]","\frac{1}{6} \left(-\frac{3 i a b^3 \log \left(\frac{4 \left(1-a^2\right)^{3/2} \left(\sqrt{1-a^2} \sqrt{a+b x-1} \sqrt{a+b x+1}+i a^2+i a b x-i\right)}{a b^3 x}\right)}{\left(1-a^2\right)^{5/2}}+\frac{\sqrt{a+b x-1} \sqrt{a+b x+1} \left(-2 a^4-a^3 b x+a^2 \left(b^2 x^2+4\right)+a b x+2 b^2 x^2-2\right)}{\left(a^2-1\right)^2 x^3}-\frac{2 a}{x^3}-\frac{3 b}{x^2}\right)","-\frac{a b^3 \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{\left(1-a^2\right)^{5/2}}+\frac{a b^2 \sqrt{a+b x-1} \sqrt{a+b x+1}}{2 \left(1-a^2\right)^2 x}+\frac{(a+b x-1)^{3/2} (a+b x+1)^{3/2}}{3 \left(1-a^2\right) x^3}-\frac{a b \sqrt{a+b x-1} (a+b x+1)^{3/2}}{2 (1-a) (a+1)^2 x^2}-\frac{a}{3 x^3}-\frac{b}{2 x^2}",1,"((-2*a)/x^3 - (3*b)/x^2 + (Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]*(-2 - 2*a^4 + a*b*x - a^3*b*x + 2*b^2*x^2 + a^2*(4 + b^2*x^2)))/((-1 + a^2)^2*x^3) - ((3*I)*a*b^3*Log[(4*(1 - a^2)^(3/2)*(-I + I*a^2 + I*a*b*x + Sqrt[1 - a^2]*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]))/(a*b^3*x)])/(1 - a^2)^(5/2))/6","C",0
283,1,198,238,0.2793951,"\int \frac{e^{\cosh ^{-1}(a+b x)}}{x^5} \, dx","Integrate[E^ArcCosh[a + b*x]/x^5,x]","\frac{1}{24} \left(-\frac{3 i \left(4 a^2+1\right) b^4 \log \left(\frac{16 i \left(1-a^2\right)^{5/2} \left(-i \sqrt{1-a^2} \sqrt{a+b x-1} \sqrt{a+b x+1}+a^2+a b x-1\right)}{b^4 \left(4 a^2 x+x\right)}\right)}{\left(1-a^2\right)^{7/2}}-\frac{\sqrt{a+b x-1} \sqrt{a+b x+1} \left(\frac{a \left(2 a^2+13\right) b^3 x^3}{\left(a^2-1\right)^3}-\frac{\left(2 a^2+3\right) b^2 x^2}{\left(a^2-1\right)^2}+\frac{2 a b x}{a^2-1}+6\right)}{x^4}-\frac{6 a}{x^4}-\frac{8 b}{x^3}\right)","-\frac{\left(4 a^2+1\right) b^4 \tan ^{-1}\left(\frac{\sqrt{1-a} \sqrt{a+b x+1}}{\sqrt{a+1} \sqrt{a+b x-1}}\right)}{4 \left(1-a^2\right)^{7/2}}+\frac{a \left(2 a^2+13\right) b^3 \sqrt{a+b x-1} \sqrt{a+b x+1}}{24 \left(1-a^2\right)^3 x}+\frac{\left(2 a^2+3\right) b^2 \sqrt{a+b x-1} \sqrt{a+b x+1}}{24 \left(1-a^2\right)^2 x^2}+\frac{a b \sqrt{a+b x-1} \sqrt{a+b x+1}}{12 \left(1-a^2\right) x^3}-\frac{\sqrt{a+b x-1} \sqrt{a+b x+1}}{4 x^4}-\frac{a}{4 x^4}-\frac{b}{3 x^3}",1,"((-6*a)/x^4 - (8*b)/x^3 - (Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]*(6 + (2*a*b*x)/(-1 + a^2) - ((3 + 2*a^2)*b^2*x^2)/(-1 + a^2)^2 + (a*(13 + 2*a^2)*b^3*x^3)/(-1 + a^2)^3))/x^4 - ((3*I)*(1 + 4*a^2)*b^4*Log[((16*I)*(1 - a^2)^(5/2)*(-1 + a^2 + a*b*x - I*Sqrt[1 - a^2]*Sqrt[-1 + a + b*x]*Sqrt[1 + a + b*x]))/(b^4*(x + 4*a^2*x))])/(1 - a^2)^(7/2))/24","C",0
284,1,198,359,0.3977378,"\int e^{\cosh ^{-1}(a+b x)^2} x^3 \, dx","Integrate[E^ArcCosh[a + b*x]^2*x^3,x]","\frac{\sqrt{\pi } \left(-8 e^{15/4} a^3 \text{erfi}\left(\cosh ^{-1}(a+b x)+\frac{1}{2}\right)+12 e^3 a^2 \text{erfi}\left(\cosh ^{-1}(a+b x)+1\right)-2 e^{15/4} \left(4 a^2+3\right) a \text{erfi}\left(\frac{1}{2}-\cosh ^{-1}(a+b x)\right)+2 e^3 \left(6 a^2+1\right) \text{erfi}\left(1-\cosh ^{-1}(a+b x)\right)-6 e^{7/4} a \text{erfi}\left(\frac{3}{2}-\cosh ^{-1}(a+b x)\right)-6 e^{15/4} a \text{erfi}\left(\cosh ^{-1}(a+b x)+\frac{1}{2}\right)-6 e^{7/4} a \text{erfi}\left(\cosh ^{-1}(a+b x)+\frac{3}{2}\right)+\text{erfi}\left(2-\cosh ^{-1}(a+b x)\right)+2 e^3 \text{erfi}\left(\cosh ^{-1}(a+b x)+1\right)+\text{erfi}\left(\cosh ^{-1}(a+b x)+2\right)\right)}{32 e^4 b^4}","\frac{\sqrt{\pi } a^3 \text{erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b^4}-\frac{\sqrt{\pi } a^3 \text{erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b^4}+\frac{3 \sqrt{\pi } a^2 \text{erfi}\left(1-\cosh ^{-1}(a+b x)\right)}{8 e b^4}+\frac{3 \sqrt{\pi } a^2 \text{erfi}\left(\cosh ^{-1}(a+b x)+1\right)}{8 e b^4}+\frac{3 \sqrt{\pi } a \text{erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-3\right)\right)}{16 e^{9/4} b^4}+\frac{3 \sqrt{\pi } a \text{erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{16 \sqrt[4]{e} b^4}-\frac{3 \sqrt{\pi } a \text{erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{16 \sqrt[4]{e} b^4}-\frac{3 \sqrt{\pi } a \text{erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+3\right)\right)}{16 e^{9/4} b^4}+\frac{\sqrt{\pi } \text{erfi}\left(1-\cosh ^{-1}(a+b x)\right)}{16 e b^4}+\frac{\sqrt{\pi } \text{erfi}\left(2-\cosh ^{-1}(a+b x)\right)}{32 e^4 b^4}+\frac{\sqrt{\pi } \text{erfi}\left(\cosh ^{-1}(a+b x)+1\right)}{16 e b^4}+\frac{\sqrt{\pi } \text{erfi}\left(\cosh ^{-1}(a+b x)+2\right)}{32 e^4 b^4}",1,"(Sqrt[Pi]*(-2*a*(3 + 4*a^2)*E^(15/4)*Erfi[1/2 - ArcCosh[a + b*x]] + 2*(1 + 6*a^2)*E^3*Erfi[1 - ArcCosh[a + b*x]] - 6*a*E^(7/4)*Erfi[3/2 - ArcCosh[a + b*x]] + Erfi[2 - ArcCosh[a + b*x]] - 6*a*E^(15/4)*Erfi[1/2 + ArcCosh[a + b*x]] - 8*a^3*E^(15/4)*Erfi[1/2 + ArcCosh[a + b*x]] + 2*E^3*Erfi[1 + ArcCosh[a + b*x]] + 12*a^2*E^3*Erfi[1 + ArcCosh[a + b*x]] - 6*a*E^(7/4)*Erfi[3/2 + ArcCosh[a + b*x]] + Erfi[2 + ArcCosh[a + b*x]]))/(32*b^4*E^4)","A",1
285,1,136,251,0.2283784,"\int e^{\cosh ^{-1}(a+b x)^2} x^2 \, dx","Integrate[E^ArcCosh[a + b*x]^2*x^2,x]","\frac{\sqrt{\pi } \left(4 e^2 a^2 \text{erfi}\left(\cosh ^{-1}(a+b x)+\frac{1}{2}\right)+e^2 \left(4 a^2+1\right) \text{erfi}\left(\frac{1}{2}-\cosh ^{-1}(a+b x)\right)-4 e^{5/4} a \text{erfi}\left(1-\cosh ^{-1}(a+b x)\right)-4 e^{5/4} a \text{erfi}\left(\cosh ^{-1}(a+b x)+1\right)+\text{erfi}\left(\frac{3}{2}-\cosh ^{-1}(a+b x)\right)+e^2 \text{erfi}\left(\cosh ^{-1}(a+b x)+\frac{1}{2}\right)+\text{erfi}\left(\cosh ^{-1}(a+b x)+\frac{3}{2}\right)\right)}{16 e^{9/4} b^3}","-\frac{\sqrt{\pi } a^2 \text{erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b^3}+\frac{\sqrt{\pi } a^2 \text{erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b^3}-\frac{\sqrt{\pi } a \text{erfi}\left(1-\cosh ^{-1}(a+b x)\right)}{4 e b^3}-\frac{\sqrt{\pi } a \text{erfi}\left(\cosh ^{-1}(a+b x)+1\right)}{4 e b^3}-\frac{\sqrt{\pi } \text{erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-3\right)\right)}{16 e^{9/4} b^3}-\frac{\sqrt{\pi } \text{erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{16 \sqrt[4]{e} b^3}+\frac{\sqrt{\pi } \text{erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{16 \sqrt[4]{e} b^3}+\frac{\sqrt{\pi } \text{erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+3\right)\right)}{16 e^{9/4} b^3}",1,"(Sqrt[Pi]*((1 + 4*a^2)*E^2*Erfi[1/2 - ArcCosh[a + b*x]] - 4*a*E^(5/4)*Erfi[1 - ArcCosh[a + b*x]] + Erfi[3/2 - ArcCosh[a + b*x]] + E^2*Erfi[1/2 + ArcCosh[a + b*x]] + 4*a^2*E^2*Erfi[1/2 + ArcCosh[a + b*x]] - 4*a*E^(5/4)*Erfi[1 + ArcCosh[a + b*x]] + Erfi[3/2 + ArcCosh[a + b*x]]))/(16*b^3*E^(9/4))","A",1
286,1,76,117,0.1385057,"\int e^{\cosh ^{-1}(a+b x)^2} x \, dx","Integrate[E^ArcCosh[a + b*x]^2*x,x]","\frac{\sqrt{\pi } \left(-2 e^{3/4} a \text{erfi}\left(\frac{1}{2}-\cosh ^{-1}(a+b x)\right)+\text{erfi}\left(1-\cosh ^{-1}(a+b x)\right)-2 e^{3/4} a \text{erfi}\left(\cosh ^{-1}(a+b x)+\frac{1}{2}\right)+\text{erfi}\left(\cosh ^{-1}(a+b x)+1\right)\right)}{8 e b^2}","\frac{\sqrt{\pi } \text{erfi}\left(1-\cosh ^{-1}(a+b x)\right)}{8 e b^2}+\frac{\sqrt{\pi } \text{erfi}\left(\cosh ^{-1}(a+b x)+1\right)}{8 e b^2}+\frac{\sqrt{\pi } a \text{erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b^2}-\frac{\sqrt{\pi } a \text{erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b^2}",1,"(Sqrt[Pi]*(-2*a*E^(3/4)*Erfi[1/2 - ArcCosh[a + b*x]] + Erfi[1 - ArcCosh[a + b*x]] - 2*a*E^(3/4)*Erfi[1/2 + ArcCosh[a + b*x]] + Erfi[1 + ArcCosh[a + b*x]]))/(8*b^2*E)","A",1
287,1,42,65,0.0378725,"\int e^{\cosh ^{-1}(a+b x)^2} \, dx","Integrate[E^ArcCosh[a + b*x]^2,x]","\frac{\sqrt{\pi } \left(\text{erfi}\left(\frac{1}{2}-\cosh ^{-1}(a+b x)\right)+\text{erfi}\left(\cosh ^{-1}(a+b x)+\frac{1}{2}\right)\right)}{4 \sqrt[4]{e} b}","\frac{\sqrt{\pi } \text{erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)+1\right)\right)}{4 \sqrt[4]{e} b}-\frac{\sqrt{\pi } \text{erfi}\left(\frac{1}{2} \left(2 \cosh ^{-1}(a+b x)-1\right)\right)}{4 \sqrt[4]{e} b}",1,"(Sqrt[Pi]*(Erfi[1/2 - ArcCosh[a + b*x]] + Erfi[1/2 + ArcCosh[a + b*x]]))/(4*b*E^(1/4))","A",1
288,0,0,17,0.1519551,"\int \frac{e^{\cosh ^{-1}(a+b x)^2}}{x} \, dx","Integrate[E^ArcCosh[a + b*x]^2/x,x]","\int \frac{e^{\cosh ^{-1}(a+b x)^2}}{x} \, dx","\text{Int}\left(\frac{e^{\cosh ^{-1}(a+b x)^2}}{x},x\right)",0,"Integrate[E^ArcCosh[a + b*x]^2/x, x]","A",-1
289,0,0,17,0.4734947,"\int \frac{e^{\cosh ^{-1}(a+b x)^2}}{x^2} \, dx","Integrate[E^ArcCosh[a + b*x]^2/x^2,x]","\int \frac{e^{\cosh ^{-1}(a+b x)^2}}{x^2} \, dx","\text{Int}\left(\frac{e^{\cosh ^{-1}(a+b x)^2}}{x^2},x\right)",0,"Integrate[E^ArcCosh[a + b*x]^2/x^2, x]","A",-1
290,1,53,60,0.045447,"\int \frac{\cosh ^{-1}(a+b x)}{\frac{a d}{b}+d x} \, dx","Integrate[ArcCosh[a + b*x]/((a*d)/b + d*x),x]","\frac{\cosh ^{-1}(a+b x) \left(\cosh ^{-1}(a+b x)+2 \log \left(e^{-2 \cosh ^{-1}(a+b x)}+1\right)\right)-\text{Li}_2\left(-e^{-2 \cosh ^{-1}(a+b x)}\right)}{2 d}","\frac{\text{Li}_2\left(-e^{2 \cosh ^{-1}(a+b x)}\right)}{2 d}-\frac{\cosh ^{-1}(a+b x)^2}{2 d}+\frac{\cosh ^{-1}(a+b x) \log \left(e^{2 \cosh ^{-1}(a+b x)}+1\right)}{d}",1,"(ArcCosh[a + b*x]*(ArcCosh[a + b*x] + 2*Log[1 + E^(-2*ArcCosh[a + b*x])]) - PolyLog[2, -E^(-2*ArcCosh[a + b*x])])/(2*d)","A",0
291,1,19,3,0.0628945,"\int \frac{x}{\sqrt{-1+x} \sqrt{1+x} \cosh ^{-1}(x)} \, dx","Integrate[x/(Sqrt[-1 + x]*Sqrt[1 + x]*ArcCosh[x]),x]","\frac{1}{2} (x-1) \text{Chi}\left(\cosh ^{-1}(x)\right) \text{csch}^2\left(\frac{1}{2} \cosh ^{-1}(x)\right)","\text{Chi}\left(\cosh ^{-1}(x)\right)",1,"((-1 + x)*CoshIntegral[ArcCosh[x]]*Csch[ArcCosh[x]/2]^2)/2","B",1
292,1,50,54,0.0361261,"\int x^3 \cosh ^{-1}\left(a+b x^4\right) \, dx","Integrate[x^3*ArcCosh[a + b*x^4],x]","\frac{\left(a+b x^4\right) \cosh ^{-1}\left(a+b x^4\right)-\sqrt{a+b x^4-1} \sqrt{a+b x^4+1}}{4 b}","\frac{\left(a+b x^4\right) \cosh ^{-1}\left(a+b x^4\right)}{4 b}-\frac{\sqrt{a+b x^4-1} \sqrt{a+b x^4+1}}{4 b}",1,"(-(Sqrt[-1 + a + b*x^4]*Sqrt[1 + a + b*x^4]) + (a + b*x^4)*ArcCosh[a + b*x^4])/(4*b)","A",1
293,1,50,55,0.0478507,"\int x^{-1+n} \cosh ^{-1}\left(a+b x^n\right) \, dx","Integrate[x^(-1 + n)*ArcCosh[a + b*x^n],x]","\frac{\left(a+b x^n\right) \cosh ^{-1}\left(a+b x^n\right)-\sqrt{a+b x^n-1} \sqrt{a+b x^n+1}}{b n}","\frac{\left(a+b x^n\right) \cosh ^{-1}\left(a+b x^n\right)}{b n}-\frac{\sqrt{a+b x^n-1} \sqrt{a+b x^n+1}}{b n}",1,"(-(Sqrt[-1 + a + b*x^n]*Sqrt[1 + a + b*x^n]) + (a + b*x^n)*ArcCosh[a + b*x^n])/(b*n)","A",1
294,1,180,58,0.5573144,"\int \cosh ^{-1}\left(\frac{c}{a+b x}\right) \, dx","Integrate[ArcCosh[c/(a + b*x)],x]","\frac{2 c \sqrt{-\frac{a+b x-c}{a+b x+c}} \left(a \sqrt{b} \sqrt{a+b x+c} \tanh ^{-1}\left(\frac{\sqrt{-b c} \sqrt{a+b x-c}}{\sqrt{b c} \sqrt{a+b x+c}}\right)-c \sqrt{-b c} \sqrt{\frac{a+b x+c}{c}} \sinh ^{-1}\left(\frac{\sqrt{b} \sqrt{a+b x-c}}{\sqrt{2} \sqrt{b c}}\right)\right)}{\sqrt{b} \sqrt{-b^2 c^2} \sqrt{a+b x-c}}+x \cosh ^{-1}\left(\frac{c}{a+b x}\right)","\frac{(a+b x) \text{sech}^{-1}\left(\frac{a}{c}+\frac{b x}{c}\right)}{b}-\frac{2 c \tan ^{-1}\left(\sqrt{\frac{c \left(1-\frac{a}{c}\right)-b x}{a+b x+c}}\right)}{b}",1,"x*ArcCosh[c/(a + b*x)] + (2*c*Sqrt[-((a - c + b*x)/(a + c + b*x))]*(-(c*Sqrt[-(b*c)]*Sqrt[(a + c + b*x)/c]*ArcSinh[(Sqrt[b]*Sqrt[a - c + b*x])/(Sqrt[2]*Sqrt[b*c])]) + a*Sqrt[b]*Sqrt[a + c + b*x]*ArcTanh[(Sqrt[-(b*c)]*Sqrt[a - c + b*x])/(Sqrt[b*c]*Sqrt[a + c + b*x])]))/(Sqrt[b]*Sqrt[-(b^2*c^2)]*Sqrt[a - c + b*x])","B",0
295,1,62,62,0.1998925,"\int \frac{\cosh ^{-1}\left(\sqrt{1+b x^2}\right)^n}{\sqrt{1+b x^2}} \, dx","Integrate[ArcCosh[Sqrt[1 + b*x^2]]^n/Sqrt[1 + b*x^2],x]","\frac{\sqrt{\sqrt{b x^2+1}-1} \sqrt{\sqrt{b x^2+1}+1} \cosh ^{-1}\left(\sqrt{b x^2+1}\right)^{n+1}}{b (n+1) x}","\frac{\sqrt{\sqrt{b x^2+1}-1} \sqrt{\sqrt{b x^2+1}+1} \cosh ^{-1}\left(\sqrt{b x^2+1}\right)^{n+1}}{b (n+1) x}",1,"(Sqrt[-1 + Sqrt[1 + b*x^2]]*Sqrt[1 + Sqrt[1 + b*x^2]]*ArcCosh[Sqrt[1 + b*x^2]]^(1 + n))/(b*(1 + n)*x)","A",1
296,1,54,54,0.0948515,"\int \frac{1}{\sqrt{1+b x^2} \cosh ^{-1}\left(\sqrt{1+b x^2}\right)} \, dx","Integrate[1/(Sqrt[1 + b*x^2]*ArcCosh[Sqrt[1 + b*x^2]]),x]","\frac{\sqrt{\sqrt{b x^2+1}-1} \sqrt{\sqrt{b x^2+1}+1} \log \left(\cosh ^{-1}\left(\sqrt{b x^2+1}\right)\right)}{b x}","\frac{\sqrt{\sqrt{b x^2+1}-1} \sqrt{\sqrt{b x^2+1}+1} \log \left(\cosh ^{-1}\left(\sqrt{b x^2+1}\right)\right)}{b x}",1,"(Sqrt[-1 + Sqrt[1 + b*x^2]]*Sqrt[1 + Sqrt[1 + b*x^2]]*Log[ArcCosh[Sqrt[1 + b*x^2]]])/(b*x)","A",1