1,1,21,10,0.0082197,"\int \sinh (a+b x) \, dx","Integrate[Sinh[a + b*x],x]","\frac{\sinh (a) \sinh (b x)}{b}+\frac{\cosh (a) \cosh (b x)}{b}","\frac{\cosh (a+b x)}{b}",1,"(Cosh[a]*Cosh[b*x])/b + (Sinh[a]*Sinh[b*x])/b","B",1
2,1,23,25,0.0233959,"\int \sinh ^2(a+b x) \, dx","Integrate[Sinh[a + b*x]^2,x]","\frac{\sinh (2 (a+b x))-2 (a+b x)}{4 b}","\frac{\sinh (a+b x) \cosh (a+b x)}{2 b}-\frac{x}{2}",1,"(-2*(a + b*x) + Sinh[2*(a + b*x)])/(4*b)","A",1
3,1,29,27,0.0104614,"\int \sinh ^3(a+b x) \, dx","Integrate[Sinh[a + b*x]^3,x]","\frac{\cosh (3 (a+b x))}{12 b}-\frac{3 \cosh (a+b x)}{4 b}","\frac{\cosh ^3(a+b x)}{3 b}-\frac{\cosh (a+b x)}{b}",1,"(-3*Cosh[a + b*x])/(4*b) + Cosh[3*(a + b*x)]/(12*b)","A",1
4,1,33,46,0.041609,"\int \sinh ^4(a+b x) \, dx","Integrate[Sinh[a + b*x]^4,x]","\frac{12 (a+b x)-8 \sinh (2 (a+b x))+\sinh (4 (a+b x))}{32 b}","\frac{\sinh ^3(a+b x) \cosh (a+b x)}{4 b}-\frac{3 \sinh (a+b x) \cosh (a+b x)}{8 b}+\frac{3 x}{8}",1,"(12*(a + b*x) - 8*Sinh[2*(a + b*x)] + Sinh[4*(a + b*x)])/(32*b)","A",1
5,1,44,41,0.0142472,"\int \sinh ^5(a+b x) \, dx","Integrate[Sinh[a + b*x]^5,x]","\frac{5 \cosh (a+b x)}{8 b}-\frac{5 \cosh (3 (a+b x))}{48 b}+\frac{\cosh (5 (a+b x))}{80 b}","\frac{\cosh ^5(a+b x)}{5 b}-\frac{2 \cosh ^3(a+b x)}{3 b}+\frac{\cosh (a+b x)}{b}",1,"(5*Cosh[a + b*x])/(8*b) - (5*Cosh[3*(a + b*x)])/(48*b) + Cosh[5*(a + b*x)]/(80*b)","A",1
6,1,43,67,0.039428,"\int \sinh ^6(a+b x) \, dx","Integrate[Sinh[a + b*x]^6,x]","\frac{45 \sinh (2 (a+b x))-9 \sinh (4 (a+b x))+\sinh (6 (a+b x))-60 a-60 b x}{192 b}","\frac{\sinh ^5(a+b x) \cosh (a+b x)}{6 b}-\frac{5 \sinh ^3(a+b x) \cosh (a+b x)}{24 b}+\frac{5 \sinh (a+b x) \cosh (a+b x)}{16 b}-\frac{5 x}{16}",1,"(-60*a - 60*b*x + 45*Sinh[2*(a + b*x)] - 9*Sinh[4*(a + b*x)] + Sinh[6*(a + b*x)])/(192*b)","A",1
7,1,75,103,0.139421,"\int \sinh ^{\frac{7}{2}}(a+b x) \, dx","Integrate[Sinh[a + b*x]^(7/2),x]","\frac{-26 \sinh (2 (a+b x))+3 \sinh (4 (a+b x))+40 i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)}{84 b \sqrt{\sinh (a+b x)}}","\frac{2 \sinh ^{\frac{5}{2}}(a+b x) \cosh (a+b x)}{7 b}-\frac{10 \sqrt{\sinh (a+b x)} \cosh (a+b x)}{21 b}-\frac{10 i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{21 b \sqrt{\sinh (a+b x)}}",1,"((40*I)*EllipticF[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[I*Sinh[a + b*x]] - 26*Sinh[2*(a + b*x)] + 3*Sinh[4*(a + b*x)])/(84*b*Sqrt[Sinh[a + b*x]])","A",1
8,1,68,80,0.0752328,"\int \sinh ^{\frac{5}{2}}(a+b x) \, dx","Integrate[Sinh[a + b*x]^(5/2),x]","\frac{\sinh (a+b x) \sinh (2 (a+b x))-6 \sqrt{i \sinh (a+b x)} E\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)}{5 b \sqrt{\sinh (a+b x)}}","\frac{2 \sinh ^{\frac{3}{2}}(a+b x) \cosh (a+b x)}{5 b}+\frac{6 i \sqrt{\sinh (a+b x)} E\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{5 b \sqrt{i \sinh (a+b x)}}",1,"(-6*EllipticE[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[I*Sinh[a + b*x]] + Sinh[a + b*x]*Sinh[2*(a + b*x)])/(5*b*Sqrt[Sinh[a + b*x]])","A",1
9,1,83,80,0.0895898,"\int \sinh ^{\frac{3}{2}}(a+b x) \, dx","Integrate[Sinh[a + b*x]^(3/2),x]","\frac{\sinh (2 (a+b x))-2 \sqrt{-\sinh (2 a+2 b x)-\cosh (2 a+2 b x)+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\cosh (2 (a+b x))+\sinh (2 (a+b x))\right)}{3 b \sqrt{\sinh (a+b x)}}","\frac{2 \sqrt{\sinh (a+b x)} \cosh (a+b x)}{3 b}+\frac{2 i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{3 b \sqrt{\sinh (a+b x)}}",1,"(Sinh[2*(a + b*x)] - 2*Hypergeometric2F1[1/4, 1/2, 5/4, Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)]]*Sqrt[1 - Cosh[2*a + 2*b*x] - Sinh[2*a + 2*b*x]])/(3*b*Sqrt[Sinh[a + b*x]])","C",1
10,1,50,54,0.1049058,"\int \sqrt{\sinh (a+b x)} \, dx","Integrate[Sqrt[Sinh[a + b*x]],x]","\frac{2 \sqrt{i \sinh (a+b x)} E\left(\left.\frac{1}{2} \left(\frac{\pi }{2}-i (a+b x)\right)\right|2\right)}{b \sqrt{\sinh (a+b x)}}","-\frac{2 i \sqrt{\sinh (a+b x)} E\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{b \sqrt{i \sinh (a+b x)}}",1,"(2*EllipticE[(Pi/2 - I*(a + b*x))/2, 2]*Sqrt[I*Sinh[a + b*x]])/(b*Sqrt[Sinh[a + b*x]])","A",1
11,1,48,54,0.1203478,"\int \frac{1}{\sqrt{\sinh (a+b x)}} \, dx","Integrate[1/Sqrt[Sinh[a + b*x]],x]","-\frac{2 \sqrt{\sinh (a+b x)} F\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)}{b \sqrt{i \sinh (a+b x)}}","-\frac{2 i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{b \sqrt{\sinh (a+b x)}}",1,"(-2*EllipticF[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[Sinh[a + b*x]])/(b*Sqrt[I*Sinh[a + b*x]])","A",1
12,1,57,76,0.0531044,"\int \frac{1}{\sinh ^{\frac{3}{2}}(a+b x)} \, dx","Integrate[Sinh[a + b*x]^(-3/2),x]","-\frac{2 \left(\cosh (a+b x)-\sqrt{i \sinh (a+b x)} E\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)\right)}{b \sqrt{\sinh (a+b x)}}","-\frac{2 \cosh (a+b x)}{b \sqrt{\sinh (a+b x)}}-\frac{2 i \sqrt{\sinh (a+b x)} E\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{b \sqrt{i \sinh (a+b x)}}",1,"(-2*(Cosh[a + b*x] - EllipticE[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*Sqrt[I*Sinh[a + b*x]]))/(b*Sqrt[Sinh[a + b*x]])","A",1
13,1,86,80,0.0777283,"\int \frac{1}{\sinh ^{\frac{5}{2}}(a+b x)} \, dx","Integrate[Sinh[a + b*x]^(-5/2),x]","-\frac{2 \left(\sinh (a+b x) \sqrt{-\sinh (2 a+2 b x)-\cosh (2 a+2 b x)+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\cosh (2 (a+b x))+\sinh (2 (a+b x))\right)+\cosh (a+b x)\right)}{3 b \sinh ^{\frac{3}{2}}(a+b x)}","-\frac{2 \cosh (a+b x)}{3 b \sinh ^{\frac{3}{2}}(a+b x)}+\frac{2 i \sqrt{i \sinh (a+b x)} F\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{3 b \sqrt{\sinh (a+b x)}}",1,"(-2*(Cosh[a + b*x] + Hypergeometric2F1[1/4, 1/2, 5/4, Cosh[2*(a + b*x)] + Sinh[2*(a + b*x)]]*Sinh[a + b*x]*Sqrt[1 - Cosh[2*a + 2*b*x] - Sinh[2*a + 2*b*x]]))/(3*b*Sinh[a + b*x]^(3/2))","C",1
14,1,73,103,0.1701317,"\int \frac{1}{\sinh ^{\frac{7}{2}}(a+b x)} \, dx","Integrate[Sinh[a + b*x]^(-7/2),x]","\frac{3 \sinh (2 (a+b x))-2 \coth (a+b x)+6 i (i \sinh (a+b x))^{3/2} E\left(\left.\frac{1}{4} (-2 i a-2 i b x+\pi )\right|2\right)}{5 b \sinh ^{\frac{3}{2}}(a+b x)}","-\frac{2 \cosh (a+b x)}{5 b \sinh ^{\frac{5}{2}}(a+b x)}+\frac{6 \cosh (a+b x)}{5 b \sqrt{\sinh (a+b x)}}+\frac{6 i \sqrt{\sinh (a+b x)} E\left(\left.\frac{1}{2} \left(i a+i b x-\frac{\pi }{2}\right)\right|2\right)}{5 b \sqrt{i \sinh (a+b x)}}",1,"(-2*Coth[a + b*x] + (6*I)*EllipticE[((-2*I)*a + Pi - (2*I)*b*x)/4, 2]*(I*Sinh[a + b*x])^(3/2) + 3*Sinh[2*(a + b*x)])/(5*b*Sinh[a + b*x]^(3/2))","A",1
15,1,76,116,0.2778857,"\int (b \sinh (c+d x))^{7/2} \, dx","Integrate[(b*Sinh[c + d*x])^(7/2),x]","\frac{b^3 \sqrt{b \sinh (c+d x)} \left(-23 \cosh (c+d x)+3 \cosh (3 (c+d x))-\frac{20 F\left(\left.\frac{1}{4} (-2 i c-2 i d x+\pi )\right|2\right)}{\sqrt{i \sinh (c+d x)}}\right)}{42 d}","-\frac{10 i b^4 \sqrt{i \sinh (c+d x)} F\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right)}{21 d \sqrt{b \sinh (c+d x)}}-\frac{10 b^3 \cosh (c+d x) \sqrt{b \sinh (c+d x)}}{21 d}+\frac{2 b \cosh (c+d x) (b \sinh (c+d x))^{5/2}}{7 d}",1,"(b^3*(-23*Cosh[c + d*x] + 3*Cosh[3*(c + d*x)] - (20*EllipticF[((-2*I)*c + Pi - (2*I)*d*x)/4, 2])/Sqrt[I*Sinh[c + d*x]])*Sqrt[b*Sinh[c + d*x]])/(42*d)","A",1
16,1,68,88,0.1225378,"\int (b \sinh (c+d x))^{5/2} \, dx","Integrate[(b*Sinh[c + d*x])^(5/2),x]","\frac{b^2 \sqrt{b \sinh (c+d x)} \left(\sinh (2 (c+d x))-\frac{6 i E\left(\left.\frac{1}{4} (-2 i c-2 i d x+\pi )\right|2\right)}{\sqrt{i \sinh (c+d x)}}\right)}{5 d}","\frac{2 b \cosh (c+d x) (b \sinh (c+d x))^{3/2}}{5 d}+\frac{6 i b^2 E\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \sinh (c+d x)}}{5 d \sqrt{i \sinh (c+d x)}}",1,"(b^2*Sqrt[b*Sinh[c + d*x]]*(((-6*I)*EllipticE[((-2*I)*c + Pi - (2*I)*d*x)/4, 2])/Sqrt[I*Sinh[c + d*x]] + Sinh[2*(c + d*x)]))/(5*d)","A",1
17,1,88,88,0.1293112,"\int (b \sinh (c+d x))^{3/2} \, dx","Integrate[(b*Sinh[c + d*x])^(3/2),x]","\frac{b^2 \left(\sinh (2 (c+d x))-2 \sqrt{-\sinh (2 c+2 d x)-\cosh (2 c+2 d x)+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\cosh (2 (c+d x))+\sinh (2 (c+d x))\right)\right)}{3 d \sqrt{b \sinh (c+d x)}}","\frac{2 b \cosh (c+d x) \sqrt{b \sinh (c+d x)}}{3 d}+\frac{2 i b^2 \sqrt{i \sinh (c+d x)} F\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right)}{3 d \sqrt{b \sinh (c+d x)}}",1,"(b^2*(Sinh[2*(c + d*x)] - 2*Hypergeometric2F1[1/4, 1/2, 5/4, Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]]*Sqrt[1 - Cosh[2*c + 2*d*x] - Sinh[2*c + 2*d*x]]))/(3*d*Sqrt[b*Sinh[c + d*x]])","C",1
18,1,52,56,0.0458529,"\int \sqrt{b \sinh (c+d x)} \, dx","Integrate[Sqrt[b*Sinh[c + d*x]],x]","\frac{2 i E\left(\left.\frac{1}{4} (-2 i c-2 i d x+\pi )\right|2\right) \sqrt{b \sinh (c+d x)}}{d \sqrt{i \sinh (c+d x)}}","-\frac{2 i E\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \sinh (c+d x)}}{d \sqrt{i \sinh (c+d x)}}",1,"((2*I)*EllipticE[((-2*I)*c + Pi - (2*I)*d*x)/4, 2]*Sqrt[b*Sinh[c + d*x]])/(d*Sqrt[I*Sinh[c + d*x]])","A",1
19,1,54,56,0.0340509,"\int \frac{1}{\sqrt{b \sinh (c+d x)}} \, dx","Integrate[1/Sqrt[b*Sinh[c + d*x]],x]","\frac{2 i \sqrt{i \sinh (c+d x)} F\left(\left.\frac{1}{2} \left(\frac{\pi }{2}-i (c+d x)\right)\right|2\right)}{d \sqrt{b \sinh (c+d x)}}","-\frac{2 i \sqrt{i \sinh (c+d x)} F\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right)}{d \sqrt{b \sinh (c+d x)}}",1,"((2*I)*EllipticF[(Pi/2 - I*(c + d*x))/2, 2]*Sqrt[I*Sinh[c + d*x]])/(d*Sqrt[b*Sinh[c + d*x]])","A",1
20,1,62,86,0.0622726,"\int \frac{1}{(b \sinh (c+d x))^{3/2}} \, dx","Integrate[(b*Sinh[c + d*x])^(-3/2),x]","-\frac{2 \left(\cosh (c+d x)-\sqrt{i \sinh (c+d x)} E\left(\left.\frac{1}{4} (-2 i c-2 i d x+\pi )\right|2\right)\right)}{b d \sqrt{b \sinh (c+d x)}}","-\frac{2 \cosh (c+d x)}{b d \sqrt{b \sinh (c+d x)}}-\frac{2 i E\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \sinh (c+d x)}}{b^2 d \sqrt{i \sinh (c+d x)}}",1,"(-2*(Cosh[c + d*x] - EllipticE[((-2*I)*c + Pi - (2*I)*d*x)/4, 2]*Sqrt[I*Sinh[c + d*x]]))/(b*d*Sqrt[b*Sinh[c + d*x]])","A",1
21,1,84,90,0.0999217,"\int \frac{1}{(b \sinh (c+d x))^{5/2}} \, dx","Integrate[(b*Sinh[c + d*x])^(-5/2),x]","-\frac{2 \left(\sqrt{2} \sqrt{-\left(\sinh ^2(c+d x) (\coth (c+d x)+1)\right)} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\cosh (2 (c+d x))+\sinh (2 (c+d x))\right)+\coth (c+d x)\right)}{3 b^2 d \sqrt{b \sinh (c+d x)}}","-\frac{2 \cosh (c+d x)}{3 b d (b \sinh (c+d x))^{3/2}}+\frac{2 i \sqrt{i \sinh (c+d x)} F\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right)}{3 b^2 d \sqrt{b \sinh (c+d x)}}",1,"(-2*(Coth[c + d*x] + Sqrt[2]*Hypergeometric2F1[1/4, 1/2, 5/4, Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]]*Sqrt[-((1 + Coth[c + d*x])*Sinh[c + d*x]^2)]))/(3*b^2*d*Sqrt[b*Sinh[c + d*x]])","C",1
22,1,79,118,0.1659891,"\int \frac{1}{(b \sinh (c+d x))^{7/2}} \, dx","Integrate[(b*Sinh[c + d*x])^(-7/2),x]","-\frac{2 \left(-3 \cosh (c+d x)+\coth (c+d x) \text{csch}(c+d x)+3 \sqrt{i \sinh (c+d x)} E\left(\left.\frac{1}{4} (-2 i c-2 i d x+\pi )\right|2\right)\right)}{5 b^3 d \sqrt{b \sinh (c+d x)}}","\frac{6 i E\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right) \sqrt{b \sinh (c+d x)}}{5 b^4 d \sqrt{i \sinh (c+d x)}}+\frac{6 \cosh (c+d x)}{5 b^3 d \sqrt{b \sinh (c+d x)}}-\frac{2 \cosh (c+d x)}{5 b d (b \sinh (c+d x))^{5/2}}",1,"(-2*(-3*Cosh[c + d*x] + Coth[c + d*x]*Csch[c + d*x] + 3*EllipticE[((-2*I)*c + Pi - (2*I)*d*x)/4, 2]*Sqrt[I*Sinh[c + d*x]]))/(5*b^3*d*Sqrt[b*Sinh[c + d*x]])","A",1
23,1,65,91,0.1656794,"\int (i \sinh (c+d x))^{7/2} \, dx","Integrate[(I*Sinh[c + d*x])^(7/2),x]","\frac{i \left(20 F\left(\left.\frac{1}{4} (-2 i c-2 i d x+\pi )\right|2\right)+\sqrt{i \sinh (c+d x)} (23 \cosh (c+d x)-3 \cosh (3 (c+d x)))\right)}{42 d}","-\frac{10 i F\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right)}{21 d}+\frac{2 i (i \sinh (c+d x))^{5/2} \cosh (c+d x)}{7 d}+\frac{10 i \sqrt{i \sinh (c+d x)} \cosh (c+d x)}{21 d}",1,"((I/42)*(20*EllipticF[((-2*I)*c + Pi - (2*I)*d*x)/4, 2] + (23*Cosh[c + d*x] - 3*Cosh[3*(c + d*x)])*Sqrt[I*Sinh[c + d*x]]))/d","A",1
24,1,55,62,0.0592189,"\int (i \sinh (c+d x))^{5/2} \, dx","Integrate[(I*Sinh[c + d*x])^(5/2),x]","\frac{6 i E\left(\left.\frac{1}{4} (-2 i c-2 i d x+\pi )\right|2\right)-\sqrt{i \sinh (c+d x)} \sinh (2 (c+d x))}{5 d}","\frac{2 i (i \sinh (c+d x))^{3/2} \cosh (c+d x)}{5 d}-\frac{6 i E\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right)}{5 d}",1,"((6*I)*EllipticE[((-2*I)*c + Pi - (2*I)*d*x)/4, 2] - Sqrt[I*Sinh[c + d*x]]*Sinh[2*(c + d*x)])/(5*d)","A",1
25,1,94,62,0.1378384,"\int (i \sinh (c+d x))^{3/2} \, dx","Integrate[(I*Sinh[c + d*x])^(3/2),x]","-\frac{2 i \sqrt{i \sinh (c+d x)} \left(\text{csch}(c+d x) \sqrt{-\sinh (2 c+2 d x)-\cosh (2 c+2 d x)+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\cosh (2 (c+d x))+\sinh (2 (c+d x))\right)-\cosh (c+d x)\right)}{3 d}","\frac{2 i \sqrt{i \sinh (c+d x)} \cosh (c+d x)}{3 d}-\frac{2 i F\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right)}{3 d}",1,"(((-2*I)/3)*Sqrt[I*Sinh[c + d*x]]*(-Cosh[c + d*x] + Csch[c + d*x]*Hypergeometric2F1[1/4, 1/2, 5/4, Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]]*Sqrt[1 - Cosh[2*c + 2*d*x] - Sinh[2*c + 2*d*x]]))/d","C",1
26,1,28,30,0.020751,"\int \sqrt{i \sinh (c+d x)} \, dx","Integrate[Sqrt[I*Sinh[c + d*x]],x]","\frac{2 i E\left(\left.\frac{1}{2} \left(\frac{\pi }{2}-i (c+d x)\right)\right|2\right)}{d}","-\frac{2 i E\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right)}{d}",1,"((2*I)*EllipticE[(Pi/2 - I*(c + d*x))/2, 2])/d","A",1
27,1,28,30,0.0244908,"\int \frac{1}{\sqrt{i \sinh (c+d x)}} \, dx","Integrate[1/Sqrt[I*Sinh[c + d*x]],x]","\frac{2 i F\left(\left.\frac{1}{2} \left(\frac{\pi }{2}-i (c+d x)\right)\right|2\right)}{d}","-\frac{2 i F\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right)}{d}",1,"((2*I)*EllipticF[(Pi/2 - I*(c + d*x))/2, 2])/d","A",1
28,1,50,58,0.0990696,"\int \frac{1}{(i \sinh (c+d x))^{3/2}} \, dx","Integrate[(I*Sinh[c + d*x])^(-3/2),x]","\frac{2 \left(\sqrt{i \sinh (c+d x)} \coth (c+d x)-i E\left(\left.\frac{1}{4} (-2 i c-2 i d x+\pi )\right|2\right)\right)}{d}","\frac{2 i E\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right)}{d}+\frac{2 i \cosh (c+d x)}{d \sqrt{i \sinh (c+d x)}}",1,"(2*((-I)*EllipticE[((-2*I)*c + Pi - (2*I)*d*x)/4, 2] + Coth[c + d*x]*Sqrt[I*Sinh[c + d*x]]))/d","A",1
29,1,83,62,0.0616896,"\int \frac{1}{(i \sinh (c+d x))^{5/2}} \, dx","Integrate[(I*Sinh[c + d*x])^(-5/2),x]","\frac{2 \left(\sqrt{2} \sqrt{-\left(\sinh ^2(c+d x) (\coth (c+d x)+1)\right)} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\cosh (2 (c+d x))+\sinh (2 (c+d x))\right)+\coth (c+d x)\right)}{3 d \sqrt{i \sinh (c+d x)}}","\frac{2 i \cosh (c+d x)}{3 d (i \sinh (c+d x))^{3/2}}-\frac{2 i F\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right)}{3 d}",1,"(2*(Coth[c + d*x] + Sqrt[2]*Hypergeometric2F1[1/4, 1/2, 5/4, Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]]*Sqrt[-((1 + Coth[c + d*x])*Sinh[c + d*x]^2)]))/(3*d*Sqrt[I*Sinh[c + d*x]])","C",1
30,1,80,91,0.1337749,"\int \frac{1}{(i \sinh (c+d x))^{7/2}} \, dx","Integrate[(I*Sinh[c + d*x])^(-7/2),x]","-\frac{2 i \left(-3 \cosh (c+d x)+\coth (c+d x) \text{csch}(c+d x)+3 \sqrt{i \sinh (c+d x)} E\left(\left.\frac{1}{4} (-2 i c-2 i d x+\pi )\right|2\right)\right)}{5 d \sqrt{i \sinh (c+d x)}}","\frac{6 i E\left(\left.\frac{1}{2} \left(i c+i d x-\frac{\pi }{2}\right)\right|2\right)}{5 d}+\frac{6 i \cosh (c+d x)}{5 d \sqrt{i \sinh (c+d x)}}+\frac{2 i \cosh (c+d x)}{5 d (i \sinh (c+d x))^{5/2}}",1,"(((-2*I)/5)*(-3*Cosh[c + d*x] + Coth[c + d*x]*Csch[c + d*x] + 3*EllipticE[((-2*I)*c + Pi - (2*I)*d*x)/4, 2]*Sqrt[I*Sinh[c + d*x]]))/(d*Sqrt[I*Sinh[c + d*x]])","A",1
31,1,57,60,0.053585,"\int (b \sinh (c+d x))^{4/3} \, dx","Integrate[(b*Sinh[c + d*x])^(4/3),x]","\frac{3 \sqrt{\cosh ^2(c+d x)} \tanh (c+d x) (b \sinh (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};-\sinh ^2(c+d x)\right)}{7 d}","\frac{3 \cosh (c+d x) (b \sinh (c+d x))^{7/3} \, _2F_1\left(\frac{1}{2},\frac{7}{6};\frac{13}{6};-\sinh ^2(c+d x)\right)}{7 b d \sqrt{\cosh ^2(c+d x)}}",1,"(3*Sqrt[Cosh[c + d*x]^2]*Hypergeometric2F1[1/2, 7/6, 13/6, -Sinh[c + d*x]^2]*(b*Sinh[c + d*x])^(4/3)*Tanh[c + d*x])/(7*d)","A",1
32,1,57,60,0.0373197,"\int (b \sinh (c+d x))^{2/3} \, dx","Integrate[(b*Sinh[c + d*x])^(2/3),x]","\frac{3 \sqrt{\cosh ^2(c+d x)} \tanh (c+d x) (b \sinh (c+d x))^{2/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};-\sinh ^2(c+d x)\right)}{5 d}","\frac{3 \cosh (c+d x) (b \sinh (c+d x))^{5/3} \, _2F_1\left(\frac{1}{2},\frac{5}{6};\frac{11}{6};-\sinh ^2(c+d x)\right)}{5 b d \sqrt{\cosh ^2(c+d x)}}",1,"(3*Sqrt[Cosh[c + d*x]^2]*Hypergeometric2F1[1/2, 5/6, 11/6, -Sinh[c + d*x]^2]*(b*Sinh[c + d*x])^(2/3)*Tanh[c + d*x])/(5*d)","A",1
33,1,57,60,0.0345464,"\int \sqrt[3]{b \sinh (c+d x)} \, dx","Integrate[(b*Sinh[c + d*x])^(1/3),x]","\frac{3 \sqrt{\cosh ^2(c+d x)} \tanh (c+d x) \sqrt[3]{b \sinh (c+d x)} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};-\sinh ^2(c+d x)\right)}{4 d}","\frac{3 \cosh (c+d x) (b \sinh (c+d x))^{4/3} \, _2F_1\left(\frac{1}{2},\frac{2}{3};\frac{5}{3};-\sinh ^2(c+d x)\right)}{4 b d \sqrt{\cosh ^2(c+d x)}}",1,"(3*Sqrt[Cosh[c + d*x]^2]*Hypergeometric2F1[1/2, 2/3, 5/3, -Sinh[c + d*x]^2]*(b*Sinh[c + d*x])^(1/3)*Tanh[c + d*x])/(4*d)","A",1
34,1,57,60,0.0396111,"\int \frac{1}{\sqrt[3]{b \sinh (c+d x)}} \, dx","Integrate[(b*Sinh[c + d*x])^(-1/3),x]","\frac{3 \sqrt{\cosh ^2(c+d x)} \tanh (c+d x) \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-\sinh ^2(c+d x)\right)}{2 d \sqrt[3]{b \sinh (c+d x)}}","\frac{3 \cosh (c+d x) (b \sinh (c+d x))^{2/3} \, _2F_1\left(\frac{1}{3},\frac{1}{2};\frac{4}{3};-\sinh ^2(c+d x)\right)}{2 b d \sqrt{\cosh ^2(c+d x)}}",1,"(3*Sqrt[Cosh[c + d*x]^2]*Hypergeometric2F1[1/3, 1/2, 4/3, -Sinh[c + d*x]^2]*Tanh[c + d*x])/(2*d*(b*Sinh[c + d*x])^(1/3))","A",1
35,1,55,58,0.040996,"\int \frac{1}{(b \sinh (c+d x))^{2/3}} \, dx","Integrate[(b*Sinh[c + d*x])^(-2/3),x]","\frac{3 \sqrt{\cosh ^2(c+d x)} \tanh (c+d x) \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\sinh ^2(c+d x)\right)}{d (b \sinh (c+d x))^{2/3}}","\frac{3 \cosh (c+d x) \sqrt[3]{b \sinh (c+d x)} \, _2F_1\left(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\sinh ^2(c+d x)\right)}{b d \sqrt{\cosh ^2(c+d x)}}",1,"(3*Sqrt[Cosh[c + d*x]^2]*Hypergeometric2F1[1/6, 1/2, 7/6, -Sinh[c + d*x]^2]*Tanh[c + d*x])/(d*(b*Sinh[c + d*x])^(2/3))","A",1
36,1,55,58,0.0386688,"\int \frac{1}{(b \sinh (c+d x))^{4/3}} \, dx","Integrate[(b*Sinh[c + d*x])^(-4/3),x]","-\frac{3 \sqrt{\cosh ^2(c+d x)} \tanh (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};-\sinh ^2(c+d x)\right)}{d (b \sinh (c+d x))^{4/3}}","-\frac{3 \cosh (c+d x) \, _2F_1\left(-\frac{1}{6},\frac{1}{2};\frac{5}{6};-\sinh ^2(c+d x)\right)}{b d \sqrt{\cosh ^2(c+d x)} \sqrt[3]{b \sinh (c+d x)}}",1,"(-3*Sqrt[Cosh[c + d*x]^2]*Hypergeometric2F1[-1/6, 1/2, 5/6, -Sinh[c + d*x]^2]*Tanh[c + d*x])/(d*(b*Sinh[c + d*x])^(4/3))","A",1
37,1,65,70,0.0437026,"\int (b \sinh (c+d x))^n \, dx","Integrate[(b*Sinh[c + d*x])^n,x]","\frac{\sqrt{\cosh ^2(c+d x)} \tanh (c+d x) (b \sinh (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};-\sinh ^2(c+d x)\right)}{d (n+1)}","\frac{\cosh (c+d x) (b \sinh (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};-\sinh ^2(c+d x)\right)}{b d (n+1) \sqrt{\cosh ^2(c+d x)}}",1,"(Sqrt[Cosh[c + d*x]^2]*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, -Sinh[c + d*x]^2]*(b*Sinh[c + d*x])^n*Tanh[c + d*x])/(d*(1 + n))","A",1
38,1,67,72,0.0409617,"\int (i \sinh (c+d x))^n \, dx","Integrate[(I*Sinh[c + d*x])^n,x]","\frac{\sqrt{\cosh ^2(c+d x)} \tanh (c+d x) (i \sinh (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};-\sinh ^2(c+d x)\right)}{d (n+1)}","-\frac{i \cosh (c+d x) (i \sinh (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};-\sinh ^2(c+d x)\right)}{d (n+1) \sqrt{\cosh ^2(c+d x)}}",1,"(Sqrt[Cosh[c + d*x]^2]*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, -Sinh[c + d*x]^2]*(I*Sinh[c + d*x])^n*Tanh[c + d*x])/(d*(1 + n))","A",1
39,1,67,72,0.0418023,"\int (-i \sinh (c+d x))^n \, dx","Integrate[((-I)*Sinh[c + d*x])^n,x]","\frac{\sqrt{\cosh ^2(c+d x)} \tanh (c+d x) (-i \sinh (c+d x))^n \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};-\sinh ^2(c+d x)\right)}{d (n+1)}","\frac{i \cosh (c+d x) (-i \sinh (c+d x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};-\sinh ^2(c+d x)\right)}{d (n+1) \sqrt{\cosh ^2(c+d x)}}",1,"(Sqrt[Cosh[c + d*x]^2]*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, -Sinh[c + d*x]^2]*((-I)*Sinh[c + d*x])^n*Tanh[c + d*x])/(d*(1 + n))","A",1
40,1,134,46,0.1911502,"\int \frac{\sinh ^4(x)}{i+\sinh (x)} \, dx","Integrate[Sinh[x]^4/(I + Sinh[x]),x]","\frac{\cosh (x) \left(i \sinh ^{-1}(\sinh (x)) (\sinh (x)+i)+2 \sinh ^3(x) \sqrt{\cosh ^2(x)}-i \sinh ^2(x) \sqrt{\cosh ^2(x)}-\sinh (x) \left(7 \sqrt{\cosh ^2(x)}+16 \sin ^{-1}\left(\frac{\sqrt{1-i \sinh (x)}}{\sqrt{2}}\right)\right)-16 i \left(\sqrt{\cosh ^2(x)}+\sin ^{-1}\left(\frac{\sqrt{1-i \sinh (x)}}{\sqrt{2}}\right)\right)\right)}{6 (\sinh (x)+i) \sqrt{\cosh ^2(x)}}","\frac{3 i x}{2}+\frac{4 \cosh ^3(x)}{3}-4 \cosh (x)-\frac{\sinh ^3(x) \cosh (x)}{\sinh (x)+i}-\frac{3}{2} i \sinh (x) \cosh (x)",1,"(Cosh[x]*((-16*I)*(ArcSin[Sqrt[1 - I*Sinh[x]]/Sqrt[2]] + Sqrt[Cosh[x]^2]) - (16*ArcSin[Sqrt[1 - I*Sinh[x]]/Sqrt[2]] + 7*Sqrt[Cosh[x]^2])*Sinh[x] - I*Sqrt[Cosh[x]^2]*Sinh[x]^2 + 2*Sqrt[Cosh[x]^2]*Sinh[x]^3 + I*ArcSinh[Sinh[x]]*(I + Sinh[x])))/(6*Sqrt[Cosh[x]^2]*(I + Sinh[x]))","B",1
41,1,41,36,0.1105166,"\int \frac{\sinh ^3(x)}{i+\sinh (x)} \, dx","Integrate[Sinh[x]^3/(I + Sinh[x]),x]","\frac{1}{2} \cosh (x) \left(-\frac{3 \sinh ^{-1}(\sinh (x))}{\sqrt{\cosh ^2(x)}}+\frac{\sinh ^2(x)-i \sinh (x)+4}{\sinh (x)+i}\right)","-\frac{3 x}{2}-2 i \cosh (x)-\frac{\sinh ^2(x) \cosh (x)}{\sinh (x)+i}+\frac{3}{2} \sinh (x) \cosh (x)",1,"(Cosh[x]*((-3*ArcSinh[Sinh[x]])/Sqrt[Cosh[x]^2] + (4 - I*Sinh[x] + Sinh[x]^2)/(I + Sinh[x])))/2","A",1
42,1,79,22,0.1113911,"\int \frac{\sinh ^2(x)}{i+\sinh (x)} \, dx","Integrate[Sinh[x]^2/(I + Sinh[x]),x]","\frac{\cosh (x) \left(\sinh (x)+\frac{2 \sinh (x) \sin ^{-1}\left(\frac{\sqrt{1-i \sinh (x)}}{\sqrt{2}}\right)}{\sqrt{\cosh ^2(x)}}+\frac{2 i \sin ^{-1}\left(\frac{\sqrt{1-i \sinh (x)}}{\sqrt{2}}\right)}{\sqrt{\cosh ^2(x)}}+2 i\right)}{\sinh (x)+i}","-i x+\cosh (x)+\frac{i \cosh (x)}{\sinh (x)+i}",1,"(Cosh[x]*(2*I + ((2*I)*ArcSin[Sqrt[1 - I*Sinh[x]]/Sqrt[2]])/Sqrt[Cosh[x]^2] + Sinh[x] + (2*ArcSin[Sqrt[1 - I*Sinh[x]]/Sqrt[2]]*Sinh[x])/Sqrt[Cosh[x]^2]))/(I + Sinh[x])","B",1
43,1,43,14,0.0570249,"\int \frac{\sinh (x)}{i+\sinh (x)} \, dx","Integrate[Sinh[x]/(I + Sinh[x]),x]","i \text{sech}(x) \left(i \sinh (x)+2 \sqrt{\cosh ^2(x)} \sin ^{-1}\left(\frac{\sqrt{1-i \sinh (x)}}{\sqrt{2}}\right)+1\right)","x-\frac{\cosh (x)}{\sinh (x)+i}",1,"I*Sech[x]*(1 + 2*ArcSin[Sqrt[1 - I*Sinh[x]]/Sqrt[2]]*Sqrt[Cosh[x]^2] + I*Sinh[x])","B",1
44,1,30,19,0.0198722,"\int \frac{\text{csch}(x)}{i+\sinh (x)} \, dx","Integrate[Csch[x]/(I + Sinh[x]),x]","\text{sech}(x) \left(\sinh (x)+i \sqrt{\cosh ^2(x)} \tanh ^{-1}\left(\sqrt{\cosh ^2(x)}\right)-i\right)","\frac{\cosh (x)}{\sinh (x)+i}+i \tanh ^{-1}(\cosh (x))",1,"Sech[x]*(-I + I*ArcTanh[Sqrt[Cosh[x]^2]]*Sqrt[Cosh[x]^2] + Sinh[x])","A",1
45,1,36,23,0.0420419,"\int \frac{\text{csch}^2(x)}{i+\sinh (x)} \, dx","Integrate[Csch[x]^2/(I + Sinh[x]),x]","\text{sech}(x) \left(2 i \sinh (x)+i \text{csch}(x)-\sqrt{\cosh ^2(x)} \tanh ^{-1}\left(\sqrt{\cosh ^2(x)}\right)+1\right)","2 i \coth (x)-\tanh ^{-1}(\cosh (x))+\frac{\coth (x)}{\sinh (x)+i}",1,"Sech[x]*(1 - ArcTanh[Sqrt[Cosh[x]^2]]*Sqrt[Cosh[x]^2] + I*Csch[x] + (2*I)*Sinh[x])","A",1
46,1,49,37,0.1889138,"\int \frac{\text{csch}^3(x)}{i+\sinh (x)} \, dx","Integrate[Csch[x]^3/(I + Sinh[x]),x]","\frac{1}{2} i \tanh (x) \left(\text{csch}^3(x)+2 i \text{csch}^2(x)+3 \text{csch}(x)-3 \sqrt{\cosh ^2(x)} \text{csch}(x) \tanh ^{-1}\left(\sqrt{\cosh ^2(x)}\right)+4 i\right)","-2 \coth (x)-\frac{3}{2} i \tanh ^{-1}(\cosh (x))+\frac{3}{2} i \coth (x) \text{csch}(x)+\frac{\coth (x) \text{csch}(x)}{\sinh (x)+i}",1,"(I/2)*(4*I + 3*Csch[x] - 3*ArcTanh[Sqrt[Cosh[x]^2]]*Sqrt[Cosh[x]^2]*Csch[x] + (2*I)*Csch[x]^2 + Csch[x]^3)*Tanh[x]","A",1
47,1,53,47,0.2362606,"\int \frac{\text{csch}^4(x)}{i+\sinh (x)} \, dx","Integrate[Csch[x]^4/(I + Sinh[x]),x]","\frac{1}{6} \text{sech}(x) \left(-16 i \sinh (x)+2 i \text{csch}^3(x)-3 \text{csch}^2(x)-8 i \text{csch}(x)+9 \sqrt{\cosh ^2(x)} \tanh ^{-1}\left(\sqrt{\cosh ^2(x)}\right)-9\right)","\frac{4}{3} i \coth ^3(x)-4 i \coth (x)+\frac{3}{2} \tanh ^{-1}(\cosh (x))-\frac{3}{2} \coth (x) \text{csch}(x)+\frac{\coth (x) \text{csch}^2(x)}{\sinh (x)+i}",1,"(Sech[x]*(-9 + 9*ArcTanh[Sqrt[Cosh[x]^2]]*Sqrt[Cosh[x]^2] - (8*I)*Csch[x] - 3*Csch[x]^2 + (2*I)*Csch[x]^3 - (16*I)*Sinh[x]))/6","A",1
48,1,147,58,0.1899539,"\int \frac{\sinh ^4(x)}{(i+\sinh (x))^2} \, dx","Integrate[Sinh[x]^4/(I + Sinh[x])^2,x]","-\frac{\sinh ^3(x) \cosh (x)}{2 (1-i \sinh (x))^2}-\frac{i \sqrt{2} \sqrt{1+\frac{1}{2} (-1+i \sinh (x))} \cosh (x)}{\sqrt{1+i \sinh (x)}}-\frac{31 i \cosh (x)}{6 (1-i \sinh (x))}+\frac{5 i \cosh (x)}{6 (1-i \sinh (x))^2}-\frac{7 i \cosh (x) \sin ^{-1}\left(\frac{\sqrt{1-i \sinh (x)}}{\sqrt{2}}\right)}{\sqrt{1-i \sinh (x)} \sqrt{1+i \sinh (x)}}","-\frac{7 x}{2}-\frac{16}{3} i \cosh (x)-\frac{\sinh ^3(x) \cosh (x)}{3 (\sinh (x)+i)^2}-\frac{8 \sinh ^2(x) \cosh (x)}{3 (\sinh (x)+i)}+\frac{7}{2} \sinh (x) \cosh (x)",1,"(((5*I)/6)*Cosh[x])/(1 - I*Sinh[x])^2 - (((31*I)/6)*Cosh[x])/(1 - I*Sinh[x]) - (I*Sqrt[2]*Cosh[x]*Sqrt[1 + (-1 + I*Sinh[x])/2])/Sqrt[1 + I*Sinh[x]] - ((7*I)*ArcSin[Sqrt[1 - I*Sinh[x]]/Sqrt[2]]*Cosh[x])/(Sqrt[1 - I*Sinh[x]]*Sqrt[1 + I*Sinh[x]]) - (Cosh[x]*Sinh[x]^3)/(2*(1 - I*Sinh[x])^2)","B",1
49,1,45,44,0.1286685,"\int \frac{\sinh ^3(x)}{(i+\sinh (x))^2} \, dx","Integrate[Sinh[x]^3/(I + Sinh[x])^2,x]","\frac{1}{3} \cosh (x) \left(\frac{3 \sinh ^2(x)+14 i \sinh (x)-10}{(\sinh (x)+i)^2}-\frac{6 i \sinh ^{-1}(\sinh (x))}{\sqrt{\cosh ^2(x)}}\right)","-2 i x+\frac{4 \cosh (x)}{3}-\frac{\sinh ^2(x) \cosh (x)}{3 (\sinh (x)+i)^2}+\frac{2 i \cosh (x)}{\sinh (x)+i}",1,"(Cosh[x]*(((-6*I)*ArcSinh[Sinh[x]])/Sqrt[Cosh[x]^2] + (-10 + (14*I)*Sinh[x] + 3*Sinh[x]^2)/(I + Sinh[x])^2))/3","A",1
50,1,55,32,0.1500193,"\int \frac{\sinh ^2(x)}{(i+\sinh (x))^2} \, dx","Integrate[Sinh[x]^2/(I + Sinh[x])^2,x]","-\frac{1}{3} i \cosh (x) \left(\frac{4-5 i \sinh (x)}{(\sinh (x)+i)^2}-\frac{6 \sin ^{-1}\left(\frac{\sqrt{1-i \sinh (x)}}{\sqrt{2}}\right)}{\sqrt{\cosh ^2(x)}}\right)","x-\frac{5 \cosh (x)}{3 (\sinh (x)+i)}+\frac{i \cosh (x)}{3 (\sinh (x)+i)^2}",1,"(-1/3*I)*Cosh[x]*((-6*ArcSin[Sqrt[1 - I*Sinh[x]]/Sqrt[2]])/Sqrt[Cosh[x]^2] + (4 - (5*I)*Sinh[x])/(I + Sinh[x])^2)","A",1
51,1,22,31,0.0091211,"\int \frac{\sinh (x)}{(i+\sinh (x))^2} \, dx","Integrate[Sinh[x]/(I + Sinh[x])^2,x]","\frac{(1-2 i \sinh (x)) \cosh (x)}{3 (\sinh (x)+i)^2}","-\frac{2 i \cosh (x)}{3 (\sinh (x)+i)}-\frac{\cosh (x)}{3 (\sinh (x)+i)^2}",1,"(Cosh[x]*(1 - (2*I)*Sinh[x]))/(3*(I + Sinh[x])^2)","A",1
52,1,91,34,0.0893067,"\int \frac{\text{csch}(x)}{(i+\sinh (x))^2} \, dx","Integrate[Csch[x]/(I + Sinh[x])^2,x]","\frac{\cosh \left(\frac{x}{2}\right) \left(6-9 \log \left(\tanh \left(\frac{x}{2}\right)\right)\right)+\cosh \left(\frac{3 x}{2}\right) \left(3 \log \left(\tanh \left(\frac{x}{2}\right)\right)-8\right)+6 i \sinh \left(\frac{x}{2}\right) \left(2 \log \left(\tanh \left(\frac{x}{2}\right)\right)+\cosh (x) \log \left(\tanh \left(\frac{x}{2}\right)\right)-3\right)}{6 \left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right)^3}","-\frac{4 i \cosh (x)}{3 (\sinh (x)+i)}+\frac{\cosh (x)}{3 (\sinh (x)+i)^2}+\tanh ^{-1}(\cosh (x))",1,"(Cosh[x/2]*(6 - 9*Log[Tanh[x/2]]) + Cosh[(3*x)/2]*(-8 + 3*Log[Tanh[x/2]]) + (6*I)*(-3 + 2*Log[Tanh[x/2]] + Cosh[x]*Log[Tanh[x/2]])*Sinh[x/2])/(6*(Cosh[x/2] - I*Sinh[x/2])^3)","B",1
53,1,88,42,0.394961,"\int \frac{\text{csch}^2(x)}{(i+\sinh (x))^2} \, dx","Integrate[Csch[x]^2/(I + Sinh[x])^2,x]","\frac{1}{6} \left(\frac{2}{\sinh (x)+i}+3 \tanh \left(\frac{x}{2}\right)+3 \coth \left(\frac{x}{2}\right)-12 i \log \left(\sinh \left(\frac{x}{2}\right)\right)+12 i \log \left(\cosh \left(\frac{x}{2}\right)\right)-\frac{4 \sinh \left(\frac{x}{2}\right) (7 \sinh (x)+8 i)}{\left(\sinh \left(\frac{x}{2}\right)+i \cosh \left(\frac{x}{2}\right)\right)^3}\right)","\frac{10 \coth (x)}{3}+2 i \tanh ^{-1}(\cosh (x))-\frac{2 i \coth (x)}{\sinh (x)+i}+\frac{\coth (x)}{3 (\sinh (x)+i)^2}",1,"(3*Coth[x/2] + (12*I)*Log[Cosh[x/2]] - (12*I)*Log[Sinh[x/2]] + 2/(I + Sinh[x]) - (4*Sinh[x/2]*(8*I + 7*Sinh[x]))/(I*Cosh[x/2] + Sinh[x/2])^3 + 3*Tanh[x/2])/6","B",1
54,1,131,58,0.3716202,"\int \frac{\text{csch}^3(x)}{(i+\sinh (x))^2} \, dx","Integrate[Csch[x]^3/(I + Sinh[x])^2,x]","\frac{1}{24} \left(24 i \tanh \left(\frac{x}{2}\right)+24 i \coth \left(\frac{x}{2}\right)+3 \text{csch}^2\left(\frac{x}{2}\right)+3 \text{sech}^2\left(\frac{x}{2}\right)+84 \log \left(\tanh \left(\frac{x}{2}\right)\right)+\frac{160 i \sinh \left(\frac{x}{2}\right)}{\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)}+\frac{8}{\left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right)^2}+\frac{16 \sinh \left(\frac{x}{2}\right)}{\left(\sinh \left(\frac{x}{2}\right)+i \cosh \left(\frac{x}{2}\right)\right)^3}\right)","\frac{16}{3} i \coth (x)-\frac{7}{2} \tanh ^{-1}(\cosh (x))+\frac{7}{2} \coth (x) \text{csch}(x)-\frac{8 i \coth (x) \text{csch}(x)}{3 (\sinh (x)+i)}+\frac{\coth (x) \text{csch}(x)}{3 (\sinh (x)+i)^2}",1,"((24*I)*Coth[x/2] + 3*Csch[x/2]^2 + 84*Log[Tanh[x/2]] + 3*Sech[x/2]^2 + 8/(Cosh[x/2] - I*Sinh[x/2])^2 + ((160*I)*Sinh[x/2])/(Cosh[x/2] - I*Sinh[x/2]) + (16*Sinh[x/2])/(I*Cosh[x/2] + Sinh[x/2])^3 + (24*I)*Tanh[x/2])/24","B",1
55,1,143,64,1.8697729,"\int \frac{\text{csch}^4(x)}{(i+\sinh (x))^2} \, dx","Integrate[Csch[x]^4/(I + Sinh[x])^2,x]","\frac{1}{24} \left(-44 \coth \left(\frac{x}{2}\right)+6 i \text{csch}^2\left(\frac{x}{2}\right)+\frac{1}{2} \sinh (x) \text{csch}^4\left(\frac{x}{2}\right)+2 \left(-\frac{4}{\sinh (x)+i}-22 \tanh \left(\frac{x}{2}\right)+3 i \text{sech}^2\left(\frac{x}{2}\right)+60 i \log \left(\sinh \left(\frac{x}{2}\right)\right)-60 i \log \left(\cosh \left(\frac{x}{2}\right)\right)+\frac{8 (13 \sinh (x)+14 i) \sinh \left(\frac{x}{2}\right)}{\left(\sinh \left(\frac{x}{2}\right)+i \cosh \left(\frac{x}{2}\right)\right)^3}-4 \sinh ^4\left(\frac{x}{2}\right) \text{csch}^3(x)\right)\right)","4 \coth ^3(x)-12 \coth (x)-5 i \tanh ^{-1}(\cosh (x))+5 i \coth (x) \text{csch}(x)-\frac{10 i \coth (x) \text{csch}^2(x)}{3 (\sinh (x)+i)}+\frac{\coth (x) \text{csch}^2(x)}{3 (\sinh (x)+i)^2}",1,"(-44*Coth[x/2] + (6*I)*Csch[x/2]^2 + (Csch[x/2]^4*Sinh[x])/2 + 2*((-60*I)*Log[Cosh[x/2]] + (60*I)*Log[Sinh[x/2]] + (3*I)*Sech[x/2]^2 - 4*Csch[x]^3*Sinh[x/2]^4 - 4/(I + Sinh[x]) + (8*Sinh[x/2]*(14*I + 13*Sinh[x]))/(I*Cosh[x/2] + Sinh[x/2])^3 - 22*Tanh[x/2]))/24","B",1
56,1,42,27,0.0529142,"\int \frac{1}{1+i \sinh (c+d x)} \, dx","Integrate[(1 + I*Sinh[c + d*x])^(-1),x]","\frac{2 \sinh \left(\frac{1}{2} (c+d x)\right)}{d \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}","\frac{i \cosh (c+d x)}{d (1+i \sinh (c+d x))}",1,"(2*Sinh[(c + d*x)/2])/(d*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]))","A",1
57,1,61,59,0.1031192,"\int \frac{1}{(1+i \sinh (c+d x))^2} \, dx","Integrate[(1 + I*Sinh[c + d*x])^(-2),x]","\frac{-4 \sinh (c+d x)+\sinh (2 (c+d x))-4 i \cosh (c+d x)-i \cosh (2 (c+d x))+3 i}{6 d (\sinh (c+d x)-i)^2}","\frac{i \cosh (c+d x)}{3 d (1+i \sinh (c+d x))}+\frac{i \cosh (c+d x)}{3 d (1+i \sinh (c+d x))^2}",1,"(3*I - (4*I)*Cosh[c + d*x] - I*Cosh[2*(c + d*x)] - 4*Sinh[c + d*x] + Sinh[2*(c + d*x)])/(6*d*(-I + Sinh[c + d*x])^2)","A",1
58,1,81,88,0.1258349,"\int \frac{1}{(1+i \sinh (c+d x))^3} \, dx","Integrate[(1 + I*Sinh[c + d*x])^(-3),x]","\frac{15 i \sinh (c+d x)-6 i \sinh (2 (c+d x))-i \sinh (3 (c+d x))-15 \cosh (c+d x)-6 \cosh (2 (c+d x))+\cosh (3 (c+d x))+10}{30 d (\sinh (c+d x)-i)^3}","\frac{2 i \cosh (c+d x)}{15 d (1+i \sinh (c+d x))}+\frac{2 i \cosh (c+d x)}{15 d (1+i \sinh (c+d x))^2}+\frac{i \cosh (c+d x)}{5 d (1+i \sinh (c+d x))^3}",1,"(10 - 15*Cosh[c + d*x] - 6*Cosh[2*(c + d*x)] + Cosh[3*(c + d*x)] + (15*I)*Sinh[c + d*x] - (6*I)*Sinh[2*(c + d*x)] - I*Sinh[3*(c + d*x)])/(30*d*(-I + Sinh[c + d*x])^3)","A",1
59,1,87,117,0.1698425,"\int \frac{1}{(1+i \sinh (c+d x))^4} \, dx","Integrate[(1 + I*Sinh[c + d*x])^(-4),x]","\frac{35 \sinh \left(\frac{1}{2} (c+d x)\right)-7 \sinh \left(\frac{5}{2} (c+d x)\right)+21 i \cosh \left(\frac{3}{2} (c+d x)\right)-i \cosh \left(\frac{7}{2} (c+d x)\right)}{70 d \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^7}","\frac{2 i \cosh (c+d x)}{35 d (1+i \sinh (c+d x))}+\frac{2 i \cosh (c+d x)}{35 d (1+i \sinh (c+d x))^2}+\frac{3 i \cosh (c+d x)}{35 d (1+i \sinh (c+d x))^3}+\frac{i \cosh (c+d x)}{7 d (1+i \sinh (c+d x))^4}",1,"((21*I)*Cosh[(3*(c + d*x))/2] - I*Cosh[(7*(c + d*x))/2] + 35*Sinh[(c + d*x)/2] - 7*Sinh[(5*(c + d*x))/2])/(70*d*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^7)","A",1
60,1,42,27,0.0629158,"\int \frac{1}{1-i \sinh (c+d x)} \, dx","Integrate[(1 - I*Sinh[c + d*x])^(-1),x]","\frac{2 \sinh \left(\frac{1}{2} (c+d x)\right)}{d \left(\cosh \left(\frac{1}{2} (c+d x)\right)-i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}","-\frac{i \cosh (c+d x)}{d (1-i \sinh (c+d x))}",1,"(2*Sinh[(c + d*x)/2])/(d*(Cosh[(c + d*x)/2] - I*Sinh[(c + d*x)/2]))","A",1
61,1,59,59,0.0754625,"\int \frac{1}{(1-i \sinh (c+d x))^2} \, dx","Integrate[(1 - I*Sinh[c + d*x])^(-2),x]","-\frac{\cosh \left(\frac{3}{2} (c+d x)\right)+3 i \sinh \left(\frac{1}{2} (c+d x)\right)}{3 d \left(\sinh \left(\frac{1}{2} (c+d x)\right)+i \cosh \left(\frac{1}{2} (c+d x)\right)\right)^3}","-\frac{i \cosh (c+d x)}{3 d (1-i \sinh (c+d x))}-\frac{i \cosh (c+d x)}{3 d (1-i \sinh (c+d x))^2}",1,"-1/3*(Cosh[(3*(c + d*x))/2] + (3*I)*Sinh[(c + d*x)/2])/(d*(I*Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2])^3)","A",1
62,1,81,88,0.1229665,"\int \frac{1}{(1-i \sinh (c+d x))^3} \, dx","Integrate[(1 - I*Sinh[c + d*x])^(-3),x]","\frac{-15 i \sinh (c+d x)+6 i \sinh (2 (c+d x))+i \sinh (3 (c+d x))-15 \cosh (c+d x)-6 \cosh (2 (c+d x))+\cosh (3 (c+d x))+10}{30 d (\sinh (c+d x)+i)^3}","-\frac{2 i \cosh (c+d x)}{15 d (1-i \sinh (c+d x))}-\frac{2 i \cosh (c+d x)}{15 d (1-i \sinh (c+d x))^2}-\frac{i \cosh (c+d x)}{5 d (1-i \sinh (c+d x))^3}",1,"(10 - 15*Cosh[c + d*x] - 6*Cosh[2*(c + d*x)] + Cosh[3*(c + d*x)] - (15*I)*Sinh[c + d*x] + (6*I)*Sinh[2*(c + d*x)] + I*Sinh[3*(c + d*x)])/(30*d*(I + Sinh[c + d*x])^3)","A",1
63,1,87,117,0.1517973,"\int \frac{1}{(1-i \sinh (c+d x))^4} \, dx","Integrate[(1 - I*Sinh[c + d*x])^(-4),x]","\frac{35 \sinh \left(\frac{1}{2} (c+d x)\right)-7 \sinh \left(\frac{5}{2} (c+d x)\right)-21 i \cosh \left(\frac{3}{2} (c+d x)\right)+i \cosh \left(\frac{7}{2} (c+d x)\right)}{70 d \left(\cosh \left(\frac{1}{2} (c+d x)\right)-i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^7}","-\frac{2 i \cosh (c+d x)}{35 d (1-i \sinh (c+d x))}-\frac{2 i \cosh (c+d x)}{35 d (1-i \sinh (c+d x))^2}-\frac{3 i \cosh (c+d x)}{35 d (1-i \sinh (c+d x))^3}-\frac{i \cosh (c+d x)}{7 d (1-i \sinh (c+d x))^4}",1,"((-21*I)*Cosh[(3*(c + d*x))/2] + I*Cosh[(7*(c + d*x))/2] + 35*Sinh[(c + d*x)/2] - 7*Sinh[(5*(c + d*x))/2])/(70*d*(Cosh[(c + d*x)/2] - I*Sinh[(c + d*x)/2])^7)","A",1
64,1,75,57,0.0727391,"\int \frac{\sinh (x)}{\sqrt{a+i a \sinh (x)}} \, dx","Integrate[Sinh[x]/Sqrt[a + I*a*Sinh[x]],x]","\frac{2 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right) \left(-i \sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right)+(1+i) \sqrt[4]{-1} \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{4}\right)+i}{\sqrt{2}}\right)\right)}{\sqrt{a+i a \sinh (x)}}","\frac{2 \cosh (x)}{\sqrt{a+i a \sinh (x)}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (x)}{\sqrt{2} \sqrt{a+i a \sinh (x)}}\right)}{\sqrt{a}}",1,"(2*((1 + I)*(-1)^(1/4)*ArcTan[(I + Tanh[x/4])/Sqrt[2]] + Cosh[x/2] - I*Sinh[x/2])*(Cosh[x/2] + I*Sinh[x/2]))/Sqrt[a + I*a*Sinh[x]]","A",1
65,1,76,57,0.0775757,"\int \frac{\sinh (x)}{\sqrt{a-i a \sinh (x)}} \, dx","Integrate[Sinh[x]/Sqrt[a - I*a*Sinh[x]],x]","\frac{2 \left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right) \left(\cosh \left(\frac{x}{2}\right)+i \left(\sinh \left(\frac{x}{2}\right)+(1+i) (-1)^{3/4} \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{4}\right)-i}{\sqrt{2}}\right)\right)\right)}{\sqrt{a-i a \sinh (x)}}","\frac{2 \cosh (x)}{\sqrt{a-i a \sinh (x)}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (x)}{\sqrt{2} \sqrt{a-i a \sinh (x)}}\right)}{\sqrt{a}}",1,"(2*(Cosh[x/2] - I*Sinh[x/2])*(Cosh[x/2] + I*((1 + I)*(-1)^(3/4)*ArcTan[(-I + Tanh[x/4])/Sqrt[2]] + Sinh[x/2])))/Sqrt[a - I*a*Sinh[x]]","A",1
66,1,145,104,0.4607016,"\int (a+i a \sinh (c+d x))^{5/2} \, dx","Integrate[(a + I*a*Sinh[c + d*x])^(5/2),x]","\frac{a^2 (\sinh (c+d x)-i)^2 \sqrt{a+i a \sinh (c+d x)} \left(-150 \sinh \left(\frac{1}{2} (c+d x)\right)+25 \sinh \left(\frac{3}{2} (c+d x)\right)+3 \sinh \left(\frac{5}{2} (c+d x)\right)-150 i \cosh \left(\frac{1}{2} (c+d x)\right)-25 i \cosh \left(\frac{3}{2} (c+d x)\right)+3 i \cosh \left(\frac{5}{2} (c+d x)\right)\right)}{30 d \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^5}","\frac{64 i a^3 \cosh (c+d x)}{15 d \sqrt{a+i a \sinh (c+d x)}}+\frac{16 i a^2 \cosh (c+d x) \sqrt{a+i a \sinh (c+d x)}}{15 d}+\frac{2 i a \cosh (c+d x) (a+i a \sinh (c+d x))^{3/2}}{5 d}",1,"(a^2*(-I + Sinh[c + d*x])^2*Sqrt[a + I*a*Sinh[c + d*x]]*((-150*I)*Cosh[(c + d*x)/2] - (25*I)*Cosh[(3*(c + d*x))/2] + (3*I)*Cosh[(5*(c + d*x))/2] - 150*Sinh[(c + d*x)/2] + 25*Sinh[(3*(c + d*x))/2] + 3*Sinh[(5*(c + d*x))/2]))/(30*d*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^5)","A",1
67,1,113,69,0.2051793,"\int (a+i a \sinh (c+d x))^{3/2} \, dx","Integrate[(a + I*a*Sinh[c + d*x])^(3/2),x]","-\frac{a (\sinh (c+d x)-i) \sqrt{a+i a \sinh (c+d x)} \left(-9 i \sinh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{3}{2} (c+d x)\right)+9 \cosh \left(\frac{1}{2} (c+d x)\right)+\cosh \left(\frac{3}{2} (c+d x)\right)\right)}{3 d \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^3}","\frac{8 i a^2 \cosh (c+d x)}{3 d \sqrt{a+i a \sinh (c+d x)}}+\frac{2 i a \cosh (c+d x) \sqrt{a+i a \sinh (c+d x)}}{3 d}",1,"-1/3*(a*(-I + Sinh[c + d*x])*Sqrt[a + I*a*Sinh[c + d*x]]*(9*Cosh[(c + d*x)/2] + Cosh[(3*(c + d*x))/2] - (9*I)*Sinh[(c + d*x)/2] + I*Sinh[(3*(c + d*x))/2]))/(d*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^3)","A",1
68,1,74,31,0.0412821,"\int \sqrt{a+i a \sinh (c+d x)} \, dx","Integrate[Sqrt[a + I*a*Sinh[c + d*x]],x]","\frac{2 \sqrt{a+i a \sinh (c+d x)} \left(\sinh \left(\frac{1}{2} (c+d x)\right)+i \cosh \left(\frac{1}{2} (c+d x)\right)\right)}{d \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}","\frac{2 i a \cosh (c+d x)}{d \sqrt{a+i a \sinh (c+d x)}}",1,"(2*(I*Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2])*Sqrt[a + I*a*Sinh[c + d*x]])/(d*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]))","B",1
69,1,84,52,0.0857696,"\int \frac{1}{\sqrt{a+i a \sinh (c+d x)}} \, dx","Integrate[1/Sqrt[a + I*a*Sinh[c + d*x]],x]","\frac{(2+2 i) \sqrt[4]{-1} \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt[4]{-1} \left(1-i \tanh \left(\frac{1}{4} (c+d x)\right)\right)\right) \left(\sinh \left(\frac{1}{2} (c+d x)\right)-i \cosh \left(\frac{1}{2} (c+d x)\right)\right)}{d \sqrt{a+i a \sinh (c+d x)}}","\frac{i \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{2} \sqrt{a+i a \sinh (c+d x)}}\right)}{\sqrt{a} d}",1,"((2 + 2*I)*(-1)^(1/4)*ArcTan[(1/2 + I/2)*(-1)^(1/4)*(1 - I*Tanh[(c + d*x)/4])]*((-I)*Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2]))/(d*Sqrt[a + I*a*Sinh[c + d*x]])","A",1
70,1,156,87,0.2356038,"\int \frac{1}{(a+i a \sinh (c+d x))^{3/2}} \, dx","Integrate[(a + I*a*Sinh[c + d*x])^(-3/2),x]","\frac{\left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)-i \left(\sinh \left(\frac{1}{2} (c+d x)\right)+(1-i) \sqrt[4]{-1} \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt[4]{-1} \left(1-i \tanh \left(\frac{1}{4} (c+d x)\right)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2\right)\right)}{2 a d (\sinh (c+d x)-i) \sqrt{a+i a \sinh (c+d x)}}","\frac{i \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{2} \sqrt{a+i a \sinh (c+d x)}}\right)}{2 \sqrt{2} a^{3/2} d}+\frac{i \cosh (c+d x)}{2 d (a+i a \sinh (c+d x))^{3/2}}",1,"((Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])*(Cosh[(c + d*x)/2] - I*((1 - I)*(-1)^(1/4)*ArcTan[(1/2 + I/2)*(-1)^(1/4)*(1 - I*Tanh[(c + d*x)/4])]*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2 + Sinh[(c + d*x)/2])))/(2*a*d*(-I + Sinh[c + d*x])*Sqrt[a + I*a*Sinh[c + d*x]])","A",1
71,1,210,122,0.2041638,"\int \frac{1}{(a+i a \sinh (c+d x))^{5/2}} \, dx","Integrate[(a + I*a*Sinh[c + d*x])^(-5/2),x]","\frac{\left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right) \left(4 \sinh \left(\frac{1}{2} (c+d x)\right)+4 i \cosh \left(\frac{1}{2} (c+d x)\right)+6 \sinh \left(\frac{1}{2} (c+d x)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2+3 \left(\sinh \left(\frac{1}{2} (c+d x)\right)-i \cosh \left(\frac{1}{2} (c+d x)\right)\right)^3+(3-3 i) \sqrt[4]{-1} \tan ^{-1}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt[4]{-1} \left(1-i \tanh \left(\frac{1}{4} (c+d x)\right)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^4\right)}{16 d (a+i a \sinh (c+d x))^{5/2}}","\frac{3 i \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (c+d x)}{\sqrt{2} \sqrt{a+i a \sinh (c+d x)}}\right)}{16 \sqrt{2} a^{5/2} d}+\frac{3 i \cosh (c+d x)}{16 a d (a+i a \sinh (c+d x))^{3/2}}+\frac{i \cosh (c+d x)}{4 d (a+i a \sinh (c+d x))^{5/2}}",1,"((Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])*((4*I)*Cosh[(c + d*x)/2] + (3 - 3*I)*(-1)^(1/4)*ArcTan[(1/2 + I/2)*(-1)^(1/4)*(1 - I*Tanh[(c + d*x)/4])]*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^4 + 4*Sinh[(c + d*x)/2] + 6*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2*Sinh[(c + d*x)/2] + 3*((-I)*Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2])^3))/(16*d*(a + I*a*Sinh[c + d*x])^(5/2))","A",1
72,1,105,108,0.4361185,"\int \frac{\sinh ^4(x)}{a+b \sinh (x)} \, dx","Integrate[Sinh[x]^4/(a + b*Sinh[x]),x]","\frac{3 b \left(4 a^2-3 b^2\right) \cosh (x)+3 a \left(-4 a^2 x+\frac{8 a^3 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+2 b^2 x-b^2 \sinh (2 x)\right)+b^3 \cosh (3 x)}{12 b^4}","-\frac{\left(2-\frac{3 a^2}{b^2}\right) \cosh (x)}{3 b}-\frac{a x \left(2 a^2-b^2\right)}{2 b^4}-\frac{2 a^4 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b^4 \sqrt{a^2+b^2}}-\frac{a \sinh (x) \cosh (x)}{2 b^2}+\frac{\sinh ^2(x) \cosh (x)}{3 b}",1,"(3*b*(4*a^2 - 3*b^2)*Cosh[x] + b^3*Cosh[3*x] + 3*a*(-4*a^2*x + 2*b^2*x + (8*a^3*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - b^2*Sinh[2*x]))/(12*b^4)","A",1
73,1,82,82,0.1410607,"\int \frac{\sinh ^3(x)}{a+b \sinh (x)} \, dx","Integrate[Sinh[x]^3/(a + b*Sinh[x]),x]","\frac{4 a^2 x-\frac{8 a^3 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}-4 a b \cosh (x)-2 b^2 x+b^2 \sinh (2 x)}{4 b^3}","\frac{x \left(2 a^2-b^2\right)}{2 b^3}+\frac{2 a^3 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b^3 \sqrt{a^2+b^2}}-\frac{a \cosh (x)}{b^2}+\frac{\sinh (x) \cosh (x)}{2 b}",1,"(4*a^2*x - 2*b^2*x - (8*a^3*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 4*a*b*Cosh[x] + b^2*Sinh[2*x])/(4*b^3)","A",1
74,1,61,57,0.0968112,"\int \frac{\sinh ^2(x)}{a+b \sinh (x)} \, dx","Integrate[Sinh[x]^2/(a + b*Sinh[x]),x]","\frac{a \left(\frac{2 a \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}-x\right)+b \cosh (x)}{b^2}","-\frac{2 a^2 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b^2 \sqrt{a^2+b^2}}-\frac{a x}{b^2}+\frac{\cosh (x)}{b}",1,"(a*(-x + (2*a*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2]) + b*Cosh[x])/b^2","A",1
75,1,52,47,0.0502977,"\int \frac{\sinh (x)}{a+b \sinh (x)} \, dx","Integrate[Sinh[x]/(a + b*Sinh[x]),x]","\frac{x-\frac{2 a \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}}{b}","\frac{2 a \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b \sqrt{a^2+b^2}}+\frac{x}{b}",1,"(x - (2*a*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2])/b","A",1
76,1,58,50,0.0517223,"\int \frac{\text{csch}(x)}{a+b \sinh (x)} \, dx","Integrate[Csch[x]/(a + b*Sinh[x]),x]","\frac{\log \left(\tanh \left(\frac{x}{2}\right)\right)-\frac{2 b \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}}{a}","\frac{2 b \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a \sqrt{a^2+b^2}}-\frac{\tanh ^{-1}(\cosh (x))}{a}",1,"((-2*b*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + Log[Tanh[x/2]])/a","A",1
77,1,81,59,0.4036037,"\int \frac{\text{csch}^2(x)}{a+b \sinh (x)} \, dx","Integrate[Csch[x]^2/(a + b*Sinh[x]),x]","-\frac{2 b \left(\log \left(\tanh \left(\frac{x}{2}\right)\right)-\frac{2 b \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}\right)+a \tanh \left(\frac{x}{2}\right)+a \coth \left(\frac{x}{2}\right)}{2 a^2}","-\frac{2 b^2 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a^2 \sqrt{a^2+b^2}}+\frac{b \tanh ^{-1}(\cosh (x))}{a^2}-\frac{\coth (x)}{a}",1,"-1/2*(a*Coth[x/2] + 2*b*((-2*b*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + Log[Tanh[x/2]]) + a*Tanh[x/2])/a^2","A",1
78,1,118,81,0.5438089,"\int \frac{\text{csch}^3(x)}{a+b \sinh (x)} \, dx","Integrate[Csch[x]^3/(a + b*Sinh[x]),x]","-\frac{4 \left(a^2-2 b^2\right) \log \left(\tanh \left(\frac{x}{2}\right)\right)+\frac{16 b^3 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+a^2 \text{csch}^2\left(\frac{x}{2}\right)+a^2 \text{sech}^2\left(\frac{x}{2}\right)-4 a b \tanh \left(\frac{x}{2}\right)-4 a b \coth \left(\frac{x}{2}\right)}{8 a^3}","\frac{b \coth (x)}{a^2}+\frac{\left(a^2-2 b^2\right) \tanh ^{-1}(\cosh (x))}{2 a^3}+\frac{2 b^3 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a^3 \sqrt{a^2+b^2}}-\frac{\coth (x) \text{csch}(x)}{2 a}",1,"-1/8*((16*b^3*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 4*a*b*Coth[x/2] + a^2*Csch[x/2]^2 + 4*(a^2 - 2*b^2)*Log[Tanh[x/2]] + a^2*Sech[x/2]^2 - 4*a*b*Tanh[x/2])/a^3","A",1
79,1,186,109,0.9446316,"\int \frac{\text{csch}^4(x)}{a+b \sinh (x)} \, dx","Integrate[Csch[x]^4/(a + b*Sinh[x]),x]","\frac{8 a^3 \tanh \left(\frac{x}{2}\right)-\frac{1}{2} a^3 \sinh (x) \text{csch}^4\left(\frac{x}{2}\right)+8 a^3 \sinh ^4\left(\frac{x}{2}\right) \text{csch}^3(x)+4 a \left(2 a^2-3 b^2\right) \coth \left(\frac{x}{2}\right)+\frac{48 b^4 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+3 a^2 b \text{csch}^2\left(\frac{x}{2}\right)+3 a^2 b \text{sech}^2\left(\frac{x}{2}\right)+12 a^2 b \log \left(\tanh \left(\frac{x}{2}\right)\right)-12 a b^2 \tanh \left(\frac{x}{2}\right)-24 b^3 \log \left(\tanh \left(\frac{x}{2}\right)\right)}{24 a^4}","\frac{b \coth (x) \text{csch}(x)}{2 a^2}-\frac{b \left(a^2-2 b^2\right) \tanh ^{-1}(\cosh (x))}{2 a^4}-\frac{2 b^4 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a^4 \sqrt{a^2+b^2}}+\frac{\left(2 a^2-3 b^2\right) \coth (x)}{3 a^3}-\frac{\coth (x) \text{csch}^2(x)}{3 a}",1,"((48*b^4*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + 4*a*(2*a^2 - 3*b^2)*Coth[x/2] + 3*a^2*b*Csch[x/2]^2 + 12*a^2*b*Log[Tanh[x/2]] - 24*b^3*Log[Tanh[x/2]] + 3*a^2*b*Sech[x/2]^2 + 8*a^3*Csch[x]^3*Sinh[x/2]^4 - (a^3*Csch[x/2]^4*Sinh[x])/2 + 8*a^3*Tanh[x/2] - 12*a*b^2*Tanh[x/2])/(24*a^4)","A",1
80,1,118,162,0.4364519,"\int \frac{\sinh ^4(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Sinh[x]^4/(a + b*Sinh[x])^2,x]","\frac{-2 x \left(b^2-6 a^2\right)-\frac{4 a^4 b \cosh (x)}{\left(a^2+b^2\right) (a+b \sinh (x))}+\frac{8 a^3 \left(3 a^2+4 b^2\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{3/2}}-8 a b \cosh (x)+b^2 \sinh (2 x)}{4 b^4}","-\frac{a^2 \sinh ^2(x) \cosh (x)}{b \left(a^2+b^2\right) (a+b \sinh (x))}+\frac{\left(3 a^2+b^2\right) \sinh (x) \cosh (x)}{2 b^2 \left(a^2+b^2\right)}+\frac{x \left(6 a^2-b^2\right)}{2 b^4}-\frac{a \left(3 a^2+2 b^2\right) \cosh (x)}{b^3 \left(a^2+b^2\right)}+\frac{2 a^3 \left(3 a^2+4 b^2\right) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b^4 \left(a^2+b^2\right)^{3/2}}",1,"(-2*(-6*a^2 + b^2)*x + (8*a^3*(3*a^2 + 4*b^2)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/(-a^2 - b^2)^(3/2) - 8*a*b*Cosh[x] - (4*a^4*b*Cosh[x])/((a^2 + b^2)*(a + b*Sinh[x])) + b^2*Sinh[2*x])/(4*b^4)","A",1
81,1,95,115,0.3695295,"\int \frac{\sinh ^3(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Sinh[x]^3/(a + b*Sinh[x])^2,x]","\frac{-\frac{2 a^2 \left(2 a^2+3 b^2\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{3/2}}+\cosh (x) \left(\frac{a^3 b}{\left(a^2+b^2\right) (a+b \sinh (x))}+b\right)-2 a x}{b^3}","\frac{\left(2 a^2+b^2\right) \cosh (x)}{b^2 \left(a^2+b^2\right)}-\frac{a^2 \sinh (x) \cosh (x)}{b \left(a^2+b^2\right) (a+b \sinh (x))}-\frac{2 a^2 \left(2 a^2+3 b^2\right) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b^3 \left(a^2+b^2\right)^{3/2}}-\frac{2 a x}{b^3}",1,"(-2*a*x - (2*a^2*(2*a^2 + 3*b^2)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/(-a^2 - b^2)^(3/2) + Cosh[x]*(b + (a^3*b)/((a^2 + b^2)*(a + b*Sinh[x]))))/b^3","A",1
82,1,86,83,0.1899091,"\int \frac{\sinh ^2(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Sinh[x]^2/(a + b*Sinh[x])^2,x]","\frac{\frac{2 a \left(a^2+2 b^2\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{3/2}}-\frac{a^2 b \cosh (x)}{\left(a^2+b^2\right) (a+b \sinh (x))}+x}{b^2}","\frac{2 a \left(a^2+2 b^2\right) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b^2 \left(a^2+b^2\right)^{3/2}}-\frac{a^2 \cosh (x)}{b \left(a^2+b^2\right) (a+b \sinh (x))}+\frac{x}{b^2}",1,"(x + (2*a*(a^2 + 2*b^2)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/(-a^2 - b^2)^(3/2) - (a^2*b*Cosh[x])/((a^2 + b^2)*(a + b*Sinh[x])))/b^2","A",1
83,1,68,60,0.1067885,"\int \frac{\sinh (x)}{(a+b \sinh (x))^2} \, dx","Integrate[Sinh[x]/(a + b*Sinh[x])^2,x]","\frac{a \cosh (x)}{\left(a^2+b^2\right) (a+b \sinh (x))}-\frac{2 b \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{3/2}}","\frac{a \cosh (x)}{\left(a^2+b^2\right) (a+b \sinh (x))}-\frac{2 b \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{3/2}}",1,"(-2*b*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/(-a^2 - b^2)^(3/2) + (a*Cosh[x])/((a^2 + b^2)*(a + b*Sinh[x]))","A",1
84,1,91,85,0.196249,"\int \frac{\text{csch}(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Csch[x]/(a + b*Sinh[x])^2,x]","\frac{\frac{2 b \left(2 a^2+b^2\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{3/2}}+\frac{a b^2 \cosh (x)}{\left(a^2+b^2\right) (a+b \sinh (x))}+\log \left(\tanh \left(\frac{x}{2}\right)\right)}{a^2}","\frac{2 b \left(2 a^2+b^2\right) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a^2 \left(a^2+b^2\right)^{3/2}}+\frac{b^2 \cosh (x)}{a \left(a^2+b^2\right) (a+b \sinh (x))}-\frac{\tanh ^{-1}(\cosh (x))}{a^2}",1,"((2*b*(2*a^2 + b^2)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/(-a^2 - b^2)^(3/2) + Log[Tanh[x/2]] + (a*b^2*Cosh[x])/((a^2 + b^2)*(a + b*Sinh[x])))/a^2","A",1
85,1,118,115,0.6782537,"\int \frac{\text{csch}^2(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Csch[x]^2/(a + b*Sinh[x])^2,x]","-\frac{\frac{4 b^2 \left(3 a^2+2 b^2\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{3/2}}+\frac{2 a b^3 \cosh (x)}{\left(a^2+b^2\right) (a+b \sinh (x))}+a \tanh \left(\frac{x}{2}\right)+a \coth \left(\frac{x}{2}\right)+4 b \log \left(\tanh \left(\frac{x}{2}\right)\right)}{2 a^3}","\frac{2 b \tanh ^{-1}(\cosh (x))}{a^3}-\frac{\left(a^2+2 b^2\right) \coth (x)}{a^2 \left(a^2+b^2\right)}+\frac{b^2 \coth (x)}{a \left(a^2+b^2\right) (a+b \sinh (x))}-\frac{2 b^2 \left(3 a^2+2 b^2\right) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a^3 \left(a^2+b^2\right)^{3/2}}",1,"-1/2*((4*b^2*(3*a^2 + 2*b^2)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/(-a^2 - b^2)^(3/2) + a*Coth[x/2] + 4*b*Log[Tanh[x/2]] + (2*a*b^3*Cosh[x])/((a^2 + b^2)*(a + b*Sinh[x])) + a*Tanh[x/2])/a^3","A",1
86,1,156,158,0.7377167,"\int \frac{\text{csch}^3(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Csch[x]^3/(a + b*Sinh[x])^2,x]","\frac{-4 \left(a^2-6 b^2\right) \log \left(\tanh \left(\frac{x}{2}\right)\right)+\frac{8 a b^4 \cosh (x)}{\left(a^2+b^2\right) (a+b \sinh (x))}+\frac{16 b^3 \left(4 a^2+3 b^2\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{3/2}}-a^2 \text{csch}^2\left(\frac{x}{2}\right)-a^2 \text{sech}^2\left(\frac{x}{2}\right)+8 a b \tanh \left(\frac{x}{2}\right)+8 a b \coth \left(\frac{x}{2}\right)}{8 a^4}","-\frac{\left(a^2+3 b^2\right) \coth (x) \text{csch}(x)}{2 a^2 \left(a^2+b^2\right)}+\frac{b^2 \coth (x) \text{csch}(x)}{a \left(a^2+b^2\right) (a+b \sinh (x))}+\frac{\left(a^2-6 b^2\right) \tanh ^{-1}(\cosh (x))}{2 a^4}+\frac{2 b^3 \left(4 a^2+3 b^2\right) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a^4 \left(a^2+b^2\right)^{3/2}}+\frac{b \left(2 a^2+3 b^2\right) \coth (x)}{a^3 \left(a^2+b^2\right)}",1,"((16*b^3*(4*a^2 + 3*b^2)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/(-a^2 - b^2)^(3/2) + 8*a*b*Coth[x/2] - a^2*Csch[x/2]^2 - 4*(a^2 - 6*b^2)*Log[Tanh[x/2]] - a^2*Sech[x/2]^2 + (8*a*b^4*Cosh[x])/((a^2 + b^2)*(a + b*Sinh[x])) + 8*a*b*Tanh[x/2])/(8*a^4)","A",1
87,1,214,198,0.9569019,"\int \frac{\text{csch}^4(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Csch[x]^4/(a + b*Sinh[x])^2,x]","\frac{-\frac{1}{2} a^3 \sinh (x) \text{csch}^4\left(\frac{x}{2}\right)+8 a^3 \sinh ^4\left(\frac{x}{2}\right) \text{csch}^3(x)+4 a \left(2 a^2-9 b^2\right) \tanh \left(\frac{x}{2}\right)+4 a \left(2 a^2-9 b^2\right) \coth \left(\frac{x}{2}\right)-\frac{24 a b^5 \cosh (x)}{\left(a^2+b^2\right) (a+b \sinh (x))}-\frac{48 b^4 \left(5 a^2+4 b^2\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{3/2}}+6 a^2 b \text{csch}^2\left(\frac{x}{2}\right)+6 a^2 b \text{sech}^2\left(\frac{x}{2}\right)+24 b (a-2 b) (a+2 b) \log \left(\tanh \left(\frac{x}{2}\right)\right)}{24 a^5}","-\frac{\left(a^2+4 b^2\right) \coth (x) \text{csch}^2(x)}{3 a^2 \left(a^2+b^2\right)}+\frac{b^2 \coth (x) \text{csch}^2(x)}{a \left(a^2+b^2\right) (a+b \sinh (x))}-\frac{b \left(a^2-4 b^2\right) \tanh ^{-1}(\cosh (x))}{a^5}-\frac{2 b^4 \left(5 a^2+4 b^2\right) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a^5 \left(a^2+b^2\right)^{3/2}}+\frac{\left(2 a^4-7 a^2 b^2-12 b^4\right) \coth (x)}{3 a^4 \left(a^2+b^2\right)}+\frac{b \left(a^2+2 b^2\right) \coth (x) \text{csch}(x)}{a^3 \left(a^2+b^2\right)}",1,"((-48*b^4*(5*a^2 + 4*b^2)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/(-a^2 - b^2)^(3/2) + 4*a*(2*a^2 - 9*b^2)*Coth[x/2] + 6*a^2*b*Csch[x/2]^2 + 24*(a - 2*b)*b*(a + 2*b)*Log[Tanh[x/2]] + 6*a^2*b*Sech[x/2]^2 + 8*a^3*Csch[x]^3*Sinh[x/2]^4 - (a^3*Csch[x/2]^4*Sinh[x])/2 - (24*a*b^5*Cosh[x])/((a^2 + b^2)*(a + b*Sinh[x])) + 4*a*(2*a^2 - 9*b^2)*Tanh[x/2])/(24*a^5)","A",1
88,1,81,73,0.0344243,"\int \frac{1}{3+5 i \sinh (c+d x)} \, dx","Integrate[(3 + (5*I)*Sinh[c + d*x])^(-1),x]","\frac{\tan ^{-1}\left(3 \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{i \log (4-5 \cosh (c+d x))}{8 d}+\frac{i \log (5 \cosh (c+d x)+4)}{8 d}+\frac{\tan ^{-1}\left(3 \coth \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}","\frac{i \log \left(3 \cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}-\frac{i \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)+3 i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}{4 d}",1,"ArcTan[3*Coth[(c + d*x)/2]]/(4*d) + ArcTan[3*Tanh[(c + d*x)/2]]/(4*d) - ((I/8)*Log[4 - 5*Cosh[c + d*x]])/d + ((I/8)*Log[4 + 5*Cosh[c + d*x]])/d","A",1
89,1,142,102,0.2639705,"\int \frac{1}{(3+5 i \sinh (c+d x))^2} \, dx","Integrate[(3 + (5*I)*Sinh[c + d*x])^(-2),x]","\frac{40 \sinh \left(\frac{1}{2} (c+d x)\right) \left(\frac{3}{\cosh \left(\frac{1}{2} (c+d x)\right)+3 i \sinh \left(\frac{1}{2} (c+d x)\right)}+\frac{1}{3 \cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)}\right)-9 \left(2 \tan ^{-1}\left(3 \tanh \left(\frac{1}{2} (c+d x)\right)\right)-i \log (4-5 \cosh (c+d x))+i \log (5 \cosh (c+d x)+4)+2 \tan ^{-1}\left(3 \coth \left(\frac{1}{2} (c+d x)\right)\right)\right)}{384 d}","\frac{5 i \cosh (c+d x)}{16 d (3+5 i \sinh (c+d x))}-\frac{3 i \log \left(3 \cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}+\frac{3 i \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)+3 i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}{64 d}",1,"(-9*(2*ArcTan[3*Coth[(c + d*x)/2]] + 2*ArcTan[3*Tanh[(c + d*x)/2]] - I*Log[4 - 5*Cosh[c + d*x]] + I*Log[4 + 5*Cosh[c + d*x]]) + 40*((3*Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^(-1) + 3/(Cosh[(c + d*x)/2] + (3*I)*Sinh[(c + d*x)/2]))*Sinh[(c + d*x)/2])/(384*d)","A",1
90,1,204,131,0.5139618,"\int \frac{1}{(3+5 i \sinh (c+d x))^3} \, dx","Integrate[(3 + (5*I)*Sinh[c + d*x])^(-3),x]","\frac{86 \tan ^{-1}\left(3 \tanh \left(\frac{1}{2} (c+d x)\right)\right)-43 i \log (4-5 \cosh (c+d x))+43 i \log (5 \cosh (c+d x)+4)+\sinh \left(\frac{1}{2} (c+d x)\right) \left(-\frac{360}{\cosh \left(\frac{1}{2} (c+d x)\right)+3 i \sinh \left(\frac{1}{2} (c+d x)\right)}-\frac{120}{3 \cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)}\right)-\frac{80 i}{\left(3 \cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}+\frac{80 i}{\left(\cosh \left(\frac{1}{2} (c+d x)\right)+3 i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}+86 \tan ^{-1}\left(3 \coth \left(\frac{1}{2} (c+d x)\right)\right)}{4096 d}","-\frac{45 i \cosh (c+d x)}{512 d (3+5 i \sinh (c+d x))}+\frac{5 i \cosh (c+d x)}{32 d (3+5 i \sinh (c+d x))^2}+\frac{43 i \log \left(3 \cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}-\frac{43 i \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)+3 i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}{2048 d}",1,"(86*ArcTan[3*Coth[(c + d*x)/2]] + 86*ArcTan[3*Tanh[(c + d*x)/2]] - (43*I)*Log[4 - 5*Cosh[c + d*x]] + (43*I)*Log[4 + 5*Cosh[c + d*x]] - (80*I)/(3*Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2 + (80*I)/(Cosh[(c + d*x)/2] + (3*I)*Sinh[(c + d*x)/2])^2 + (-120/(3*Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) - 360/(Cosh[(c + d*x)/2] + (3*I)*Sinh[(c + d*x)/2]))*Sinh[(c + d*x)/2])/(4096*d)","A",1
91,1,265,160,0.6344055,"\int \frac{1}{(3+5 i \sinh (c+d x))^4} \, dx","Integrate[(3 + (5*I)*Sinh[c + d*x])^(-4),x]","\frac{-5022 \tan ^{-1}\left(3 \tanh \left(\frac{1}{2} (c+d x)\right)\right)+2511 i \log (4-5 \cosh (c+d x))-2511 i \log (5 \cosh (c+d x)+4)+40 \sinh \left(\frac{1}{2} (c+d x)\right) \left(\frac{597}{\cosh \left(\frac{1}{2} (c+d x)\right)+3 i \sinh \left(\frac{1}{2} (c+d x)\right)}+\frac{240}{\left(\cosh \left(\frac{1}{2} (c+d x)\right)+3 i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^3}+\frac{199}{3 \cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)}+\frac{80}{\left(3 \cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^3}\right)+\frac{4640 i}{\left(3 \cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}-\frac{1440 i}{\left(\cosh \left(\frac{1}{2} (c+d x)\right)+3 i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}-5022 \tan ^{-1}\left(3 \coth \left(\frac{1}{2} (c+d x)\right)\right)}{589824 d}","\frac{995 i \cosh (c+d x)}{24576 d (3+5 i \sinh (c+d x))}-\frac{25 i \cosh (c+d x)}{512 d (3+5 i \sinh (c+d x))^2}+\frac{5 i \cosh (c+d x)}{48 d (3+5 i \sinh (c+d x))^3}-\frac{279 i \log \left(3 \cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}+\frac{279 i \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)+3 i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}{32768 d}",1,"(-5022*ArcTan[3*Coth[(c + d*x)/2]] - 5022*ArcTan[3*Tanh[(c + d*x)/2]] + (2511*I)*Log[4 - 5*Cosh[c + d*x]] - (2511*I)*Log[4 + 5*Cosh[c + d*x]] + (4640*I)/(3*Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2 - (1440*I)/(Cosh[(c + d*x)/2] + (3*I)*Sinh[(c + d*x)/2])^2 + 40*(80/(3*Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^3 + 199/(3*Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) + 240/(Cosh[(c + d*x)/2] + (3*I)*Sinh[(c + d*x)/2])^3 + 597/(Cosh[(c + d*x)/2] + (3*I)*Sinh[(c + d*x)/2]))*Sinh[(c + d*x)/2])/(589824*d)","A",1
92,1,171,37,0.0318018,"\int \frac{1}{5+3 i \sinh (c+d x)} \, dx","Integrate[(5 + (3*I)*Sinh[c + d*x])^(-1),x]","-\frac{\log (5 \cosh (c+d x)-4 \sinh (c+d x))}{8 d}+\frac{\log (4 \sinh (c+d x)+5 \cosh (c+d x))}{8 d}-\frac{i \tan ^{-1}\left(\frac{2 \cosh \left(\frac{1}{2} (c+d x)\right)-\sinh \left(\frac{1}{2} (c+d x)\right)}{\cosh \left(\frac{1}{2} (c+d x)\right)-2 \sinh \left(\frac{1}{2} (c+d x)\right)}\right)}{4 d}+\frac{i \tan ^{-1}\left(\frac{2 \sinh \left(\frac{1}{2} (c+d x)\right)+\cosh \left(\frac{1}{2} (c+d x)\right)}{\sinh \left(\frac{1}{2} (c+d x)\right)+2 \cosh \left(\frac{1}{2} (c+d x)\right)}\right)}{4 d}","\frac{x}{4}-\frac{i \tan ^{-1}\left(\frac{\cosh (c+d x)}{3+i \sinh (c+d x)}\right)}{2 d}",1,"((-1/4*I)*ArcTan[(2*Cosh[(c + d*x)/2] - Sinh[(c + d*x)/2])/(Cosh[(c + d*x)/2] - 2*Sinh[(c + d*x)/2])])/d + ((I/4)*ArcTan[(Cosh[(c + d*x)/2] + 2*Sinh[(c + d*x)/2])/(2*Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2])])/d - Log[5*Cosh[c + d*x] - 4*Sinh[c + d*x]]/(8*d) + Log[5*Cosh[c + d*x] + 4*Sinh[c + d*x]]/(8*d)","B",1
93,1,183,66,0.247079,"\int \frac{1}{(5+3 i \sinh (c+d x))^2} \, dx","Integrate[(5 + (3*I)*Sinh[c + d*x])^(-2),x]","\frac{-\frac{120 \cosh (c+d x)}{3 \sinh (c+d x)-5 i}-25 \log (5 \cosh (c+d x)-4 \sinh (c+d x))+25 \log (4 \sinh (c+d x)+5 \cosh (c+d x))-50 i \tan ^{-1}\left(\frac{2 \cosh \left(\frac{1}{2} (c+d x)\right)-\sinh \left(\frac{1}{2} (c+d x)\right)}{\cosh \left(\frac{1}{2} (c+d x)\right)-2 \sinh \left(\frac{1}{2} (c+d x)\right)}\right)+50 i \tan ^{-1}\left(\frac{2 \sinh \left(\frac{1}{2} (c+d x)\right)+\cosh \left(\frac{1}{2} (c+d x)\right)}{\sinh \left(\frac{1}{2} (c+d x)\right)+2 \cosh \left(\frac{1}{2} (c+d x)\right)}\right)+24 i}{640 d}","-\frac{3 i \cosh (c+d x)}{16 d (5+3 i \sinh (c+d x))}-\frac{5 i \tan ^{-1}\left(\frac{\cosh (c+d x)}{3+i \sinh (c+d x)}\right)}{32 d}+\frac{5 x}{64}",1,"(24*I - (50*I)*ArcTan[(2*Cosh[(c + d*x)/2] - Sinh[(c + d*x)/2])/(Cosh[(c + d*x)/2] - 2*Sinh[(c + d*x)/2])] + (50*I)*ArcTan[(Cosh[(c + d*x)/2] + 2*Sinh[(c + d*x)/2])/(2*Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2])] - 25*Log[5*Cosh[c + d*x] - 4*Sinh[c + d*x]] + 25*Log[5*Cosh[c + d*x] + 4*Sinh[c + d*x]] - (120*Cosh[c + d*x])/(-5*I + 3*Sinh[c + d*x]))/(640*d)","B",1
94,1,277,95,0.6899652,"\int \frac{1}{(5+3 i \sinh (c+d x))^3} \, dx","Integrate[(5 + (3*I)*Sinh[c + d*x])^(-3),x]","\frac{-\frac{144 \sinh \left(\frac{1}{2} (c+d x)\right) \left(5 \sinh \left(\frac{1}{2} (c+d x)\right)-3 i \cosh \left(\frac{1}{2} (c+d x)\right)\right)}{3 \sinh (c+d x)-5 i}+\frac{48}{\left((1+2 i) \cosh \left(\frac{1}{2} (c+d x)\right)-(2+i) \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}+\frac{48}{\left((1+2 i) \sinh \left(\frac{1}{2} (c+d x)\right)+(2+i) \cosh \left(\frac{1}{2} (c+d x)\right)\right)^2}-59 \log (5 \cosh (c+d x)-4 \sinh (c+d x))+59 \log (4 \sinh (c+d x)+5 \cosh (c+d x))-118 i \tan ^{-1}\left(\frac{2 \cosh \left(\frac{1}{2} (c+d x)\right)-\sinh \left(\frac{1}{2} (c+d x)\right)}{\cosh \left(\frac{1}{2} (c+d x)\right)-2 \sinh \left(\frac{1}{2} (c+d x)\right)}\right)+118 i \tan ^{-1}\left(\frac{2 \sinh \left(\frac{1}{2} (c+d x)\right)+\cosh \left(\frac{1}{2} (c+d x)\right)}{\sinh \left(\frac{1}{2} (c+d x)\right)+2 \cosh \left(\frac{1}{2} (c+d x)\right)}\right)}{4096 d}","-\frac{45 i \cosh (c+d x)}{512 d (5+3 i \sinh (c+d x))}-\frac{3 i \cosh (c+d x)}{32 d (5+3 i \sinh (c+d x))^2}-\frac{59 i \tan ^{-1}\left(\frac{\cosh (c+d x)}{3+i \sinh (c+d x)}\right)}{1024 d}+\frac{59 x}{2048}",1,"((-118*I)*ArcTan[(2*Cosh[(c + d*x)/2] - Sinh[(c + d*x)/2])/(Cosh[(c + d*x)/2] - 2*Sinh[(c + d*x)/2])] + (118*I)*ArcTan[(Cosh[(c + d*x)/2] + 2*Sinh[(c + d*x)/2])/(2*Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2])] - 59*Log[5*Cosh[c + d*x] - 4*Sinh[c + d*x]] + 59*Log[5*Cosh[c + d*x] + 4*Sinh[c + d*x]] + 48/((1 + 2*I)*Cosh[(c + d*x)/2] - (2 + I)*Sinh[(c + d*x)/2])^2 + 48/((2 + I)*Cosh[(c + d*x)/2] + (1 + 2*I)*Sinh[(c + d*x)/2])^2 - (144*Sinh[(c + d*x)/2]*((-3*I)*Cosh[(c + d*x)/2] + 5*Sinh[(c + d*x)/2]))/(-5*I + 3*Sinh[c + d*x]))/(4096*d)","B",1
95,1,308,124,1.9253592,"\int \frac{1}{(5+3 i \sinh (c+d x))^4} \, dx","Integrate[(5 + (3*I)*Sinh[c + d*x])^(-4),x]","\frac{\frac{2 (-298563 i \sinh (c+d x)+89364 i \sinh (2 (c+d x))+8397 i \sinh (3 (c+d x))+166615 \cosh (c+d x)+82530 \cosh (2 (c+d x))-13995 \cosh (3 (c+d x))-235150)}{(3 \sinh (c+d x)-5 i)^3}+\frac{2656-192 i}{\left((1+2 i) \cosh \left(\frac{1}{2} (c+d x)\right)-(2+i) \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}+\frac{2656+192 i}{\left((1+2 i) \sinh \left(\frac{1}{2} (c+d x)\right)+(2+i) \cosh \left(\frac{1}{2} (c+d x)\right)\right)^2}-1925 \log (5 \cosh (c+d x)-4 \sinh (c+d x))+1925 \log (4 \sinh (c+d x)+5 \cosh (c+d x))-3850 i \tan ^{-1}\left(\frac{2 \cosh \left(\frac{1}{2} (c+d x)\right)-\sinh \left(\frac{1}{2} (c+d x)\right)}{\cosh \left(\frac{1}{2} (c+d x)\right)-2 \sinh \left(\frac{1}{2} (c+d x)\right)}\right)+3850 i \tan ^{-1}\left(\frac{2 \sinh \left(\frac{1}{2} (c+d x)\right)+\cosh \left(\frac{1}{2} (c+d x)\right)}{\sinh \left(\frac{1}{2} (c+d x)\right)+2 \cosh \left(\frac{1}{2} (c+d x)\right)}\right)}{327680 d}","-\frac{311 i \cosh (c+d x)}{8192 d (5+3 i \sinh (c+d x))}-\frac{25 i \cosh (c+d x)}{512 d (5+3 i \sinh (c+d x))^2}-\frac{i \cosh (c+d x)}{16 d (5+3 i \sinh (c+d x))^3}-\frac{385 i \tan ^{-1}\left(\frac{\cosh (c+d x)}{3+i \sinh (c+d x)}\right)}{16384 d}+\frac{385 x}{32768}",1,"((-3850*I)*ArcTan[(2*Cosh[(c + d*x)/2] - Sinh[(c + d*x)/2])/(Cosh[(c + d*x)/2] - 2*Sinh[(c + d*x)/2])] + (3850*I)*ArcTan[(Cosh[(c + d*x)/2] + 2*Sinh[(c + d*x)/2])/(2*Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2])] - 1925*Log[5*Cosh[c + d*x] - 4*Sinh[c + d*x]] + 1925*Log[5*Cosh[c + d*x] + 4*Sinh[c + d*x]] + (2656 - 192*I)/((1 + 2*I)*Cosh[(c + d*x)/2] - (2 + I)*Sinh[(c + d*x)/2])^2 + (2656 + 192*I)/((2 + I)*Cosh[(c + d*x)/2] + (1 + 2*I)*Sinh[(c + d*x)/2])^2 + (2*(-235150 + 166615*Cosh[c + d*x] + 82530*Cosh[2*(c + d*x)] - 13995*Cosh[3*(c + d*x)] - (298563*I)*Sinh[c + d*x] + (89364*I)*Sinh[2*(c + d*x)] + (8397*I)*Sinh[3*(c + d*x)]))/(-5*I + 3*Sinh[c + d*x])^3)/(327680*d)","B",1
96,1,138,183,0.6509192,"\int (a+b \sinh (c+d x))^5 \, dx","Integrate[(a + b*Sinh[c + d*x])^5,x]","\frac{50 \left(8 a^2 b^3-b^5\right) \cosh (3 (c+d x))+15 a \left(40 \left(2 a^2 b^2-b^4\right) \sinh (2 (c+d x))+4 \left(8 a^4-40 a^2 b^2+15 b^4\right) (c+d x)+5 b^4 \sinh (4 (c+d x))\right)+300 b \left(8 a^4-12 a^2 b^2+b^4\right) \cosh (c+d x)+6 b^5 \cosh (5 (c+d x))}{480 d}","\frac{b \left(47 a^2-16 b^2\right) \cosh (c+d x) (a+b \sinh (c+d x))^2}{60 d}+\frac{7 a b^2 \left(22 a^2-23 b^2\right) \sinh (c+d x) \cosh (c+d x)}{120 d}+\frac{b \left(107 a^4-192 a^2 b^2+16 b^4\right) \cosh (c+d x)}{30 d}+\frac{1}{8} a x \left(8 a^4-40 a^2 b^2+15 b^4\right)+\frac{b \cosh (c+d x) (a+b \sinh (c+d x))^4}{5 d}+\frac{9 a b \cosh (c+d x) (a+b \sinh (c+d x))^3}{20 d}",1,"(300*b*(8*a^4 - 12*a^2*b^2 + b^4)*Cosh[c + d*x] + 50*(8*a^2*b^3 - b^5)*Cosh[3*(c + d*x)] + 6*b^5*Cosh[5*(c + d*x)] + 15*a*(4*(8*a^4 - 40*a^2*b^2 + 15*b^4)*(c + d*x) + 40*(2*a^2*b^2 - b^4)*Sinh[2*(c + d*x)] + 5*b^4*Sinh[4*(c + d*x)]))/(480*d)","A",1
97,1,108,137,0.3695616,"\int (a+b \sinh (c+d x))^4 \, dx","Integrate[(a + b*Sinh[c + d*x])^4,x]","\frac{96 a b \left(4 a^2-3 b^2\right) \cosh (c+d x)+3 \left(8 \left(6 a^2 b^2-b^4\right) \sinh (2 (c+d x))+4 \left(8 a^4-24 a^2 b^2+3 b^4\right) (c+d x)+b^4 \sinh (4 (c+d x))\right)+32 a b^3 \cosh (3 (c+d x))}{96 d}","\frac{a b \left(19 a^2-16 b^2\right) \cosh (c+d x)}{6 d}+\frac{b^2 \left(26 a^2-9 b^2\right) \sinh (c+d x) \cosh (c+d x)}{24 d}+\frac{1}{8} x \left(8 a^4-24 a^2 b^2+3 b^4\right)+\frac{b \cosh (c+d x) (a+b \sinh (c+d x))^3}{4 d}+\frac{7 a b \cosh (c+d x) (a+b \sinh (c+d x))^2}{12 d}",1,"(96*a*b*(4*a^2 - 3*b^2)*Cosh[c + d*x] + 32*a*b^3*Cosh[3*(c + d*x)] + 3*(4*(8*a^4 - 24*a^2*b^2 + 3*b^4)*(c + d*x) + 8*(6*a^2*b^2 - b^4)*Sinh[2*(c + d*x)] + b^4*Sinh[4*(c + d*x)]))/(96*d)","A",1
98,1,71,92,0.1806212,"\int (a+b \sinh (c+d x))^3 \, dx","Integrate[(a + b*Sinh[c + d*x])^3,x]","\frac{6 a \left(2 a^2-3 b^2\right) (c+d x)-9 b \left(b^2-4 a^2\right) \cosh (c+d x)+9 a b^2 \sinh (2 (c+d x))+b^3 \cosh (3 (c+d x))}{12 d}","\frac{2 b \left(4 a^2-b^2\right) \cosh (c+d x)}{3 d}+\frac{1}{2} a x \left(2 a^2-3 b^2\right)+\frac{5 a b^2 \sinh (c+d x) \cosh (c+d x)}{6 d}+\frac{b \cosh (c+d x) (a+b \sinh (c+d x))^2}{3 d}",1,"(6*a*(2*a^2 - 3*b^2)*(c + d*x) - 9*b*(-4*a^2 + b^2)*Cosh[c + d*x] + b^3*Cosh[3*(c + d*x)] + 9*a*b^2*Sinh[2*(c + d*x)])/(12*d)","A",1
99,1,48,52,0.0801712,"\int (a+b \sinh (c+d x))^2 \, dx","Integrate[(a + b*Sinh[c + d*x])^2,x]","\frac{2 \left(2 a^2-b^2\right) (c+d x)+8 a b \cosh (c+d x)+b^2 \sinh (2 (c+d x))}{4 d}","\frac{1}{2} x \left(2 a^2-b^2\right)+\frac{2 a b \cosh (c+d x)}{d}+\frac{b^2 \sinh (c+d x) \cosh (c+d x)}{2 d}",1,"(2*(2*a^2 - b^2)*(c + d*x) + 8*a*b*Cosh[c + d*x] + b^2*Sinh[2*(c + d*x)])/(4*d)","A",1
100,1,26,15,0.0084202,"\int (a+b \sinh (c+d x)) \, dx","Integrate[a + b*Sinh[c + d*x],x]","a x+\frac{b \sinh (c) \sinh (d x)}{d}+\frac{b \cosh (c) \cosh (d x)}{d}","a x+\frac{b \cosh (c+d x)}{d}",1,"a*x + (b*Cosh[c]*Cosh[d*x])/d + (b*Sinh[c]*Sinh[d*x])/d","A",1
101,1,52,44,0.0352437,"\int \frac{1}{a+b \sinh (c+d x)} \, dx","Integrate[(a + b*Sinh[c + d*x])^(-1),x]","\frac{2 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{d \sqrt{-a^2-b^2}}","-\frac{2 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{d \sqrt{a^2+b^2}}",1,"(2*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(Sqrt[-a^2 - b^2]*d)","A",1
102,1,85,79,0.2634688,"\int \frac{1}{(a+b \sinh (c+d x))^2} \, dx","Integrate[(a + b*Sinh[c + d*x])^(-2),x]","-\frac{\frac{2 a \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{3/2}}+\frac{b \cosh (c+d x)}{\left(a^2+b^2\right) (a+b \sinh (c+d x))}}{d}","-\frac{2 a \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{d \left(a^2+b^2\right)^{3/2}}-\frac{b \cosh (c+d x)}{d \left(a^2+b^2\right) (a+b \sinh (c+d x))}",1,"-(((2*a*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(-a^2 - b^2)^(3/2) + (b*Cosh[c + d*x])/((a^2 + b^2)*(a + b*Sinh[c + d*x])))/d)","A",1
103,1,117,127,0.2777404,"\int \frac{1}{(a+b \sinh (c+d x))^3} \, dx","Integrate[(a + b*Sinh[c + d*x])^(-3),x]","\frac{\frac{2 \left(2 a^2-b^2\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}-\frac{b \cosh (c+d x) \left(4 a^2+3 a b \sinh (c+d x)+b^2\right)}{(a+b \sinh (c+d x))^2}}{2 d \left(a^2+b^2\right)^2}","-\frac{\left(2 a^2-b^2\right) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{d \left(a^2+b^2\right)^{5/2}}-\frac{3 a b \cosh (c+d x)}{2 d \left(a^2+b^2\right)^2 (a+b \sinh (c+d x))}-\frac{b \cosh (c+d x)}{2 d \left(a^2+b^2\right) (a+b \sinh (c+d x))^2}",1,"((2*(2*a^2 - b^2)*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - (b*Cosh[c + d*x]*(4*a^2 + b^2 + 3*a*b*Sinh[c + d*x]))/(a + b*Sinh[c + d*x])^2)/(2*(a^2 + b^2)^2*d)","A",1
104,1,159,174,0.7239335,"\int \frac{1}{(a+b \sinh (c+d x))^4} \, dx","Integrate[(a + b*Sinh[c + d*x])^(-4),x]","\frac{\frac{6 a \left(2 a^2-3 b^2\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+\frac{b \cosh (c+d x) \left(-18 a^4+3 a b \left(b^2-9 a^2\right) \sinh (c+d x)-5 a^2 b^2+\left(4 b^4-11 a^2 b^2\right) \sinh ^2(c+d x)-2 b^4\right)}{(a+b \sinh (c+d x))^3}}{6 d \left(a^2+b^2\right)^3}","-\frac{a \left(2 a^2-3 b^2\right) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{d \left(a^2+b^2\right)^{7/2}}-\frac{b \left(11 a^2-4 b^2\right) \cosh (c+d x)}{6 d \left(a^2+b^2\right)^3 (a+b \sinh (c+d x))}-\frac{5 a b \cosh (c+d x)}{6 d \left(a^2+b^2\right)^2 (a+b \sinh (c+d x))^2}-\frac{b \cosh (c+d x)}{3 d \left(a^2+b^2\right) (a+b \sinh (c+d x))^3}",1,"((6*a*(2*a^2 - 3*b^2)*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + (b*Cosh[c + d*x]*(-18*a^4 - 5*a^2*b^2 - 2*b^4 + 3*a*b*(-9*a^2 + b^2)*Sinh[c + d*x] + (-11*a^2*b^2 + 4*b^4)*Sinh[c + d*x]^2))/(a + b*Sinh[c + d*x])^3)/(6*(a^2 + b^2)^3*d)","A",1
105,1,178,179,0.4342827,"\int (a+b \sinh (x))^{5/2} \, dx","Integrate[(a + b*Sinh[x])^(5/2),x]","\frac{b \cosh (x) \left(22 a^2+28 a b \sinh (x)+3 b^2 \cosh (2 x)-3 b^2\right)-16 i a \left(a^2+b^2\right) \sqrt{\frac{a+b \sinh (x)}{a-i b}} F\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)+2 \left(23 i a^3+23 a^2 b-9 i a b^2-9 b^3\right) \sqrt{\frac{a+b \sinh (x)}{a-i b}} E\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)}{15 \sqrt{a+b \sinh (x)}}","-\frac{16 i a \left(a^2+b^2\right) \sqrt{\frac{a+b \sinh (x)}{a-i b}} F\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{15 \sqrt{a+b \sinh (x)}}+\frac{2 i \left(23 a^2-9 b^2\right) \sqrt{a+b \sinh (x)} E\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{15 \sqrt{\frac{a+b \sinh (x)}{a-i b}}}+\frac{2}{5} b \cosh (x) (a+b \sinh (x))^{3/2}+\frac{16}{15} a b \cosh (x) \sqrt{a+b \sinh (x)}",1,"(2*((23*I)*a^3 + 23*a^2*b - (9*I)*a*b^2 - 9*b^3)*EllipticE[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)]*Sqrt[(a + b*Sinh[x])/(a - I*b)] - (16*I)*a*(a^2 + b^2)*EllipticF[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)]*Sqrt[(a + b*Sinh[x])/(a - I*b)] + b*Cosh[x]*(22*a^2 - 3*b^2 + 3*b^2*Cosh[2*x] + 28*a*b*Sinh[x]))/(15*Sqrt[a + b*Sinh[x]])","A",1
106,1,139,150,0.382157,"\int (a+b \sinh (x))^{3/2} \, dx","Integrate[(a + b*Sinh[x])^(3/2),x]","\frac{-2 i \left(a^2+b^2\right) \sqrt{\frac{a+b \sinh (x)}{a-i b}} F\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)+2 b \cosh (x) (a+b \sinh (x))+8 a (b+i a) \sqrt{\frac{a+b \sinh (x)}{a-i b}} E\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)}{3 \sqrt{a+b \sinh (x)}}","-\frac{2 i \left(a^2+b^2\right) \sqrt{\frac{a+b \sinh (x)}{a-i b}} F\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{3 \sqrt{a+b \sinh (x)}}+\frac{2}{3} b \cosh (x) \sqrt{a+b \sinh (x)}+\frac{8 i a \sqrt{a+b \sinh (x)} E\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{3 \sqrt{\frac{a+b \sinh (x)}{a-i b}}}",1,"(2*b*Cosh[x]*(a + b*Sinh[x]) + 8*a*(I*a + b)*EllipticE[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)]*Sqrt[(a + b*Sinh[x])/(a - I*b)] - (2*I)*(a^2 + b^2)*EllipticF[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)]*Sqrt[(a + b*Sinh[x])/(a - I*b)])/(3*Sqrt[a + b*Sinh[x]])","A",1
107,1,65,60,0.1884675,"\int \sqrt{a+b \sinh (x)} \, dx","Integrate[Sqrt[a + b*Sinh[x]],x]","\frac{2 (b+i a) \sqrt{\frac{a+b \sinh (x)}{a-i b}} E\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)}{\sqrt{a+b \sinh (x)}}","\frac{2 i \sqrt{a+b \sinh (x)} E\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{\sqrt{\frac{a+b \sinh (x)}{a-i b}}}",1,"(2*(I*a + b)*EllipticE[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)]*Sqrt[(a + b*Sinh[x])/(a - I*b)])/Sqrt[a + b*Sinh[x]]","A",1
108,1,60,60,0.1933202,"\int \frac{1}{\sqrt{a+b \sinh (x)}} \, dx","Integrate[1/Sqrt[a + b*Sinh[x]],x]","\frac{2 i \sqrt{\frac{a+b \sinh (x)}{a-i b}} F\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)}{\sqrt{a+b \sinh (x)}}","\frac{2 i \sqrt{\frac{a+b \sinh (x)}{a-i b}} F\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{\sqrt{a+b \sinh (x)}}",1,"((2*I)*EllipticF[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)]*Sqrt[(a + b*Sinh[x])/(a - I*b)])/Sqrt[a + b*Sinh[x]]","A",1
109,1,81,94,0.1557624,"\int \frac{1}{(a+b \sinh (x))^{3/2}} \, dx","Integrate[(a + b*Sinh[x])^(-3/2),x]","\frac{-2 b \cosh (x)+2 (b+i a) \sqrt{\frac{a+b \sinh (x)}{a-i b}} E\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)}{\left(a^2+b^2\right) \sqrt{a+b \sinh (x)}}","-\frac{2 b \cosh (x)}{\left(a^2+b^2\right) \sqrt{a+b \sinh (x)}}+\frac{2 i \sqrt{a+b \sinh (x)} E\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{\left(a^2+b^2\right) \sqrt{\frac{a+b \sinh (x)}{a-i b}}}",1,"(-2*b*Cosh[x] + 2*(I*a + b)*EllipticE[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)]*Sqrt[(a + b*Sinh[x])/(a - I*b)])/((a^2 + b^2)*Sqrt[a + b*Sinh[x]])","A",1
110,1,166,197,0.6439156,"\int \frac{1}{(a+b \sinh (x))^{5/2}} \, dx","Integrate[(a + b*Sinh[x])^(-5/2),x]","\frac{-2 b \cosh (x) \left(5 a^2+4 a b \sinh (x)+b^2\right)-2 i \left(a^2+b^2\right) \sqrt{\frac{a+b \sinh (x)}{a-i b}} (a+b \sinh (x)) F\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)+\frac{8 i a (a+b \sinh (x))^2 E\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)}{\sqrt{\frac{a+b \sinh (x)}{a-i b}}}}{3 \left(a^2+b^2\right)^2 (a+b \sinh (x))^{3/2}}","-\frac{8 a b \cosh (x)}{3 \left(a^2+b^2\right)^2 \sqrt{a+b \sinh (x)}}-\frac{2 b \cosh (x)}{3 \left(a^2+b^2\right) (a+b \sinh (x))^{3/2}}-\frac{2 i \sqrt{\frac{a+b \sinh (x)}{a-i b}} F\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{3 \left(a^2+b^2\right) \sqrt{a+b \sinh (x)}}+\frac{8 i a \sqrt{a+b \sinh (x)} E\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{3 \left(a^2+b^2\right)^2 \sqrt{\frac{a+b \sinh (x)}{a-i b}}}",1,"(((8*I)*a*EllipticE[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)]*(a + b*Sinh[x])^2)/Sqrt[(a + b*Sinh[x])/(a - I*b)] - (2*I)*(a^2 + b^2)*EllipticF[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)]*(a + b*Sinh[x])*Sqrt[(a + b*Sinh[x])/(a - I*b)] - 2*b*Cosh[x]*(5*a^2 + b^2 + 4*a*b*Sinh[x]))/(3*(a^2 + b^2)^2*(a + b*Sinh[x])^(3/2))","A",1
111,1,101,128,0.363045,"\int \frac{\sinh (x)}{\sqrt{a+b \sinh (x)}} \, dx","Integrate[Sinh[x]/Sqrt[a + b*Sinh[x]],x]","\frac{2 \sqrt{\frac{a+b \sinh (x)}{a-i b}} \left((b+i a) E\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)-i a F\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)\right)}{b \sqrt{a+b \sinh (x)}}","\frac{2 i \sqrt{a+b \sinh (x)} E\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{b \sqrt{\frac{a+b \sinh (x)}{a-i b}}}-\frac{2 i a \sqrt{\frac{a+b \sinh (x)}{a-i b}} F\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{b \sqrt{a+b \sinh (x)}}",1,"(2*((I*a + b)*EllipticE[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)] - I*a*EllipticF[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)])*Sqrt[(a + b*Sinh[x])/(a - I*b)])/(b*Sqrt[a + b*Sinh[x]])","A",1
112,1,100,112,0.3578961,"\int (a+i a \sinh (x))^{5/2} (A+B \sinh (x)) \, dx","Integrate[(a + I*a*Sinh[x])^(5/2)*(A + B*Sinh[x]),x]","\frac{a^2 \sqrt{a+i a \sinh (x)} \left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right) ((-392 A+505 i B) \sinh (x)+(-120 B-42 i A) \cosh (2 x)+1246 i A-15 i B \sinh (3 x)+1040 B)}{210 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)}","\frac{64 a^3 (5 B+7 i A) \cosh (x)}{105 \sqrt{a+i a \sinh (x)}}+\frac{16}{105} a^2 (5 B+7 i A) \cosh (x) \sqrt{a+i a \sinh (x)}+\frac{2}{35} a (5 B+7 i A) \cosh (x) (a+i a \sinh (x))^{3/2}+\frac{2}{7} B \cosh (x) (a+i a \sinh (x))^{5/2}",1,"(a^2*(Cosh[x/2] - I*Sinh[x/2])*Sqrt[a + I*a*Sinh[x]]*((1246*I)*A + 1040*B + ((-42*I)*A - 120*B)*Cosh[2*x] + (-392*A + (505*I)*B)*Sinh[x] - (15*I)*B*Sinh[3*x]))/(210*(Cosh[x/2] + I*Sinh[x/2]))","A",1
113,1,83,81,0.2196172,"\int (a+i a \sinh (x))^{3/2} (A+B \sinh (x)) \, dx","Integrate[(a + I*a*Sinh[x])^(3/2)*(A + B*Sinh[x]),x]","-\frac{a \sqrt{a+i a \sinh (x)} \left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right) (2 (5 A-9 i B) \sinh (x)-50 i A+3 B \cosh (2 x)-39 B)}{15 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)}","\frac{8 a^2 (3 B+5 i A) \cosh (x)}{15 \sqrt{a+i a \sinh (x)}}+\frac{2}{15} a (3 B+5 i A) \cosh (x) \sqrt{a+i a \sinh (x)}+\frac{2}{5} B \cosh (x) (a+i a \sinh (x))^{3/2}",1,"-1/15*(a*(Cosh[x/2] - I*Sinh[x/2])*Sqrt[a + I*a*Sinh[x]]*((-50*I)*A - 39*B + 3*B*Cosh[2*x] + 2*(5*A - (9*I)*B)*Sinh[x]))/(Cosh[x/2] + I*Sinh[x/2])","A",1
114,1,66,48,0.0742399,"\int \sqrt{a+i a \sinh (x)} (A+B \sinh (x)) \, dx","Integrate[Sqrt[a + I*a*Sinh[x]]*(A + B*Sinh[x]),x]","\frac{2 \sqrt{a+i a \sinh (x)} \left(\sinh \left(\frac{x}{2}\right)+i \cosh \left(\frac{x}{2}\right)\right) (3 A+B \sinh (x)-2 i B)}{3 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)}","\frac{2 a (B+3 i A) \cosh (x)}{3 \sqrt{a+i a \sinh (x)}}+\frac{2}{3} B \cosh (x) \sqrt{a+i a \sinh (x)}",1,"(2*(I*Cosh[x/2] + Sinh[x/2])*Sqrt[a + I*a*Sinh[x]]*(3*A - (2*I)*B + B*Sinh[x]))/(3*(Cosh[x/2] + I*Sinh[x/2]))","A",1
115,1,53,23,0.2487931,"\int \frac{A+B \sinh (x)}{i+\sinh (x)} \, dx","Integrate[(A + B*Sinh[x])/(I + Sinh[x]),x]","\cosh (x) \left(\frac{2 i B \sin ^{-1}\left(\frac{\sqrt{1-i \sinh (x)}}{\sqrt{2}}\right)}{\sqrt{\cosh ^2(x)}}-\frac{B+i A}{\sinh (x)+i}\right)","B x-\frac{(B+i A) \cosh (x)}{\sinh (x)+i}",1,"Cosh[x]*(((2*I)*B*ArcSin[Sqrt[1 - I*Sinh[x]]/Sqrt[2]])/Sqrt[Cosh[x]^2] - (I*A + B)/(I + Sinh[x]))","B",1
116,1,32,43,0.0299925,"\int \frac{A+B \sinh (x)}{(i+\sinh (x))^2} \, dx","Integrate[(A + B*Sinh[x])/(I + Sinh[x])^2,x]","\frac{\cosh (x) (-(A+2 i B) \sinh (x)-2 i A+B)}{3 (\sinh (x)+i)^2}","-\frac{(A+2 i B) \cosh (x)}{3 (\sinh (x)+i)}-\frac{(B+i A) \cosh (x)}{3 (\sinh (x)+i)^2}",1,"(Cosh[x]*((-2*I)*A + B - (A + (2*I)*B)*Sinh[x]))/(3*(I + Sinh[x])^2)","A",1
117,1,50,68,0.0396574,"\int \frac{A+B \sinh (x)}{(i+\sinh (x))^3} \, dx","Integrate[(A + B*Sinh[x])/(I + Sinh[x])^3,x]","\frac{\cosh (x) \left((-3 B+2 i A) \sinh ^2(x)-3 (2 A+3 i B) \sinh (x)-7 i A+3 B\right)}{15 (\sinh (x)+i)^3}","\frac{(-3 B+2 i A) \cosh (x)}{15 (\sinh (x)+i)}-\frac{(2 A+3 i B) \cosh (x)}{15 (\sinh (x)+i)^2}-\frac{(B+i A) \cosh (x)}{5 (\sinh (x)+i)^3}",1,"(Cosh[x]*((-7*I)*A + 3*B - 3*(2*A + (3*I)*B)*Sinh[x] + ((2*I)*A - 3*B)*Sinh[x]^2))/(15*(I + Sinh[x])^3)","A",1
118,1,67,91,0.0509158,"\int \frac{A+B \sinh (x)}{(i+\sinh (x))^4} \, dx","Integrate[(A + B*Sinh[x])/(I + Sinh[x])^4,x]","\frac{\cosh (x) \left((6 A+8 i B) \sinh ^3(x)+8 i (3 A+4 i B) \sinh ^2(x)-13 (3 A+4 i B) \sinh (x)-36 i A+13 B\right)}{105 (\sinh (x)+i)^4}","\frac{2 (3 A+4 i B) \cosh (x)}{105 (\sinh (x)+i)}+\frac{2 (-4 B+3 i A) \cosh (x)}{105 (\sinh (x)+i)^2}-\frac{(3 A+4 i B) \cosh (x)}{35 (\sinh (x)+i)^3}-\frac{(B+i A) \cosh (x)}{7 (\sinh (x)+i)^4}",1,"(Cosh[x]*((-36*I)*A + 13*B - 13*(3*A + (4*I)*B)*Sinh[x] + (8*I)*(3*A + (4*I)*B)*Sinh[x]^2 + (6*A + (8*I)*B)*Sinh[x]^3))/(105*(I + Sinh[x])^4)","A",1
119,1,59,27,0.0794175,"\int \frac{A+B \sinh (x)}{i-\sinh (x)} \, dx","Integrate[(A + B*Sinh[x])/(I - Sinh[x]),x]","\frac{\left(-\sinh \left(\frac{x}{2}\right)+i \cosh \left(\frac{x}{2}\right)\right) \left(B x \cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right) (2 A+B (x+2 i))\right)}{\sinh (x)-i}","-B x+\frac{(-B+i A) \cosh (x)}{-\sinh (x)+i}",1,"((I*Cosh[x/2] - Sinh[x/2])*(B*x*Cosh[x/2] + I*(2*A + B*(2*I + x))*Sinh[x/2]))/(-I + Sinh[x])","B",1
120,1,32,49,0.0290424,"\int \frac{A+B \sinh (x)}{(i-\sinh (x))^2} \, dx","Integrate[(A + B*Sinh[x])/(I - Sinh[x])^2,x]","\frac{\cosh (x) (-(A-2 i B) \sinh (x)+2 i A+B)}{3 (\sinh (x)-i)^2}","\frac{(A-2 i B) \cosh (x)}{3 (-\sinh (x)+i)}+\frac{(-B+i A) \cosh (x)}{3 (-\sinh (x)+i)^2}",1,"(Cosh[x]*((2*I)*A + B - (A - (2*I)*B)*Sinh[x]))/(3*(-I + Sinh[x])^2)","A",1
121,1,92,76,0.2228425,"\int \frac{A+B \sinh (x)}{(i-\sinh (x))^3} \, dx","Integrate[(A + B*Sinh[x])/(I - Sinh[x])^3,x]","-\frac{5 (2 A-3 i B) \cosh \left(\frac{3 x}{2}\right)-20 i A \sinh \left(\frac{x}{2}\right)+2 i A \sinh \left(\frac{5 x}{2}\right)-15 B \sinh \left(\frac{x}{2}\right)+3 B \sinh \left(\frac{5 x}{2}\right)+15 i B \cosh \left(\frac{x}{2}\right)}{30 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)^5}","-\frac{(3 B+2 i A) \cosh (x)}{15 (-\sinh (x)+i)}+\frac{(2 A-3 i B) \cosh (x)}{15 (-\sinh (x)+i)^2}+\frac{(-B+i A) \cosh (x)}{5 (-\sinh (x)+i)^3}",1,"-1/30*((15*I)*B*Cosh[x/2] + 5*(2*A - (3*I)*B)*Cosh[(3*x)/2] - (20*I)*A*Sinh[x/2] - 15*B*Sinh[x/2] + (2*I)*A*Sinh[(5*x)/2] + 3*B*Sinh[(5*x)/2])/(Cosh[x/2] + I*Sinh[x/2])^5","A",1
122,1,63,101,0.0505726,"\int \frac{A+B \sinh (x)}{(i-\sinh (x))^4} \, dx","Integrate[(A + B*Sinh[x])/(I - Sinh[x])^4,x]","\frac{\cosh (x) \left((6 A-8 i B) \sinh ^3(x)+(-32 B-24 i A) \sinh ^2(x)+(-39 A+52 i B) \sinh (x)+36 i A+13 B\right)}{105 (\sinh (x)-i)^4}","-\frac{2 (3 A-4 i B) \cosh (x)}{105 (-\sinh (x)+i)}-\frac{2 (4 B+3 i A) \cosh (x)}{105 (-\sinh (x)+i)^2}+\frac{(3 A-4 i B) \cosh (x)}{35 (-\sinh (x)+i)^3}+\frac{(-B+i A) \cosh (x)}{7 (-\sinh (x)+i)^4}",1,"(Cosh[x]*((36*I)*A + 13*B + (-39*A + (52*I)*B)*Sinh[x] + ((-24*I)*A - 32*B)*Sinh[x]^2 + (6*A - (8*I)*B)*Sinh[x]^3))/(105*(-I + Sinh[x])^4)","A",1
123,1,85,66,0.1235902,"\int \frac{A+B \sinh (x)}{\sqrt{a+i a \sinh (x)}} \, dx","Integrate[(A + B*Sinh[x])/Sqrt[a + I*a*Sinh[x]],x]","\frac{2 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right) \left((1+i) \sqrt[4]{-1} (B-i A) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{4}\right)+i}{\sqrt{2}}\right)-i B \sinh \left(\frac{x}{2}\right)+B \cosh \left(\frac{x}{2}\right)\right)}{\sqrt{a+i a \sinh (x)}}","\frac{\sqrt{2} (-B+i A) \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (x)}{\sqrt{2} \sqrt{a+i a \sinh (x)}}\right)}{\sqrt{a}}+\frac{2 B \cosh (x)}{\sqrt{a+i a \sinh (x)}}",1,"(2*(Cosh[x/2] + I*Sinh[x/2])*((1 + I)*(-1)^(1/4)*((-I)*A + B)*ArcTan[(I + Tanh[x/4])/Sqrt[2]] + B*Cosh[x/2] - I*B*Sinh[x/2]))/Sqrt[a + I*a*Sinh[x]]","A",1
124,1,105,79,0.2467079,"\int \frac{A+B \sinh (x)}{(a+i a \sinh (x))^{3/2}} \, dx","Integrate[(A + B*Sinh[x])/(a + I*a*Sinh[x])^(3/2),x]","\frac{\left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right) \left((A+i B) \sinh \left(\frac{x}{2}\right)+i (A+i B) \cosh \left(\frac{x}{2}\right)+(1+i) \sqrt[4]{-1} (A-3 i B) (\sinh (x)-i) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{4}\right)+i}{\sqrt{2}}\right)\right)}{2 (a+i a \sinh (x))^{3/2}}","\frac{(3 B+i A) \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (x)}{\sqrt{2} \sqrt{a+i a \sinh (x)}}\right)}{2 \sqrt{2} a^{3/2}}+\frac{(-B+i A) \cosh (x)}{2 (a+i a \sinh (x))^{3/2}}",1,"((Cosh[x/2] + I*Sinh[x/2])*(I*(A + I*B)*Cosh[x/2] + (A + I*B)*Sinh[x/2] + (1 + I)*(-1)^(1/4)*(A - (3*I)*B)*ArcTan[(I + Tanh[x/4])/Sqrt[2]]*(-I + Sinh[x])))/(2*(a + I*a*Sinh[x])^(3/2))","A",1
125,1,184,110,0.2217065,"\int \frac{A+B \sinh (x)}{(a+i a \sinh (x))^{5/2}} \, dx","Integrate[(A + B*Sinh[x])/(a + I*a*Sinh[x])^(5/2),x]","\frac{\left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right) \left(8 (A+i B) \sinh \left(\frac{x}{2}\right)+2 (5 B+3 i A) \sinh \left(\frac{x}{2}\right) (\sinh (x)-i)+(5 B+3 i A) \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)^3+4 i (A+i B) \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)+(1-i) \sqrt[4]{-1} (3 A-5 i B) \tan ^{-1}\left(\frac{\tanh \left(\frac{x}{4}\right)+i}{\sqrt{2}}\right) \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)^4\right)}{16 (a+i a \sinh (x))^{5/2}}","\frac{(5 B+3 i A) \tanh ^{-1}\left(\frac{\sqrt{a} \cosh (x)}{\sqrt{2} \sqrt{a+i a \sinh (x)}}\right)}{16 \sqrt{2} a^{5/2}}+\frac{(5 B+3 i A) \cosh (x)}{16 a (a+i a \sinh (x))^{3/2}}+\frac{(-B+i A) \cosh (x)}{4 (a+i a \sinh (x))^{5/2}}",1,"((Cosh[x/2] + I*Sinh[x/2])*((4*I)*(A + I*B)*(Cosh[x/2] + I*Sinh[x/2]) + ((3*I)*A + 5*B)*(Cosh[x/2] + I*Sinh[x/2])^3 + (1 - I)*(-1)^(1/4)*(3*A - (5*I)*B)*ArcTan[(I + Tanh[x/4])/Sqrt[2]]*(Cosh[x/2] + I*Sinh[x/2])^4 + 8*(A + I*B)*Sinh[x/2] + 2*((3*I)*A + 5*B)*Sinh[x/2]*(-I + Sinh[x])))/(16*(a + I*a*Sinh[x])^(5/2))","A",1
126,1,241,259,0.802414,"\int (a+b \sinh (x))^{5/2} (A+B \sinh (x)) \, dx","Integrate[(a + b*Sinh[x])^(5/2)*(A + B*Sinh[x]),x]","\frac{\cosh (x) (a+b \sinh (x)) \left(90 a^2 B+6 b \sinh (x) (15 a B+7 A b)+154 a A b+15 b^2 B \cosh (2 x)-65 b^2 B\right)+\frac{2 i \sqrt{\frac{a+b \sinh (x)}{a-i b}} \left(b \left(105 a^3 A-135 a^2 b B-119 a A b^2+25 b^3 B\right) F\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)+\left(15 a^3 B+161 a^2 A b-145 a b^2 B-63 A b^3\right) \left((a-i b) E\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)-a F\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)\right)\right)}{b}}{105 \sqrt{a+b \sinh (x)}}","\frac{2}{105} \cosh (x) \left(15 a^2 B+56 a A b-25 b^2 B\right) \sqrt{a+b \sinh (x)}-\frac{2 i \left(a^2+b^2\right) \left(15 a^2 B+56 a A b-25 b^2 B\right) \sqrt{\frac{a+b \sinh (x)}{a-i b}} F\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{105 b \sqrt{a+b \sinh (x)}}+\frac{2 i \left(15 a^3 B+161 a^2 A b-145 a b^2 B-63 A b^3\right) \sqrt{a+b \sinh (x)} E\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{105 b \sqrt{\frac{a+b \sinh (x)}{a-i b}}}+\frac{2}{35} \cosh (x) (5 a B+7 A b) (a+b \sinh (x))^{3/2}+\frac{2}{7} B \cosh (x) (a+b \sinh (x))^{5/2}",1,"(((2*I)*(b*(105*a^3*A - 119*a*A*b^2 - 135*a^2*b*B + 25*b^3*B)*EllipticF[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)] + (161*a^2*A*b - 63*A*b^3 + 15*a^3*B - 145*a*b^2*B)*((a - I*b)*EllipticE[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)] - a*EllipticF[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)]))*Sqrt[(a + b*Sinh[x])/(a - I*b)])/b + Cosh[x]*(a + b*Sinh[x])*(154*a*A*b + 90*a^2*B - 65*b^2*B + 15*b^2*B*Cosh[2*x] + 6*b*(7*A*b + 15*a*B)*Sinh[x]))/(105*Sqrt[a + b*Sinh[x]])","A",1
127,1,196,207,0.5678737,"\int (a+b \sinh (x))^{3/2} (A+B \sinh (x)) \, dx","Integrate[(a + b*Sinh[x])^(3/2)*(A + B*Sinh[x]),x]","\frac{2 \left(\cosh (x) (a+b \sinh (x)) (6 a B+5 A b+3 b B \sinh (x))+\frac{i \sqrt{\frac{a+b \sinh (x)}{a-i b}} \left(b \left(15 a^2 A-12 a b B-5 A b^2\right) F\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)+\left(3 a^2 B+20 a A b-9 b^2 B\right) \left((a-i b) E\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)-a F\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)\right)\right)}{b}\right)}{15 \sqrt{a+b \sinh (x)}}","-\frac{2 i \left(a^2+b^2\right) (3 a B+5 A b) \sqrt{\frac{a+b \sinh (x)}{a-i b}} F\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{15 b \sqrt{a+b \sinh (x)}}+\frac{2 i \left(3 a^2 B+20 a A b-9 b^2 B\right) \sqrt{a+b \sinh (x)} E\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{15 b \sqrt{\frac{a+b \sinh (x)}{a-i b}}}+\frac{2}{15} \cosh (x) (3 a B+5 A b) \sqrt{a+b \sinh (x)}+\frac{2}{5} B \cosh (x) (a+b \sinh (x))^{3/2}",1,"(2*((I*(b*(15*a^2*A - 5*A*b^2 - 12*a*b*B)*EllipticF[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)] + (20*a*A*b + 3*a^2*B - 9*b^2*B)*((a - I*b)*EllipticE[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)] - a*EllipticF[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)]))*Sqrt[(a + b*Sinh[x])/(a - I*b)])/b + Cosh[x]*(a + b*Sinh[x])*(5*A*b + 6*a*B + 3*b*B*Sinh[x])))/(15*Sqrt[a + b*Sinh[x]])","A",1
128,1,151,164,0.4072105,"\int \sqrt{a+b \sinh (x)} (A+B \sinh (x)) \, dx","Integrate[Sqrt[a + b*Sinh[x]]*(A + B*Sinh[x]),x]","\frac{-2 i B \left(a^2+b^2\right) \sqrt{\frac{a+b \sinh (x)}{a-i b}} F\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)+2 (b+i a) (a B+3 A b) \sqrt{\frac{a+b \sinh (x)}{a-i b}} E\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)+2 b B \cosh (x) (a+b \sinh (x))}{3 b \sqrt{a+b \sinh (x)}}","-\frac{2 i B \left(a^2+b^2\right) \sqrt{\frac{a+b \sinh (x)}{a-i b}} F\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{3 b \sqrt{a+b \sinh (x)}}+\frac{2 i (a B+3 A b) \sqrt{a+b \sinh (x)} E\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{3 b \sqrt{\frac{a+b \sinh (x)}{a-i b}}}+\frac{2}{3} B \cosh (x) \sqrt{a+b \sinh (x)}",1,"(2*b*B*Cosh[x]*(a + b*Sinh[x]) + 2*(I*a + b)*(3*A*b + a*B)*EllipticE[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)]*Sqrt[(a + b*Sinh[x])/(a - I*b)] - (2*I)*(a^2 + b^2)*B*EllipticF[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)]*Sqrt[(a + b*Sinh[x])/(a - I*b)])/(3*b*Sqrt[a + b*Sinh[x]])","A",1
129,1,61,55,0.1064967,"\int \frac{A+B \sinh (x)}{a+b \sinh (x)} \, dx","Integrate[(A + B*Sinh[x])/(a + b*Sinh[x]),x]","\frac{\frac{2 (A b-a B) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+B x}{b}","\frac{B x}{b}-\frac{2 (A b-a B) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b \sqrt{a^2+b^2}}",1,"(B*x + (2*(A*b - a*B)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2])/b","A",1
130,1,82,74,0.1534129,"\int \frac{A+B \sinh (x)}{(a+b \sinh (x))^2} \, dx","Integrate[(A + B*Sinh[x])/(a + b*Sinh[x])^2,x]","\frac{\frac{2 (a A+b B) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+\frac{\cosh (x) (a B-A b)}{a+b \sinh (x)}}{a^2+b^2}","-\frac{2 (a A+b B) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{3/2}}-\frac{\cosh (x) (A b-a B)}{\left(a^2+b^2\right) (a+b \sinh (x))}",1,"((2*(a*A + b*B)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + ((-(A*b) + a*B)*Cosh[x])/(a + b*Sinh[x]))/(a^2 + b^2)","A",1
131,1,131,128,0.2888124,"\int \frac{A+B \sinh (x)}{(a+b \sinh (x))^3} \, dx","Integrate[(A + B*Sinh[x])/(a + b*Sinh[x])^3,x]","\frac{\frac{2 \left(2 a^2 A+3 a b B-A b^2\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+\frac{\cosh (x) \left(a^2 B-3 a A b-2 b^2 B\right)}{a+b \sinh (x)}+\frac{\left(a^2+b^2\right) \cosh (x) (a B-A b)}{(a+b \sinh (x))^2}}{2 \left(a^2+b^2\right)^2}","-\frac{\left(2 a^2 A+3 a b B-A b^2\right) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{5/2}}-\frac{\cosh (x) \left(a^2 (-B)+3 a A b+2 b^2 B\right)}{2 \left(a^2+b^2\right)^2 (a+b \sinh (x))}-\frac{\cosh (x) (A b-a B)}{2 \left(a^2+b^2\right) (a+b \sinh (x))^2}",1,"((2*(2*a^2*A - A*b^2 + 3*a*b*B)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + ((a^2 + b^2)*(-(A*b) + a*B)*Cosh[x])/(a + b*Sinh[x])^2 + ((-3*a*A*b + a^2*B - 2*b^2*B)*Cosh[x])/(a + b*Sinh[x]))/(2*(a^2 + b^2)^2)","A",1
132,1,189,187,0.4869931,"\int \frac{A+B \sinh (x)}{(a+b \sinh (x))^4} \, dx","Integrate[(A + B*Sinh[x])/(a + b*Sinh[x])^4,x]","\frac{\frac{2 \left(a^2+b^2\right)^2 \cosh (x) (a B-A b)}{(a+b \sinh (x))^3}+\frac{\left(a^2+b^2\right) \cosh (x) \left(2 a^2 B-5 a A b-3 b^2 B\right)}{(a+b \sinh (x))^2}+\frac{6 \left(2 a^3 A+4 a^2 b B-3 a A b^2-b^3 B\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+\frac{\cosh (x) \left(2 a^3 B-11 a^2 A b-13 a b^2 B+4 A b^3\right)}{a+b \sinh (x)}}{6 \left(a^2+b^2\right)^3}","-\frac{\cosh (x) \left(-2 a^2 B+5 a A b+3 b^2 B\right)}{6 \left(a^2+b^2\right)^2 (a+b \sinh (x))^2}-\frac{\cosh (x) (A b-a B)}{3 \left(a^2+b^2\right) (a+b \sinh (x))^3}-\frac{\left(2 a^3 A+4 a^2 b B-3 a A b^2-b^3 B\right) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{7/2}}-\frac{\cosh (x) \left(-2 a^3 B+11 a^2 A b+13 a b^2 B-4 A b^3\right)}{6 \left(a^2+b^2\right)^3 (a+b \sinh (x))}",1,"((6*(2*a^3*A - 3*a*A*b^2 + 4*a^2*b*B - b^3*B)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + (2*(a^2 + b^2)^2*(-(A*b) + a*B)*Cosh[x])/(a + b*Sinh[x])^3 + ((a^2 + b^2)*(-5*a*A*b + 2*a^2*B - 3*b^2*B)*Cosh[x])/(a + b*Sinh[x])^2 + ((-11*a^2*A*b + 4*A*b^3 + 2*a^3*B - 13*a*b^2*B)*Cosh[x])/(a + b*Sinh[x]))/(6*(a^2 + b^2)^3)","A",1
133,1,66,60,0.072262,"\int \frac{\frac{b B}{a}+B \sinh (x)}{a+b \sinh (x)} \, dx","Integrate[((b*B)/a + B*Sinh[x])/(a + b*Sinh[x]),x]","\frac{B \left(a x-\frac{2 \left(a^2-b^2\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}\right)}{a b}","\frac{2 B \left(a^2-b^2\right) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a b \sqrt{a^2+b^2}}+\frac{B x}{b}",1,"(B*(a*x - (2*(a^2 - b^2)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2]))/(a*b)","A",1
134,1,6,6,0.000443,"\int \frac{\frac{a B}{b}+B \sinh (x)}{a+b \sinh (x)} \, dx","Integrate[((a*B)/b + B*Sinh[x])/(a + b*Sinh[x]),x]","\frac{B x}{b}","\frac{B x}{b}",1,"(B*x)/b","A",1
135,1,12,12,0.0351104,"\int \frac{a-b \sinh (x)}{(b+a \sinh (x))^2} \, dx","Integrate[(a - b*Sinh[x])/(b + a*Sinh[x])^2,x]","-\frac{\cosh (x)}{a \sinh (x)+b}","-\frac{\cosh (x)}{a \sinh (x)+b}",1,"-(Cosh[x]/(b + a*Sinh[x]))","A",1
136,1,28,34,0.0884323,"\int \frac{2-\sinh (x)}{2+\sinh (x)} \, dx","Integrate[(2 - Sinh[x])/(2 + Sinh[x]),x]","-x-\frac{8 \tanh ^{-1}\left(\frac{1-2 \tanh \left(\frac{x}{2}\right)}{\sqrt{5}}\right)}{\sqrt{5}}","\frac{4 x}{\sqrt{5}}-x-\frac{8 \tanh ^{-1}\left(\frac{\cosh (x)}{\sinh (x)+\sqrt{5}+2}\right)}{\sqrt{5}}",1,"-x - (8*ArcTanh[(1 - 2*Tanh[x/2])/Sqrt[5]])/Sqrt[5]","A",1
137,1,109,136,0.5245204,"\int \frac{A+B \sinh (x)}{\sqrt{a+b \sinh (x)}} \, dx","Integrate[(A + B*Sinh[x])/Sqrt[a + b*Sinh[x]],x]","\frac{2 \sqrt{\frac{a+b \sinh (x)}{a-i b}} \left(i (A b-a B) F\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)+B (b+i a) E\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)\right)}{b \sqrt{a+b \sinh (x)}}","\frac{2 i (A b-a B) \sqrt{\frac{a+b \sinh (x)}{a-i b}} F\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{b \sqrt{a+b \sinh (x)}}+\frac{2 i B \sqrt{a+b \sinh (x)} E\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{b \sqrt{\frac{a+b \sinh (x)}{a-i b}}}",1,"(2*((I*a + b)*B*EllipticE[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)] + I*(A*b - a*B)*EllipticF[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)])*Sqrt[(a + b*Sinh[x])/(a - I*b)])/(b*Sqrt[a + b*Sinh[x]])","A",1
138,1,159,176,0.653516,"\int \frac{A+B \sinh (x)}{(a+b \sinh (x))^{3/2}} \, dx","Integrate[(A + B*Sinh[x])/(a + b*Sinh[x])^(3/2),x]","\frac{2 i B \left(a^2+b^2\right) \sqrt{\frac{a+b \sinh (x)}{a-i b}} F\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)+2 b \cosh (x) (a B-A b)+\frac{2 i (A b-a B) (a+b \sinh (x)) E\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)}{\sqrt{\frac{a+b \sinh (x)}{a-i b}}}}{b \left(a^2+b^2\right) \sqrt{a+b \sinh (x)}}","-\frac{2 \cosh (x) (A b-a B)}{\left(a^2+b^2\right) \sqrt{a+b \sinh (x)}}+\frac{2 i (A b-a B) \sqrt{a+b \sinh (x)} E\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{b \left(a^2+b^2\right) \sqrt{\frac{a+b \sinh (x)}{a-i b}}}+\frac{2 i B \sqrt{\frac{a+b \sinh (x)}{a-i b}} F\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{b \sqrt{a+b \sinh (x)}}",1,"(2*b*(-(A*b) + a*B)*Cosh[x] + ((2*I)*(A*b - a*B)*EllipticE[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)]*(a + b*Sinh[x]))/Sqrt[(a + b*Sinh[x])/(a - I*b)] + (2*I)*(a^2 + b^2)*B*EllipticF[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)]*Sqrt[(a + b*Sinh[x])/(a - I*b)])/(b*(a^2 + b^2)*Sqrt[a + b*Sinh[x]])","A",1
139,1,236,251,0.8246215,"\int \frac{A+B \sinh (x)}{(a+b \sinh (x))^{5/2}} \, dx","Integrate[(A + B*Sinh[x])/(a + b*Sinh[x])^(5/2),x]","\frac{2 i \left(i b \cosh (x) \left(-\left(a^2 B-4 a A b-3 b^2 B\right) (a+b \sinh (x))-\left(\left(a^2+b^2\right) (a B-A b)\right)\right)+\sqrt{\frac{a+b \sinh (x)}{a-i b}} (a+b \sinh (x)) \left(b \left(3 a^2 A+4 a b B-A b^2\right) F\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)+\left(a^2 (-B)+4 a A b+3 b^2 B\right) \left((a-i b) E\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)-a F\left(\frac{1}{4} (\pi -2 i x)|-\frac{2 i b}{a-i b}\right)\right)\right)\right)}{3 b \left(a^2+b^2\right)^2 (a+b \sinh (x))^{3/2}}","-\frac{2 \cosh (x) \left(a^2 (-B)+4 a A b+3 b^2 B\right)}{3 \left(a^2+b^2\right)^2 \sqrt{a+b \sinh (x)}}-\frac{2 \cosh (x) (A b-a B)}{3 \left(a^2+b^2\right) (a+b \sinh (x))^{3/2}}-\frac{2 i (A b-a B) \sqrt{\frac{a+b \sinh (x)}{a-i b}} F\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{3 b \left(a^2+b^2\right) \sqrt{a+b \sinh (x)}}+\frac{2 i \left(a^2 (-B)+4 a A b+3 b^2 B\right) \sqrt{a+b \sinh (x)} E\left(\frac{\pi }{4}-\frac{i x}{2}|\frac{2 b}{i a+b}\right)}{3 b \left(a^2+b^2\right)^2 \sqrt{\frac{a+b \sinh (x)}{a-i b}}}",1,"(((2*I)/3)*((b*(3*a^2*A - A*b^2 + 4*a*b*B)*EllipticF[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)] + (4*a*A*b - a^2*B + 3*b^2*B)*((a - I*b)*EllipticE[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)] - a*EllipticF[(Pi - (2*I)*x)/4, ((-2*I)*b)/(a - I*b)]))*(a + b*Sinh[x])*Sqrt[(a + b*Sinh[x])/(a - I*b)] + I*b*Cosh[x]*(-((a^2 + b^2)*(-(A*b) + a*B)) - (-4*a*A*b + a^2*B - 3*b^2*B)*(a + b*Sinh[x]))))/(b*(a^2 + b^2)^2*(a + b*Sinh[x])^(3/2))","A",1
140,1,36,53,0.0410233,"\int \left(a \sinh ^2(x)\right)^{5/2} \, dx","Integrate[(a*Sinh[x]^2)^(5/2),x]","\frac{1}{240} a^2 (150 \cosh (x)-25 \cosh (3 x)+3 \cosh (5 x)) \text{csch}(x) \sqrt{a \sinh ^2(x)}","\frac{8}{15} a^2 \coth (x) \sqrt{a \sinh ^2(x)}+\frac{1}{5} \coth (x) \left(a \sinh ^2(x)\right)^{5/2}-\frac{4}{15} a \coth (x) \left(a \sinh ^2(x)\right)^{3/2}",1,"(a^2*(150*Cosh[x] - 25*Cosh[3*x] + 3*Cosh[5*x])*Csch[x]*Sqrt[a*Sinh[x]^2])/240","A",1
141,1,26,34,0.037744,"\int \left(a \sinh ^2(x)\right)^{3/2} \, dx","Integrate[(a*Sinh[x]^2)^(3/2),x]","\frac{1}{12} a (\cosh (3 x)-9 \cosh (x)) \text{csch}(x) \sqrt{a \sinh ^2(x)}","\frac{1}{3} \coth (x) \left(a \sinh ^2(x)\right)^{3/2}-\frac{2}{3} a \coth (x) \sqrt{a \sinh ^2(x)}",1,"(a*(-9*Cosh[x] + Cosh[3*x])*Csch[x]*Sqrt[a*Sinh[x]^2])/12","A",1
142,1,13,13,0.0044951,"\int \sqrt{a \sinh ^2(x)} \, dx","Integrate[Sqrt[a*Sinh[x]^2],x]","\coth (x) \sqrt{a \sinh ^2(x)}","\coth (x) \sqrt{a \sinh ^2(x)}",1,"Coth[x]*Sqrt[a*Sinh[x]^2]","A",1
143,1,20,17,0.0058928,"\int \frac{1}{\sqrt{a \sinh ^2(x)}} \, dx","Integrate[1/Sqrt[a*Sinh[x]^2],x]","\frac{\sinh (x) \log \left(\tanh \left(\frac{x}{2}\right)\right)}{\sqrt{a \sinh ^2(x)}}","-\frac{\sinh (x) \tanh ^{-1}(\cosh (x))}{\sqrt{a \sinh ^2(x)}}",1,"(Log[Tanh[x/2]]*Sinh[x])/Sqrt[a*Sinh[x]^2]","A",1
144,1,44,42,0.0402034,"\int \frac{1}{\left(a \sinh ^2(x)\right)^{3/2}} \, dx","Integrate[(a*Sinh[x]^2)^(-3/2),x]","-\frac{\sinh ^3(x) \left(\text{csch}^2\left(\frac{x}{2}\right)+\text{sech}^2\left(\frac{x}{2}\right)+4 \log \left(\tanh \left(\frac{x}{2}\right)\right)\right)}{8 \left(a \sinh ^2(x)\right)^{3/2}}","\frac{\sinh (x) \tanh ^{-1}(\cosh (x))}{2 a \sqrt{a \sinh ^2(x)}}-\frac{\coth (x)}{2 a \sqrt{a \sinh ^2(x)}}",1,"-1/8*((Csch[x/2]^2 + 4*Log[Tanh[x/2]] + Sech[x/2]^2)*Sinh[x]^3)/(a*Sinh[x]^2)^(3/2)","A",1
145,1,67,61,0.1010104,"\int \frac{1}{\left(a \sinh ^2(x)\right)^{5/2}} \, dx","Integrate[(a*Sinh[x]^2)^(-5/2),x]","-\frac{\text{csch}(x) \sqrt{a \sinh ^2(x)} \left(\text{csch}^4\left(\frac{x}{2}\right)-6 \text{csch}^2\left(\frac{x}{2}\right)-\text{sech}^4\left(\frac{x}{2}\right)-6 \text{sech}^2\left(\frac{x}{2}\right)-24 \log \left(\tanh \left(\frac{x}{2}\right)\right)\right)}{64 a^3}","\frac{3 \coth (x)}{8 a^2 \sqrt{a \sinh ^2(x)}}-\frac{3 \sinh (x) \tanh ^{-1}(\cosh (x))}{8 a^2 \sqrt{a \sinh ^2(x)}}-\frac{\coth (x)}{4 a \left(a \sinh ^2(x)\right)^{3/2}}",1,"-1/64*(Csch[x]*(-6*Csch[x/2]^2 + Csch[x/2]^4 - 24*Log[Tanh[x/2]] - 6*Sech[x/2]^2 - Sech[x/2]^4)*Sqrt[a*Sinh[x]^2])/a^3","A",1
146,1,67,135,0.1850461,"\int \left(a \sinh ^3(x)\right)^{5/2} \, dx","Integrate[(a*Sinh[x]^3)^(5/2),x]","\frac{a^2 \text{csch}(x) \sqrt{a \sinh ^3(x)} \left(-15465 \cosh (x)+3657 \cosh (3 x)-749 \cosh (5 x)+77 \cosh (7 x)-\frac{12480 F\left(\left.\frac{1}{4} (\pi -2 i x)\right|2\right)}{\sqrt{i \sinh (x)}}\right)}{36960}","-\frac{26}{165} a^2 \sinh ^3(x) \cosh (x) \sqrt{a \sinh ^3(x)}+\frac{78}{385} a^2 \sinh (x) \cosh (x) \sqrt{a \sinh ^3(x)}+\frac{2}{15} a^2 \sinh ^5(x) \cosh (x) \sqrt{a \sinh ^3(x)}-\frac{26}{77} a^2 \coth (x) \sqrt{a \sinh ^3(x)}+\frac{26}{77} i a^2 \sqrt{i \sinh (x)} \text{csch}^2(x) F\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right) \sqrt{a \sinh ^3(x)}",1,"(a^2*Csch[x]*(-15465*Cosh[x] + 3657*Cosh[3*x] - 749*Cosh[5*x] + 77*Cosh[7*x] - (12480*EllipticF[(Pi - (2*I)*x)/4, 2])/Sqrt[I*Sinh[x]])*Sqrt[a*Sinh[x]^3])/36960","A",1
147,1,57,83,0.0643855,"\int \left(a \sinh ^3(x)\right)^{3/2} \, dx","Integrate[(a*Sinh[x]^3)^(3/2),x]","\frac{1}{180} a \text{csch}(x) \sqrt{a \sinh ^3(x)} \left(-38 \sinh (2 x)+5 \sinh (4 x)+168 \sqrt{i \sinh (x)} \text{csch}(x) E\left(\left.\frac{1}{4} (\pi -2 i x)\right|2\right)\right)","-\frac{14}{45} a \cosh (x) \sqrt{a \sinh ^3(x)}+\frac{2}{9} a \sinh ^2(x) \cosh (x) \sqrt{a \sinh ^3(x)}+\frac{14 i a \text{csch}(x) E\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right) \sqrt{a \sinh ^3(x)}}{15 \sqrt{i \sinh (x)}}",1,"(a*Csch[x]*Sqrt[a*Sinh[x]^3]*(168*Csch[x]*EllipticE[(Pi - (2*I)*x)/4, 2]*Sqrt[I*Sinh[x]] - 38*Sinh[2*x] + 5*Sinh[4*x]))/180","A",1
148,1,60,62,0.0864531,"\int \sqrt{a \sinh ^3(x)} \, dx","Integrate[Sqrt[a*Sinh[x]^3],x]","\frac{2}{3} \sqrt{a \sinh ^3(x)} \left(\coth (x)-\sqrt{2} \text{csch}^2(x) \sqrt{-\sinh (x) (\sinh (x)+\cosh (x))} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\cosh (2 x)+\sinh (2 x)\right)\right)","\frac{2}{3} \coth (x) \sqrt{a \sinh ^3(x)}-\frac{2}{3} i \sqrt{i \sinh (x)} \text{csch}^2(x) F\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right) \sqrt{a \sinh ^3(x)}",1,"(2*Sqrt[a*Sinh[x]^3]*(Coth[x] - Sqrt[2]*Csch[x]^2*Hypergeometric2F1[1/4, 1/2, 5/4, Cosh[2*x] + Sinh[2*x]]*Sqrt[-(Sinh[x]*(Cosh[x] + Sinh[x]))]))/3","C",1
149,1,42,60,0.0287633,"\int \frac{1}{\sqrt{a \sinh ^3(x)}} \, dx","Integrate[1/Sqrt[a*Sinh[x]^3],x]","-\frac{2 \sinh (x) \left(\cosh (x)-\sqrt{i \sinh (x)} E\left(\left.\frac{1}{4} (\pi -2 i x)\right|2\right)\right)}{\sqrt{a \sinh ^3(x)}}","-\frac{2 \sinh (x) \cosh (x)}{\sqrt{a \sinh ^3(x)}}+\frac{2 i \sinh ^2(x) E\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right)}{\sqrt{i \sinh (x)} \sqrt{a \sinh ^3(x)}}",1,"(-2*(Cosh[x] - EllipticE[(Pi - (2*I)*x)/4, 2]*Sqrt[I*Sinh[x]])*Sinh[x])/Sqrt[a*Sinh[x]^3]","A",1
150,1,53,87,0.0855169,"\int \frac{1}{\left(a \sinh ^3(x)\right)^{3/2}} \, dx","Integrate[(a*Sinh[x]^3)^(-3/2),x]","\frac{2 \left(5 \cosh (x)-3 \coth (x) \text{csch}(x)+5 (i \sinh (x))^{3/2} F\left(\left.\frac{1}{4} (\pi -2 i x)\right|2\right)\right)}{21 a \sqrt{a \sinh ^3(x)}}","\frac{10 \cosh (x)}{21 a \sqrt{a \sinh ^3(x)}}+\frac{10 i \sqrt{i \sinh (x)} \sinh (x) F\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right)}{21 a \sqrt{a \sinh ^3(x)}}-\frac{2 \coth (x) \text{csch}(x)}{7 a \sqrt{a \sinh ^3(x)}}",1,"(2*(5*Cosh[x] - 3*Coth[x]*Csch[x] + 5*EllipticF[(Pi - (2*I)*x)/4, 2]*(I*Sinh[x])^(3/2)))/(21*a*Sqrt[a*Sinh[x]^3])","A",1
151,1,69,135,0.2037938,"\int \frac{1}{\left(a \sinh ^3(x)\right)^{5/2}} \, dx","Integrate[(a*Sinh[x]^3)^(-5/2),x]","\frac{462 \sinh (x) \cosh (x)-2 \coth (x) \left(45 \text{csch}^4(x)-55 \text{csch}^2(x)+77\right)+462 i (i \sinh (x))^{3/2} E\left(\left.\frac{1}{4} (\pi -2 i x)\right|2\right)}{585 a^2 \sqrt{a \sinh ^3(x)}}","\frac{154 \sinh (x) \cosh (x)}{195 a^2 \sqrt{a \sinh ^3(x)}}-\frac{154 \coth (x)}{585 a^2 \sqrt{a \sinh ^3(x)}}-\frac{154 i \sinh ^2(x) E\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right)}{195 a^2 \sqrt{i \sinh (x)} \sqrt{a \sinh ^3(x)}}-\frac{2 \coth (x) \text{csch}^4(x)}{13 a^2 \sqrt{a \sinh ^3(x)}}+\frac{22 \coth (x) \text{csch}^2(x)}{117 a^2 \sqrt{a \sinh ^3(x)}}",1,"(-2*Coth[x]*(77 - 55*Csch[x]^2 + 45*Csch[x]^4) + (462*I)*EllipticE[(Pi - (2*I)*x)/4, 2]*(I*Sinh[x])^(3/2) + 462*Cosh[x]*Sinh[x])/(585*a^2*Sqrt[a*Sinh[x]^3])","A",1
152,1,53,132,0.1615558,"\int \left(a \sinh ^4(x)\right)^{5/2} \, dx","Integrate[(a*Sinh[x]^4)^(5/2),x]","\frac{a (-2520 x+2100 \sinh (2 x)-600 \sinh (4 x)+150 \sinh (6 x)-25 \sinh (8 x)+2 \sinh (10 x)) \text{csch}^6(x) \left(a \sinh ^4(x)\right)^{3/2}}{10240}","-\frac{21}{128} a^2 \sinh (x) \cosh (x) \sqrt{a \sinh ^4(x)}+\frac{1}{10} a^2 \sinh ^7(x) \cosh (x) \sqrt{a \sinh ^4(x)}-\frac{9}{80} a^2 \sinh ^5(x) \cosh (x) \sqrt{a \sinh ^4(x)}+\frac{21}{160} a^2 \sinh ^3(x) \cosh (x) \sqrt{a \sinh ^4(x)}+\frac{63}{256} a^2 \coth (x) \sqrt{a \sinh ^4(x)}-\frac{63}{256} a^2 x \text{csch}^2(x) \sqrt{a \sinh ^4(x)}",1,"(a*Csch[x]^6*(a*Sinh[x]^4)^(3/2)*(-2520*x + 2100*Sinh[2*x] - 600*Sinh[4*x] + 150*Sinh[6*x] - 25*Sinh[8*x] + 2*Sinh[10*x]))/10240","A",1
153,1,38,78,0.0894142,"\int \left(a \sinh ^4(x)\right)^{3/2} \, dx","Integrate[(a*Sinh[x]^4)^(3/2),x]","\frac{1}{192} (-60 x+45 \sinh (2 x)-9 \sinh (4 x)+\sinh (6 x)) \text{csch}^6(x) \left(a \sinh ^4(x)\right)^{3/2}","-\frac{5}{24} a \sinh (x) \cosh (x) \sqrt{a \sinh ^4(x)}+\frac{1}{6} a \sinh ^3(x) \cosh (x) \sqrt{a \sinh ^4(x)}+\frac{5}{16} a \coth (x) \sqrt{a \sinh ^4(x)}-\frac{5}{16} a x \text{csch}^2(x) \sqrt{a \sinh ^4(x)}",1,"(Csch[x]^6*(a*Sinh[x]^4)^(3/2)*(-60*x + 45*Sinh[2*x] - 9*Sinh[4*x] + Sinh[6*x]))/192","A",1
154,1,24,36,0.0372832,"\int \sqrt{a \sinh ^4(x)} \, dx","Integrate[Sqrt[a*Sinh[x]^4],x]","\frac{1}{2} \sqrt{a \sinh ^4(x)} \left(\coth (x)-x \text{csch}^2(x)\right)","\frac{1}{2} \coth (x) \sqrt{a \sinh ^4(x)}-\frac{1}{2} x \text{csch}^2(x) \sqrt{a \sinh ^4(x)}",1,"((Coth[x] - x*Csch[x]^2)*Sqrt[a*Sinh[x]^4])/2","A",1
155,1,16,16,0.0058342,"\int \frac{1}{\sqrt{a \sinh ^4(x)}} \, dx","Integrate[1/Sqrt[a*Sinh[x]^4],x]","-\frac{\sinh (x) \cosh (x)}{\sqrt{a \sinh ^4(x)}}","-\frac{\sinh (x) \cosh (x)}{\sqrt{a \sinh ^4(x)}}",1,"-((Cosh[x]*Sinh[x])/Sqrt[a*Sinh[x]^4])","A",1
156,1,34,68,0.0389072,"\int \frac{1}{\left(a \sinh ^4(x)\right)^{3/2}} \, dx","Integrate[(a*Sinh[x]^4)^(-3/2),x]","-\frac{\sinh ^5(x) \cosh (x) \left(3 \text{csch}^4(x)-4 \text{csch}^2(x)+8\right)}{15 \left(a \sinh ^4(x)\right)^{3/2}}","-\frac{\sinh (x) \cosh (x)}{a \sqrt{a \sinh ^4(x)}}-\frac{\cosh ^2(x) \coth ^3(x)}{5 a \sqrt{a \sinh ^4(x)}}+\frac{2 \cosh ^2(x) \coth (x)}{3 a \sqrt{a \sinh ^4(x)}}",1,"-1/15*(Cosh[x]*(8 - 4*Csch[x]^2 + 3*Csch[x]^4)*Sinh[x]^5)/(a*Sinh[x]^4)^(3/2)","A",1
157,1,47,118,0.0595076,"\int \frac{1}{\left(a \sinh ^4(x)\right)^{5/2}} \, dx","Integrate[(a*Sinh[x]^4)^(-5/2),x]","-\frac{\sinh (x) \cosh (x) \left(35 \text{csch}^8(x)-40 \text{csch}^6(x)+48 \text{csch}^4(x)-64 \text{csch}^2(x)+128\right)}{315 a^2 \sqrt{a \sinh ^4(x)}}","-\frac{\sinh (x) \cosh (x)}{a^2 \sqrt{a \sinh ^4(x)}}-\frac{\cosh ^2(x) \coth ^7(x)}{9 a^2 \sqrt{a \sinh ^4(x)}}+\frac{4 \cosh ^2(x) \coth ^5(x)}{7 a^2 \sqrt{a \sinh ^4(x)}}-\frac{6 \cosh ^2(x) \coth ^3(x)}{5 a^2 \sqrt{a \sinh ^4(x)}}+\frac{4 \cosh ^2(x) \coth (x)}{3 a^2 \sqrt{a \sinh ^4(x)}}",1,"-1/315*(Cosh[x]*(128 - 64*Csch[x]^2 + 48*Csch[x]^4 - 40*Csch[x]^6 + 35*Csch[x]^8)*Sinh[x])/(a^2*Sqrt[a*Sinh[x]^4])","A",1
158,1,219,50,0.160132,"\int \frac{\cosh ^8(x)}{i+\sinh (x)} \, dx","Integrate[Cosh[x]^8/(I + Sinh[x]),x]","\frac{\cosh ^9(x) \left(48 \sqrt{1+i \sinh (x)} \sinh ^7(x)-8 i \sqrt{1+i \sinh (x)} \sinh ^6(x)+200 \sqrt{1+i \sinh (x)} \sinh ^5(x)-38 i \sqrt{1+i \sinh (x)} \sinh ^4(x)+326 \sqrt{1+i \sinh (x)} \sinh ^3(x)-87 i \sqrt{1+i \sinh (x)} \sinh ^2(x)+279 \sqrt{1+i \sinh (x)} \sinh (x)+6 i \left(8 \sqrt{1+i \sinh (x)}+35 \sqrt{1-i \sinh (x)} \sin ^{-1}\left(\frac{\sqrt{1-i \sinh (x)}}{\sqrt{2}}\right)\right)\right)}{336 \sqrt{1+i \sinh (x)} (\sinh (x)-i)^4 (\sinh (x)+i)^5}","-\frac{5 i x}{16}+\frac{\cosh ^7(x)}{7}-\frac{1}{6} i \sinh (x) \cosh ^5(x)-\frac{5}{24} i \sinh (x) \cosh ^3(x)-\frac{5}{16} i \sinh (x) \cosh (x)",1,"(Cosh[x]^9*((6*I)*(35*ArcSin[Sqrt[1 - I*Sinh[x]]/Sqrt[2]]*Sqrt[1 - I*Sinh[x]] + 8*Sqrt[1 + I*Sinh[x]]) + 279*Sqrt[1 + I*Sinh[x]]*Sinh[x] - (87*I)*Sqrt[1 + I*Sinh[x]]*Sinh[x]^2 + 326*Sqrt[1 + I*Sinh[x]]*Sinh[x]^3 - (38*I)*Sqrt[1 + I*Sinh[x]]*Sinh[x]^4 + 200*Sqrt[1 + I*Sinh[x]]*Sinh[x]^5 - (8*I)*Sqrt[1 + I*Sinh[x]]*Sinh[x]^6 + 48*Sqrt[1 + I*Sinh[x]]*Sinh[x]^7))/(336*Sqrt[1 + I*Sinh[x]]*(-I + Sinh[x])^4*(I + Sinh[x])^5)","B",1
159,1,42,43,0.0306117,"\int \frac{\cosh ^7(x)}{i+\sinh (x)} \, dx","Integrate[Cosh[x]^7/(I + Sinh[x]),x]","\frac{1}{30} \sinh (x) \left(5 \sinh ^5(x)-6 i \sinh ^4(x)+15 \sinh ^3(x)-20 i \sinh ^2(x)+15 \sinh (x)-30 i\right)","\frac{1}{6} (-\sinh (x)+i)^6-\frac{4}{5} i (-\sinh (x)+i)^5-(-\sinh (x)+i)^4",1,"(Sinh[x]*(-30*I + 15*Sinh[x] - (20*I)*Sinh[x]^2 + 15*Sinh[x]^3 - (6*I)*Sinh[x]^4 + 5*Sinh[x]^5))/30","A",1
160,1,131,38,0.2412168,"\int \frac{\cosh ^6(x)}{i+\sinh (x)} \, dx","Integrate[Cosh[x]^6/(I + Sinh[x]),x]","-\frac{i \cosh ^7(x) \left(8 \sinh ^5(x)-2 i \sinh ^4(x)+26 \sinh ^3(x)-9 i \sinh ^2(x)+33 \sinh (x)+\frac{30 i \sqrt{1-i \sinh (x)} \sin ^{-1}\left(\frac{\sqrt{1-i \sinh (x)}}{\sqrt{2}}\right)}{\sqrt{1+i \sinh (x)}}+8 i\right)}{40 \left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right)^8 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)^6}","-\frac{3 i x}{8}+\frac{\cosh ^5(x)}{5}-\frac{1}{4} i \sinh (x) \cosh ^3(x)-\frac{3}{8} i \sinh (x) \cosh (x)",1,"((-1/40*I)*Cosh[x]^7*(8*I + ((30*I)*ArcSin[Sqrt[1 - I*Sinh[x]]/Sqrt[2]]*Sqrt[1 - I*Sinh[x]])/Sqrt[1 + I*Sinh[x]] + 33*Sinh[x] - (9*I)*Sinh[x]^2 + 26*Sinh[x]^3 - (2*I)*Sinh[x]^4 + 8*Sinh[x]^5))/((Cosh[x/2] - I*Sinh[x/2])^8*(Cosh[x/2] + I*Sinh[x/2])^6)","B",1
161,1,28,33,0.0206228,"\int \frac{\cosh ^5(x)}{i+\sinh (x)} \, dx","Integrate[Cosh[x]^5/(I + Sinh[x]),x]","\frac{1}{12} \sinh (x) \left(3 \sinh ^3(x)-4 i \sinh ^2(x)+6 \sinh (x)-12 i\right)","\frac{\sinh ^4(x)}{4}-\frac{1}{3} i \sinh ^3(x)+\frac{\sinh ^2(x)}{2}-i \sinh (x)",1,"(Sinh[x]*(-12*I + 6*Sinh[x] - (4*I)*Sinh[x]^2 + 3*Sinh[x]^3))/12","A",1
162,1,93,26,0.1599923,"\int \frac{\cosh ^4(x)}{i+\sinh (x)} \, dx","Integrate[Cosh[x]^4/(I + Sinh[x]),x]","\frac{\cosh ^5(x) \left(2 \sinh ^3(x)-i \sinh ^2(x)+5 \sinh (x)+\frac{6 i \sqrt{1-i \sinh (x)} \sin ^{-1}\left(\frac{\sqrt{1-i \sinh (x)}}{\sqrt{2}}\right)}{\sqrt{1+i \sinh (x)}}+2 i\right)}{6 (\sinh (x)-i)^2 (\sinh (x)+i)^3}","-\frac{i x}{2}+\frac{\cosh ^3(x)}{3}-\frac{1}{2} i \sinh (x) \cosh (x)",1,"(Cosh[x]^5*(2*I + ((6*I)*ArcSin[Sqrt[1 - I*Sinh[x]]/Sqrt[2]]*Sqrt[1 - I*Sinh[x]])/Sqrt[1 + I*Sinh[x]] + 5*Sinh[x] - I*Sinh[x]^2 + 2*Sinh[x]^3))/(6*(-I + Sinh[x])^2*(I + Sinh[x])^3)","B",1
163,1,12,15,0.010539,"\int \frac{\cosh ^3(x)}{i+\sinh (x)} \, dx","Integrate[Cosh[x]^3/(I + Sinh[x]),x]","\frac{1}{2} \sinh (x) (\sinh (x)-2 i)","\frac{\sinh ^2(x)}{2}-i \sinh (x)",1,"(Sinh[x]*(-2*I + Sinh[x]))/2","A",1
164,1,34,8,0.0466103,"\int \frac{\cosh ^2(x)}{i+\sinh (x)} \, dx","Integrate[Cosh[x]^2/(I + Sinh[x]),x]","\cosh (x)+2 \sqrt{\cosh ^2(x)} \text{sech}(x) \sin ^{-1}\left(\frac{\sqrt{1-i \sinh (x)}}{\sqrt{2}}\right)","\cosh (x)-i x",1,"Cosh[x] + 2*ArcSin[Sqrt[1 - I*Sinh[x]]/Sqrt[2]]*Sqrt[Cosh[x]^2]*Sech[x]","B",1
165,1,7,7,0.0058663,"\int \frac{\cosh (x)}{i+\sinh (x)} \, dx","Integrate[Cosh[x]/(I + Sinh[x]),x]","\log (\sinh (x)+i)","\log (\sinh (x)+i)",1,"Log[I + Sinh[x]]","A",1
166,1,18,24,0.0229245,"\int \frac{\text{sech}(x)}{i+\sinh (x)} \, dx","Integrate[Sech[x]/(I + Sinh[x]),x]","-\frac{1}{2} i \left(\tan ^{-1}(\sinh (x))+\frac{1}{\sinh (x)+i}\right)","-\frac{i}{2 (\sinh (x)+i)}-\frac{1}{2} i \tan ^{-1}(\sinh (x))",1,"(-1/2*I)*(ArcTan[Sinh[x]] + (I + Sinh[x])^(-1))","A",1
167,1,22,25,0.0341858,"\int \frac{\text{sech}^2(x)}{i+\sinh (x)} \, dx","Integrate[Sech[x]^2/(I + Sinh[x]),x]","-\frac{1}{3} i \left(2 \tanh (x)+\frac{\text{sech}(x)}{\sinh (x)+i}\right)","-\frac{2}{3} i \tanh (x)-\frac{i \text{sech}(x)}{3 (\sinh (x)+i)}",1,"(-1/3*I)*(Sech[x]/(I + Sinh[x]) + 2*Tanh[x])","A",1
168,1,61,52,0.0450091,"\int \frac{\text{sech}^3(x)}{i+\sinh (x)} \, dx","Integrate[Sech[x]^3/(I + Sinh[x]),x]","-\frac{i \text{sech}^2(x) \left(3 \sinh ^3(x) \tan ^{-1}(\sinh (x))+\sinh ^2(x) \left(3+3 i \tan ^{-1}(\sinh (x))\right)+3 \sinh (x) \left(\tan ^{-1}(\sinh (x))+i\right)+3 i \tan ^{-1}(\sinh (x))+2\right)}{8 (\sinh (x)+i)}","\frac{i}{8 (-\sinh (x)+i)}-\frac{i}{4 (\sinh (x)+i)}+\frac{1}{8 (\sinh (x)+i)^2}-\frac{3}{8} i \tan ^{-1}(\sinh (x))",1,"((-1/8*I)*Sech[x]^2*(2 + (3*I)*ArcTan[Sinh[x]] + 3*(I + ArcTan[Sinh[x]])*Sinh[x] + (3 + (3*I)*ArcTan[Sinh[x]])*Sinh[x]^2 + 3*ArcTan[Sinh[x]]*Sinh[x]^3))/(I + Sinh[x])","A",1
169,1,35,37,0.0687526,"\int \frac{\text{sech}^4(x)}{i+\sinh (x)} \, dx","Integrate[Sech[x]^4/(I + Sinh[x]),x]","-\frac{1}{15} i \left(8 \tanh ^3(x)+\frac{3 \text{sech}^3(x)}{\sinh (x)+i}+12 \tanh (x) \text{sech}^2(x)\right)","\frac{4}{15} i \tanh ^3(x)-\frac{4}{5} i \tanh (x)-\frac{i \text{sech}^3(x)}{5 (\sinh (x)+i)}",1,"(-1/15*I)*((3*Sech[x]^3)/(I + Sinh[x]) + 12*Sech[x]^2*Tanh[x] + 8*Tanh[x]^3)","A",1
170,1,94,80,0.0717027,"\int \frac{\text{sech}^5(x)}{i+\sinh (x)} \, dx","Integrate[Sech[x]^5/(I + Sinh[x]),x]","-\frac{i \text{sech}^4(x) \left(15 \sinh ^5(x) \tan ^{-1}(\sinh (x))+15 \sinh ^4(x) \left(1+i \tan ^{-1}(\sinh (x))\right)+15 \sinh ^3(x) \left(2 \tan ^{-1}(\sinh (x))+i\right)+5 \sinh ^2(x) \left(5+6 i \tan ^{-1}(\sinh (x))\right)+5 \sinh (x) \left(3 \tan ^{-1}(\sinh (x))+5 i\right)+15 i \tan ^{-1}(\sinh (x))+8\right)}{48 (\sinh (x)+i)}","\frac{i}{8 (-\sinh (x)+i)}-\frac{3 i}{16 (\sinh (x)+i)}-\frac{1}{32 (-\sinh (x)+i)^2}+\frac{3}{32 (\sinh (x)+i)^2}+\frac{i}{24 (\sinh (x)+i)^3}-\frac{5}{16} i \tan ^{-1}(\sinh (x))",1,"((-1/48*I)*Sech[x]^4*(8 + (15*I)*ArcTan[Sinh[x]] + 5*(5*I + 3*ArcTan[Sinh[x]])*Sinh[x] + 5*(5 + (6*I)*ArcTan[Sinh[x]])*Sinh[x]^2 + 15*(I + 2*ArcTan[Sinh[x]])*Sinh[x]^3 + 15*(1 + I*ArcTan[Sinh[x]])*Sinh[x]^4 + 15*ArcTan[Sinh[x]]*Sinh[x]^5))/(I + Sinh[x])","A",1
171,1,121,40,0.1883819,"\int \frac{\cosh ^6(x)}{(i+\sinh (x))^2} \, dx","Integrate[Cosh[x]^6/(I + Sinh[x])^2,x]","-\frac{i \cosh ^7(x) \left(6 \sinh ^4(x)-10 i \sinh ^3(x)+7 \sinh ^2(x)-25 i \sinh (x)+\frac{30 \sqrt{1-i \sinh (x)} \sin ^{-1}\left(\frac{\sqrt{1-i \sinh (x)}}{\sqrt{2}}\right)}{\sqrt{1+i \sinh (x)}}+16\right)}{24 \left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right)^8 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)^6}","-\frac{5 x}{8}-\frac{5}{12} i \cosh ^3(x)+\frac{\cosh ^5(x)}{4 (\sinh (x)+i)}-\frac{5}{8} \sinh (x) \cosh (x)",1,"((-1/24*I)*Cosh[x]^7*(16 + (30*ArcSin[Sqrt[1 - I*Sinh[x]]/Sqrt[2]]*Sqrt[1 - I*Sinh[x]])/Sqrt[1 + I*Sinh[x]] - (25*I)*Sinh[x] + 7*Sinh[x]^2 - (10*I)*Sinh[x]^3 + 6*Sinh[x]^4))/((Cosh[x/2] - I*Sinh[x/2])^8*(Cosh[x/2] + I*Sinh[x/2])^6)","B",1
172,1,18,14,0.0197601,"\int \frac{\cosh ^5(x)}{(i+\sinh (x))^2} \, dx","Integrate[Cosh[x]^5/(I + Sinh[x])^2,x]","\frac{1}{6} \sinh (x) (-6 i \sinh (x)+\cosh (2 x)-7)","-\frac{1}{3} (-\sinh (x)+i)^3",1,"((-7 + Cosh[2*x] - (6*I)*Sinh[x])*Sinh[x])/6","A",1
173,1,46,30,0.0783792,"\int \frac{\cosh ^4(x)}{(i+\sinh (x))^2} \, dx","Integrate[Cosh[x]^4/(I + Sinh[x])^2,x]","\frac{1}{2} (\sinh (x)-4 i) \cosh (x)-3 i \sqrt{\cosh ^2(x)} \text{sech}(x) \sin ^{-1}\left(\frac{\sqrt{1-i \sinh (x)}}{\sqrt{2}}\right)","-\frac{3 x}{2}-\frac{3}{2} i \cosh (x)+\frac{\cosh ^3(x)}{2 (\sinh (x)+i)}",1,"(-3*I)*ArcSin[Sqrt[1 - I*Sinh[x]]/Sqrt[2]]*Sqrt[Cosh[x]^2]*Sech[x] + (Cosh[x]*(-4*I + Sinh[x]))/2","A",1
174,1,14,14,0.0128457,"\int \frac{\cosh ^3(x)}{(i+\sinh (x))^2} \, dx","Integrate[Cosh[x]^3/(I + Sinh[x])^2,x]","\sinh (x)-2 i \log (\sinh (x)+i)","\sinh (x)-2 i \log (\sinh (x)+i)",1,"(-2*I)*Log[I + Sinh[x]] + Sinh[x]","A",1
175,1,69,14,0.0548685,"\int \frac{\cosh ^2(x)}{(i+\sinh (x))^2} \, dx","Integrate[Cosh[x]^2/(I + Sinh[x])^2,x]","\frac{2 \cosh ^3(x) \left(-1-\frac{\sqrt{1-i \sinh (x)} \sin ^{-1}\left(\frac{\sqrt{1-i \sinh (x)}}{\sqrt{2}}\right)}{\sqrt{1+i \sinh (x)}}\right)}{(\sinh (x)-i) (\sinh (x)+i)^2}","x-\frac{2 \cosh (x)}{\sinh (x)+i}",1,"(2*Cosh[x]^3*(-1 - (ArcSin[Sqrt[1 - I*Sinh[x]]/Sqrt[2]]*Sqrt[1 - I*Sinh[x]])/Sqrt[1 + I*Sinh[x]]))/((-I + Sinh[x])*(I + Sinh[x])^2)","B",1
176,1,10,10,0.0103625,"\int \frac{\cosh (x)}{(i+\sinh (x))^2} \, dx","Integrate[Cosh[x]/(I + Sinh[x])^2,x]","-\frac{1}{\sinh (x)+i}","-\frac{1}{\sinh (x)+i}",1,"-(I + Sinh[x])^(-1)","A",1
177,1,26,34,0.0438056,"\int \frac{\text{sech}(x)}{(i+\sinh (x))^2} \, dx","Integrate[Sech[x]/(I + Sinh[x])^2,x]","\frac{1}{4} \left(-\tan ^{-1}(\sinh (x))-\frac{\sinh (x)+2 i}{(\sinh (x)+i)^2}\right)","-\frac{1}{4 (\sinh (x)+i)}-\frac{i}{4 (\sinh (x)+i)^2}-\frac{1}{4} \tan ^{-1}(\sinh (x))",1,"(-ArcTan[Sinh[x]] - (2*I + Sinh[x])/(I + Sinh[x])^2)/4","A",1
178,1,31,37,0.0218306,"\int \frac{\text{sech}^2(x)}{(i+\sinh (x))^2} \, dx","Integrate[Sech[x]^2/(I + Sinh[x])^2,x]","-\frac{\text{sech}(x) (-5 \sinh (x)+\sinh (3 x)+4 i \cosh (2 x))}{10 (\sinh (x)+i)^2}","-\frac{2 \tanh (x)}{5}-\frac{\text{sech}(x)}{5 (\sinh (x)+i)}-\frac{i \text{sech}(x)}{5 (\sinh (x)+i)^2}",1,"-1/10*(Sech[x]*((4*I)*Cosh[2*x] - 5*Sinh[x] + Sinh[3*x]))/(I + Sinh[x])^2","A",1
179,1,68,60,0.0484954,"\int \frac{\text{sech}^3(x)}{(i+\sinh (x))^2} \, dx","Integrate[Sech[x]^3/(I + Sinh[x])^2,x]","-\frac{\text{sech}^2(x) \left(6 i \sinh ^2(x)+3 \sinh ^4(x) \tan ^{-1}(\sinh (x))+\sinh ^3(x) \left(3+6 i \tan ^{-1}(\sinh (x))\right)+\sinh (x) \left(-1+6 i \tan ^{-1}(\sinh (x))\right)-3 \tan ^{-1}(\sinh (x))+4 i\right)}{12 (\sinh (x)+i)^2}","\frac{1}{16 (-\sinh (x)+i)}-\frac{3}{16 (\sinh (x)+i)}-\frac{i}{8 (\sinh (x)+i)^2}+\frac{1}{12 (\sinh (x)+i)^3}-\frac{1}{4} \tan ^{-1}(\sinh (x))",1,"-1/12*(Sech[x]^2*(4*I - 3*ArcTan[Sinh[x]] + (-1 + (6*I)*ArcTan[Sinh[x]])*Sinh[x] + (6*I)*Sinh[x]^2 + (3 + (6*I)*ArcTan[Sinh[x]])*Sinh[x]^3 + 3*ArcTan[Sinh[x]]*Sinh[x]^4))/(I + Sinh[x])^2","A",1
180,1,47,49,0.040046,"\int \frac{\text{sech}^4(x)}{(i+\sinh (x))^2} \, dx","Integrate[Sech[x]^4/(I + Sinh[x])^2,x]","-\frac{\text{sech}^3(x) (-14 \sinh (x)-3 \sinh (3 x)+\sinh (5 x)+8 i \cosh (2 x)+4 i \cosh (4 x))}{42 (\sinh (x)+i)^2}","\frac{4 \tanh ^3(x)}{21}-\frac{4 \tanh (x)}{7}-\frac{\text{sech}^3(x)}{7 (\sinh (x)+i)}-\frac{i \text{sech}^3(x)}{7 (\sinh (x)+i)^2}",1,"-1/42*(Sech[x]^3*((8*I)*Cosh[2*x] + (4*I)*Cosh[4*x] - 14*Sinh[x] - 3*Sinh[3*x] + Sinh[5*x]))/(I + Sinh[x])^2","A",1
181,1,45,28,0.0896323,"\int \frac{\cosh ^3(x)}{(1+i \sinh (x))^3} \, dx","Integrate[Cosh[x]^3/(1 + I*Sinh[x])^3,x]","\frac{2 i \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+\log (\cosh (x))+\sinh (x) \left(-2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+i \log (\cosh (x))\right)+2}{\sinh (x)-i}","\frac{2 i}{1+i \sinh (x)}+i \log (-\sinh (x)+i)",1,"(2 + (2*I)*ArcTan[Tanh[x/2]] + Log[Cosh[x]] + (-2*ArcTan[Tanh[x/2]] + I*Log[Cosh[x]])*Sinh[x])/(-I + Sinh[x])","A",1
182,1,40,20,0.0651163,"\int \frac{\cosh ^2(x)}{(1+i \sinh (x))^3} \, dx","Integrate[Cosh[x]^2/(1 + I*Sinh[x])^3,x]","-\frac{i \left(\cosh \left(\frac{3 x}{2}\right)-3 \cosh \left(\frac{x}{2}\right)\right)}{3 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)^3}","\frac{i \cosh ^3(x)}{3 (1+i \sinh (x))^3}",1,"((-1/3*I)*(-3*Cosh[x/2] + Cosh[(3*x)/2]))/(Cosh[x/2] + I*Sinh[x/2])^3","A",1
183,1,14,16,0.0257786,"\int \frac{\cosh (x)}{(1+i \sinh (x))^3} \, dx","Integrate[Cosh[x]/(1 + I*Sinh[x])^3,x]","-\frac{i}{2 (\sinh (x)-i)^2}","\frac{i}{2 (1+i \sinh (x))^2}",1,"(-1/2*I)/(-I + Sinh[x])^2","A",1
184,1,45,26,0.0847161,"\int \frac{\cosh ^3(x)}{(1-i \sinh (x))^3} \, dx","Integrate[Cosh[x]^3/(1 - I*Sinh[x])^3,x]","\frac{-2 i \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+\log (\cosh (x))-2 \sinh (x) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)-i \sinh (x) \log (\cosh (x))+2}{\sinh (x)+i}","-\frac{2 i}{1-i \sinh (x)}-i \log (\sinh (x)+i)",1,"(2 - (2*I)*ArcTan[Tanh[x/2]] + Log[Cosh[x]] - 2*ArcTan[Tanh[x/2]]*Sinh[x] - I*Log[Cosh[x]]*Sinh[x])/(I + Sinh[x])","A",1
185,1,38,20,0.0642522,"\int \frac{\cosh ^2(x)}{(1-i \sinh (x))^3} \, dx","Integrate[Cosh[x]^2/(1 - I*Sinh[x])^3,x]","\frac{\cosh \left(\frac{3 x}{2}\right)-3 \cosh \left(\frac{x}{2}\right)}{3 \left(\sinh \left(\frac{x}{2}\right)+i \cosh \left(\frac{x}{2}\right)\right)^3}","-\frac{i \cosh ^3(x)}{3 (1-i \sinh (x))^3}",1,"(-3*Cosh[x/2] + Cosh[(3*x)/2])/(3*(I*Cosh[x/2] + Sinh[x/2])^3)","A",1
186,1,14,16,0.0273103,"\int \frac{\cosh (x)}{(1-i \sinh (x))^3} \, dx","Integrate[Cosh[x]/(1 - I*Sinh[x])^3,x]","\frac{i}{2 (\sinh (x)+i)^2}","-\frac{i}{2 (1-i \sinh (x))^2}",1,"(I/2)/(I + Sinh[x])^2","A",1
187,1,121,138,0.158729,"\int \frac{\cosh ^7(x)}{a+b \sinh (x)} \, dx","Integrate[Cosh[x]^7/(a + b*Sinh[x]),x]","\frac{30 b^2 \left(a^2+b^2\right)^2 \sinh ^2(x)+60 \left(a^2+b^2\right)^3 \log (a+b \sinh (x))+15 b^4 \left(a^2+b^2\right) \cosh ^4(x)-20 a b^3 \left(a^2+3 b^2\right) \sinh ^3(x)-60 a b \left(a^4+3 a^2 b^2+3 b^4\right) \sinh (x)-12 a b^5 \sinh ^5(x)+10 b^6 \cosh ^6(x)}{60 b^7}","\frac{\left(a^2+b^2\right)^3 \log (a+b \sinh (x))}{b^7}-\frac{a \left(a^2+3 b^2\right) \sinh ^3(x)}{3 b^4}+\frac{\left(a^2+3 b^2\right) \sinh ^4(x)}{4 b^3}-\frac{a \left(a^4+3 a^2 b^2+3 b^4\right) \sinh (x)}{b^6}+\frac{\left(a^4+3 a^2 b^2+3 b^4\right) \sinh ^2(x)}{2 b^5}-\frac{a \sinh ^5(x)}{5 b^2}+\frac{\sinh ^6(x)}{6 b}",1,"(15*b^4*(a^2 + b^2)*Cosh[x]^4 + 10*b^6*Cosh[x]^6 + 60*(a^2 + b^2)^3*Log[a + b*Sinh[x]] - 60*a*b*(a^4 + 3*a^2*b^2 + 3*b^4)*Sinh[x] + 30*b^2*(a^2 + b^2)^2*Sinh[x]^2 - 20*a*b^3*(a^2 + 3*b^2)*Sinh[x]^3 - 12*a*b^5*Sinh[x]^5)/(60*b^7)","A",1
188,1,463,145,5.8308403,"\int \frac{\cosh ^6(x)}{a+b \sinh (x)} \, dx","Integrate[Cosh[x]^6/(a + b*Sinh[x]),x]","\frac{\cosh (x) \left(8 b^2 \left(5 a^2+11 b^2\right) \sinh ^2(x)-15 a b \left(4 a^2+9 b^2\right) \sinh (x)-\frac{240 \left(a^2+b^2\right)^2 \tanh ^{-1}\left(\frac{\sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{-\frac{b (\sinh (x)-i)}{a+i b}}}\right)}{\sqrt{-\frac{b (\sinh (x)-i)}{a+i b}} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}+8 \left(15 a^4+35 a^2 b^2+23 b^4\right)-\frac{30 (-1)^{3/4} \sqrt{b} \left(8 a^4-4 i a^3 b+16 a^2 b^2-7 i a b^3+8 b^4\right) \sin ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{a-i b} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{b}}\right)}{\sqrt{a-i b} \sqrt{1+i \sinh (x)} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}-30 a b^3 \sinh ^3(x)+\frac{240 (a-i b)^{5/2} (a+i b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a-i b} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{a+i b} \sqrt{-\frac{b (\sinh (x)-i)}{a+i b}}}\right)}{\sqrt{-\frac{b (\sinh (x)-i)}{a+i b}} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}+24 b^4 \sinh ^4(x)\right)}{120 b^5}","-\frac{2 \left(a^2+b^2\right)^{5/2} \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b^6}+\frac{\cosh (x) \left(8 \left(a^2+b^2\right)^2-a b \left(4 a^2+7 b^2\right) \sinh (x)\right)}{8 b^5}+\frac{\cosh ^3(x) \left(4 \left(a^2+b^2\right)-3 a b \sinh (x)\right)}{12 b^3}-\frac{a x \left(8 a^4+20 a^2 b^2+15 b^4\right)}{8 b^6}+\frac{\cosh ^5(x)}{5 b}",1,"(Cosh[x]*(8*(15*a^4 + 35*a^2*b^2 + 23*b^4) - 15*a*b*(4*a^2 + 9*b^2)*Sinh[x] + 8*b^2*(5*a^2 + 11*b^2)*Sinh[x]^2 - 30*a*b^3*Sinh[x]^3 + 24*b^4*Sinh[x]^4 - (30*(-1)^(3/4)*Sqrt[b]*(8*a^4 - (4*I)*a^3*b + 16*a^2*b^2 - (7*I)*a*b^3 + 8*b^4)*ArcSin[((1/2 + I/2)*Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])/Sqrt[b]])/(Sqrt[a - I*b]*Sqrt[1 + I*Sinh[x]]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))]) - (240*(a^2 + b^2)^2*ArcTanh[Sqrt[-((b*(I + Sinh[x]))/(a - I*b))]/Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))]])/(Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))]) + (240*(a - I*b)^(5/2)*(a + I*b)^(3/2)*ArcTanh[(Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])/(Sqrt[a + I*b]*Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))])])/(Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])))/(120*b^5)","C",1
189,1,76,81,0.091117,"\int \frac{\cosh ^5(x)}{a+b \sinh (x)} \, dx","Integrate[Cosh[x]^5/(a + b*Sinh[x]),x]","\frac{6 b^2 \left(a^2+b^2\right) \sinh ^2(x)-12 a b \left(a^2+2 b^2\right) \sinh (x)+12 \left(a^2+b^2\right)^2 \log (a+b \sinh (x))-4 a b^3 \sinh ^3(x)+3 b^4 \cosh ^4(x)}{12 b^5}","\frac{\left(a^2+b^2\right)^2 \log (a+b \sinh (x))}{b^5}-\frac{a \left(a^2+2 b^2\right) \sinh (x)}{b^4}+\frac{\left(a^2+2 b^2\right) \sinh ^2(x)}{2 b^3}-\frac{a \sinh ^3(x)}{3 b^2}+\frac{\sinh ^4(x)}{4 b}",1,"(3*b^4*Cosh[x]^4 + 12*(a^2 + b^2)^2*Log[a + b*Sinh[x]] - 12*a*b*(a^2 + 2*b^2)*Sinh[x] + 6*b^2*(a^2 + b^2)*Sinh[x]^2 - 4*a*b^3*Sinh[x]^3)/(12*b^5)","A",1
190,1,553,97,2.2454816,"\int \frac{\cosh ^4(x)}{a+b \sinh (x)} \, dx","Integrate[Cosh[x]^4/(a + b*Sinh[x]),x]","\frac{\cosh ^3(x) \left(\sqrt{a+i b} \sqrt{-\frac{b (\sinh (x)-i)}{a+i b}} \left(2 \sqrt{a-i b} \left(3 a^2+4 b^2\right) \sqrt{1+i \sinh (x)} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}+(3-3 i) \sqrt{2} \sqrt{b} \left(2 a^2-i a b+2 b^2\right) \sin ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{a-i b} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{b}}\right)+2 b^2 \sqrt{a-i b} \sqrt{1+i \sinh (x)} \sinh ^2(x) \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}-3 a b \sqrt{a-i b} \sqrt{1+i \sinh (x)} \sinh (x) \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}\right)-12 \sqrt{a+i b} \left(a^2+b^2\right) \sqrt{a-i b} \sqrt{1+i \sinh (x)} \tanh ^{-1}\left(\frac{\sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{-\frac{b (\sinh (x)-i)}{a+i b}}}\right)+12 (a+i b) (a-i b)^2 \sqrt{1+i \sinh (x)} \tanh ^{-1}\left(\frac{\sqrt{a-i b} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{a+i b} \sqrt{-\frac{b (\sinh (x)-i)}{a+i b}}}\right)\right)}{6 b (a-i b)^{3/2} (a+i b)^{3/2} \sqrt{1+i \sinh (x)} \left(-\frac{b (\sinh (x)-i)}{a+i b}\right)^{3/2} \left(-\frac{b (\sinh (x)+i)}{a-i b}\right)^{3/2}}","-\frac{a x \left(2 a^2+3 b^2\right)}{2 b^4}-\frac{2 \left(a^2+b^2\right)^{3/2} \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b^4}+\frac{\cosh (x) \left(2 \left(a^2+b^2\right)-a b \sinh (x)\right)}{2 b^3}+\frac{\cosh ^3(x)}{3 b}",1,"(Cosh[x]^3*(-12*Sqrt[a - I*b]*Sqrt[a + I*b]*(a^2 + b^2)*ArcTanh[Sqrt[-((b*(I + Sinh[x]))/(a - I*b))]/Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))]]*Sqrt[1 + I*Sinh[x]] + 12*(a - I*b)^2*(a + I*b)*ArcTanh[(Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])/(Sqrt[a + I*b]*Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))])]*Sqrt[1 + I*Sinh[x]] + Sqrt[a + I*b]*Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))]*((3 - 3*I)*Sqrt[2]*Sqrt[b]*(2*a^2 - I*a*b + 2*b^2)*ArcSin[((1/2 + I/2)*Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])/Sqrt[b]] + 2*Sqrt[a - I*b]*(3*a^2 + 4*b^2)*Sqrt[1 + I*Sinh[x]]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))] - 3*a*Sqrt[a - I*b]*b*Sqrt[1 + I*Sinh[x]]*Sinh[x]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))] + 2*Sqrt[a - I*b]*b^2*Sqrt[1 + I*Sinh[x]]*Sinh[x]^2*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])))/(6*(a - I*b)^(3/2)*(a + I*b)^(3/2)*b*Sqrt[1 + I*Sinh[x]]*(-((b*(-I + Sinh[x]))/(a + I*b)))^(3/2)*(-((b*(I + Sinh[x]))/(a - I*b)))^(3/2))","C",1
191,1,38,38,0.0357986,"\int \frac{\cosh ^3(x)}{a+b \sinh (x)} \, dx","Integrate[Cosh[x]^3/(a + b*Sinh[x]),x]","-\frac{-\left(a^2+b^2\right) \log (a+b \sinh (x))+a b \sinh (x)-\frac{1}{2} b^2 \sinh ^2(x)}{b^3}","\frac{\left(a^2+b^2\right) \log (a+b \sinh (x))}{b^3}-\frac{a \sinh (x)}{b^2}+\frac{\sinh ^2(x)}{2 b}",1,"-((-((a^2 + b^2)*Log[a + b*Sinh[x]]) + a*b*Sinh[x] - (b^2*Sinh[x]^2)/2)/b^3)","A",1
192,1,396,54,0.7679019,"\int \frac{\cosh ^2(x)}{a+b \sinh (x)} \, dx","Integrate[Cosh[x]^2/(a + b*Sinh[x]),x]","\frac{\cosh (x) \left(\sqrt{a+i b} \sqrt{-\frac{b (\sinh (x)-i)}{a+i b}} \left(\sqrt{a-i b} \sqrt{1+i \sinh (x)} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}-2 (-1)^{3/4} \sqrt{b} \sin ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{a-i b} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{b}}\right)\right)-2 \sqrt{a-i b} \sqrt{a+i b} \sqrt{1+i \sinh (x)} \tanh ^{-1}\left(\frac{\sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{-\frac{b (\sinh (x)-i)}{a+i b}}}\right)+2 (a-i b) \sqrt{1+i \sinh (x)} \tanh ^{-1}\left(\frac{\sqrt{a-i b} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{a+i b} \sqrt{-\frac{b (\sinh (x)-i)}{a+i b}}}\right)\right)}{b \sqrt{a-i b} \sqrt{a+i b} \sqrt{1+i \sinh (x)} \sqrt{-\frac{b (\sinh (x)-i)}{a+i b}} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}","-\frac{2 \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b^2}-\frac{a x}{b^2}+\frac{\cosh (x)}{b}",1,"(Cosh[x]*(-2*Sqrt[a - I*b]*Sqrt[a + I*b]*ArcTanh[Sqrt[-((b*(I + Sinh[x]))/(a - I*b))]/Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))]]*Sqrt[1 + I*Sinh[x]] + 2*(a - I*b)*ArcTanh[(Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])/(Sqrt[a + I*b]*Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))])]*Sqrt[1 + I*Sinh[x]] + Sqrt[a + I*b]*Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))]*(-2*(-1)^(3/4)*Sqrt[b]*ArcSin[((1/2 + I/2)*Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])/Sqrt[b]] + Sqrt[a - I*b]*Sqrt[1 + I*Sinh[x]]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])))/(Sqrt[a - I*b]*Sqrt[a + I*b]*b*Sqrt[1 + I*Sinh[x]]*Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])","C",1
193,1,11,11,0.0059857,"\int \frac{\cosh (x)}{a+b \sinh (x)} \, dx","Integrate[Cosh[x]/(a + b*Sinh[x]),x]","\frac{\log (a+b \sinh (x))}{b}","\frac{\log (a+b \sinh (x))}{b}",1,"Log[a + b*Sinh[x]]/b","A",1
194,1,99,48,0.095694,"\int \frac{\text{sech}(x)}{a+b \sinh (x)} \, dx","Integrate[Sech[x]/(a + b*Sinh[x]),x]","-\frac{b \left(\left(\sqrt{-b^2}-a\right) \log \left(\sqrt{-b^2}-b \sinh (x)\right)-2 \sqrt{-b^2} \log (a+b \sinh (x))+\left(a+\sqrt{-b^2}\right) \log \left(\sqrt{-b^2}+b \sinh (x)\right)\right)}{2 \sqrt{-b^2} \left(a^2+b^2\right)}","\frac{b \log (a+b \sinh (x))}{a^2+b^2}+\frac{a \tan ^{-1}(\sinh (x))}{a^2+b^2}-\frac{b \log (\cosh (x))}{a^2+b^2}",1,"-1/2*(b*((-a + Sqrt[-b^2])*Log[Sqrt[-b^2] - b*Sinh[x]] - 2*Sqrt[-b^2]*Log[a + b*Sinh[x]] + (a + Sqrt[-b^2])*Log[Sqrt[-b^2] + b*Sinh[x]]))/(Sqrt[-b^2]*(a^2 + b^2))","B",1
195,1,67,59,0.1697204,"\int \frac{\text{sech}^2(x)}{a+b \sinh (x)} \, dx","Integrate[Sech[x]^2/(a + b*Sinh[x]),x]","\frac{\frac{2 b^2 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+a \tanh (x)+b \text{sech}(x)}{a^2+b^2}","\frac{\text{sech}(x) (a \sinh (x)+b)}{a^2+b^2}-\frac{2 b^2 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{3/2}}",1,"((2*b^2*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + b*Sech[x] + a*Tanh[x])/(a^2 + b^2)","A",1
196,1,77,87,0.1293713,"\int \frac{\text{sech}^3(x)}{a+b \sinh (x)} \, dx","Integrate[Sech[x]^3/(a + b*Sinh[x]),x]","\frac{b \left(a^2+b^2\right) \text{sech}^2(x)+2 a \left(a^2+3 b^2\right) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+a \left(a^2+b^2\right) \tanh (x) \text{sech}(x)+2 b^3 (\log (a+b \sinh (x))-\log (\cosh (x)))}{2 \left(a^2+b^2\right)^2}","\frac{a \left(a^2+3 b^2\right) \tan ^{-1}(\sinh (x))}{2 \left(a^2+b^2\right)^2}+\frac{\text{sech}^2(x) (a \sinh (x)+b)}{2 \left(a^2+b^2\right)}+\frac{b^3 \log (a+b \sinh (x))}{\left(a^2+b^2\right)^2}-\frac{b^3 \log (\cosh (x))}{\left(a^2+b^2\right)^2}",1,"(2*a*(a^2 + 3*b^2)*ArcTan[Tanh[x/2]] + 2*b^3*(-Log[Cosh[x]] + Log[a + b*Sinh[x]]) + b*(a^2 + b^2)*Sech[x]^2 + a*(a^2 + b^2)*Sech[x]*Tanh[x])/(2*(a^2 + b^2)^2)","A",1
197,1,102,100,0.3434192,"\int \frac{\text{sech}^4(x)}{a+b \sinh (x)} \, dx","Integrate[Sech[x]^4/(a + b*Sinh[x]),x]","\frac{a \left(2 a^2+5 b^2\right) \tanh (x)+\left(a^2+b^2\right) \text{sech}^3(x) (a \sinh (x)+b)+\frac{6 b^4 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+3 b^3 \text{sech}(x)}{3 \left(a^2+b^2\right)^2}","\frac{\text{sech}^3(x) (a \sinh (x)+b)}{3 \left(a^2+b^2\right)}-\frac{2 b^4 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{5/2}}+\frac{\text{sech}(x) \left(a \left(2 a^2+5 b^2\right) \sinh (x)+3 b^3\right)}{3 \left(a^2+b^2\right)^2}",1,"((6*b^4*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + 3*b^3*Sech[x] + (a^2 + b^2)*Sech[x]^3*(b + a*Sinh[x]) + a*(2*a^2 + 5*b^2)*Tanh[x])/(3*(a^2 + b^2)^2)","A",1
198,1,135,135,0.2363946,"\int \frac{\text{sech}^5(x)}{a+b \sinh (x)} \, dx","Integrate[Sech[x]^5/(a + b*Sinh[x]),x]","\frac{2 b \left(a^2+b^2\right)^2 \text{sech}^4(x)+2 a \left(a^2+b^2\right)^2 \tanh (x) \text{sech}^3(x)+4 b^3 \left(a^2+b^2\right) \text{sech}^2(x)+\left(6 a^5+20 a^3 b^2+30 a b^4\right) \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+a \left(3 a^4+10 a^2 b^2+7 b^4\right) \tanh (x) \text{sech}(x)+8 b^5 (\log (a+b \sinh (x))-\log (\cosh (x)))}{8 \left(a^2+b^2\right)^3}","\frac{\text{sech}^4(x) (a \sinh (x)+b)}{4 \left(a^2+b^2\right)}+\frac{b^5 \log (a+b \sinh (x))}{\left(a^2+b^2\right)^3}-\frac{b^5 \log (\cosh (x))}{\left(a^2+b^2\right)^3}+\frac{\text{sech}^2(x) \left(a \left(3 a^2+7 b^2\right) \sinh (x)+4 b^3\right)}{8 \left(a^2+b^2\right)^2}+\frac{a \left(3 a^4+10 a^2 b^2+15 b^4\right) \tan ^{-1}(\sinh (x))}{8 \left(a^2+b^2\right)^3}",1,"((6*a^5 + 20*a^3*b^2 + 30*a*b^4)*ArcTan[Tanh[x/2]] + 8*b^5*(-Log[Cosh[x]] + Log[a + b*Sinh[x]]) + 4*b^3*(a^2 + b^2)*Sech[x]^2 + 2*b*(a^2 + b^2)^2*Sech[x]^4 + a*(3*a^4 + 10*a^2*b^2 + 7*b^4)*Sech[x]*Tanh[x] + 2*a*(a^2 + b^2)^2*Sech[x]^3*Tanh[x])/(8*(a^2 + b^2)^3)","A",1
199,1,146,146,0.4496642,"\int \frac{\text{sech}^6(x)}{a+b \sinh (x)} \, dx","Integrate[Sech[x]^6/(a + b*Sinh[x]),x]","\frac{3 \left(a^2+b^2\right)^2 \text{sech}^5(x) (a \sinh (x)+b)+\frac{30 b^6 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+\left(a^2+b^2\right) \text{sech}^3(x) \left(a \left(4 a^2+9 b^2\right) \sinh (x)+5 b^3\right)+a \left(8 a^4+26 a^2 b^2+33 b^4\right) \tanh (x)+15 b^5 \text{sech}(x)}{15 \left(a^2+b^2\right)^3}","\frac{\text{sech}^5(x) (a \sinh (x)+b)}{5 \left(a^2+b^2\right)}-\frac{2 b^6 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{7/2}}+\frac{\text{sech}^3(x) \left(a \left(4 a^2+9 b^2\right) \sinh (x)+5 b^3\right)}{15 \left(a^2+b^2\right)^2}+\frac{\text{sech}(x) \left(a \left(8 a^4+26 a^2 b^2+33 b^4\right) \sinh (x)+15 b^5\right)}{15 \left(a^2+b^2\right)^3}",1,"((30*b^6*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + 15*b^5*Sech[x] + 3*(a^2 + b^2)^2*Sech[x]^5*(b + a*Sinh[x]) + (a^2 + b^2)*Sech[x]^3*(5*b^3 + a*(4*a^2 + 9*b^2)*Sinh[x]) + a*(8*a^4 + 26*a^2*b^2 + 33*b^4)*Tanh[x])/(15*(a^2 + b^2)^3)","A",1
200,1,660,94,4.4615469,"\int \frac{\cosh ^4(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Cosh[x]^4/(a + b*Sinh[x])^2,x]","\frac{\cosh ^3(x) \left(-12 a \left(a^2+b^2\right) \sqrt{1+i \sinh (x)} (a+b \sinh (x)) \tanh ^{-1}\left(\frac{\sqrt{a-i b} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{a+i b} \sqrt{-\frac{b (\sinh (x)-i)}{a+i b}}}\right)+\sqrt{a+i b} \sqrt{-\frac{b (\sinh (x)-i)}{a+i b}} \left(6 (-1)^{3/4} a \sqrt{b} \left(2 a^2+i a b+b^2\right) \sin ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{a-i b} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{b}}\right)+6 (-1)^{3/4} b^{3/2} \left(2 a^2+i a b+b^2\right) \sinh (x) \sin ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{a-i b} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{b}}\right)-2 \sqrt{a-i b} \left(3 a^3+3 i a^2 b+a b^2+i b^3\right) \sqrt{1+i \sinh (x)} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}+b^2 \sqrt{a-i b} (a+i b) \sqrt{1+i \sinh (x)} \sinh ^2(x) \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}-3 a b \sqrt{a-i b} (a+i b) \sqrt{1+i \sinh (x)} \sinh (x) \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}\right)+12 a \sqrt{a-i b} (a+i b)^{3/2} \sqrt{1+i \sinh (x)} (a+b \sinh (x)) \tanh ^{-1}\left(\frac{\sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{-\frac{b (\sinh (x)-i)}{a+i b}}}\right)\right)}{2 b (a-i b)^{3/2} (a+i b)^{5/2} \sqrt{1+i \sinh (x)} \left(-\frac{b (\sinh (x)-i)}{a+i b}\right)^{3/2} \left(-\frac{b (\sinh (x)+i)}{a-i b}\right)^{3/2} (a+b \sinh (x))}","\frac{3 x \left(2 a^2+b^2\right)}{2 b^4}+\frac{6 a \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b^4}-\frac{3 \cosh (x) (2 a-b \sinh (x))}{2 b^3}-\frac{\cosh ^3(x)}{b (a+b \sinh (x))}",1,"(Cosh[x]^3*(12*a*Sqrt[a - I*b]*(a + I*b)^(3/2)*ArcTanh[Sqrt[-((b*(I + Sinh[x]))/(a - I*b))]/Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))]]*Sqrt[1 + I*Sinh[x]]*(a + b*Sinh[x]) - 12*a*(a^2 + b^2)*ArcTanh[(Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])/(Sqrt[a + I*b]*Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))])]*Sqrt[1 + I*Sinh[x]]*(a + b*Sinh[x]) + Sqrt[a + I*b]*Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))]*(6*(-1)^(3/4)*a*Sqrt[b]*(2*a^2 + I*a*b + b^2)*ArcSin[((1/2 + I/2)*Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])/Sqrt[b]] + 6*(-1)^(3/4)*b^(3/2)*(2*a^2 + I*a*b + b^2)*ArcSin[((1/2 + I/2)*Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])/Sqrt[b]]*Sinh[x] - 2*Sqrt[a - I*b]*(3*a^3 + (3*I)*a^2*b + a*b^2 + I*b^3)*Sqrt[1 + I*Sinh[x]]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))] - 3*a*Sqrt[a - I*b]*(a + I*b)*b*Sqrt[1 + I*Sinh[x]]*Sinh[x]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))] + Sqrt[a - I*b]*(a + I*b)*b^2*Sqrt[1 + I*Sinh[x]]*Sinh[x]^2*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])))/(2*(a - I*b)^(3/2)*(a + I*b)^(5/2)*b*Sqrt[1 + I*Sinh[x]]*(-((b*(-I + Sinh[x]))/(a + I*b)))^(3/2)*(-((b*(I + Sinh[x]))/(a - I*b)))^(3/2)*(a + b*Sinh[x]))","C",1
201,1,37,40,0.0672758,"\int \frac{\cosh ^3(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Cosh[x]^3/(a + b*Sinh[x])^2,x]","-\frac{\frac{a^2+b^2}{a+b \sinh (x)}+2 a \log (a+b \sinh (x))-b \sinh (x)}{b^3}","-\frac{a^2+b^2}{b^3 (a+b \sinh (x))}-\frac{2 a \log (a+b \sinh (x))}{b^3}+\frac{\sinh (x)}{b^2}",1,"-((2*a*Log[a + b*Sinh[x]] - b*Sinh[x] + (a^2 + b^2)/(a + b*Sinh[x]))/b^3)","A",1
202,1,502,62,1.7905086,"\int \frac{\cosh ^2(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Cosh[x]^2/(a + b*Sinh[x])^2,x]","\frac{\cosh (x) \left(\sqrt{a+i b} \sqrt{-\frac{b (\sinh (x)-i)}{a+i b}} \left(-\sqrt{a-i b} \left(a^2+b^2\right) \sqrt{1+i \sinh (x)} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}+2 \sqrt[4]{-1} b^{3/2} (b+i a) \sinh (x) \sin ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{a-i b} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{b}}\right)+2 \sqrt[4]{-1} a \sqrt{b} (b+i a) \sin ^{-1}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{a-i b} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{b}}\right)\right)+2 a \sqrt{a-i b} \sqrt{a+i b} \sqrt{1+i \sinh (x)} (a+b \sinh (x)) \tanh ^{-1}\left(\frac{\sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{-\frac{b (\sinh (x)-i)}{a+i b}}}\right)-2 a (a-i b) \sqrt{1+i \sinh (x)} (a+b \sinh (x)) \tanh ^{-1}\left(\frac{\sqrt{a-i b} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}}}{\sqrt{a+i b} \sqrt{-\frac{b (\sinh (x)-i)}{a+i b}}}\right)\right)}{b (a-i b)^{3/2} (a+i b)^{3/2} \sqrt{1+i \sinh (x)} \sqrt{-\frac{b (\sinh (x)-i)}{a+i b}} \sqrt{-\frac{b (\sinh (x)+i)}{a-i b}} (a+b \sinh (x))}","\frac{2 a \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{b^2 \sqrt{a^2+b^2}}-\frac{\cosh (x)}{b (a+b \sinh (x))}+\frac{x}{b^2}",1,"(Cosh[x]*(2*a*Sqrt[a - I*b]*Sqrt[a + I*b]*ArcTanh[Sqrt[-((b*(I + Sinh[x]))/(a - I*b))]/Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))]]*Sqrt[1 + I*Sinh[x]]*(a + b*Sinh[x]) - 2*a*(a - I*b)*ArcTanh[(Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])/(Sqrt[a + I*b]*Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))])]*Sqrt[1 + I*Sinh[x]]*(a + b*Sinh[x]) + Sqrt[a + I*b]*Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))]*(2*(-1)^(1/4)*a*Sqrt[b]*(I*a + b)*ArcSin[((1/2 + I/2)*Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])/Sqrt[b]] + 2*(-1)^(1/4)*b^(3/2)*(I*a + b)*ArcSin[((1/2 + I/2)*Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])/Sqrt[b]]*Sinh[x] - Sqrt[a - I*b]*(a^2 + b^2)*Sqrt[1 + I*Sinh[x]]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))])))/((a - I*b)^(3/2)*(a + I*b)^(3/2)*b*Sqrt[1 + I*Sinh[x]]*Sqrt[-((b*(-I + Sinh[x]))/(a + I*b))]*Sqrt[-((b*(I + Sinh[x]))/(a - I*b))]*(a + b*Sinh[x]))","C",1
203,1,13,13,0.0119501,"\int \frac{\cosh (x)}{(a+b \sinh (x))^2} \, dx","Integrate[Cosh[x]/(a + b*Sinh[x])^2,x]","-\frac{1}{b (a+b \sinh (x))}","-\frac{1}{b (a+b \sinh (x))}",1,"-(1/(b*(a + b*Sinh[x])))","A",1
204,1,121,79,0.4558901,"\int \frac{\text{sech}(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Sech[x]/(a + b*Sinh[x])^2,x]","-\frac{b \left(\frac{2 \left(a^2+b^2\right)}{a+b \sinh (x)}+\left(\frac{b^2-a^2}{\sqrt{-b^2}}+2 a\right) \log \left(\sqrt{-b^2}-b \sinh (x)\right)+\left(\frac{a^2-b^2}{\sqrt{-b^2}}+2 a\right) \log \left(\sqrt{-b^2}+b \sinh (x)\right)-4 a \log (a+b \sinh (x))\right)}{2 \left(a^2+b^2\right)^2}","-\frac{b}{\left(a^2+b^2\right) (a+b \sinh (x))}+\frac{2 a b \log (a+b \sinh (x))}{\left(a^2+b^2\right)^2}+\frac{\left(a^2-b^2\right) \tan ^{-1}(\sinh (x))}{\left(a^2+b^2\right)^2}-\frac{2 a b \log (\cosh (x))}{\left(a^2+b^2\right)^2}",1,"-1/2*(b*((2*a + (-a^2 + b^2)/Sqrt[-b^2])*Log[Sqrt[-b^2] - b*Sinh[x]] - 4*a*Log[a + b*Sinh[x]] + (2*a + (a^2 - b^2)/Sqrt[-b^2])*Log[Sqrt[-b^2] + b*Sinh[x]] + (2*(a^2 + b^2))/(a + b*Sinh[x])))/(a^2 + b^2)^2","A",1
205,1,94,93,0.2348615,"\int \frac{\text{sech}^2(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Sech[x]^2/(a + b*Sinh[x])^2,x]","\frac{\frac{6 a b^2 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+a^2 \tanh (x)-\frac{b^3 \cosh (x)}{a+b \sinh (x)}+2 a b \text{sech}(x)-b^2 \tanh (x)}{\left(a^2+b^2\right)^2}","-\frac{6 a b^2 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{5/2}}-\frac{b \text{sech}(x)}{\left(a^2+b^2\right) (a+b \sinh (x))}+\frac{\text{sech}(x) \left(\left(a^2-2 b^2\right) \sinh (x)+3 a b\right)}{\left(a^2+b^2\right)^2}",1,"((6*a*b^2*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + 2*a*b*Sech[x] - (b^3*Cosh[x])/(a + b*Sinh[x]) + a^2*Tanh[x] - b^2*Tanh[x])/(a^2 + b^2)^2","A",1
206,1,260,136,2.4376135,"\int \frac{\text{sech}^3(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Sech[x]^3/(a + b*Sinh[x])^2,x]","-\frac{\frac{b \left(\frac{2 a \left(a^2+b^2\right) \left(\left(\sqrt{-b^2}-a\right) \log \left(\sqrt{-b^2}-b \sinh (x)\right)-2 \sqrt{-b^2} \log (a+b \sinh (x))+\left(a+\sqrt{-b^2}\right) \log \left(\sqrt{-b^2}+b \sinh (x)\right)\right)}{\sqrt{-b^2}}+\left(3 b^2-a^2\right) \left(\frac{2 \left(a^2+b^2\right)}{a+b \sinh (x)}+\left(\frac{b^2-a^2}{\sqrt{-b^2}}+2 a\right) \log \left(\sqrt{-b^2}-b \sinh (x)\right)+\left(\frac{a^2-b^2}{\sqrt{-b^2}}+2 a\right) \log \left(\sqrt{-b^2}+b \sinh (x)\right)-4 a \log (a+b \sinh (x))\right)\right)}{\left(a^2+b^2\right)^2}-\frac{2 \text{sech}^2(x) (a \sinh (x)+b)}{a+b \sinh (x)}}{4 \left(a^2+b^2\right)}","\frac{b \left(a^2-3 b^2\right)}{2 \left(a^2+b^2\right)^2 (a+b \sinh (x))}+\frac{\text{sech}^2(x) (a \sinh (x)+b)}{2 \left(a^2+b^2\right) (a+b \sinh (x))}+\frac{4 a b^3 \log (a+b \sinh (x))}{\left(a^2+b^2\right)^3}-\frac{4 a b^3 \log (\cosh (x))}{\left(a^2+b^2\right)^3}+\frac{\left(a^4+6 a^2 b^2-3 b^4\right) \tan ^{-1}(\sinh (x))}{2 \left(a^2+b^2\right)^3}",1,"-1/4*((-2*Sech[x]^2*(b + a*Sinh[x]))/(a + b*Sinh[x]) + (b*((2*a*(a^2 + b^2)*((-a + Sqrt[-b^2])*Log[Sqrt[-b^2] - b*Sinh[x]] - 2*Sqrt[-b^2]*Log[a + b*Sinh[x]] + (a + Sqrt[-b^2])*Log[Sqrt[-b^2] + b*Sinh[x]]))/Sqrt[-b^2] + (-a^2 + 3*b^2)*((2*a + (-a^2 + b^2)/Sqrt[-b^2])*Log[Sqrt[-b^2] - b*Sinh[x]] - 4*a*Log[a + b*Sinh[x]] + (2*a + (a^2 - b^2)/Sqrt[-b^2])*Log[Sqrt[-b^2] + b*Sinh[x]] + (2*(a^2 + b^2))/(a + b*Sinh[x]))))/(a^2 + b^2)^2)/(a^2 + b^2)","A",1
207,1,137,144,0.4423664,"\int \frac{\text{sech}^4(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Sech[x]^4/(a + b*Sinh[x])^2,x]","\frac{\left(a^2+b^2\right) \text{sech}^3(x) \left(\left(a^2-b^2\right) \sinh (x)+2 a b\right)+\frac{30 a b^4 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+\left(2 a^4+9 a^2 b^2-5 b^4\right) \tanh (x)-\frac{3 b^5 \cosh (x)}{a+b \sinh (x)}+12 a b^3 \text{sech}(x)}{3 \left(a^2+b^2\right)^3}","-\frac{b \text{sech}^3(x)}{\left(a^2+b^2\right) (a+b \sinh (x))}+\frac{\text{sech}^3(x) \left(\left(a^2-4 b^2\right) \sinh (x)+5 a b\right)}{3 \left(a^2+b^2\right)^2}-\frac{10 a b^4 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{7/2}}+\frac{\text{sech}(x) \left(\left(2 a^4+9 a^2 b^2-8 b^4\right) \sinh (x)+15 a b^3\right)}{3 \left(a^2+b^2\right)^3}",1,"((30*a*b^4*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + 12*a*b^3*Sech[x] - (3*b^5*Cosh[x])/(a + b*Sinh[x]) + (a^2 + b^2)*Sech[x]^3*(2*a*b + (a^2 - b^2)*Sinh[x]) + (2*a^4 + 9*a^2*b^2 - 5*b^4)*Tanh[x])/(3*(a^2 + b^2)^3)","A",1
208,1,96,31,0.1423349,"\int \frac{\tanh ^4(x)}{i+\sinh (x)} \, dx","Integrate[Tanh[x]^4/(I + Sinh[x]),x]","-\frac{64 i \sinh (x)+178 i \sinh (2 x)-192 i \sinh (3 x)+89 i \sinh (4 x)-534 \cosh (x)+288 \cosh (2 x)-178 \cosh (3 x)+24 \cosh (4 x)+200}{960 \left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right)^5 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)^3}","-\frac{1}{5} i \tanh ^5(x)-\frac{1}{5} \text{sech}^5(x)+\frac{2 \text{sech}^3(x)}{3}-\text{sech}(x)",1,"-1/960*(200 - 534*Cosh[x] + 288*Cosh[2*x] - 178*Cosh[3*x] + 24*Cosh[4*x] + (64*I)*Sinh[x] + (178*I)*Sinh[2*x] - (192*I)*Sinh[3*x] + (89*I)*Sinh[4*x])/((Cosh[x/2] - I*Sinh[x/2])^5*(Cosh[x/2] + I*Sinh[x/2])^3)","B",1
209,1,42,36,0.0813376,"\int \frac{\tanh ^3(x)}{i+\sinh (x)} \, dx","Integrate[Tanh[x]^3/(I + Sinh[x]),x]","\frac{1}{8} \left(3 \tan ^{-1}(\sinh (x))-\frac{5 \sinh ^2(x)+i \sinh (x)+2}{(\sinh (x)-i) (\sinh (x)+i)^2}\right)","-\frac{1}{4} i \tanh ^4(x)+\frac{3}{8} \tan ^{-1}(\sinh (x))-\frac{1}{4} \tanh ^3(x) \text{sech}(x)-\frac{3}{8} \tanh (x) \text{sech}(x)",1,"(3*ArcTan[Sinh[x]] - (2 + I*Sinh[x] + 5*Sinh[x]^2)/((-I + Sinh[x])*(I + Sinh[x])^2))/8","A",1
210,1,67,23,0.0584402,"\int \frac{\tanh ^2(x)}{i+\sinh (x)} \, dx","Integrate[Tanh[x]^2/(I + Sinh[x]),x]","\frac{4 i \sinh (x)-\cosh (2 x)+(5-5 i \sinh (x)) \cosh (x)-3}{6 \left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right)^3 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)}","-\frac{1}{3} i \tanh ^3(x)+\frac{\text{sech}^3(x)}{3}-\text{sech}(x)",1,"(-3 - Cosh[2*x] + Cosh[x]*(5 - (5*I)*Sinh[x]) + (4*I)*Sinh[x])/(6*(Cosh[x/2] - I*Sinh[x/2])^3*(Cosh[x/2] + I*Sinh[x/2]))","B",1
211,1,20,26,0.0211321,"\int \frac{\tanh (x)}{i+\sinh (x)} \, dx","Integrate[Tanh[x]/(I + Sinh[x]),x]","\frac{1}{2} \tan ^{-1}(\sinh (x))-\frac{1}{2 (\sinh (x)+i)}","\frac{1}{2} i \text{sech}^2(x)+\frac{1}{2} \tan ^{-1}(\sinh (x))-\frac{1}{2} \tanh (x) \text{sech}(x)",1,"ArcTan[Sinh[x]]/2 - 1/(2*(I + Sinh[x]))","A",1
212,1,19,19,0.0080603,"\int \frac{\coth (x)}{i+\sinh (x)} \, dx","Integrate[Coth[x]/(I + Sinh[x]),x]","i \log (\sinh (x)+i)-i \log (\sinh (x))","i \log (\sinh (x)+i)-i \log (\sinh (x))",1,"(-I)*Log[Sinh[x]] + I*Log[I + Sinh[x]]","A",1
213,1,32,12,0.0344203,"\int \frac{\coth ^2(x)}{i+\sinh (x)} \, dx","Integrate[Coth[x]^2/(I + Sinh[x]),x]","\frac{1}{2} i \tanh \left(\frac{x}{2}\right)+\frac{1}{2} i \coth \left(\frac{x}{2}\right)+\log \left(\tanh \left(\frac{x}{2}\right)\right)","-\tanh ^{-1}(\cosh (x))+i \coth (x)",1,"(I/2)*Coth[x/2] + Log[Tanh[x/2]] + (I/2)*Tanh[x/2]","B",1
214,1,15,15,0.0109903,"\int \frac{\coth ^3(x)}{i+\sinh (x)} \, dx","Integrate[Coth[x]^3/(I + Sinh[x]),x]","-\text{csch}(x)+\frac{1}{2} i \text{csch}^2(x)","-\text{csch}(x)+\frac{1}{2} i \text{csch}^2(x)",1,"-Csch[x] + (I/2)*Csch[x]^2","A",1
215,1,100,26,0.0376963,"\int \frac{\coth ^4(x)}{i+\sinh (x)} \, dx","Integrate[Coth[x]^4/(I + Sinh[x]),x]","\frac{1}{6} i \tanh \left(\frac{x}{2}\right)+\frac{1}{6} i \coth \left(\frac{x}{2}\right)-\frac{1}{8} \text{csch}^2\left(\frac{x}{2}\right)-\frac{1}{8} \text{sech}^2\left(\frac{x}{2}\right)+\frac{1}{2} \log \left(\tanh \left(\frac{x}{2}\right)\right)+\frac{1}{24} i \coth \left(\frac{x}{2}\right) \text{csch}^2\left(\frac{x}{2}\right)-\frac{1}{24} i \tanh \left(\frac{x}{2}\right) \text{sech}^2\left(\frac{x}{2}\right)","\frac{1}{3} i \coth ^3(x)-\frac{1}{2} \tanh ^{-1}(\cosh (x))-\frac{1}{2} \coth (x) \text{csch}(x)",1,"(I/6)*Coth[x/2] - Csch[x/2]^2/8 + (I/24)*Coth[x/2]*Csch[x/2]^2 + Log[Tanh[x/2]]/2 - Sech[x/2]^2/8 + (I/6)*Tanh[x/2] - (I/24)*Sech[x/2]^2*Tanh[x/2]","B",1
216,1,33,23,0.0102248,"\int \frac{\coth ^5(x)}{i+\sinh (x)} \, dx","Integrate[Coth[x]^5/(I + Sinh[x]),x]","\frac{1}{4} i \text{csch}^4(x)-\frac{\text{csch}^3(x)}{3}+\frac{1}{2} i \text{csch}^2(x)-\text{csch}(x)","\frac{1}{4} i \coth ^4(x)-\frac{\text{csch}^3(x)}{3}-\text{csch}(x)",1,"-Csch[x] + (I/2)*Csch[x]^2 - Csch[x]^3/3 + (I/4)*Csch[x]^4","A",1
217,1,164,36,0.0400082,"\int \frac{\coth ^6(x)}{i+\sinh (x)} \, dx","Integrate[Coth[x]^6/(I + Sinh[x]),x]","\frac{1}{10} i \tanh \left(\frac{x}{2}\right)+\frac{1}{10} i \coth \left(\frac{x}{2}\right)-\frac{1}{64} \text{csch}^4\left(\frac{x}{2}\right)-\frac{5}{32} \text{csch}^2\left(\frac{x}{2}\right)+\frac{1}{64} \text{sech}^4\left(\frac{x}{2}\right)-\frac{5}{32} \text{sech}^2\left(\frac{x}{2}\right)+\frac{3}{8} \log \left(\tanh \left(\frac{x}{2}\right)\right)+\frac{1}{160} i \coth \left(\frac{x}{2}\right) \text{csch}^4\left(\frac{x}{2}\right)+\frac{7}{160} i \coth \left(\frac{x}{2}\right) \text{csch}^2\left(\frac{x}{2}\right)+\frac{1}{160} i \tanh \left(\frac{x}{2}\right) \text{sech}^4\left(\frac{x}{2}\right)-\frac{7}{160} i \tanh \left(\frac{x}{2}\right) \text{sech}^2\left(\frac{x}{2}\right)","\frac{1}{5} i \coth ^5(x)-\frac{3}{8} \tanh ^{-1}(\cosh (x))-\frac{1}{4} \coth ^3(x) \text{csch}(x)-\frac{3}{8} \coth (x) \text{csch}(x)",1,"(I/10)*Coth[x/2] - (5*Csch[x/2]^2)/32 + ((7*I)/160)*Coth[x/2]*Csch[x/2]^2 - Csch[x/2]^4/64 + (I/160)*Coth[x/2]*Csch[x/2]^4 + (3*Log[Tanh[x/2]])/8 - (5*Sech[x/2]^2)/32 + Sech[x/2]^4/64 + (I/10)*Tanh[x/2] - ((7*I)/160)*Sech[x/2]^2*Tanh[x/2] + (I/160)*Sech[x/2]^4*Tanh[x/2]","B",1
218,1,112,47,0.1522295,"\int \frac{\tanh ^4(x)}{(i+\sinh (x))^2} \, dx","Integrate[Tanh[x]^4/(I + Sinh[x])^2,x]","-\frac{1232 \sinh (x)+824 \sinh (2 x)-1896 \sinh (3 x)+412 \sinh (4 x)+72 \sinh (5 x)+1442 i \cosh (x)-1664 i \cosh (2 x)+309 i \cosh (3 x)+288 i \cosh (4 x)-103 i \cosh (5 x)-672 i}{13440 \left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right)^7 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)^3}","\frac{2 \tanh ^7(x)}{7}-\frac{\tanh ^5(x)}{5}+\frac{2}{7} i \text{sech}^7(x)-\frac{4}{5} i \text{sech}^5(x)+\frac{2}{3} i \text{sech}^3(x)",1,"-1/13440*(-672*I + (1442*I)*Cosh[x] - (1664*I)*Cosh[2*x] + (309*I)*Cosh[3*x] + (288*I)*Cosh[4*x] - (103*I)*Cosh[5*x] + 1232*Sinh[x] + 824*Sinh[2*x] - 1896*Sinh[3*x] + 412*Sinh[4*x] + 72*Sinh[5*x])/((Cosh[x/2] - I*Sinh[x/2])^7*(Cosh[x/2] + I*Sinh[x/2])^3)","B",1
219,1,52,66,0.1022783,"\int \frac{\tanh ^3(x)}{(i+\sinh (x))^2} \, dx","Integrate[Tanh[x]^3/(I + Sinh[x])^2,x]","\frac{1}{48} \left(\frac{2 \left(-3 i \sinh ^3(x)-6 \sinh ^2(x)-7 i \sinh (x)+2\right)}{(\sinh (x)-i) (\sinh (x)+i)^3}-6 i \tan ^{-1}(\sinh (x))\right)","-\frac{i}{16 (-\sinh (x)+i)}-\frac{3 i}{16 (\sinh (x)+i)}-\frac{1}{4 (\sinh (x)+i)^2}+\frac{i}{12 (\sinh (x)+i)^3}-\frac{1}{8} i \tan ^{-1}(\sinh (x))",1,"((-6*I)*ArcTan[Sinh[x]] + (2*(2 - (7*I)*Sinh[x] - 6*Sinh[x]^2 - (3*I)*Sinh[x]^3))/((-I + Sinh[x])*(I + Sinh[x])^3))/48","A",1
220,1,84,37,0.0962627,"\int \frac{\tanh ^2(x)}{(i+\sinh (x))^2} \, dx","Integrate[Tanh[x]^2/(I + Sinh[x])^2,x]","\frac{140 \sinh (x)-44 \sinh (2 x)-4 \sinh (3 x)-55 i \cosh (x)-16 i \cosh (2 x)+11 i \cosh (3 x)+80 i}{240 \left(\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)\right)^5 \left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right)}","\frac{2 \tanh ^5(x)}{5}-\frac{\tanh ^3(x)}{3}-\frac{2}{5} i \text{sech}^5(x)+\frac{2}{3} i \text{sech}^3(x)",1,"(80*I - (55*I)*Cosh[x] - (16*I)*Cosh[2*x] + (11*I)*Cosh[3*x] + 140*Sinh[x] - 44*Sinh[2*x] - 4*Sinh[3*x])/(240*(Cosh[x/2] - I*Sinh[x/2])^5*(Cosh[x/2] + I*Sinh[x/2]))","B",1
221,1,29,36,0.0305815,"\int \frac{\tanh (x)}{(i+\sinh (x))^2} \, dx","Integrate[Tanh[x]/(I + Sinh[x])^2,x]","-\frac{i \left(\sinh (x)+(\sinh (x)+i)^2 \tan ^{-1}(\sinh (x))\right)}{4 (\sinh (x)+i)^2}","-\frac{i}{4 (\sinh (x)+i)}-\frac{1}{4 (\sinh (x)+i)^2}-\frac{1}{4} i \tan ^{-1}(\sinh (x))",1,"((-1/4*I)*(Sinh[x] + ArcTan[Sinh[x]]*(I + Sinh[x])^2))/(I + Sinh[x])^2","A",1
222,1,25,25,0.0292281,"\int \frac{\coth (x)}{(i+\sinh (x))^2} \, dx","Integrate[Coth[x]/(I + Sinh[x])^2,x]","-\frac{i}{\sinh (x)+i}-\log (\sinh (x))+\log (\sinh (x)+i)","-\frac{i}{\sinh (x)+i}-\log (\sinh (x))+\log (\sinh (x)+i)",1,"-Log[Sinh[x]] + Log[I + Sinh[x]] - I/(I + Sinh[x])","A",1
223,1,66,26,0.1455137,"\int \frac{\coth ^2(x)}{(i+\sinh (x))^2} \, dx","Integrate[Coth[x]^2/(I + Sinh[x])^2,x]","\frac{1}{2} \left(\tanh \left(\frac{x}{2}\right)+\coth \left(\frac{x}{2}\right)-4 i \log \left(\sinh \left(\frac{x}{2}\right)\right)+4 i \log \left(\cosh \left(\frac{x}{2}\right)\right)+\frac{8 \sinh \left(\frac{x}{2}\right)}{\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)}\right)","\coth (x)+2 i \tanh ^{-1}(\cosh (x))+\frac{2 i \coth (x)}{-\text{csch}(x)+i}",1,"(Coth[x/2] + (4*I)*Log[Cosh[x/2]] - (4*I)*Log[Sinh[x/2]] + (8*Sinh[x/2])/(Cosh[x/2] - I*Sinh[x/2]) + Tanh[x/2])/2","B",1
224,1,29,29,0.0158846,"\int \frac{\coth ^3(x)}{(i+\sinh (x))^2} \, dx","Integrate[Coth[x]^3/(I + Sinh[x])^2,x]","\frac{\text{csch}^2(x)}{2}+2 i \text{csch}(x)+2 \log (\sinh (x))-2 \log (\sinh (x)+i)","\frac{\text{csch}^2(x)}{2}+2 i \text{csch}(x)+2 \log (\sinh (x))-2 \log (\sinh (x)+i)",1,"(2*I)*Csch[x] + Csch[x]^2/2 + 2*Log[Sinh[x]] - 2*Log[I + Sinh[x]]","A",1
225,1,107,28,0.0561141,"\int \frac{\coth ^4(x)}{(i+\sinh (x))^2} \, dx","Integrate[Coth[x]^4/(I + Sinh[x])^2,x]","-\frac{5}{6} \tanh \left(\frac{x}{2}\right)-\frac{5}{6} \coth \left(\frac{x}{2}\right)+\frac{1}{4} i \text{csch}^2\left(\frac{x}{2}\right)+\frac{1}{4} i \text{sech}^2\left(\frac{x}{2}\right)+i \log \left(\sinh \left(\frac{x}{2}\right)\right)-i \log \left(\cosh \left(\frac{x}{2}\right)\right)+\frac{1}{24} \coth \left(\frac{x}{2}\right) \text{csch}^2\left(\frac{x}{2}\right)-\frac{1}{24} \tanh \left(\frac{x}{2}\right) \text{sech}^2\left(\frac{x}{2}\right)","\frac{\coth ^3(x)}{3}-2 \coth (x)-i \tanh ^{-1}(\cosh (x))+i \coth (x) \text{csch}(x)",1,"(-5*Coth[x/2])/6 + (I/4)*Csch[x/2]^2 + (Coth[x/2]*Csch[x/2]^2)/24 - I*Log[Cosh[x/2]] + I*Log[Sinh[x/2]] + (I/4)*Sech[x/2]^2 - (5*Tanh[x/2])/6 - (Sech[x/2]^2*Tanh[x/2])/24","B",1
226,1,27,27,0.0126542,"\int \frac{\coth ^5(x)}{(i+\sinh (x))^2} \, dx","Integrate[Coth[x]^5/(I + Sinh[x])^2,x]","\frac{\text{csch}^4(x)}{4}+\frac{2}{3} i \text{csch}^3(x)-\frac{\text{csch}^2(x)}{2}","\frac{\text{csch}^4(x)}{4}+\frac{2}{3} i \text{csch}^3(x)-\frac{\text{csch}^2(x)}{2}",1,"-1/2*Csch[x]^2 + ((2*I)/3)*Csch[x]^3 + Csch[x]^4/4","A",1
227,1,175,48,0.061434,"\int \frac{\coth ^6(x)}{(i+\sinh (x))^2} \, dx","Integrate[Coth[x]^6/(I + Sinh[x])^2,x]","-\frac{7}{30} \tanh \left(\frac{x}{2}\right)-\frac{7}{30} \coth \left(\frac{x}{2}\right)+\frac{1}{32} i \text{csch}^4\left(\frac{x}{2}\right)+\frac{1}{16} i \text{csch}^2\left(\frac{x}{2}\right)-\frac{1}{32} i \text{sech}^4\left(\frac{x}{2}\right)+\frac{1}{16} i \text{sech}^2\left(\frac{x}{2}\right)+\frac{1}{4} i \log \left(\sinh \left(\frac{x}{2}\right)\right)-\frac{1}{4} i \log \left(\cosh \left(\frac{x}{2}\right)\right)+\frac{1}{160} \coth \left(\frac{x}{2}\right) \text{csch}^4\left(\frac{x}{2}\right)-\frac{19}{480} \coth \left(\frac{x}{2}\right) \text{csch}^2\left(\frac{x}{2}\right)+\frac{1}{160} \tanh \left(\frac{x}{2}\right) \text{sech}^4\left(\frac{x}{2}\right)+\frac{19}{480} \tanh \left(\frac{x}{2}\right) \text{sech}^2\left(\frac{x}{2}\right)","\frac{\coth ^5(x)}{5}-\frac{2 \coth ^3(x)}{3}-\frac{1}{4} i \tanh ^{-1}(\cosh (x))+\frac{1}{2} i \coth (x) \text{csch}^3(x)+\frac{1}{4} i \coth (x) \text{csch}(x)",1,"(-7*Coth[x/2])/30 + (I/16)*Csch[x/2]^2 - (19*Coth[x/2]*Csch[x/2]^2)/480 + (I/32)*Csch[x/2]^4 + (Coth[x/2]*Csch[x/2]^4)/160 - (I/4)*Log[Cosh[x/2]] + (I/4)*Log[Sinh[x/2]] + (I/16)*Sech[x/2]^2 - (I/32)*Sech[x/2]^4 - (7*Tanh[x/2])/30 + (19*Sech[x/2]^2*Tanh[x/2])/480 + (Sech[x/2]^4*Tanh[x/2])/160","B",1
228,1,108,124,0.3659167,"\int \frac{\tanh ^4(x)}{a+b \sinh (x)} \, dx","Integrate[Tanh[x]^4/(a + b*Sinh[x]),x]","\frac{-a \left(4 a^2+b^2\right) \tanh (x)-3 b \left(2 a^2+b^2\right) \text{sech}(x)+\left(a^2+b^2\right) \text{sech}^3(x) (a \sinh (x)+b)+\frac{6 a^4 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}}{3 \left(a^2+b^2\right)^2}","-\frac{a \tanh ^3(x)}{3 \left(a^2+b^2\right)}+\frac{b \text{sech}^3(x)}{3 \left(a^2+b^2\right)}-\frac{a^2 b \text{sech}(x)}{\left(a^2+b^2\right)^2}-\frac{b \text{sech}(x)}{a^2+b^2}-\frac{2 a^4 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{5/2}}-\frac{a^3 \tanh (x)}{\left(a^2+b^2\right)^2}",1,"((6*a^4*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 3*b*(2*a^2 + b^2)*Sech[x] + (a^2 + b^2)*Sech[x]^3*(b + a*Sinh[x]) - a*(4*a^2 + b^2)*Tanh[x])/(3*(a^2 + b^2)^2)","A",1
229,1,153,88,0.1865578,"\int \frac{\tanh ^3(x)}{a+b \sinh (x)} \, dx","Integrate[Tanh[x]^3/(a + b*Sinh[x]),x]","\frac{a \text{sech}^2(x)}{2 \left(a^2+b^2\right)}-\frac{b \tan ^{-1}(\sinh (x))}{2 \left(a^2+b^2\right)}-\frac{b \tanh (x) \text{sech}(x)}{2 \left(a^2+b^2\right)}-\frac{a^3 \log (a+b \sinh (x))}{\left(a^2+b^2\right)^2}+\frac{\left(a^3-i \left(2 a^2 b+b^3\right)\right) \log (-\sinh (x)+i)}{2 \left(a^2+b^2\right)^2}+\frac{\left(a^3+i \left(2 a^2 b+b^3\right)\right) \log (\sinh (x)+i)}{2 \left(a^2+b^2\right)^2}","\frac{b \left(3 a^2+b^2\right) \tan ^{-1}(\sinh (x))}{2 \left(a^2+b^2\right)^2}+\frac{\text{sech}^2(x) (a-b \sinh (x))}{2 \left(a^2+b^2\right)}-\frac{a^3 \log (a+b \sinh (x))}{\left(a^2+b^2\right)^2}+\frac{a^3 \log (\cosh (x))}{\left(a^2+b^2\right)^2}",1,"-1/2*(b*ArcTan[Sinh[x]])/(a^2 + b^2) + ((a^3 - I*(2*a^2*b + b^3))*Log[I - Sinh[x]])/(2*(a^2 + b^2)^2) + ((a^3 + I*(2*a^2*b + b^3))*Log[I + Sinh[x]])/(2*(a^2 + b^2)^2) - (a^3*Log[a + b*Sinh[x]])/(a^2 + b^2)^2 + (a*Sech[x]^2)/(2*(a^2 + b^2)) - (b*Sech[x]*Tanh[x])/(2*(a^2 + b^2))","C",1
230,1,69,69,0.1951105,"\int \frac{\tanh ^2(x)}{a+b \sinh (x)} \, dx","Integrate[Tanh[x]^2/(a + b*Sinh[x]),x]","\frac{a \left(\frac{2 a \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}-\tanh (x)\right)-b \text{sech}(x)}{a^2+b^2}","-\frac{2 a^2 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{3/2}}-\frac{a \tanh (x)}{a^2+b^2}-\frac{b \text{sech}(x)}{a^2+b^2}",1,"(-(b*Sech[x]) + a*((2*a*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - Tanh[x]))/(a^2 + b^2)","A",1
231,1,36,48,0.0596548,"\int \frac{\tanh (x)}{a+b \sinh (x)} \, dx","Integrate[Tanh[x]/(a + b*Sinh[x]),x]","\frac{-a \log (a+b \sinh (x))+a \log (\cosh (x))+2 b \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)}{a^2+b^2}","-\frac{a \log (a+b \sinh (x))}{a^2+b^2}+\frac{b \tan ^{-1}(\sinh (x))}{a^2+b^2}+\frac{a \log (\cosh (x))}{a^2+b^2}",1,"(2*b*ArcTan[Tanh[x/2]] + a*Log[Cosh[x]] - a*Log[a + b*Sinh[x]])/(a^2 + b^2)","A",1
232,1,20,20,0.0099673,"\int \frac{\coth (x)}{a+b \sinh (x)} \, dx","Integrate[Coth[x]/(a + b*Sinh[x]),x]","\frac{\log (\sinh (x))}{a}-\frac{\log (a+b \sinh (x))}{a}","\frac{\log (\sinh (x))}{a}-\frac{\log (a+b \sinh (x))}{a}",1,"Log[Sinh[x]]/a - Log[a + b*Sinh[x]]/a","A",1
233,1,82,56,0.1828729,"\int \frac{\coth ^2(x)}{a+b \sinh (x)} \, dx","Integrate[Coth[x]^2/(a + b*Sinh[x]),x]","-\frac{\text{csch}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \left(\sinh (x) \left(2 \sqrt{-a^2-b^2} \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)+b \log \left(\tanh \left(\frac{x}{2}\right)\right)\right)+a \cosh (x)\right)}{2 a^2}","-\frac{2 \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a^2}+\frac{b \tanh ^{-1}(\cosh (x))}{a^2}-\frac{\coth (x)}{a}",1,"-1/2*(Csch[x/2]*Sech[x/2]*(a*Cosh[x] + (2*Sqrt[-a^2 - b^2]*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]] + b*Log[Tanh[x/2]])*Sinh[x]))/a^2","A",1
234,1,45,52,0.0626709,"\int \frac{\coth ^3(x)}{a+b \sinh (x)} \, dx","Integrate[Coth[x]^3/(a + b*Sinh[x]),x]","\frac{2 \left(a^2+b^2\right) (\log (\sinh (x))-\log (a+b \sinh (x)))-a^2 \text{csch}^2(x)+2 a b \text{csch}(x)}{2 a^3}","\frac{b \text{csch}(x)}{a^2}+\frac{\left(a^2+b^2\right) \log (\sinh (x))}{a^3}-\frac{\left(a^2+b^2\right) \log (a+b \sinh (x))}{a^3}-\frac{\text{csch}^2(x)}{2 a}",1,"(2*a*b*Csch[x] - a^2*Csch[x]^2 + 2*(a^2 + b^2)*(Log[Sinh[x]] - Log[a + b*Sinh[x]]))/(2*a^3)","A",1
235,1,176,108,0.4293415,"\int \frac{\coth ^4(x)}{a+b \sinh (x)} \, dx","Integrate[Coth[x]^4/(a + b*Sinh[x]),x]","\frac{-\frac{1}{2} a^3 \sinh (x) \text{csch}^4\left(\frac{x}{2}\right)+8 a^3 \sinh ^4\left(\frac{x}{2}\right) \text{csch}^3(x)-4 a \left(4 a^2+3 b^2\right) \tanh \left(\frac{x}{2}\right)-4 a \left(4 a^2+3 b^2\right) \coth \left(\frac{x}{2}\right)-12 b \left(3 a^2+2 b^2\right) \log \left(\tanh \left(\frac{x}{2}\right)\right)+48 \left(-a^2-b^2\right)^{3/2} \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)+3 a^2 b \text{csch}^2\left(\frac{x}{2}\right)+3 a^2 b \text{sech}^2\left(\frac{x}{2}\right)}{24 a^4}","\frac{b \coth (x) \text{csch}(x)}{2 a^2}-\frac{2 \left(a^2+b^2\right)^{3/2} \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a^4}+\frac{b \left(3 a^2+2 b^2\right) \tanh ^{-1}(\cosh (x))}{2 a^4}-\frac{\left(4 a^2+3 b^2\right) \coth (x)}{3 a^3}-\frac{\coth (x) \text{csch}^2(x)}{3 a}",1,"(48*(-a^2 - b^2)^(3/2)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]] - 4*a*(4*a^2 + 3*b^2)*Coth[x/2] + 3*a^2*b*Csch[x/2]^2 - 12*b*(3*a^2 + 2*b^2)*Log[Tanh[x/2]] + 3*a^2*b*Sech[x/2]^2 + 8*a^3*Csch[x]^3*Sinh[x/2]^4 - (a^3*Csch[x/2]^4*Sinh[x])/2 - 4*a*(4*a^2 + 3*b^2)*Tanh[x/2])/(24*a^4)","A",1
236,1,144,224,0.4122757,"\int \frac{\tanh ^4(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Tanh[x]^4/(a + b*Sinh[x])^2,x]","\frac{-\frac{3 a^4 b \cosh (x)}{a+b \sinh (x)}-12 a^3 b \text{sech}(x)+\left(a^2+b^2\right) \text{sech}^3(x) \left(\left(a^2-b^2\right) \sinh (x)+2 a b\right)+\left(-4 a^4+9 a^2 b^2+b^4\right) \tanh (x)+\frac{6 a^3 \left(a^2-4 b^2\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}}{3 \left(a^2+b^2\right)^3}","-\frac{\left(a^2-b^2\right) \tanh ^3(x)}{3 \left(a^2+b^2\right)^2}+\frac{\left(a^2-b^2\right) \tanh (x)}{\left(a^2+b^2\right)^2}+\frac{2 a b \text{sech}^3(x)}{3 \left(a^2+b^2\right)^2}-\frac{2 a^5 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{7/2}}-\frac{a^4 b \cosh (x)}{\left(a^2+b^2\right)^3 (a+b \sinh (x))}-\frac{\left(2 a^4-3 a^2 b^2-b^4\right) \tanh (x)}{\left(a^2+b^2\right)^3}+\frac{8 a^3 b^2 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{7/2}}-\frac{4 a^3 b \text{sech}(x)}{\left(a^2+b^2\right)^3}",1,"((6*a^3*(a^2 - 4*b^2)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 12*a^3*b*Sech[x] - (3*a^4*b*Cosh[x])/(a + b*Sinh[x]) + (a^2 + b^2)*Sech[x]^3*(2*a*b + (a^2 - b^2)*Sinh[x]) + (-4*a^4 + 9*a^2*b^2 + b^4)*Tanh[x])/(3*(a^2 + b^2)^3)","A",1
237,1,150,135,0.7004199,"\int \frac{\tanh ^3(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Tanh[x]^3/(a + b*Sinh[x])^2,x]","\frac{\left(a^4-b^4\right) \text{sech}^2(x)-2 a^2 \left(a^2-3 b^2\right) \log (a+b \sinh (x))-2 a b \left(a^2+b^2\right) \tan ^{-1}(\sinh (x))-2 a b \left(a^2+b^2\right) \tanh (x) \text{sech}(x)+a^2 (a-i b) (a-3 i b) \log (-\sinh (x)+i)+a^2 (a+i b) (a+3 i b) \log (\sinh (x)+i)+\frac{2 a^3 \left(a^2+b^2\right)}{a+b \sinh (x)}}{2 \left(a^2+b^2\right)^3}","-\frac{a^2 \left(a^2-3 b^2\right) \log (a+b \sinh (x))}{\left(a^2+b^2\right)^3}+\frac{a b \left(3 a^2-b^2\right) \tan ^{-1}(\sinh (x))}{\left(a^2+b^2\right)^3}+\frac{a^2 \left(a^2-3 b^2\right) \log (\cosh (x))}{\left(a^2+b^2\right)^3}+\frac{\text{sech}^2(x) \left(a^2-2 a b \sinh (x)-b^2\right)}{2 \left(a^2+b^2\right)^2}+\frac{a^3}{\left(a^2+b^2\right)^2 (a+b \sinh (x))}",1,"(-2*a*b*(a^2 + b^2)*ArcTan[Sinh[x]] + a^2*(a - I*b)*(a - (3*I)*b)*Log[I - Sinh[x]] + a^2*(a + I*b)*(a + (3*I)*b)*Log[I + Sinh[x]] - 2*a^2*(a^2 - 3*b^2)*Log[a + b*Sinh[x]] + (a^4 - b^4)*Sech[x]^2 + (2*a^3*(a^2 + b^2))/(a + b*Sinh[x]) - 2*a*b*(a^2 + b^2)*Sech[x]*Tanh[x])/(2*(a^2 + b^2)^3)","C",1
238,1,100,144,0.2696981,"\int \frac{\tanh ^2(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Tanh[x]^2/(a + b*Sinh[x])^2,x]","\frac{\left(b^2-a^2\right) \tanh (x)+\frac{2 a \left(a^2-2 b^2\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}-\frac{a^2 b \cosh (x)}{a+b \sinh (x)}-2 a b \text{sech}(x)}{\left(a^2+b^2\right)^2}","\frac{4 a b^2 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{5/2}}-\frac{\left(a^2-b^2\right) \tanh (x)}{\left(a^2+b^2\right)^2}-\frac{2 a b \text{sech}(x)}{\left(a^2+b^2\right)^2}-\frac{a^2 b \cosh (x)}{\left(a^2+b^2\right)^2 (a+b \sinh (x))}-\frac{2 a^3 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\left(a^2+b^2\right)^{5/2}}",1,"((2*a*(a^2 - 2*b^2)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 2*a*b*Sech[x] - (a^2*b*Cosh[x])/(a + b*Sinh[x]) + (-a^2 + b^2)*Tanh[x])/(a^2 + b^2)^2","A",1
239,1,146,85,0.2391966,"\int \frac{\tanh (x)}{(a+b \sinh (x))^2} \, dx","Integrate[Tanh[x]/(a + b*Sinh[x])^2,x]","\frac{a \left(2 \left(\left(b^2-a^2\right) \log (a+b \sinh (x))+a^2+b^2\right)+(a-i b)^2 \log (-\sinh (x)+i)+(a+i b)^2 \log (\sinh (x)+i)\right)+b \sinh (x) \left(2 \left(b^2-a^2\right) \log (a+b \sinh (x))+(a-i b)^2 \log (-\sinh (x)+i)+(a+i b)^2 \log (\sinh (x)+i)\right)}{2 \left(a^2+b^2\right)^2 (a+b \sinh (x))}","\frac{a}{\left(a^2+b^2\right) (a+b \sinh (x))}-\frac{\left(a^2-b^2\right) \log (a+b \sinh (x))}{\left(a^2+b^2\right)^2}+\frac{2 a b \tan ^{-1}(\sinh (x))}{\left(a^2+b^2\right)^2}+\frac{\left(a^2-b^2\right) \log (\cosh (x))}{\left(a^2+b^2\right)^2}",1,"(a*((a - I*b)^2*Log[I - Sinh[x]] + (a + I*b)^2*Log[I + Sinh[x]] + 2*(a^2 + b^2 + (-a^2 + b^2)*Log[a + b*Sinh[x]])) + b*((a - I*b)^2*Log[I - Sinh[x]] + (a + I*b)^2*Log[I + Sinh[x]] + 2*(-a^2 + b^2)*Log[a + b*Sinh[x]])*Sinh[x])/(2*(a^2 + b^2)^2*(a + b*Sinh[x]))","C",1
240,1,27,32,0.0511626,"\int \frac{\coth (x)}{(a+b \sinh (x))^2} \, dx","Integrate[Coth[x]/(a + b*Sinh[x])^2,x]","\frac{\frac{a}{a+b \sinh (x)}-\log (a+b \sinh (x))+\log (\sinh (x))}{a^2}","-\frac{\log (a+b \sinh (x))}{a^2}+\frac{\log (\sinh (x))}{a^2}+\frac{1}{a (a+b \sinh (x))}",1,"(Log[Sinh[x]] - Log[a + b*Sinh[x]] + a/(a + b*Sinh[x]))/a^2","A",1
241,1,102,80,0.4787622,"\int \frac{\coth ^2(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Coth[x]^2/(a + b*Sinh[x])^2,x]","-\frac{-\frac{4 \left(a^2+2 b^2\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+\frac{2 a b \cosh (x)}{a+b \sinh (x)}+a \tanh \left(\frac{x}{2}\right)+a \coth \left(\frac{x}{2}\right)+4 b \log \left(\tanh \left(\frac{x}{2}\right)\right)}{2 a^3}","\frac{2 b \tanh ^{-1}(\cosh (x))}{a^3}-\frac{2 \coth (x)}{a^2}-\frac{2 \left(a^2+2 b^2\right) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a^3 \sqrt{a^2+b^2}}+\frac{\coth (x)}{a (a+b \sinh (x))}",1,"-1/2*((-4*(a^2 + 2*b^2)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + a*Coth[x/2] + 4*b*Log[Tanh[x/2]] + (2*a*b*Cosh[x])/(a + b*Sinh[x]) + a*Tanh[x/2])/a^3","A",1
242,1,73,76,0.2129958,"\int \frac{\coth ^3(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Coth[x]^3/(a + b*Sinh[x])^2,x]","\frac{\frac{2 a \left(a^2+b^2\right)}{a+b \sinh (x)}+2 \left(a^2+3 b^2\right) \log (\sinh (x))-2 \left(a^2+3 b^2\right) \log (a+b \sinh (x))-a^2 \text{csch}^2(x)+4 a b \text{csch}(x)}{2 a^4}","\frac{2 b \text{csch}(x)}{a^3}-\frac{\text{csch}^2(x)}{2 a^2}+\frac{\left(a^2+3 b^2\right) \log (\sinh (x))}{a^4}-\frac{\left(a^2+3 b^2\right) \log (a+b \sinh (x))}{a^4}+\frac{a^2+b^2}{a^3 (a+b \sinh (x))}",1,"(4*a*b*Csch[x] - a^2*Csch[x]^2 + 2*(a^2 + 3*b^2)*Log[Sinh[x]] - 2*(a^2 + 3*b^2)*Log[a + b*Sinh[x]] + (2*a*(a^2 + b^2))/(a + b*Sinh[x]))/(2*a^4)","A",1
243,1,214,159,0.8232215,"\int \frac{\coth ^4(x)}{(a+b \sinh (x))^2} \, dx","Integrate[Coth[x]^4/(a + b*Sinh[x])^2,x]","\frac{-\frac{1}{2} a^3 \sinh (x) \text{csch}^4\left(\frac{x}{2}\right)+8 a^3 \sinh ^4\left(\frac{x}{2}\right) \text{csch}^3(x)-4 a \left(4 a^2+9 b^2\right) \tanh \left(\frac{x}{2}\right)-4 a \left(4 a^2+9 b^2\right) \coth \left(\frac{x}{2}\right)-24 b \left(3 a^2+4 b^2\right) \log \left(\tanh \left(\frac{x}{2}\right)\right)-\frac{24 a b \left(a^2+b^2\right) \cosh (x)}{a+b \sinh (x)}+6 a^2 b \text{csch}^2\left(\frac{x}{2}\right)+6 a^2 b \text{sech}^2\left(\frac{x}{2}\right)+\frac{48 \left(a^4+5 a^2 b^2+4 b^4\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}}{24 a^5}","-\frac{\left(\frac{4 b^2}{a^2}+3\right) \coth (x) \text{csch}(x)}{3 b (a+b \sinh (x))}-\frac{2 \sqrt{a^2+b^2} \left(a^2+4 b^2\right) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a^5}+\frac{b \left(3 a^2+4 b^2\right) \tanh ^{-1}(\cosh (x))}{a^5}-\frac{\left(7 a^2+12 b^2\right) \coth (x)}{3 a^4}+\frac{\left(a^2+2 b^2\right) \coth (x) \text{csch}(x)}{a^3 b}-\frac{\coth (x) \text{csch}^2(x)}{3 a (a+b \sinh (x))}",1,"((48*(a^4 + 5*a^2*b^2 + 4*b^4)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 4*a*(4*a^2 + 9*b^2)*Coth[x/2] + 6*a^2*b*Csch[x/2]^2 - 24*b*(3*a^2 + 4*b^2)*Log[Tanh[x/2]] + 6*a^2*b*Sech[x/2]^2 + 8*a^3*Csch[x]^3*Sinh[x/2]^4 - (a^3*Csch[x/2]^4*Sinh[x])/2 - (24*a*b*(a^2 + b^2)*Cosh[x])/(a + b*Sinh[x]) - 4*a*(4*a^2 + 9*b^2)*Tanh[x/2])/(24*a^5)","A",1
244,1,37,37,0.0226224,"\int \coth (x) \sqrt{a+b \sinh (x)} \, dx","Integrate[Coth[x]*Sqrt[a + b*Sinh[x]],x]","2 \sqrt{a+b \sinh (x)}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh (x)}}{\sqrt{a}}\right)","2 \sqrt{a+b \sinh (x)}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh (x)}}{\sqrt{a}}\right)",1,"-2*Sqrt[a]*ArcTanh[Sqrt[a + b*Sinh[x]]/Sqrt[a]] + 2*Sqrt[a + b*Sinh[x]]","A",1
245,1,24,24,0.0132433,"\int \frac{\coth (x)}{\sqrt{a+b \sinh (x)}} \, dx","Integrate[Coth[x]/Sqrt[a + b*Sinh[x]],x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh (x)}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sinh (x)}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(-2*ArcTanh[Sqrt[a + b*Sinh[x]]/Sqrt[a]])/Sqrt[a]","A",1
246,1,59,51,0.0787212,"\int \frac{A+B \cosh (x)}{a+b \sinh (x)} \, dx","Integrate[(A + B*Cosh[x])/(a + b*Sinh[x]),x]","\frac{2 A \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+\frac{B \log (a+b \sinh (x))}{b}","\frac{B \log (a+b \sinh (x))}{b}-\frac{2 A \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}",1,"(2*A*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + (B*Log[a + b*Sinh[x]])/b","A",1
247,1,48,25,0.0692144,"\int \frac{A+B \cosh (x)}{i+\sinh (x)} \, dx","Integrate[(A + B*Cosh[x])/(I + Sinh[x]),x]","-\frac{2 i A \sinh \left(\frac{x}{2}\right)}{\cosh \left(\frac{x}{2}\right)-i \sinh \left(\frac{x}{2}\right)}-2 i B \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+B \log (\cosh (x))","B \log (\sinh (x)+i)-\frac{A \cosh (x)}{1-i \sinh (x)}",1,"(-2*I)*B*ArcTan[Tanh[x/2]] + B*Log[Cosh[x]] - ((2*I)*A*Sinh[x/2])/(Cosh[x/2] - I*Sinh[x/2])","A",1
248,1,81,27,0.094961,"\int \frac{A+B \cosh (x)}{i-\sinh (x)} \, dx","Integrate[(A + B*Cosh[x])/(I - Sinh[x]),x]","-\frac{\left(\cosh \left(\frac{x}{2}\right)+i \sinh \left(\frac{x}{2}\right)\right) \left(\sinh \left(\frac{x}{2}\right) \left(2 A+2 i B \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+B \log (\cosh (x))\right)+B \cosh \left(\frac{x}{2}\right) \left(2 \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)-i \log (\cosh (x))\right)\right)}{\sinh (x)-i}","\frac{A \cosh (x)}{1+i \sinh (x)}-B \log (-\sinh (x)+i)",1,"-(((Cosh[x/2] + I*Sinh[x/2])*(B*Cosh[x/2]*(2*ArcTan[Tanh[x/2]] - I*Log[Cosh[x]]) + (2*A + (2*I)*B*ArcTan[Tanh[x/2]] + B*Log[Cosh[x]])*Sinh[x/2]))/(-I + Sinh[x]))","B",1
249,1,132,89,0.3684862,"\int \frac{A+B \tanh (x)}{a+b \sinh (x)} \, dx","Integrate[(A + B*Tanh[x])/(a + b*Sinh[x]),x]","-\frac{\cosh (x) (A+B \tanh (x)) \left(2 A \left(a^2+b^2\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)+2 b B \sqrt{-a^2-b^2} \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)+a B \sqrt{-a^2-b^2} (\log (\cosh (x))-\log (a+b \sinh (x)))\right)}{\left(-a^2-b^2\right)^{3/2} (A \cosh (x)+B \sinh (x))}","-\frac{2 A \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}-\frac{a B \log (a+b \sinh (x))}{a^2+b^2}+\frac{b B \tan ^{-1}(\sinh (x))}{a^2+b^2}+\frac{a B \log (\cosh (x))}{a^2+b^2}",1,"-((Cosh[x]*(2*b*Sqrt[-a^2 - b^2]*B*ArcTan[Tanh[x/2]] + 2*A*(a^2 + b^2)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]] + a*Sqrt[-a^2 - b^2]*B*(Log[Cosh[x]] - Log[a + b*Sinh[x]]))*(A + B*Tanh[x]))/((-a^2 - b^2)^(3/2)*(A*Cosh[x] + B*Sinh[x])))","A",1
250,1,65,60,0.16523,"\int \frac{A+B \coth (x)}{a+b \sinh (x)} \, dx","Integrate[(A + B*Coth[x])/(a + b*Sinh[x]),x]","\frac{2 A \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+\frac{B (\log (\sinh (x))-\log (a+b \sinh (x)))}{a}","-\frac{2 A \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}-\frac{B \log (a+b \sinh (x))}{a}+\frac{B \log (\sinh (x))}{a}",1,"(2*A*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + (B*(Log[Sinh[x]] - Log[a + b*Sinh[x]]))/a","A",1
251,1,93,89,0.2496674,"\int \frac{A+B \text{sech}(x)}{a+b \sinh (x)} \, dx","Integrate[(A + B*Sech[x])/(a + b*Sinh[x]),x]","\frac{2 A \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+\frac{2 a B \tan ^{-1}\left(\tanh \left(\frac{x}{2}\right)\right)}{a^2+b^2}-\frac{b B (\log (\cosh (x))-\log (a+b \sinh (x)))}{a^2+b^2}","-\frac{2 A \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}+\frac{b B \log (a+b \sinh (x))}{a^2+b^2}+\frac{a B \tan ^{-1}(\sinh (x))}{a^2+b^2}-\frac{b B \log (\cosh (x))}{a^2+b^2}",1,"(2*a*B*ArcTan[Tanh[x/2]])/(a^2 + b^2) + (2*A*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - (b*B*(Log[Cosh[x]] - Log[a + b*Sinh[x]]))/(a^2 + b^2)","A",1
252,1,67,58,0.1175577,"\int \frac{A+B \text{csch}(x)}{a+b \sinh (x)} \, dx","Integrate[(A + B*Csch[x])/(a + b*Sinh[x]),x]","\frac{\frac{2 (a A-b B) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+B \log \left(\tanh \left(\frac{x}{2}\right)\right)}{a}","-\frac{2 (a A-b B) \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{x}{2}\right)}{\sqrt{a^2+b^2}}\right)}{a \sqrt{a^2+b^2}}-\frac{B \tanh ^{-1}(\cosh (x))}{a}",1,"((2*(a*A - b*B)*ArcTan[(b - a*Tanh[x/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + B*Log[Tanh[x/2]])/a","A",1
253,1,85,81,0.2903945,"\int \frac{A+B \cosh (d+e x)+C \sinh (d+e x)}{a+c \sinh (d+e x)} \, dx","Integrate[(A + B*Cosh[d + e*x] + C*Sinh[d + e*x])/(a + c*Sinh[d + e*x]),x]","\frac{\frac{2 (A c-a C) \tan ^{-1}\left(\frac{c-a \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{-a^2-c^2}}\right)}{\sqrt{-a^2-c^2}}+B \log (a+c \sinh (d+e x))+C (d+e x)}{c e}","-\frac{2 (A c-a C) \tanh ^{-1}\left(\frac{c-a \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{a^2+c^2}}\right)}{c e \sqrt{a^2+c^2}}+\frac{B \log (a+c \sinh (d+e x))}{c e}+\frac{C x}{c}",1,"(C*(d + e*x) + (2*(A*c - a*C)*ArcTan[(c - a*Tanh[(d + e*x)/2])/Sqrt[-a^2 - c^2]])/Sqrt[-a^2 - c^2] + B*Log[a + c*Sinh[d + e*x]])/(c*e)","A",1
254,1,113,113,0.518665,"\int \frac{A+B \cosh (d+e x)+C \sinh (d+e x)}{(a+c \sinh (d+e x))^2} \, dx","Integrate[(A + B*Cosh[d + e*x] + C*Sinh[d + e*x])/(a + c*Sinh[d + e*x])^2,x]","\frac{\frac{2 (a A+c C) \tan ^{-1}\left(\frac{c-a \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{-a^2-c^2}}\right)}{\sqrt{-a^2-c^2}}-\frac{B \left(a^2+c^2\right)+c (A c-a C) \cosh (d+e x)}{c (a+c \sinh (d+e x))}}{e \left(a^2+c^2\right)}","-\frac{2 (a A+c C) \tanh ^{-1}\left(\frac{c-a \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{a^2+c^2}}\right)}{e \left(a^2+c^2\right)^{3/2}}-\frac{(A c-a C) \cosh (d+e x)}{e \left(a^2+c^2\right) (a+c \sinh (d+e x))}-\frac{B}{c e (a+c \sinh (d+e x))}",1,"((2*(a*A + c*C)*ArcTan[(c - a*Tanh[(d + e*x)/2])/Sqrt[-a^2 - c^2]])/Sqrt[-a^2 - c^2] - (B*(a^2 + c^2) + c*(A*c - a*C)*Cosh[d + e*x])/(c*(a + c*Sinh[d + e*x])))/((a^2 + c^2)*e)","A",1
255,1,170,180,0.6852456,"\int \frac{A+B \cosh (d+e x)+C \sinh (d+e x)}{(a+c \sinh (d+e x))^3} \, dx","Integrate[(A + B*Cosh[d + e*x] + C*Sinh[d + e*x])/(a + c*Sinh[d + e*x])^3,x]","\frac{-\frac{\left(a^2+c^2\right) \left(B \left(a^2+c^2\right)+c (A c-a C) \cosh (d+e x)\right)}{c (a+c \sinh (d+e x))^2}+\frac{2 \left(2 a^2 A+3 a c C-A c^2\right) \tan ^{-1}\left(\frac{c-a \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{-a^2-c^2}}\right)}{\sqrt{-a^2-c^2}}+\frac{\left(a^2 C-3 a A c-2 c^2 C\right) \cosh (d+e x)}{a+c \sinh (d+e x)}}{2 e \left(a^2+c^2\right)^2}","-\frac{\left(2 a^2 A+3 a c C-A c^2\right) \tanh ^{-1}\left(\frac{c-a \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{a^2+c^2}}\right)}{e \left(a^2+c^2\right)^{5/2}}-\frac{\left(a^2 (-C)+3 a A c+2 c^2 C\right) \cosh (d+e x)}{2 e \left(a^2+c^2\right)^2 (a+c \sinh (d+e x))}-\frac{(A c-a C) \cosh (d+e x)}{2 e \left(a^2+c^2\right) (a+c \sinh (d+e x))^2}-\frac{B}{2 c e (a+c \sinh (d+e x))^2}",1,"((2*(2*a^2*A - A*c^2 + 3*a*c*C)*ArcTan[(c - a*Tanh[(d + e*x)/2])/Sqrt[-a^2 - c^2]])/Sqrt[-a^2 - c^2] - ((a^2 + c^2)*(B*(a^2 + c^2) + c*(A*c - a*C)*Cosh[d + e*x]))/(c*(a + c*Sinh[d + e*x])^2) + ((-3*a*A*c + a^2*C - 2*c^2*C)*Cosh[d + e*x])/(a + c*Sinh[d + e*x]))/(2*(a^2 + c^2)^2*e)","A",1
256,1,235,250,1.5801365,"\int \frac{A+B \cosh (d+e x)+C \sinh (d+e x)}{(a+c \sinh (d+e x))^4} \, dx","Integrate[(A + B*Cosh[d + e*x] + C*Sinh[d + e*x])/(a + c*Sinh[d + e*x])^4,x]","\frac{-\frac{2 \left(a^2+c^2\right)^2 \left(B \left(a^2+c^2\right)+c (A c-a C) \cosh (d+e x)\right)}{c (a+c \sinh (d+e x))^3}+\frac{\left(a^2+c^2\right) \left(2 a^2 C-5 a A c-3 c^2 C\right) \cosh (d+e x)}{(a+c \sinh (d+e x))^2}+\frac{6 \left(2 a^3 A+4 a^2 c C-3 a A c^2-c^3 C\right) \tan ^{-1}\left(\frac{c-a \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{-a^2-c^2}}\right)}{\sqrt{-a^2-c^2}}+\frac{\left(2 a^3 C-11 a^2 A c-13 a c^2 C+4 A c^3\right) \cosh (d+e x)}{a+c \sinh (d+e x)}}{6 e \left(a^2+c^2\right)^3}","-\frac{\left(-2 a^2 C+5 a A c+3 c^2 C\right) \cosh (d+e x)}{6 e \left(a^2+c^2\right)^2 (a+c \sinh (d+e x))^2}-\frac{(A c-a C) \cosh (d+e x)}{3 e \left(a^2+c^2\right) (a+c \sinh (d+e x))^3}-\frac{\left(2 a^3 A+4 a^2 c C-3 a A c^2-c^3 C\right) \tanh ^{-1}\left(\frac{c-a \tanh \left(\frac{1}{2} (d+e x)\right)}{\sqrt{a^2+c^2}}\right)}{e \left(a^2+c^2\right)^{7/2}}-\frac{\left(-2 a^3 C+11 a^2 A c+13 a c^2 C-4 A c^3\right) \cosh (d+e x)}{6 e \left(a^2+c^2\right)^3 (a+c \sinh (d+e x))}-\frac{B}{3 c e (a+c \sinh (d+e x))^3}",1,"((6*(2*a^3*A - 3*a*A*c^2 + 4*a^2*c*C - c^3*C)*ArcTan[(c - a*Tanh[(d + e*x)/2])/Sqrt[-a^2 - c^2]])/Sqrt[-a^2 - c^2] - (2*(a^2 + c^2)^2*(B*(a^2 + c^2) + c*(A*c - a*C)*Cosh[d + e*x]))/(c*(a + c*Sinh[d + e*x])^3) + ((a^2 + c^2)*(-5*a*A*c + 2*a^2*C - 3*c^2*C)*Cosh[d + e*x])/(a + c*Sinh[d + e*x])^2 + ((-11*a^2*A*c + 4*A*c^3 + 2*a^3*C - 13*a*c^2*C)*Cosh[d + e*x])/(a + c*Sinh[d + e*x]))/(6*(a^2 + c^2)^3*e)","A",1
257,1,319,439,0.8588608,"\int \frac{x^3}{a+b \sinh ^2(x)} \, dx","Integrate[x^3/(a + b*Sinh[x]^2),x]","\frac{-6 x^2 \text{Li}_2\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a-b} \sqrt{a}-b}\right)+6 x^2 \text{Li}_2\left(\frac{b e^{2 x}}{-2 a+2 \sqrt{a-b} \sqrt{a}+b}\right)+6 x \text{Li}_3\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a-b} \sqrt{a}-b}\right)-6 x \text{Li}_3\left(\frac{b e^{2 x}}{-2 a+2 \sqrt{a-b} \sqrt{a}+b}\right)-3 \text{Li}_4\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a-b} \sqrt{a}-b}\right)+3 \text{Li}_4\left(\frac{b e^{2 x}}{-2 a+2 \sqrt{a-b} \sqrt{a}+b}\right)-4 x^3 \log \left(\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a-b}+2 a-b}+1\right)+4 x^3 \log \left(1-\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a-b}-2 a+b}\right)}{8 \sqrt{a} \sqrt{a-b}}","\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a-b} \sqrt{a}-b}\right)}{4 \sqrt{a} \sqrt{a-b}}-\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a-b} \sqrt{a}-b}\right)}{4 \sqrt{a} \sqrt{a-b}}-\frac{3 x \text{Li}_3\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a-b} \sqrt{a}-b}\right)}{4 \sqrt{a} \sqrt{a-b}}+\frac{3 x \text{Li}_3\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a-b} \sqrt{a}-b}\right)}{4 \sqrt{a} \sqrt{a-b}}+\frac{3 \text{Li}_4\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a-b} \sqrt{a}-b}\right)}{8 \sqrt{a} \sqrt{a-b}}-\frac{3 \text{Li}_4\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a-b} \sqrt{a}-b}\right)}{8 \sqrt{a} \sqrt{a-b}}+\frac{x^3 \log \left(\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a-b}+2 a-b}+1\right)}{2 \sqrt{a} \sqrt{a-b}}-\frac{x^3 \log \left(\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a-b}+2 a-b}+1\right)}{2 \sqrt{a} \sqrt{a-b}}",1,"(-4*x^3*Log[1 + (b*E^(2*x))/(2*a + 2*Sqrt[a]*Sqrt[a - b] - b)] + 4*x^3*Log[1 - (b*E^(2*x))/(-2*a + 2*Sqrt[a]*Sqrt[a - b] + b)] - 6*x^2*PolyLog[2, -((b*E^(2*x))/(2*a + 2*Sqrt[a]*Sqrt[a - b] - b))] + 6*x^2*PolyLog[2, (b*E^(2*x))/(-2*a + 2*Sqrt[a]*Sqrt[a - b] + b)] + 6*x*PolyLog[3, -((b*E^(2*x))/(2*a + 2*Sqrt[a]*Sqrt[a - b] - b))] - 6*x*PolyLog[3, (b*E^(2*x))/(-2*a + 2*Sqrt[a]*Sqrt[a - b] + b)] - 3*PolyLog[4, -((b*E^(2*x))/(2*a + 2*Sqrt[a]*Sqrt[a - b] - b))] + 3*PolyLog[4, (b*E^(2*x))/(-2*a + 2*Sqrt[a]*Sqrt[a - b] + b)])/(8*Sqrt[a]*Sqrt[a - b])","A",1
258,1,240,327,0.7544216,"\int \frac{x^2}{a+b \sinh ^2(x)} \, dx","Integrate[x^2/(a + b*Sinh[x]^2),x]","\frac{-2 x \text{Li}_2\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a-b} \sqrt{a}-b}\right)+2 x \text{Li}_2\left(\frac{b e^{2 x}}{-2 a+2 \sqrt{a-b} \sqrt{a}+b}\right)+\text{Li}_3\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a-b} \sqrt{a}-b}\right)-\text{Li}_3\left(\frac{b e^{2 x}}{-2 a+2 \sqrt{a-b} \sqrt{a}+b}\right)-2 x^2 \log \left(\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a-b}+2 a-b}+1\right)+2 x^2 \log \left(1-\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a-b}-2 a+b}\right)}{4 \sqrt{a} \sqrt{a-b}}","\frac{x \text{Li}_2\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a-b} \sqrt{a}-b}\right)}{2 \sqrt{a} \sqrt{a-b}}-\frac{x \text{Li}_2\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a-b} \sqrt{a}-b}\right)}{2 \sqrt{a} \sqrt{a-b}}-\frac{\text{Li}_3\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a-b} \sqrt{a}-b}\right)}{4 \sqrt{a} \sqrt{a-b}}+\frac{\text{Li}_3\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a-b} \sqrt{a}-b}\right)}{4 \sqrt{a} \sqrt{a-b}}+\frac{x^2 \log \left(\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a-b}+2 a-b}+1\right)}{2 \sqrt{a} \sqrt{a-b}}-\frac{x^2 \log \left(\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a-b}+2 a-b}+1\right)}{2 \sqrt{a} \sqrt{a-b}}",1,"(-2*x^2*Log[1 + (b*E^(2*x))/(2*a + 2*Sqrt[a]*Sqrt[a - b] - b)] + 2*x^2*Log[1 - (b*E^(2*x))/(-2*a + 2*Sqrt[a]*Sqrt[a - b] + b)] - 2*x*PolyLog[2, -((b*E^(2*x))/(2*a + 2*Sqrt[a]*Sqrt[a - b] - b))] + 2*x*PolyLog[2, (b*E^(2*x))/(-2*a + 2*Sqrt[a]*Sqrt[a - b] + b)] + PolyLog[3, -((b*E^(2*x))/(2*a + 2*Sqrt[a]*Sqrt[a - b] - b))] - PolyLog[3, (b*E^(2*x))/(-2*a + 2*Sqrt[a]*Sqrt[a - b] + b)])/(4*Sqrt[a]*Sqrt[a - b])","A",1
259,1,576,215,0.8183865,"\int \frac{x}{a+b \sinh ^2(x)} \, dx","Integrate[x/(a + b*Sinh[x]^2),x]","-\frac{-2 i \cos ^{-1}\left(1-\frac{2 a}{b}\right) \tan ^{-1}\left(\frac{\sqrt{a b-a^2} \tanh (x)}{a}\right)-\log \left(\frac{2 a \left(\sqrt{a (b-a)}-i a+i b\right) (\tanh (x)-1)}{b \sqrt{a (b-a)} \tanh (x)-i a b}\right) \left(2 \tan ^{-1}\left(\frac{\sqrt{a b-a^2} \tanh (x)}{a}\right)+\cos ^{-1}\left(1-\frac{2 a}{b}\right)\right)-\log \left(\frac{2 a \left(\sqrt{a (b-a)}+i a-i b\right) (\tanh (x)+1)}{b \sqrt{a (b-a)} \tanh (x)-i a b}\right) \left(\cos ^{-1}\left(1-\frac{2 a}{b}\right)-2 \tan ^{-1}\left(\frac{\sqrt{a b-a^2} \tanh (x)}{a}\right)\right)+\log \left(\frac{\sqrt{2} e^{-x} \sqrt{a (b-a)}}{\sqrt{b} \sqrt{2 a+b \cosh (2 x)-b}}\right) \left(2 \left(\tan ^{-1}\left(\frac{\sqrt{a b-a^2} \tanh (x)}{a}\right)+\tan ^{-1}\left(\frac{a \coth (x)}{\sqrt{-a (a-b)}}\right)\right)+\cos ^{-1}\left(1-\frac{2 a}{b}\right)\right)+\log \left(\frac{\sqrt{2} e^x \sqrt{a (b-a)}}{\sqrt{b} \sqrt{2 a+b \cosh (2 x)-b}}\right) \left(\cos ^{-1}\left(1-\frac{2 a}{b}\right)-2 \left(\tan ^{-1}\left(\frac{\sqrt{a b-a^2} \tanh (x)}{a}\right)+\tan ^{-1}\left(\frac{a \coth (x)}{\sqrt{-a (a-b)}}\right)\right)\right)+i \left(\text{Li}_2\left(\frac{\left(-2 a+b+2 i \sqrt{a (b-a)}\right) \left(i a+\sqrt{a (b-a)} \tanh (x)\right)}{b \sqrt{a (b-a)} \tanh (x)-i a b}\right)-\text{Li}_2\left(\frac{\left(-2 a+b-2 i \sqrt{a (b-a)}\right) \left(i a+\sqrt{a (b-a)} \tanh (x)\right)}{b \sqrt{a (b-a)} \tanh (x)-i a b}\right)\right)+4 x \tan ^{-1}\left(\frac{a \coth (x)}{\sqrt{-a (a-b)}}\right)}{4 \sqrt{a (b-a)}}","\frac{\text{Li}_2\left(-\frac{b e^{2 x}}{2 a-2 \sqrt{a-b} \sqrt{a}-b}\right)}{4 \sqrt{a} \sqrt{a-b}}-\frac{\text{Li}_2\left(-\frac{b e^{2 x}}{2 a+2 \sqrt{a-b} \sqrt{a}-b}\right)}{4 \sqrt{a} \sqrt{a-b}}+\frac{x \log \left(\frac{b e^{2 x}}{-2 \sqrt{a} \sqrt{a-b}+2 a-b}+1\right)}{2 \sqrt{a} \sqrt{a-b}}-\frac{x \log \left(\frac{b e^{2 x}}{2 \sqrt{a} \sqrt{a-b}+2 a-b}+1\right)}{2 \sqrt{a} \sqrt{a-b}}",1,"-1/4*(4*x*ArcTan[(a*Coth[x])/Sqrt[-(a*(a - b))]] - (2*I)*ArcCos[1 - (2*a)/b]*ArcTan[(Sqrt[-a^2 + a*b]*Tanh[x])/a] + (ArcCos[1 - (2*a)/b] + 2*(ArcTan[(a*Coth[x])/Sqrt[-(a*(a - b))]] + ArcTan[(Sqrt[-a^2 + a*b]*Tanh[x])/a]))*Log[(Sqrt[2]*Sqrt[a*(-a + b)])/(Sqrt[b]*E^x*Sqrt[2*a - b + b*Cosh[2*x]])] + (ArcCos[1 - (2*a)/b] - 2*(ArcTan[(a*Coth[x])/Sqrt[-(a*(a - b))]] + ArcTan[(Sqrt[-a^2 + a*b]*Tanh[x])/a]))*Log[(Sqrt[2]*Sqrt[a*(-a + b)]*E^x)/(Sqrt[b]*Sqrt[2*a - b + b*Cosh[2*x]])] - (ArcCos[1 - (2*a)/b] + 2*ArcTan[(Sqrt[-a^2 + a*b]*Tanh[x])/a])*Log[(2*a*((-I)*a + I*b + Sqrt[a*(-a + b)])*(-1 + Tanh[x]))/((-I)*a*b + b*Sqrt[a*(-a + b)]*Tanh[x])] - (ArcCos[1 - (2*a)/b] - 2*ArcTan[(Sqrt[-a^2 + a*b]*Tanh[x])/a])*Log[(2*a*(I*a - I*b + Sqrt[a*(-a + b)])*(1 + Tanh[x]))/((-I)*a*b + b*Sqrt[a*(-a + b)]*Tanh[x])] + I*(-PolyLog[2, ((-2*a + b - (2*I)*Sqrt[a*(-a + b)])*(I*a + Sqrt[a*(-a + b)]*Tanh[x]))/((-I)*a*b + b*Sqrt[a*(-a + b)]*Tanh[x])] + PolyLog[2, ((-2*a + b + (2*I)*Sqrt[a*(-a + b)])*(I*a + Sqrt[a*(-a + b)]*Tanh[x]))/((-I)*a*b + b*Sqrt[a*(-a + b)]*Tanh[x])]))/Sqrt[a*(-a + b)]","C",1
260,1,41,47,0.1034188,"\int \frac{\cosh (a+b x) \left(-2+\sinh ^2(a+b x)\right)}{x} \, dx","Integrate[(Cosh[a + b*x]*(-2 + Sinh[a + b*x]^2))/x,x]","\frac{1}{4} (-9 \cosh (a) \text{Chi}(b x)+\cosh (3 a) \text{Chi}(3 b x)-9 \sinh (a) \text{Shi}(b x)+\sinh (3 a) \text{Shi}(3 b x))","-\frac{9}{4} \cosh (a) \text{Chi}(b x)+\frac{1}{4} \cosh (3 a) \text{Chi}(3 b x)-\frac{9}{4} \sinh (a) \text{Shi}(b x)+\frac{1}{4} \sinh (3 a) \text{Shi}(3 b x)",1,"(-9*Cosh[a]*CoshIntegral[b*x] + Cosh[3*a]*CoshIntegral[3*b*x] - 9*Sinh[a]*SinhIntegral[b*x] + Sinh[3*a]*SinhIntegral[3*b*x])/4","A",1
261,1,55,58,0.0806973,"\int \frac{\sinh ^3\left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Integrate[Sinh[Sqrt[1 - a*x]/Sqrt[1 + a*x]]^3/(1 - a^2*x^2),x]","\frac{3 \text{Shi}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)-\text{Shi}\left(\frac{3 \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{4 a}","\frac{3 \text{Shi}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)}{4 a}-\frac{\text{Shi}\left(\frac{3 \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{4 a}",1,"(3*SinhIntegral[Sqrt[1 - a*x]/Sqrt[1 + a*x]] - SinhIntegral[(3*Sqrt[1 - a*x])/Sqrt[1 + a*x]])/(4*a)","A",1
262,1,57,58,0.0367638,"\int \frac{\sinh ^2\left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Integrate[Sinh[Sqrt[1 - a*x]/Sqrt[1 + a*x]]^2/(1 - a^2*x^2),x]","-\frac{\text{Chi}\left(\frac{2 \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}+\frac{\log (1-a x)}{4 a}-\frac{\log (a x+1)}{4 a}","\frac{\log \left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}-\frac{\text{Chi}\left(\frac{2 \sqrt{1-a x}}{\sqrt{a x+1}}\right)}{2 a}",1,"-1/2*CoshIntegral[(2*Sqrt[1 - a*x])/Sqrt[1 + a*x]]/a + Log[1 - a*x]/(4*a) - Log[1 + a*x]/(4*a)","A",1
263,1,26,26,0.0308534,"\int \frac{\sinh \left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Integrate[Sinh[Sqrt[1 - a*x]/Sqrt[1 + a*x]]/(1 - a^2*x^2),x]","-\frac{\text{Shi}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}","-\frac{\text{Shi}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)}{a}",1,"-(SinhIntegral[Sqrt[1 - a*x]/Sqrt[1 + a*x]]/a)","A",1
264,0,0,40,13.0898972,"\int \frac{\text{csch}\left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Integrate[Csch[Sqrt[1 - a*x]/Sqrt[1 + a*x]]/(1 - a^2*x^2),x]","\int \frac{\text{csch}\left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","\text{Int}\left(\frac{\text{csch}\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)}{(1-a x) (a x+1)},x\right)",0,"Integrate[Csch[Sqrt[1 - a*x]/Sqrt[1 + a*x]]/(1 - a^2*x^2), x]","A",-1
265,0,0,42,38.0626572,"\int \frac{\text{csch}^2\left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","Integrate[Csch[Sqrt[1 - a*x]/Sqrt[1 + a*x]]^2/(1 - a^2*x^2),x]","\int \frac{\text{csch}^2\left(\frac{\sqrt{1-a x}}{\sqrt{1+a x}}\right)}{1-a^2 x^2} \, dx","\text{Int}\left(\frac{\text{csch}^2\left(\frac{\sqrt{1-a x}}{\sqrt{a x+1}}\right)}{(1-a x) (a x+1)},x\right)",0,"Integrate[Csch[Sqrt[1 - a*x]/Sqrt[1 + a*x]]^2/(1 - a^2*x^2), x]","A",-1
266,1,41,54,0.0704811,"\int \sinh \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Sinh[a + b*Log[c*x^n]],x]","\frac{x \left(b n \cosh \left(a+b \log \left(c x^n\right)\right)-\sinh \left(a+b \log \left(c x^n\right)\right)\right)}{b^2 n^2-1}","\frac{x \sinh \left(a+b \log \left(c x^n\right)\right)}{1-b^2 n^2}-\frac{b n x \cosh \left(a+b \log \left(c x^n\right)\right)}{1-b^2 n^2}",1,"(x*(b*n*Cosh[a + b*Log[c*x^n]] - Sinh[a + b*Log[c*x^n]]))/(-1 + b^2*n^2)","A",1
267,1,55,88,0.115174,"\int \sinh ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Sinh[a + b*Log[c*x^n]]^2,x]","-\frac{x \left(-2 b n \sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+\cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+4 b^2 n^2-1\right)}{8 b^2 n^2-2}","\frac{x \sinh ^2\left(a+b \log \left(c x^n\right)\right)}{1-4 b^2 n^2}-\frac{2 b n x \sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{1-4 b^2 n^2}+\frac{2 b^2 n^2 x}{1-4 b^2 n^2}",1,"-((x*(-1 + 4*b^2*n^2 + Cosh[2*(a + b*Log[c*x^n])] - 2*b*n*Sinh[2*(a + b*Log[c*x^n])]))/(-2 + 8*b^2*n^2))","A",1
268,1,120,149,0.5258476,"\int \sinh ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Sinh[a + b*Log[c*x^n]]^3,x]","\frac{x \left(-3 b n \left(9 b^2 n^2-1\right) \cosh \left(a+b \log \left(c x^n\right)\right)+3 b n \left(b^2 n^2-1\right) \cosh \left(3 \left(a+b \log \left(c x^n\right)\right)\right)-2 \sinh \left(a+b \log \left(c x^n\right)\right) \left(\left(b^2 n^2-1\right) \cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)-13 b^2 n^2+1\right)\right)}{36 b^4 n^4-40 b^2 n^2+4}","\frac{x \sinh ^3\left(a+b \log \left(c x^n\right)\right)}{1-9 b^2 n^2}-\frac{3 b n x \sinh ^2\left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{1-9 b^2 n^2}+\frac{6 b^2 n^2 x \sinh \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4-10 b^2 n^2+1}-\frac{6 b^3 n^3 x \cosh \left(a+b \log \left(c x^n\right)\right)}{9 b^4 n^4-10 b^2 n^2+1}",1,"(x*(-3*b*n*(-1 + 9*b^2*n^2)*Cosh[a + b*Log[c*x^n]] + 3*b*n*(-1 + b^2*n^2)*Cosh[3*(a + b*Log[c*x^n])] - 2*(1 - 13*b^2*n^2 + (-1 + b^2*n^2)*Cosh[2*(a + b*Log[c*x^n])])*Sinh[a + b*Log[c*x^n]]))/(4 - 40*b^2*n^2 + 36*b^4*n^4)","A",1
269,1,167,191,0.4420771,"\int \sinh ^4\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[Sinh[a + b*Log[c*x^n]]^4,x]","\frac{x \left(-128 b^3 n^3 \sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+16 b^3 n^3 \sinh \left(4 \left(a+b \log \left(c x^n\right)\right)\right)+\left(64 b^2 n^2-4\right) \cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+\left(1-4 b^2 n^2\right) \cosh \left(4 \left(a+b \log \left(c x^n\right)\right)\right)+8 b n \sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)-4 b n \sinh \left(4 \left(a+b \log \left(c x^n\right)\right)\right)+192 b^4 n^4-60 b^2 n^2+3\right)}{8 \left(64 b^4 n^4-20 b^2 n^2+1\right)}","\frac{x \sinh ^4\left(a+b \log \left(c x^n\right)\right)}{1-16 b^2 n^2}-\frac{4 b n x \sinh ^3\left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{1-16 b^2 n^2}+\frac{12 b^2 n^2 x \sinh ^2\left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4-20 b^2 n^2+1}-\frac{24 b^3 n^3 x \sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{64 b^4 n^4-20 b^2 n^2+1}+\frac{24 b^4 n^4 x}{64 b^4 n^4-20 b^2 n^2+1}",1,"(x*(3 - 60*b^2*n^2 + 192*b^4*n^4 + (-4 + 64*b^2*n^2)*Cosh[2*(a + b*Log[c*x^n])] + (1 - 4*b^2*n^2)*Cosh[4*(a + b*Log[c*x^n])] + 8*b*n*Sinh[2*(a + b*Log[c*x^n])] - 128*b^3*n^3*Sinh[2*(a + b*Log[c*x^n])] - 4*b*n*Sinh[4*(a + b*Log[c*x^n])] + 16*b^3*n^3*Sinh[4*(a + b*Log[c*x^n])]))/(8*(1 - 20*b^2*n^2 + 64*b^4*n^4))","A",1
270,1,54,73,0.1408396,"\int x^m \sinh \left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^m*Sinh[a + b*Log[c*x^n]],x]","\frac{x^{m+1} \left((m+1) \sinh \left(a+b \log \left(c x^n\right)\right)-b n \cosh \left(a+b \log \left(c x^n\right)\right)\right)}{(-b n+m+1) (b n+m+1)}","\frac{(m+1) x^{m+1} \sinh \left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-b^2 n^2}-\frac{b n x^{m+1} \cosh \left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-b^2 n^2}",1,"(x^(1 + m)*(-(b*n*Cosh[a + b*Log[c*x^n]]) + (1 + m)*Sinh[a + b*Log[c*x^n]]))/((1 + m - b*n)*(1 + m + b*n))","A",1
271,1,89,120,0.3022222,"\int x^m \sinh ^2\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^m*Sinh[a + b*Log[c*x^n]]^2,x]","\frac{x^{m+1} \left(-2 b (m+1) n \sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+(m+1)^2 \cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+4 b^2 n^2-m^2-2 m-1\right)}{2 (m+1) (-2 b n+m+1) (2 b n+m+1)}","\frac{(m+1) x^{m+1} \sinh ^2\left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-4 b^2 n^2}-\frac{2 b n x^{m+1} \sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-4 b^2 n^2}+\frac{2 b^2 n^2 x^{m+1}}{(m+1) \left((m+1)^2-4 b^2 n^2\right)}",1,"(x^(1 + m)*(-1 - 2*m - m^2 + 4*b^2*n^2 + (1 + m)^2*Cosh[2*(a + b*Log[c*x^n])] - 2*b*(1 + m)*n*Sinh[2*(a + b*Log[c*x^n])]))/(2*(1 + m)*(1 + m - 2*b*n)*(1 + m + 2*b*n))","A",1
272,1,292,203,1.3457849,"\int x^m \sinh ^3\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^m*Sinh[a + b*Log[c*x^n]]^3,x]","\frac{1}{4} x^{m+1} \left(-\frac{3 \cosh (b n \log (x)) \left((m+1) \sinh \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-b n \cosh \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)}{(-b n+m+1) (b n+m+1)}-\frac{3 \sinh (b n \log (x)) \left((m+1) \cosh \left(a+b \log \left(c x^n\right)-b n \log (x)\right)-b n \sinh \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)}{(-b n+m+1) (b n+m+1)}+\frac{\cosh (3 b n \log (x)) \left((m+1) \sinh \left(3 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)-3 b n \cosh \left(3 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)\right)}{(-3 b n+m+1) (3 b n+m+1)}+\frac{\sinh (3 b n \log (x)) \left((m+1) \cosh \left(3 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)-3 b n \sinh \left(3 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)\right)}{(-3 b n+m+1) (3 b n+m+1)}\right)","\frac{(m+1) x^{m+1} \sinh ^3\left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-9 b^2 n^2}+\frac{6 b^2 (m+1) n^2 x^{m+1} \sinh \left(a+b \log \left(c x^n\right)\right)}{\left((m+1)^2-9 b^2 n^2\right) \left((m+1)^2-b^2 n^2\right)}-\frac{3 b n x^{m+1} \sinh ^2\left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-9 b^2 n^2}-\frac{6 b^3 n^3 x^{m+1} \cosh \left(a+b \log \left(c x^n\right)\right)}{\left((m+1)^2-9 b^2 n^2\right) \left((m+1)^2-b^2 n^2\right)}",1,"(x^(1 + m)*((-3*Cosh[b*n*Log[x]]*(-(b*n*Cosh[a - b*n*Log[x] + b*Log[c*x^n]]) + (1 + m)*Sinh[a - b*n*Log[x] + b*Log[c*x^n]]))/((1 + m - b*n)*(1 + m + b*n)) - (3*Sinh[b*n*Log[x]]*((1 + m)*Cosh[a - b*n*Log[x] + b*Log[c*x^n]] - b*n*Sinh[a - b*n*Log[x] + b*Log[c*x^n]]))/((1 + m - b*n)*(1 + m + b*n)) + (Cosh[3*b*n*Log[x]]*(-3*b*n*Cosh[3*(a - b*n*Log[x] + b*Log[c*x^n])] + (1 + m)*Sinh[3*(a - b*n*Log[x] + b*Log[c*x^n])]))/((1 + m - 3*b*n)*(1 + m + 3*b*n)) + (Sinh[3*b*n*Log[x]]*((1 + m)*Cosh[3*(a - b*n*Log[x] + b*Log[c*x^n])] - 3*b*n*Sinh[3*(a - b*n*Log[x] + b*Log[c*x^n])]))/((1 + m - 3*b*n)*(1 + m + 3*b*n))))/4","A",1
273,1,311,266,3.4919399,"\int x^m \sinh ^4\left(a+b \log \left(c x^n\right)\right) \, dx","Integrate[x^m*Sinh[a + b*Log[c*x^n]]^4,x]","\frac{1}{8} x^{m+1} \left(-\frac{4 \sinh (2 b n \log (x)) \left((m+1) \sinh \left(2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)-2 b n \cosh \left(2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)\right)}{(-2 b n+m+1) (2 b n+m+1)}-\frac{4 \cosh (2 b n \log (x)) \left((m+1) \cosh \left(2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)-2 b n \sinh \left(2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)\right)}{(-2 b n+m+1) (2 b n+m+1)}+\frac{\sinh (4 b n \log (x)) \left((m+1) \sinh \left(4 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)-4 b n \cosh \left(4 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)\right)}{(-4 b n+m+1) (4 b n+m+1)}+\frac{\cosh (4 b n \log (x)) \left((m+1) \cosh \left(4 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)-4 b n \sinh \left(4 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)\right)\right)}{(-4 b n+m+1) (4 b n+m+1)}+\frac{3}{m+1}\right)","\frac{(m+1) x^{m+1} \sinh ^4\left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-16 b^2 n^2}+\frac{12 b^2 (m+1) n^2 x^{m+1} \sinh ^2\left(a+b \log \left(c x^n\right)\right)}{\left((m+1)^2-16 b^2 n^2\right) \left((m+1)^2-4 b^2 n^2\right)}-\frac{4 b n x^{m+1} \sinh ^3\left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{(m+1)^2-16 b^2 n^2}-\frac{24 b^3 n^3 x^{m+1} \sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{\left((m+1)^2-16 b^2 n^2\right) \left((m+1)^2-4 b^2 n^2\right)}+\frac{24 b^4 n^4 x^{m+1}}{(m+1) \left((m+1)^2-16 b^2 n^2\right) \left((m+1)^2-4 b^2 n^2\right)}",1,"(x^(1 + m)*(3/(1 + m) - (4*Sinh[2*b*n*Log[x]]*(-2*b*n*Cosh[2*(a - b*n*Log[x] + b*Log[c*x^n])] + (1 + m)*Sinh[2*(a - b*n*Log[x] + b*Log[c*x^n])]))/((1 + m - 2*b*n)*(1 + m + 2*b*n)) - (4*Cosh[2*b*n*Log[x]]*((1 + m)*Cosh[2*(a - b*n*Log[x] + b*Log[c*x^n])] - 2*b*n*Sinh[2*(a - b*n*Log[x] + b*Log[c*x^n])]))/((1 + m - 2*b*n)*(1 + m + 2*b*n)) + (Sinh[4*b*n*Log[x]]*(-4*b*n*Cosh[4*(a - b*n*Log[x] + b*Log[c*x^n])] + (1 + m)*Sinh[4*(a - b*n*Log[x] + b*Log[c*x^n])]))/((1 + m - 4*b*n)*(1 + m + 4*b*n)) + (Cosh[4*b*n*Log[x]]*((1 + m)*Cosh[4*(a - b*n*Log[x] + b*Log[c*x^n])] - 4*b*n*Sinh[4*(a - b*n*Log[x] + b*Log[c*x^n])]))/((1 + m - 4*b*n)*(1 + m + 4*b*n))))/8","A",1
274,1,37,18,0.0115423,"\int \frac{\sinh \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Sinh[a + b*Log[c*x^n]]/x,x]","\frac{\sinh (a) \sinh \left(b \log \left(c x^n\right)\right)}{b n}+\frac{\cosh (a) \cosh \left(b \log \left(c x^n\right)\right)}{b n}","\frac{\cosh \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"(Cosh[a]*Cosh[b*Log[c*x^n]])/(b*n) + (Sinh[a]*Sinh[b*Log[c*x^n]])/(b*n)","B",1
275,1,36,39,0.029498,"\int \frac{\sinh ^2\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Sinh[a + b*Log[c*x^n]]^2/x,x]","\frac{\sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)-2 \left(a+b \log \left(c x^n\right)\right)}{4 b n}","\frac{\sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{2 b n}-\frac{\log (x)}{2}",1,"(-2*(a + b*Log[c*x^n]) + Sinh[2*(a + b*Log[c*x^n])])/(4*b*n)","A",1
276,1,45,43,0.0138737,"\int \frac{\sinh ^3\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Sinh[a + b*Log[c*x^n]]^3/x,x]","\frac{\cosh \left(3 \left(a+b \log \left(c x^n\right)\right)\right)}{12 b n}-\frac{3 \cosh \left(a+b \log \left(c x^n\right)\right)}{4 b n}","\frac{\cosh ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}-\frac{\cosh \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"(-3*Cosh[a + b*Log[c*x^n]])/(4*b*n) + Cosh[3*(a + b*Log[c*x^n])]/(12*b*n)","A",1
277,1,51,73,0.0447712,"\int \frac{\sinh ^4\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Sinh[a + b*Log[c*x^n]]^4/x,x]","\frac{12 \left(a+b \log \left(c x^n\right)\right)-8 \sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+\sinh \left(4 \left(a+b \log \left(c x^n\right)\right)\right)}{32 b n}","\frac{\sinh ^3\left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{4 b n}-\frac{3 \sinh \left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{8 b n}+\frac{3 \log (x)}{8}",1,"(12*(a + b*Log[c*x^n]) - 8*Sinh[2*(a + b*Log[c*x^n])] + Sinh[4*(a + b*Log[c*x^n])])/(32*b*n)","A",1
278,1,68,65,0.0193847,"\int \frac{\sinh ^5\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Sinh[a + b*Log[c*x^n]]^5/x,x]","\frac{5 \cosh \left(a+b \log \left(c x^n\right)\right)}{8 b n}-\frac{5 \cosh \left(3 \left(a+b \log \left(c x^n\right)\right)\right)}{48 b n}+\frac{\cosh \left(5 \left(a+b \log \left(c x^n\right)\right)\right)}{80 b n}","\frac{\cosh ^5\left(a+b \log \left(c x^n\right)\right)}{5 b n}-\frac{2 \cosh ^3\left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{\cosh \left(a+b \log \left(c x^n\right)\right)}{b n}",1,"(5*Cosh[a + b*Log[c*x^n]])/(8*b*n) - (5*Cosh[3*(a + b*Log[c*x^n])])/(48*b*n) + Cosh[5*(a + b*Log[c*x^n])]/(80*b*n)","A",1
279,1,96,111,0.08978,"\int \frac{\sinh ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Sinh[a + b*Log[c*x^n]]^(5/2)/x,x]","\frac{\sinh \left(a+b \log \left(c x^n\right)\right) \sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)-6 \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{4} \left(-2 i a-2 i b \log \left(c x^n\right)+\pi \right)\right|2\right)}{5 b n \sqrt{\sinh \left(a+b \log \left(c x^n\right)\right)}}","\frac{2 \sinh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right) \cosh \left(a+b \log \left(c x^n\right)\right)}{5 b n}+\frac{6 i \sqrt{\sinh \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(i a+i b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{5 b n \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)}}",1,"(-6*EllipticE[((-2*I)*a + Pi - (2*I)*b*Log[c*x^n])/4, 2]*Sqrt[I*Sinh[a + b*Log[c*x^n]]] + Sinh[a + b*Log[c*x^n]]*Sinh[2*(a + b*Log[c*x^n])])/(5*b*n*Sqrt[Sinh[a + b*Log[c*x^n]]])","A",1
280,1,114,111,0.1384173,"\int \frac{\sinh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Integrate[Sinh[a + b*Log[c*x^n]]^(3/2)/x,x]","\frac{\sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)-2 \sqrt{-\sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)-\cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+\sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)\right)}{3 b n \sqrt{\sinh \left(a+b \log \left(c x^n\right)\right)}}","\frac{2 \sqrt{\sinh \left(a+b \log \left(c x^n\right)\right)} \cosh \left(a+b \log \left(c x^n\right)\right)}{3 b n}+\frac{2 i \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(i a+i b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{3 b n \sqrt{\sinh \left(a+b \log \left(c x^n\right)\right)}}",1,"(-2*Hypergeometric2F1[1/4, 1/2, 5/4, Cosh[2*(a + b*Log[c*x^n])] + Sinh[2*(a + b*Log[c*x^n])]]*Sqrt[1 - Cosh[2*(a + b*Log[c*x^n])] - Sinh[2*(a + b*Log[c*x^n])]] + Sinh[2*(a + b*Log[c*x^n])])/(3*b*n*Sqrt[Sinh[a + b*Log[c*x^n]]])","C",1
281,1,68,72,0.0412236,"\int \frac{\sqrt{\sinh \left(a+b \log \left(c x^n\right)\right)}}{x} \, dx","Integrate[Sqrt[Sinh[a + b*Log[c*x^n]]]/x,x]","\frac{2 \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(\frac{\pi }{2}-i \left(a+b \log \left(c x^n\right)\right)\right)\right|2\right)}{b n \sqrt{\sinh \left(a+b \log \left(c x^n\right)\right)}}","-\frac{2 i \sqrt{\sinh \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(i a+i b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)}}",1,"(2*EllipticE[(Pi/2 - I*(a + b*Log[c*x^n]))/2, 2]*Sqrt[I*Sinh[a + b*Log[c*x^n]]])/(b*n*Sqrt[Sinh[a + b*Log[c*x^n]]])","A",1
282,1,66,72,0.0451409,"\int \frac{1}{x \sqrt{\sinh \left(a+b \log \left(c x^n\right)\right)}} \, dx","Integrate[1/(x*Sqrt[Sinh[a + b*Log[c*x^n]]]),x]","-\frac{2 \sqrt{\sinh \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{4} \left(-2 i a-2 i b \log \left(c x^n\right)+\pi \right)\right|2\right)}{b n \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)}}","-\frac{2 i \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(i a+i b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n \sqrt{\sinh \left(a+b \log \left(c x^n\right)\right)}}",1,"(-2*EllipticF[((-2*I)*a + Pi - (2*I)*b*Log[c*x^n])/4, 2]*Sqrt[Sinh[a + b*Log[c*x^n]]])/(b*n*Sqrt[I*Sinh[a + b*Log[c*x^n]]])","A",1
283,1,80,107,0.0617414,"\int \frac{1}{x \sinh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x*Sinh[a + b*Log[c*x^n]]^(3/2)),x]","-\frac{2 \left(\cosh \left(a+b \log \left(c x^n\right)\right)-\sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{4} \left(-2 i a-2 i b \log \left(c x^n\right)+\pi \right)\right|2\right)\right)}{b n \sqrt{\sinh \left(a+b \log \left(c x^n\right)\right)}}","-\frac{2 \cosh \left(a+b \log \left(c x^n\right)\right)}{b n \sqrt{\sinh \left(a+b \log \left(c x^n\right)\right)}}-\frac{2 i \sqrt{\sinh \left(a+b \log \left(c x^n\right)\right)} E\left(\left.\frac{1}{2} \left(i a+i b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{b n \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)}}",1,"(-2*(Cosh[a + b*Log[c*x^n]] - EllipticE[((-2*I)*a + Pi - (2*I)*b*Log[c*x^n])/4, 2]*Sqrt[I*Sinh[a + b*Log[c*x^n]]]))/(b*n*Sqrt[Sinh[a + b*Log[c*x^n]]])","A",1
284,1,122,111,0.1279014,"\int \frac{1}{x \sinh ^{\frac{5}{2}}\left(a+b \log \left(c x^n\right)\right)} \, dx","Integrate[1/(x*Sinh[a + b*Log[c*x^n]]^(5/2)),x]","-\frac{2 \left(\sinh \left(a+b \log \left(c x^n\right)\right) \sqrt{-\sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)-\cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+1} \, _2F_1\left(\frac{1}{4},\frac{1}{2};\frac{5}{4};\cosh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)+\sinh \left(2 \left(a+b \log \left(c x^n\right)\right)\right)\right)+\cosh \left(a+b \log \left(c x^n\right)\right)\right)}{3 b n \sinh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}","-\frac{2 \cosh \left(a+b \log \left(c x^n\right)\right)}{3 b n \sinh ^{\frac{3}{2}}\left(a+b \log \left(c x^n\right)\right)}+\frac{2 i \sqrt{i \sinh \left(a+b \log \left(c x^n\right)\right)} F\left(\left.\frac{1}{2} \left(i a+i b \log \left(c x^n\right)-\frac{\pi }{2}\right)\right|2\right)}{3 b n \sqrt{\sinh \left(a+b \log \left(c x^n\right)\right)}}",1,"(-2*(Cosh[a + b*Log[c*x^n]] + Hypergeometric2F1[1/4, 1/2, 5/4, Cosh[2*(a + b*Log[c*x^n])] + Sinh[2*(a + b*Log[c*x^n])]]*Sinh[a + b*Log[c*x^n]]*Sqrt[1 - Cosh[2*(a + b*Log[c*x^n])] - Sinh[2*(a + b*Log[c*x^n])]]))/(3*b*n*Sinh[a + b*Log[c*x^n]]^(3/2))","C",1
285,1,86,209,0.4425893,"\int \sinh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right) \, dx","Integrate[Sinh[a + (2*Log[c*x^n])/n]^(5/2),x]","\frac{1}{14} e^{2 a} x \left(c x^n\right)^{4/n} \left(e^{2 a} \left(c x^n\right)^{4/n}-1\right) \, _2F_1\left(2,\frac{7}{2};\frac{9}{2};1-e^{2 a} \left(c x^n\right)^{4/n}\right) \sinh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)","-\frac{5 e^{-2 a} x \left(c x^n\right)^{-4/n} \sinh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}{4 \left(1-e^{-2 a} \left(c x^n\right)^{-4/n}\right)^2}-\frac{1}{4} x \sinh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)+\frac{5 x \sinh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}{12 \left(1-e^{-2 a} \left(c x^n\right)^{-4/n}\right)}-\frac{5 e^{-3 a} x \left(c x^n\right)^{-6/n} \csc ^{-1}\left(e^a \left(c x^n\right)^{2/n}\right) \sinh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}{4 \left(1-e^{-2 a} \left(c x^n\right)^{-4/n}\right)^{5/2}}",1,"(E^(2*a)*x*(c*x^n)^(4/n)*(-1 + E^(2*a)*(c*x^n)^(4/n))*Hypergeometric2F1[2, 7/2, 9/2, 1 - E^(2*a)*(c*x^n)^(4/n)]*Sinh[a + (2*Log[c*x^n])/n]^(5/2))/14","C",0
286,1,74,103,0.2866771,"\int \sqrt{\sinh \left(a+\frac{2 \log \left(c x^n\right)}{n}\right)} \, dx","Integrate[Sqrt[Sinh[a + (2*Log[c*x^n])/n]],x]","\frac{1}{2} x \left(1-\frac{\tan ^{-1}\left(\sqrt{e^{2 a} \left(c x^n\right)^{4/n}-1}\right)}{\sqrt{e^{2 a} \left(c x^n\right)^{4/n}-1}}\right) \sqrt{\sinh \left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}","\frac{1}{2} x \sqrt{\sinh \left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}+\frac{e^{-a} x \left(c x^n\right)^{-2/n} \csc ^{-1}\left(e^a \left(c x^n\right)^{2/n}\right) \sqrt{\sinh \left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}}{2 \sqrt{1-e^{-2 a} \left(c x^n\right)^{-4/n}}}",1,"(x*(1 - ArcTan[Sqrt[-1 + E^(2*a)*(c*x^n)^(4/n)]]/Sqrt[-1 + E^(2*a)*(c*x^n)^(4/n)])*Sqrt[Sinh[a + (2*Log[c*x^n])/n]])/2","A",0
287,1,61,43,0.1546429,"\int \frac{1}{\sinh ^{\frac{3}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)} \, dx","Integrate[Sinh[a + (2*Log[c*x^n])/n]^(-3/2),x]","\frac{\sinh \left(a+\frac{2 \log \left(c x^n\right)}{n}-2 \log (x)\right)-\cosh \left(a+\frac{2 \log \left(c x^n\right)}{n}-2 \log (x)\right)}{x \sqrt{\sinh \left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}}","-\frac{x \left(1-e^{-2 a} \left(c x^n\right)^{-4/n}\right)}{2 \sinh ^{\frac{3}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}",1,"(-Cosh[a - 2*Log[x] + (2*Log[c*x^n])/n] + Sinh[a - 2*Log[x] + (2*Log[c*x^n])/n])/(x*Sqrt[Sinh[a + (2*Log[c*x^n])/n]])","A",1
288,1,121,103,0.2729895,"\int \frac{1}{\sinh ^{\frac{7}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)} \, dx","Integrate[Sinh[a + (2*Log[c*x^n])/n]^(-7/2),x]","\frac{\left(\left(5 x^4+2\right) \sinh \left(a+\frac{2 \log \left(c x^n\right)}{n}-2 \log (x)\right)+\left(5 x^4-2\right) \cosh \left(a+\frac{2 \log \left(c x^n\right)}{n}-2 \log (x)\right)\right) \left(\sinh \left(2 a+\frac{4 \log \left(c x^n\right)}{n}-4 \log (x)\right)-\cosh \left(2 a+\frac{4 \log \left(c x^n\right)}{n}-4 \log (x)\right)\right)}{15 x^5 \sinh ^{\frac{5}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}","\frac{e^{-2 a} x \left(c x^n\right)^{-4/n} \left(1-e^{-2 a} \left(c x^n\right)^{-4/n}\right)}{15 \sinh ^{\frac{7}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}-\frac{x \left(1-e^{-2 a} \left(c x^n\right)^{-4/n}\right)}{6 \sinh ^{\frac{7}{2}}\left(a+\frac{2 \log \left(c x^n\right)}{n}\right)}",1,"(((-2 + 5*x^4)*Cosh[a - 2*Log[x] + (2*Log[c*x^n])/n] + (2 + 5*x^4)*Sinh[a - 2*Log[x] + (2*Log[c*x^n])/n])*(-Cosh[2*a - 4*Log[x] + (4*Log[c*x^n])/n] + Sinh[2*a - 4*Log[x] + (4*Log[c*x^n])/n]))/(15*x^5*Sinh[a + (2*Log[c*x^n])/n]^(5/2))","A",1
289,1,36,36,0.0195155,"\int \sinh \left(\frac{a}{c+d x}\right) \, dx","Integrate[Sinh[a/(c + d*x)],x]","\frac{(c+d x) \sinh \left(\frac{a}{c+d x}\right)}{d}-\frac{a \text{Chi}\left(\frac{a}{c+d x}\right)}{d}","\frac{(c+d x) \sinh \left(\frac{a}{c+d x}\right)}{d}-\frac{a \text{Chi}\left(\frac{a}{c+d x}\right)}{d}",1,"-((a*CoshIntegral[a/(c + d*x)])/d) + ((c + d*x)*Sinh[a/(c + d*x)])/d","A",1
290,1,37,39,0.0384536,"\int \sinh ^2\left(\frac{a}{c+d x}\right) \, dx","Integrate[Sinh[a/(c + d*x)]^2,x]","\frac{(c+d x) \sinh ^2\left(\frac{a}{c+d x}\right)-a \text{Shi}\left(\frac{2 a}{c+d x}\right)}{d}","\frac{(c+d x) \sinh ^2\left(\frac{a}{c+d x}\right)}{d}-\frac{a \text{Shi}\left(\frac{2 a}{c+d x}\right)}{d}",1,"((c + d*x)*Sinh[a/(c + d*x)]^2 - a*SinhIntegral[(2*a)/(c + d*x)])/d","A",1
291,1,54,59,0.0600298,"\int \sinh ^3\left(\frac{a}{c+d x}\right) \, dx","Integrate[Sinh[a/(c + d*x)]^3,x]","\frac{3 a \text{Chi}\left(\frac{a}{c+d x}\right)-3 a \text{Chi}\left(\frac{3 a}{c+d x}\right)+4 (c+d x) \sinh ^3\left(\frac{a}{c+d x}\right)}{4 d}","\frac{3 a \text{Chi}\left(\frac{a}{c+d x}\right)}{4 d}-\frac{3 a \text{Chi}\left(\frac{3 a}{c+d x}\right)}{4 d}+\frac{(c+d x) \sinh ^3\left(\frac{a}{c+d x}\right)}{d}",1,"(3*a*CoshIntegral[a/(c + d*x)] - 3*a*CoshIntegral[(3*a)/(c + d*x)] + 4*(c + d*x)*Sinh[a/(c + d*x)]^3)/(4*d)","A",1
292,1,70,74,0.3024842,"\int \sinh \left(\frac{b x}{c+d x}\right) \, dx","Integrate[Sinh[(b*x)/(c + d*x)],x]","\frac{b c \cosh \left(\frac{b}{d}\right) \text{Chi}\left(\frac{b c}{d (c+d x)}\right)-b c \sinh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{b c}{d (c+d x)}\right)+d (c+d x) \sinh \left(\frac{b x}{c+d x}\right)}{d^2}","\frac{b c \cosh \left(\frac{b}{d}\right) \text{Chi}\left(\frac{b c}{d (c+d x)}\right)}{d^2}-\frac{b c \sinh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{b c}{d (c+d x)}\right)}{d^2}+\frac{(c+d x) \sinh \left(\frac{b x}{c+d x}\right)}{d}",1,"(b*c*Cosh[b/d]*CoshIntegral[(b*c)/(d*(c + d*x))] + d*(c + d*x)*Sinh[(b*x)/(c + d*x)] - b*c*Sinh[b/d]*SinhIntegral[(b*c)/(d*(c + d*x))])/d^2","A",1
293,1,85,80,0.3835531,"\int \sinh ^2\left(\frac{b x}{c+d x}\right) \, dx","Integrate[Sinh[(b*x)/(c + d*x)]^2,x]","\frac{2 b c \sinh \left(\frac{2 b}{d}\right) \text{Chi}\left(\frac{2 b c}{d (c+d x)}\right)-2 b c \cosh \left(\frac{2 b}{d}\right) \text{Shi}\left(\frac{2 b c}{d (c+d x)}\right)+d \left((c+d x) \cosh \left(\frac{2 b x}{c+d x}\right)-d x\right)}{2 d^2}","\frac{b c \sinh \left(\frac{2 b}{d}\right) \text{Chi}\left(\frac{2 b c}{d (c+d x)}\right)}{d^2}-\frac{b c \cosh \left(\frac{2 b}{d}\right) \text{Shi}\left(\frac{2 b c}{d (c+d x)}\right)}{d^2}+\frac{(c+d x) \sinh ^2\left(\frac{b x}{c+d x}\right)}{d}",1,"(d*(-(d*x) + (c + d*x)*Cosh[(2*b*x)/(c + d*x)]) + 2*b*c*CoshIntegral[(2*b*c)/(d*(c + d*x))]*Sinh[(2*b)/d] - 2*b*c*Cosh[(2*b)/d]*SinhIntegral[(2*b*c)/(d*(c + d*x))])/(2*d^2)","A",1
294,1,172,143,0.4871013,"\int \sinh ^3\left(\frac{b x}{c+d x}\right) \, dx","Integrate[Sinh[(b*x)/(c + d*x)]^3,x]","\frac{-3 b c \cosh \left(\frac{b}{d}\right) \text{Chi}\left(\frac{b c}{d (c+d x)}\right)+3 b c \cosh \left(\frac{3 b}{d}\right) \text{Chi}\left(\frac{3 b c}{d (c+d x)}\right)-3 d^2 x \sinh \left(\frac{b x}{c+d x}\right)+d^2 x \sinh \left(\frac{3 b x}{c+d x}\right)+3 b c \sinh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{b c}{d (c+d x)}\right)-3 b c \sinh \left(\frac{3 b}{d}\right) \text{Shi}\left(\frac{3 b c}{d (c+d x)}\right)-3 c d \sinh \left(\frac{b x}{c+d x}\right)+c d \sinh \left(\frac{3 b x}{c+d x}\right)}{4 d^2}","-\frac{3 b c \cosh \left(\frac{b}{d}\right) \text{Chi}\left(\frac{b c}{d (c+d x)}\right)}{4 d^2}+\frac{3 b c \cosh \left(\frac{3 b}{d}\right) \text{Chi}\left(\frac{3 b c}{d (c+d x)}\right)}{4 d^2}+\frac{3 b c \sinh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{b c}{d (c+d x)}\right)}{4 d^2}-\frac{3 b c \sinh \left(\frac{3 b}{d}\right) \text{Shi}\left(\frac{3 b c}{d (c+d x)}\right)}{4 d^2}+\frac{(c+d x) \sinh ^3\left(\frac{b x}{c+d x}\right)}{d}",1,"(-3*b*c*Cosh[b/d]*CoshIntegral[(b*c)/(d*(c + d*x))] + 3*b*c*Cosh[(3*b)/d]*CoshIntegral[(3*b*c)/(d*(c + d*x))] - 3*c*d*Sinh[(b*x)/(c + d*x)] - 3*d^2*x*Sinh[(b*x)/(c + d*x)] + c*d*Sinh[(3*b*x)/(c + d*x)] + d^2*x*Sinh[(3*b*x)/(c + d*x)] + 3*b*c*Sinh[b/d]*SinhIntegral[(b*c)/(d*(c + d*x))] - 3*b*c*Sinh[(3*b)/d]*SinhIntegral[(3*b*c)/(d*(c + d*x))])/(4*d^2)","A",1
295,1,373,101,0.7129444,"\int \sinh \left(\frac{a+b x}{c+d x}\right) \, dx","Integrate[Sinh[(a + b*x)/(c + d*x)],x]","\frac{(b c-a d) \left(\cosh \left(\frac{b}{d}\right)-\sinh \left(\frac{b}{d}\right)\right) \text{Chi}\left(\frac{b c-a d}{x d^2+c d}\right)+(b c-a d) \left(\sinh \left(\frac{b}{d}\right)+\cosh \left(\frac{b}{d}\right)\right) \text{Chi}\left(\frac{a d-b c}{d (c+d x)}\right)+a d \sinh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{b c-a d}{x d^2+c d}\right)-b c \sinh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{b c-a d}{x d^2+c d}\right)-a d \cosh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{b c-a d}{x d^2+c d}\right)+b c \cosh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{b c-a d}{x d^2+c d}\right)+2 d^2 x \sinh \left(\frac{a+b x}{c+d x}\right)-a d \sinh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{a d-b c}{d (c+d x)}\right)+b c \sinh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{a d-b c}{d (c+d x)}\right)-a d \cosh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{a d-b c}{d (c+d x)}\right)+b c \cosh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{a d-b c}{d (c+d x)}\right)+2 c d \sinh \left(\frac{a+b x}{c+d x}\right)}{2 d^2}","\frac{\cosh \left(\frac{b}{d}\right) (b c-a d) \text{Chi}\left(\frac{b c-a d}{d (c+d x)}\right)}{d^2}-\frac{\sinh \left(\frac{b}{d}\right) (b c-a d) \text{Shi}\left(\frac{b c-a d}{d (c+d x)}\right)}{d^2}+\frac{(c+d x) \sinh \left(\frac{a+b x}{c+d x}\right)}{d}",1,"((b*c - a*d)*CoshIntegral[(b*c - a*d)/(c*d + d^2*x)]*(Cosh[b/d] - Sinh[b/d]) + (b*c - a*d)*CoshIntegral[(-(b*c) + a*d)/(d*(c + d*x))]*(Cosh[b/d] + Sinh[b/d]) + 2*c*d*Sinh[(a + b*x)/(c + d*x)] + 2*d^2*x*Sinh[(a + b*x)/(c + d*x)] + b*c*Cosh[b/d]*SinhIntegral[(-(b*c) + a*d)/(d*(c + d*x))] - a*d*Cosh[b/d]*SinhIntegral[(-(b*c) + a*d)/(d*(c + d*x))] + b*c*Sinh[b/d]*SinhIntegral[(-(b*c) + a*d)/(d*(c + d*x))] - a*d*Sinh[b/d]*SinhIntegral[(-(b*c) + a*d)/(d*(c + d*x))] + b*c*Cosh[b/d]*SinhIntegral[(b*c - a*d)/(c*d + d^2*x)] - a*d*Cosh[b/d]*SinhIntegral[(b*c - a*d)/(c*d + d^2*x)] - b*c*Sinh[b/d]*SinhIntegral[(b*c - a*d)/(c*d + d^2*x)] + a*d*Sinh[b/d]*SinhIntegral[(b*c - a*d)/(c*d + d^2*x)])/(2*d^2)","B",1
296,1,112,107,0.8674557,"\int \sinh ^2\left(\frac{a+b x}{c+d x}\right) \, dx","Integrate[Sinh[(a + b*x)/(c + d*x)]^2,x]","\frac{2 \sinh \left(\frac{2 b}{d}\right) (b c-a d) \text{Chi}\left(\frac{2 (a d-b c)}{d (c+d x)}\right)+2 \cosh \left(\frac{2 b}{d}\right) (b c-a d) \text{Shi}\left(\frac{2 (a d-b c)}{d (c+d x)}\right)+d \left((c+d x) \cosh \left(\frac{2 (a+b x)}{c+d x}\right)-d x\right)}{2 d^2}","\frac{\sinh \left(\frac{2 b}{d}\right) (b c-a d) \text{Chi}\left(\frac{2 (b c-a d)}{d (c+d x)}\right)}{d^2}-\frac{\cosh \left(\frac{2 b}{d}\right) (b c-a d) \text{Shi}\left(\frac{2 (b c-a d)}{d (c+d x)}\right)}{d^2}+\frac{(c+d x) \sinh ^2\left(\frac{a+b x}{c+d x}\right)}{d}",1,"(d*(-(d*x) + (c + d*x)*Cosh[(2*(a + b*x))/(c + d*x)]) + 2*(b*c - a*d)*CoshIntegral[(2*(-(b*c) + a*d))/(d*(c + d*x))]*Sinh[(2*b)/d] + 2*(b*c - a*d)*Cosh[(2*b)/d]*SinhIntegral[(2*(-(b*c) + a*d))/(d*(c + d*x))])/(2*d^2)","A",1
297,1,599,194,1.4197174,"\int \sinh ^3\left(\frac{a+b x}{c+d x}\right) \, dx","Integrate[Sinh[(a + b*x)/(c + d*x)]^3,x]","\frac{-3 a d \sinh \left(\frac{b}{d}\right) \text{Chi}\left(\frac{b c-a d}{x d^2+c d}\right)+3 b c \sinh \left(\frac{b}{d}\right) \text{Chi}\left(\frac{b c-a d}{x d^2+c d}\right)+3 a d \cosh \left(\frac{b}{d}\right) \text{Chi}\left(\frac{b c-a d}{x d^2+c d}\right)-3 b c \cosh \left(\frac{b}{d}\right) \text{Chi}\left(\frac{b c-a d}{x d^2+c d}\right)+6 \cosh \left(\frac{3 b}{d}\right) (b c-a d) \text{Chi}\left(\frac{3 (a d-b c)}{d (c+d x)}\right)-3 (b c-a d) \left(\sinh \left(\frac{b}{d}\right)+\cosh \left(\frac{b}{d}\right)\right) \text{Chi}\left(\frac{a d-b c}{d (c+d x)}\right)-3 a d \sinh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{b c-a d}{x d^2+c d}\right)+3 b c \sinh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{b c-a d}{x d^2+c d}\right)+3 a d \cosh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{b c-a d}{x d^2+c d}\right)-3 b c \cosh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{b c-a d}{x d^2+c d}\right)-6 d^2 x \sinh \left(\frac{a+b x}{c+d x}\right)+2 d^2 x \sinh \left(\frac{3 (a+b x)}{c+d x}\right)+3 a d \sinh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{a d-b c}{d (c+d x)}\right)-6 a d \sinh \left(\frac{3 b}{d}\right) \text{Shi}\left(\frac{3 (a d-b c)}{d (c+d x)}\right)-3 b c \sinh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{a d-b c}{d (c+d x)}\right)+6 b c \sinh \left(\frac{3 b}{d}\right) \text{Shi}\left(\frac{3 (a d-b c)}{d (c+d x)}\right)+3 a d \cosh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{a d-b c}{d (c+d x)}\right)-3 b c \cosh \left(\frac{b}{d}\right) \text{Shi}\left(\frac{a d-b c}{d (c+d x)}\right)-6 c d \sinh \left(\frac{a+b x}{c+d x}\right)+2 c d \sinh \left(\frac{3 (a+b x)}{c+d x}\right)}{8 d^2}","-\frac{3 \cosh \left(\frac{b}{d}\right) (b c-a d) \text{Chi}\left(\frac{b c-a d}{d (c+d x)}\right)}{4 d^2}+\frac{3 \cosh \left(\frac{3 b}{d}\right) (b c-a d) \text{Chi}\left(\frac{3 (b c-a d)}{d (c+d x)}\right)}{4 d^2}+\frac{3 \sinh \left(\frac{b}{d}\right) (b c-a d) \text{Shi}\left(\frac{b c-a d}{d (c+d x)}\right)}{4 d^2}-\frac{3 \sinh \left(\frac{3 b}{d}\right) (b c-a d) \text{Shi}\left(\frac{3 (b c-a d)}{d (c+d x)}\right)}{4 d^2}+\frac{(c+d x) \sinh ^3\left(\frac{a+b x}{c+d x}\right)}{d}",1,"(6*(b*c - a*d)*Cosh[(3*b)/d]*CoshIntegral[(3*(-(b*c) + a*d))/(d*(c + d*x))] - 3*b*c*Cosh[b/d]*CoshIntegral[(b*c - a*d)/(c*d + d^2*x)] + 3*a*d*Cosh[b/d]*CoshIntegral[(b*c - a*d)/(c*d + d^2*x)] + 3*b*c*CoshIntegral[(b*c - a*d)/(c*d + d^2*x)]*Sinh[b/d] - 3*a*d*CoshIntegral[(b*c - a*d)/(c*d + d^2*x)]*Sinh[b/d] - 3*(b*c - a*d)*CoshIntegral[(-(b*c) + a*d)/(d*(c + d*x))]*(Cosh[b/d] + Sinh[b/d]) - 6*c*d*Sinh[(a + b*x)/(c + d*x)] - 6*d^2*x*Sinh[(a + b*x)/(c + d*x)] + 2*c*d*Sinh[(3*(a + b*x))/(c + d*x)] + 2*d^2*x*Sinh[(3*(a + b*x))/(c + d*x)] - 3*b*c*Cosh[b/d]*SinhIntegral[(-(b*c) + a*d)/(d*(c + d*x))] + 3*a*d*Cosh[b/d]*SinhIntegral[(-(b*c) + a*d)/(d*(c + d*x))] - 3*b*c*Sinh[b/d]*SinhIntegral[(-(b*c) + a*d)/(d*(c + d*x))] + 3*a*d*Sinh[b/d]*SinhIntegral[(-(b*c) + a*d)/(d*(c + d*x))] + 6*b*c*Sinh[(3*b)/d]*SinhIntegral[(3*(-(b*c) + a*d))/(d*(c + d*x))] - 6*a*d*Sinh[(3*b)/d]*SinhIntegral[(3*(-(b*c) + a*d))/(d*(c + d*x))] - 3*b*c*Cosh[b/d]*SinhIntegral[(b*c - a*d)/(c*d + d^2*x)] + 3*a*d*Cosh[b/d]*SinhIntegral[(b*c - a*d)/(c*d + d^2*x)] + 3*b*c*Sinh[b/d]*SinhIntegral[(b*c - a*d)/(c*d + d^2*x)] - 3*a*d*Sinh[b/d]*SinhIntegral[(b*c - a*d)/(c*d + d^2*x)])/(8*d^2)","B",1
298,1,449,121,1.4764323,"\int \sinh \left(e+\frac{f (a+b x)}{c+d x}\right) \, dx","Integrate[Sinh[e + (f*(a + b*x))/(c + d*x)],x]","\frac{f (b c-a d) \left(\cosh \left(\frac{b f}{d}+e\right)-\sinh \left(\frac{b f}{d}+e\right)\right) \text{Chi}\left(\frac{(b c-a d) f}{d (c+d x)}\right)+f (b c-a d) \left(\sinh \left(\frac{b f}{d}+e\right)+\cosh \left(\frac{b f}{d}+e\right)\right) \text{Chi}\left(\frac{a d f-b c f}{d (c+d x)}\right)+2 d^2 x \sinh \left(\frac{a f+b f x+c e+d e x}{c+d x}\right)+a d f \sinh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{(b c-a d) f}{d (c+d x)}\right)-a d f \sinh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{a d f-b c f}{d (c+d x)}\right)-b c f \sinh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{(b c-a d) f}{d (c+d x)}\right)+b c f \sinh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{a d f-b c f}{d (c+d x)}\right)-a d f \cosh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{(b c-a d) f}{d (c+d x)}\right)-a d f \cosh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{a d f-b c f}{d (c+d x)}\right)+b c f \cosh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{(b c-a d) f}{d (c+d x)}\right)+b c f \cosh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{a d f-b c f}{d (c+d x)}\right)+2 c d \sinh \left(\frac{a f+b f x+c e+d e x}{c+d x}\right)}{2 d^2}","\frac{f (b c-a d) \cosh \left(\frac{b f}{d}+e\right) \text{Chi}\left(\frac{(b c-a d) f}{d (c+d x)}\right)}{d^2}-\frac{f (b c-a d) \sinh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{(b c-a d) f}{d (c+d x)}\right)}{d^2}+\frac{(c+d x) \sinh \left(\frac{a f+b f x+c e+d e x}{c+d x}\right)}{d}",1,"((b*c - a*d)*f*CoshIntegral[((b*c - a*d)*f)/(d*(c + d*x))]*(Cosh[e + (b*f)/d] - Sinh[e + (b*f)/d]) + (b*c - a*d)*f*CoshIntegral[(-(b*c*f) + a*d*f)/(d*(c + d*x))]*(Cosh[e + (b*f)/d] + Sinh[e + (b*f)/d]) + 2*c*d*Sinh[(c*e + a*f + d*e*x + b*f*x)/(c + d*x)] + 2*d^2*x*Sinh[(c*e + a*f + d*e*x + b*f*x)/(c + d*x)] + b*c*f*Cosh[e + (b*f)/d]*SinhIntegral[((b*c - a*d)*f)/(d*(c + d*x))] - a*d*f*Cosh[e + (b*f)/d]*SinhIntegral[((b*c - a*d)*f)/(d*(c + d*x))] - b*c*f*Sinh[e + (b*f)/d]*SinhIntegral[((b*c - a*d)*f)/(d*(c + d*x))] + a*d*f*Sinh[e + (b*f)/d]*SinhIntegral[((b*c - a*d)*f)/(d*(c + d*x))] + b*c*f*Cosh[e + (b*f)/d]*SinhIntegral[(-(b*c*f) + a*d*f)/(d*(c + d*x))] - a*d*f*Cosh[e + (b*f)/d]*SinhIntegral[(-(b*c*f) + a*d*f)/(d*(c + d*x))] + b*c*f*Sinh[e + (b*f)/d]*SinhIntegral[(-(b*c*f) + a*d*f)/(d*(c + d*x))] - a*d*f*Sinh[e + (b*f)/d]*SinhIntegral[(-(b*c*f) + a*d*f)/(d*(c + d*x))])/(2*d^2)","B",1
299,1,136,129,2.1000828,"\int \sinh ^2\left(e+\frac{f (a+b x)}{c+d x}\right) \, dx","Integrate[Sinh[e + (f*(a + b*x))/(c + d*x)]^2,x]","\frac{2 f (b c-a d) \sinh \left(2 \left(\frac{b f}{d}+e\right)\right) \text{Chi}\left(\frac{2 (a d f-b c f)}{d (c+d x)}\right)+2 f (b c-a d) \cosh \left(2 \left(\frac{b f}{d}+e\right)\right) \text{Shi}\left(\frac{2 (a d f-b c f)}{d (c+d x)}\right)+d \left((c+d x) \cosh \left(\frac{2 (a f+b f x+c e+d e x)}{c+d x}\right)-d x\right)}{2 d^2}","\frac{f (b c-a d) \sinh \left(2 \left(\frac{b f}{d}+e\right)\right) \text{Chi}\left(\frac{2 (b c-a d) f}{d (c+d x)}\right)}{d^2}-\frac{f (b c-a d) \cosh \left(2 \left(\frac{b f}{d}+e\right)\right) \text{Shi}\left(\frac{2 (b c-a d) f}{d (c+d x)}\right)}{d^2}+\frac{(c+d x) \sinh ^2\left(\frac{a f+b f x+c e+d e x}{c+d x}\right)}{d}",1,"(d*(-(d*x) + (c + d*x)*Cosh[(2*(c*e + a*f + d*e*x + b*f*x))/(c + d*x)]) + 2*(b*c - a*d)*f*CoshIntegral[(2*(-(b*c*f) + a*d*f))/(d*(c + d*x))]*Sinh[2*(e + (b*f)/d)] + 2*(b*c - a*d)*f*Cosh[2*(e + (b*f)/d)]*SinhIntegral[(2*(-(b*c*f) + a*d*f))/(d*(c + d*x))])/(2*d^2)","A",1
300,1,671,226,6.0036767,"\int \sinh ^3\left(e+\frac{f (a+b x)}{c+d x}\right) \, dx","Integrate[Sinh[e + (f*(a + b*x))/(c + d*x)]^3,x]","\frac{-6 a d f \cosh \left(3 \left(\frac{b f}{d}+e\right)\right) \text{Chi}\left(\frac{3 (a d f-b c f)}{d (c+d x)}\right)+6 b c f \cosh \left(3 \left(\frac{b f}{d}+e\right)\right) \text{Chi}\left(\frac{3 (a d f-b c f)}{d (c+d x)}\right)+3 f (b c-a d) \left(\sinh \left(\frac{b f}{d}+e\right)-\cosh \left(\frac{b f}{d}+e\right)\right) \text{Chi}\left(\frac{(b c-a d) f}{d (c+d x)}\right)-3 f (b c-a d) \left(\sinh \left(\frac{b f}{d}+e\right)+\cosh \left(\frac{b f}{d}+e\right)\right) \text{Chi}\left(\frac{a d f-b c f}{d (c+d x)}\right)-6 d^2 x \sinh \left(\frac{a f+b f x+c e+d e x}{c+d x}\right)+2 d^2 x \sinh \left(\frac{3 (a f+b f x+c e+d e x)}{c+d x}\right)-3 a d f \sinh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{(b c-a d) f}{d (c+d x)}\right)+3 a d f \sinh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{a d f-b c f}{d (c+d x)}\right)-6 a d f \sinh \left(3 \left(\frac{b f}{d}+e\right)\right) \text{Shi}\left(\frac{3 (a d f-b c f)}{d (c+d x)}\right)+3 b c f \sinh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{(b c-a d) f}{d (c+d x)}\right)-3 b c f \sinh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{a d f-b c f}{d (c+d x)}\right)+6 b c f \sinh \left(3 \left(\frac{b f}{d}+e\right)\right) \text{Shi}\left(\frac{3 (a d f-b c f)}{d (c+d x)}\right)+3 a d f \cosh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{(b c-a d) f}{d (c+d x)}\right)+3 a d f \cosh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{a d f-b c f}{d (c+d x)}\right)-3 b c f \cosh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{(b c-a d) f}{d (c+d x)}\right)-3 b c f \cosh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{a d f-b c f}{d (c+d x)}\right)-6 c d \sinh \left(\frac{a f+b f x+c e+d e x}{c+d x}\right)+2 c d \sinh \left(\frac{3 (a f+b f x+c e+d e x)}{c+d x}\right)}{8 d^2}","-\frac{3 f (b c-a d) \cosh \left(\frac{b f}{d}+e\right) \text{Chi}\left(\frac{(b c-a d) f}{d (c+d x)}\right)}{4 d^2}+\frac{3 f (b c-a d) \cosh \left(3 \left(\frac{b f}{d}+e\right)\right) \text{Chi}\left(\frac{3 (b c-a d) f}{d (c+d x)}\right)}{4 d^2}+\frac{3 f (b c-a d) \sinh \left(\frac{b f}{d}+e\right) \text{Shi}\left(\frac{(b c-a d) f}{d (c+d x)}\right)}{4 d^2}-\frac{3 f (b c-a d) \sinh \left(3 \left(\frac{b f}{d}+e\right)\right) \text{Shi}\left(\frac{3 (b c-a d) f}{d (c+d x)}\right)}{4 d^2}+\frac{(c+d x) \sinh ^3\left(\frac{a f+b f x+c e+d e x}{c+d x}\right)}{d}",1,"(6*b*c*f*Cosh[3*(e + (b*f)/d)]*CoshIntegral[(3*(-(b*c*f) + a*d*f))/(d*(c + d*x))] - 6*a*d*f*Cosh[3*(e + (b*f)/d)]*CoshIntegral[(3*(-(b*c*f) + a*d*f))/(d*(c + d*x))] + 3*(b*c - a*d)*f*CoshIntegral[((b*c - a*d)*f)/(d*(c + d*x))]*(-Cosh[e + (b*f)/d] + Sinh[e + (b*f)/d]) - 3*(b*c - a*d)*f*CoshIntegral[(-(b*c*f) + a*d*f)/(d*(c + d*x))]*(Cosh[e + (b*f)/d] + Sinh[e + (b*f)/d]) - 6*c*d*Sinh[(c*e + a*f + d*e*x + b*f*x)/(c + d*x)] - 6*d^2*x*Sinh[(c*e + a*f + d*e*x + b*f*x)/(c + d*x)] + 2*c*d*Sinh[(3*(c*e + a*f + d*e*x + b*f*x))/(c + d*x)] + 2*d^2*x*Sinh[(3*(c*e + a*f + d*e*x + b*f*x))/(c + d*x)] - 3*b*c*f*Cosh[e + (b*f)/d]*SinhIntegral[((b*c - a*d)*f)/(d*(c + d*x))] + 3*a*d*f*Cosh[e + (b*f)/d]*SinhIntegral[((b*c - a*d)*f)/(d*(c + d*x))] + 3*b*c*f*Sinh[e + (b*f)/d]*SinhIntegral[((b*c - a*d)*f)/(d*(c + d*x))] - 3*a*d*f*Sinh[e + (b*f)/d]*SinhIntegral[((b*c - a*d)*f)/(d*(c + d*x))] - 3*b*c*f*Cosh[e + (b*f)/d]*SinhIntegral[(-(b*c*f) + a*d*f)/(d*(c + d*x))] + 3*a*d*f*Cosh[e + (b*f)/d]*SinhIntegral[(-(b*c*f) + a*d*f)/(d*(c + d*x))] - 3*b*c*f*Sinh[e + (b*f)/d]*SinhIntegral[(-(b*c*f) + a*d*f)/(d*(c + d*x))] + 3*a*d*f*Sinh[e + (b*f)/d]*SinhIntegral[(-(b*c*f) + a*d*f)/(d*(c + d*x))] + 6*b*c*f*Sinh[3*(e + (b*f)/d)]*SinhIntegral[(3*(-(b*c*f) + a*d*f))/(d*(c + d*x))] - 6*a*d*f*Sinh[3*(e + (b*f)/d)]*SinhIntegral[(3*(-(b*c*f) + a*d*f))/(d*(c + d*x))])/(8*d^2)","B",0
301,1,62,83,0.0439161,"\int e^{a+b x} \sinh ^4(a+b x) \, dx","Integrate[E^(a + b*x)*Sinh[a + b*x]^4,x]","\frac{e^{-3 (a+b x)} \left(60 e^{2 (a+b x)}+90 e^{4 (a+b x)}-20 e^{6 (a+b x)}+3 e^{8 (a+b x)}-5\right)}{240 b}","-\frac{e^{-3 a-3 b x}}{48 b}+\frac{e^{-a-b x}}{4 b}+\frac{3 e^{a+b x}}{8 b}-\frac{e^{3 a+3 b x}}{12 b}+\frac{e^{5 a+5 b x}}{80 b}",1,"(-5 + 60*E^(2*(a + b*x)) + 90*E^(4*(a + b*x)) - 20*E^(6*(a + b*x)) + 3*E^(8*(a + b*x)))/(240*b*E^(3*(a + b*x)))","A",1
302,1,45,57,0.0350428,"\int e^{a+b x} \sinh ^3(a+b x) \, dx","Integrate[E^(a + b*x)*Sinh[a + b*x]^3,x]","\frac{e^{-2 (a+b x)}-3 e^{2 (a+b x)}+\frac{1}{2} e^{4 (a+b x)}+6 b x}{16 b}","\frac{e^{-2 a-2 b x}}{16 b}-\frac{3 e^{2 a+2 b x}}{16 b}+\frac{e^{4 a+4 b x}}{32 b}+\frac{3 x}{8}",1,"(E^(-2*(a + b*x)) - 3*E^(2*(a + b*x)) + E^(4*(a + b*x))/2 + 6*b*x)/(16*b)","A",1
303,1,39,49,0.0208139,"\int e^{a+b x} \sinh ^2(a+b x) \, dx","Integrate[E^(a + b*x)*Sinh[a + b*x]^2,x]","\frac{e^{-a-b x} \left(-6 e^{2 (a+b x)}+e^{4 (a+b x)}-3\right)}{12 b}","-\frac{e^{-a-b x}}{4 b}-\frac{e^{a+b x}}{2 b}+\frac{e^{3 a+3 b x}}{12 b}",1,"(E^(-a - b*x)*(-3 - 6*E^(2*(a + b*x)) + E^(4*(a + b*x))))/(12*b)","A",1
304,1,23,23,0.0116573,"\int e^{a+b x} \sinh (a+b x) \, dx","Integrate[E^(a + b*x)*Sinh[a + b*x],x]","\frac{e^{2 a+2 b x}}{4 b}-\frac{x}{2}","\frac{e^{2 a+2 b x}}{4 b}-\frac{x}{2}",1,"E^(2*a + 2*b*x)/(4*b) - x/2","A",1
305,1,19,19,0.0102417,"\int e^{a+b x} \text{csch}(a+b x) \, dx","Integrate[E^(a + b*x)*Csch[a + b*x],x]","\frac{\log \left(1-e^{2 a+2 b x}\right)}{b}","\frac{\log \left(1-e^{2 a+2 b x}\right)}{b}",1,"Log[1 - E^(2*a + 2*b*x)]/b","A",1
306,1,38,42,0.0718736,"\int e^{a+b x} \text{csch}^2(a+b x) \, dx","Integrate[E^(a + b*x)*Csch[a + b*x]^2,x]","\frac{2 \left(-\frac{e^{a+b x}}{e^{2 (a+b x)}-1}-\tanh ^{-1}\left(e^{a+b x}\right)\right)}{b}","\frac{2 e^{a+b x}}{b \left(1-e^{2 a+2 b x}\right)}-\frac{2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(2*(-(E^(a + b*x)/(-1 + E^(2*(a + b*x)))) - ArcTanh[E^(a + b*x)]))/b","A",1
307,1,29,31,0.0194055,"\int e^{a+b x} \text{csch}^3(a+b x) \, dx","Integrate[E^(a + b*x)*Csch[a + b*x]^3,x]","-\frac{2 e^{4 a+4 b x}}{b \left(e^{2 a+2 b x}-1\right)^2}","-\frac{2 e^{4 a+4 b x}}{b \left(1-e^{2 a+2 b x}\right)^2}",1,"(-2*E^(4*a + 4*b*x))/(b*(-1 + E^(2*a + 2*b*x))^2)","A",1
308,1,75,101,0.0729251,"\int e^{a+b x} \text{csch}^4(a+b x) \, dx","Integrate[E^(a + b*x)*Csch[a + b*x]^4,x]","\frac{3 e^{a+b x}-8 e^{3 (a+b x)}-3 e^{5 (a+b x)}+3 \left(e^{2 (a+b x)}-1\right)^3 \tanh ^{-1}\left(e^{a+b x}\right)}{3 b \left(e^{2 (a+b x)}-1\right)^3}","\frac{e^{a+b x}}{b \left(1-e^{2 a+2 b x}\right)}-\frac{2 e^{a+b x}}{b \left(1-e^{2 a+2 b x}\right)^2}+\frac{8 e^{3 a+3 b x}}{3 b \left(1-e^{2 a+2 b x}\right)^3}+\frac{\tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(3*E^(a + b*x) - 8*E^(3*(a + b*x)) - 3*E^(5*(a + b*x)) + 3*(-1 + E^(2*(a + b*x)))^3*ArcTanh[E^(a + b*x)])/(3*b*(-1 + E^(2*(a + b*x)))^3)","A",1
309,1,44,66,0.036597,"\int e^{a+b x} \text{csch}^5(a+b x) \, dx","Integrate[E^(a + b*x)*Csch[a + b*x]^5,x]","-\frac{4 \left(-4 e^{2 (a+b x)}+6 e^{4 (a+b x)}+1\right)}{3 b \left(e^{2 (a+b x)}-1\right)^4}","-\frac{8}{b \left(1-e^{2 a+2 b x}\right)^2}+\frac{32}{3 b \left(1-e^{2 a+2 b x}\right)^3}-\frac{4}{b \left(1-e^{2 a+2 b x}\right)^4}",1,"(-4*(1 - 4*E^(2*(a + b*x)) + 6*E^(4*(a + b*x))))/(3*b*(-1 + E^(2*(a + b*x)))^4)","A",1
310,1,26,26,0.0135169,"\int e^x \sinh ^2(2 x) \, dx","Integrate[E^x*Sinh[2*x]^2,x]","-\frac{1}{12} e^{-3 x}-\frac{e^x}{2}+\frac{e^{5 x}}{20}","-\frac{1}{12} e^{-3 x}-\frac{e^x}{2}+\frac{e^{5 x}}{20}",1,"-1/12*1/E^(3*x) - E^x/2 + E^(5*x)/20","A",1
311,1,16,19,0.0083559,"\int e^x \sinh (2 x) \, dx","Integrate[E^x*Sinh[2*x],x]","\frac{1}{6} e^{-x} \left(e^{4 x}+3\right)","\frac{e^{-x}}{2}+\frac{e^{3 x}}{6}",1,"(3 + E^(4*x))/(6*E^x)","A",1
312,1,11,11,0.0088455,"\int e^x \text{csch}(2 x) \, dx","Integrate[E^x*Csch[2*x],x]","\tan ^{-1}\left(e^x\right)-\tanh ^{-1}\left(e^x\right)","\tan ^{-1}\left(e^x\right)-\tanh ^{-1}\left(e^x\right)",1,"ArcTan[E^x] - ArcTanh[E^x]","A",1
313,1,32,32,0.0374766,"\int e^x \text{csch}^2(2 x) \, dx","Integrate[E^x*Csch[2*x]^2,x]","\frac{e^x}{1-e^{4 x}}-\frac{1}{2} \tan ^{-1}\left(e^x\right)-\frac{1}{2} \tanh ^{-1}\left(e^x\right)","\frac{e^x}{1-e^{4 x}}-\frac{1}{2} \tan ^{-1}\left(e^x\right)-\frac{1}{2} \tanh ^{-1}\left(e^x\right)",1,"E^x/(1 - E^(4*x)) - ArcTan[E^x]/2 - ArcTanh[E^x]/2","A",1
314,1,26,26,0.0157484,"\int e^x \sinh ^2(3 x) \, dx","Integrate[E^x*Sinh[3*x]^2,x]","-\frac{1}{20} e^{-5 x}-\frac{e^x}{2}+\frac{e^{7 x}}{28}","-\frac{1}{20} e^{-5 x}-\frac{e^x}{2}+\frac{e^{7 x}}{28}",1,"-1/20*1/E^(5*x) - E^x/2 + E^(7*x)/28","A",1
315,1,16,19,0.0093699,"\int e^x \sinh (3 x) \, dx","Integrate[E^x*Sinh[3*x],x]","\frac{1}{8} e^{-2 x} \left(e^{6 x}+2\right)","\frac{e^{-2 x}}{4}+\frac{e^{4 x}}{8}",1,"(2 + E^(6*x))/(8*E^(2*x))","A",1
316,1,22,54,0.0119241,"\int e^x \text{csch}(3 x) \, dx","Integrate[E^x*Csch[3*x],x]","-\frac{1}{2} e^{4 x} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};e^{6 x}\right)","\frac{1}{3} \log \left(1-e^{2 x}\right)-\frac{1}{6} \log \left(e^{2 x}+e^{4 x}+1\right)+\frac{\tan ^{-1}\left(\frac{2 e^{2 x}+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-1/2*(E^(4*x)*Hypergeometric2F1[2/3, 1, 5/3, E^(6*x)])","C",1
317,1,34,105,0.0260021,"\int e^x \text{csch}^2(3 x) \, dx","Integrate[E^x*Csch[3*x]^2,x]","\frac{2}{3} e^x \left(\frac{1}{1-e^{6 x}}-\, _2F_1\left(\frac{1}{6},1;\frac{7}{6};e^{6 x}\right)\right)","\frac{2 e^x}{3 \left(1-e^{6 x}\right)}+\frac{1}{18} \log \left(-e^x+e^{2 x}+1\right)-\frac{1}{18} \log \left(e^x+e^{2 x}+1\right)+\frac{\tan ^{-1}\left(\frac{1-2 e^x}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 e^x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{2}{9} \tanh ^{-1}\left(e^x\right)",1,"(2*E^x*((1 - E^(6*x))^(-1) - Hypergeometric2F1[1/6, 1, 7/6, E^(6*x)]))/3","C",1
318,1,26,26,0.0169664,"\int e^x \sinh ^2(4 x) \, dx","Integrate[E^x*Sinh[4*x]^2,x]","-\frac{1}{28} e^{-7 x}-\frac{e^x}{2}+\frac{e^{9 x}}{36}","-\frac{1}{28} e^{-7 x}-\frac{e^x}{2}+\frac{e^{9 x}}{36}",1,"-1/28*1/E^(7*x) - E^x/2 + E^(9*x)/36","A",1
319,1,19,19,0.0103881,"\int e^x \sinh (4 x) \, dx","Integrate[E^x*Sinh[4*x],x]","\frac{e^{-3 x}}{6}+\frac{e^{5 x}}{10}","\frac{e^{-3 x}}{6}+\frac{e^{5 x}}{10}",1,"1/(6*E^(3*x)) + E^(5*x)/10","A",1
320,1,22,113,0.0121742,"\int e^x \text{csch}(4 x) \, dx","Integrate[E^x*Csch[4*x],x]","-\frac{2}{5} e^{5 x} \, _2F_1\left(\frac{5}{8},1;\frac{13}{8};e^{8 x}\right)","-\frac{\log \left(-\sqrt{2} e^x+e^{2 x}+1\right)}{4 \sqrt{2}}+\frac{\log \left(\sqrt{2} e^x+e^{2 x}+1\right)}{4 \sqrt{2}}-\frac{1}{2} \tan ^{-1}\left(e^x\right)-\frac{\tan ^{-1}\left(1-\sqrt{2} e^x\right)}{2 \sqrt{2}}+\frac{\tan ^{-1}\left(\sqrt{2} e^x+1\right)}{2 \sqrt{2}}-\frac{1}{2} \tanh ^{-1}\left(e^x\right)",1,"(-2*E^(5*x)*Hypergeometric2F1[5/8, 1, 13/8, E^(8*x)])/5","C",1
321,1,34,131,0.0252265,"\int e^x \text{csch}^2(4 x) \, dx","Integrate[E^x*Csch[4*x]^2,x]","\frac{1}{2} e^x \left(\frac{1}{1-e^{8 x}}-\, _2F_1\left(\frac{1}{8},1;\frac{9}{8};e^{8 x}\right)\right)","\frac{e^x}{2 \left(1-e^{8 x}\right)}+\frac{\log \left(-\sqrt{2} e^x+e^{2 x}+1\right)}{16 \sqrt{2}}-\frac{\log \left(\sqrt{2} e^x+e^{2 x}+1\right)}{16 \sqrt{2}}-\frac{1}{8} \tan ^{-1}\left(e^x\right)+\frac{\tan ^{-1}\left(1-\sqrt{2} e^x\right)}{8 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} e^x+1\right)}{8 \sqrt{2}}-\frac{1}{8} \tanh ^{-1}\left(e^x\right)",1,"(E^x*((1 - E^(8*x))^(-1) - Hypergeometric2F1[1/8, 1, 9/8, E^(8*x)]))/2","C",1
322,1,157,202,0.6923013,"\int F^{c (a+b x)} \sinh ^3(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Sinh[d + e*x]^3,x]","\frac{F^{c (a+b x)} \left(3 \cosh (3 (d+e x)) \left(e^3-b^2 c^2 e \log ^2(F)\right)+3 \cosh (d+e x) \left(b^2 c^2 e \log ^2(F)-9 e^3\right)+2 b c \log (F) \sinh (d+e x) \left(\cosh (2 (d+e x)) \left(b^2 c^2 \log ^2(F)-e^2\right)-b^2 c^2 \log ^2(F)+13 e^2\right)\right)}{4 \left(b^4 c^4 \log ^4(F)-10 b^2 c^2 e^2 \log ^2(F)+9 e^4\right)}","-\frac{b c \log (F) \sinh ^3(d+e x) F^{c (a+b x)}}{9 e^2-b^2 c^2 \log ^2(F)}+\frac{3 e \sinh ^2(d+e x) \cosh (d+e x) F^{c (a+b x)}}{9 e^2-b^2 c^2 \log ^2(F)}+\frac{6 b c e^2 \log (F) \sinh (d+e x) F^{c (a+b x)}}{b^4 c^4 \log ^4(F)-10 b^2 c^2 e^2 \log ^2(F)+9 e^4}-\frac{6 e^3 \cosh (d+e x) F^{c (a+b x)}}{b^4 c^4 \log ^4(F)-10 b^2 c^2 e^2 \log ^2(F)+9 e^4}",1,"(F^(c*(a + b*x))*(3*Cosh[3*(d + e*x)]*(e^3 - b^2*c^2*e*Log[F]^2) + 3*Cosh[d + e*x]*(-9*e^3 + b^2*c^2*e*Log[F]^2) + 2*b*c*Log[F]*(13*e^2 - b^2*c^2*Log[F]^2 + Cosh[2*(d + e*x)]*(-e^2 + b^2*c^2*Log[F]^2))*Sinh[d + e*x]))/(4*(9*e^4 - 10*b^2*c^2*e^2*Log[F]^2 + b^4*c^4*Log[F]^4))","A",1
323,1,86,132,0.2061163,"\int F^{c (a+b x)} \sinh ^2(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Sinh[d + e*x]^2,x]","\frac{F^{c (a+b x)} \left(b^2 c^2 \log ^2(F) \cosh (2 (d+e x))-b^2 c^2 \log ^2(F)-2 b c e \log (F) \sinh (2 (d+e x))+4 e^2\right)}{2 b^3 c^3 \log ^3(F)-8 b c e^2 \log (F)}","-\frac{b c \log (F) \sinh ^2(d+e x) F^{c (a+b x)}}{4 e^2-b^2 c^2 \log ^2(F)}+\frac{2 e \sinh (d+e x) \cosh (d+e x) F^{c (a+b x)}}{4 e^2-b^2 c^2 \log ^2(F)}-\frac{2 e^2 F^{c (a+b x)}}{b c \log (F) \left(4 e^2-b^2 c^2 \log ^2(F)\right)}",1,"(F^(c*(a + b*x))*(4*e^2 - b^2*c^2*Log[F]^2 + b^2*c^2*Cosh[2*(d + e*x)]*Log[F]^2 - 2*b*c*e*Log[F]*Sinh[2*(d + e*x)]))/(-8*b*c*e^2*Log[F] + 2*b^3*c^3*Log[F]^3)","A",1
324,1,50,75,0.114834,"\int F^{c (a+b x)} \sinh (d+e x) \, dx","Integrate[F^(c*(a + b*x))*Sinh[d + e*x],x]","\frac{F^{c (a+b x)} (e \cosh (d+e x)-b c \log (F) \sinh (d+e x))}{(e-b c \log (F)) (b c \log (F)+e)}","\frac{e \cosh (d+e x) F^{c (a+b x)}}{e^2-b^2 c^2 \log ^2(F)}-\frac{b c \log (F) \sinh (d+e x) F^{c (a+b x)}}{e^2-b^2 c^2 \log ^2(F)}",1,"(F^(c*(a + b*x))*(e*Cosh[d + e*x] - b*c*Log[F]*Sinh[d + e*x]))/((e - b*c*Log[F])*(e + b*c*Log[F]))","A",1
325,1,93,66,5.6106591,"\int F^{c (a+b x)} \text{csch}(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Csch[d + e*x],x]","\frac{F^{c (a+b x)} \left(\, _2F_1\left(1,\frac{b c \log (F)}{e};\frac{b c \log (F)}{e}+1;-\cosh (d+e x)-\sinh (d+e x)\right)-\, _2F_1\left(1,\frac{b c \log (F)}{e};\frac{b c \log (F)}{e}+1;\cosh (d+e x)+\sinh (d+e x)\right)\right)}{b c \log (F)}","-\frac{2 e^{d+e x} F^{c (a+b x)} \, _2F_1\left(1,\frac{e+b c \log (F)}{2 e};\frac{1}{2} \left(\frac{b c \log (F)}{e}+3\right);e^{2 (d+e x)}\right)}{b c \log (F)+e}",1,"(F^(c*(a + b*x))*(Hypergeometric2F1[1, (b*c*Log[F])/e, 1 + (b*c*Log[F])/e, -Cosh[d + e*x] - Sinh[d + e*x]] - Hypergeometric2F1[1, (b*c*Log[F])/e, 1 + (b*c*Log[F])/e, Cosh[d + e*x] + Sinh[d + e*x]]))/(b*c*Log[F])","A",1
326,1,87,68,2.8158338,"\int F^{c (a+b x)} \text{csch}^2(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Csch[d + e*x]^2,x]","-\frac{2 F^{c (a+b x)} \left(\left(e^{2 d}-1\right) \, _2F_1\left(1,\frac{b c \log (F)}{2 e};\frac{b c \log (F)}{2 e}+1;e^{2 (d+e x)}\right)+\sinh (d) \text{csch}(d+e x) (\cosh (e x)-\sinh (e x))\right)}{\left(e^{2 d}-1\right) e}","\frac{4 e^{2 (d+e x)} F^{c (a+b x)} \, _2F_1\left(2,\frac{b c \log (F)}{2 e}+1;\frac{b c \log (F)}{2 e}+2;e^{2 (d+e x)}\right)}{b c \log (F)+2 e}",1,"(-2*F^(c*(a + b*x))*((-1 + E^(2*d))*Hypergeometric2F1[1, (b*c*Log[F])/(2*e), 1 + (b*c*Log[F])/(2*e), E^(2*(d + e*x))] + Csch[d + e*x]*Sinh[d]*(Cosh[e*x] - Sinh[e*x])))/(e*(-1 + E^(2*d)))","A",1
327,1,299,122,20.1959435,"\int F^{c (a+b x)} \text{csch}^3(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Csch[d + e*x]^3,x]","\frac{F^{c (a+b x)} \left(\frac{4 \left(e^2-b^2 c^2 \log ^2(F)\right) \left((\sinh (d)+\cosh (d)-1) \, _2F_1\left(1,\frac{b c \log (F)}{e};\frac{b c \log (F)}{e}+1;\cosh (d+e x)+\sinh (d+e x)\right)+1\right)}{b c \log (F) (\sinh (d)+\cosh (d)-1)}+\frac{4 \left(e^2-b^2 c^2 \log ^2(F)\right) \left(1-(\sinh (d)+\cosh (d)+1) \, _2F_1\left(1,\frac{b c \log (F)}{e};\frac{b c \log (F)}{e}+1;-\cosh (d+e x)-\sinh (d+e x)\right)\right)}{b c \log (F) (\sinh (d)+\cosh (d)+1)}+\text{csch}(d) \left(4 b c \log (F)-\frac{4 e^2}{b c \log (F)}\right)+2 b c \text{sech}\left(\frac{d}{2}\right) \log (F) \sinh \left(\frac{e x}{2}\right) \text{sech}\left(\frac{1}{2} (d+e x)\right)+2 b c \text{csch}\left(\frac{d}{2}\right) \log (F) \sinh \left(\frac{e x}{2}\right) \text{csch}\left(\frac{1}{2} (d+e x)\right)-4 b c \text{csch}(d) \log (F)-e \text{csch}^2\left(\frac{1}{2} (d+e x)\right)-e \text{sech}^2\left(\frac{1}{2} (d+e x)\right)\right)}{8 e^2}","\frac{e^{d+e x} F^{c (a+b x)} (e-b c \log (F)) \, _2F_1\left(1,\frac{e+b c \log (F)}{2 e};\frac{1}{2} \left(\frac{b c \log (F)}{e}+3\right);e^{2 (d+e x)}\right)}{e^2}-\frac{b c \log (F) \text{csch}(d+e x) F^{c (a+b x)}}{2 e^2}-\frac{\coth (d+e x) \text{csch}(d+e x) F^{c (a+b x)}}{2 e}",1,"(F^(c*(a + b*x))*(-(e*Csch[(d + e*x)/2]^2) - 4*b*c*Csch[d]*Log[F] + Csch[d]*((-4*e^2)/(b*c*Log[F]) + 4*b*c*Log[F]) - e*Sech[(d + e*x)/2]^2 + (4*(e^2 - b^2*c^2*Log[F]^2)*(1 + Hypergeometric2F1[1, (b*c*Log[F])/e, 1 + (b*c*Log[F])/e, Cosh[d + e*x] + Sinh[d + e*x]]*(-1 + Cosh[d] + Sinh[d])))/(b*c*Log[F]*(-1 + Cosh[d] + Sinh[d])) + (4*(e^2 - b^2*c^2*Log[F]^2)*(1 - Hypergeometric2F1[1, (b*c*Log[F])/e, 1 + (b*c*Log[F])/e, -Cosh[d + e*x] - Sinh[d + e*x]]*(1 + Cosh[d] + Sinh[d])))/(b*c*Log[F]*(1 + Cosh[d] + Sinh[d])) + 2*b*c*Csch[d/2]*Csch[(d + e*x)/2]*Log[F]*Sinh[(e*x)/2] + 2*b*c*Log[F]*Sech[d/2]*Sech[(d + e*x)/2]*Sinh[(e*x)/2]))/(8*e^2)","B",1
328,1,202,131,7.0617856,"\int F^{c (a+b x)} \text{csch}^4(d+e x) \, dx","Integrate[F^(c*(a + b*x))*Csch[d + e*x]^4,x]","\frac{F^{c (a+b x)} \left(4 e^2-b^2 c^2 \log ^2(F)\right) \left(2 \, _2F_1\left(1,\frac{b c \log (F)}{2 e};\frac{b c \log (F)}{2 e}+1;\cosh (2 (d+e x))+\sinh (2 (d+e x))\right)+\coth (d)-1\right)}{6 e^3}-\frac{\text{csch}(d) \sinh (e x) \text{csch}(d+e x) F^{a c+b c x} \left(4 e^2-b^2 c^2 \log ^2(F)\right)}{6 e^3}-\frac{\text{csch}(d) \text{csch}^2(d+e x) F^{a c+b c x} (b c \sinh (d) \log (F)+2 e \cosh (d))}{6 e^2}+\frac{\text{csch}(d) \sinh (e x) \text{csch}^3(d+e x) F^{a c+b c x}}{3 e}","-\frac{2 e^{2 (d+e x)} F^{c (a+b x)} (2 e-b c \log (F)) \, _2F_1\left(2,\frac{b c \log (F)}{2 e}+1;\frac{b c \log (F)}{2 e}+2;e^{2 (d+e x)}\right)}{3 e^2}-\frac{b c \log (F) \text{csch}^2(d+e x) F^{c (a+b x)}}{6 e^2}-\frac{\coth (d+e x) \text{csch}^2(d+e x) F^{c (a+b x)}}{3 e}",1,"(F^(c*(a + b*x))*(-1 + Coth[d] + 2*Hypergeometric2F1[1, (b*c*Log[F])/(2*e), 1 + (b*c*Log[F])/(2*e), Cosh[2*(d + e*x)] + Sinh[2*(d + e*x)]])*(4*e^2 - b^2*c^2*Log[F]^2))/(6*e^3) - (F^(a*c + b*c*x)*Csch[d]*Csch[d + e*x]^2*(2*e*Cosh[d] + b*c*Log[F]*Sinh[d]))/(6*e^2) + (F^(a*c + b*c*x)*Csch[d]*Csch[d + e*x]^3*Sinh[e*x])/(3*e) - (F^(a*c + b*c*x)*Csch[d]*Csch[d + e*x]*(4*e^2 - b^2*c^2*Log[F]^2)*Sinh[e*x])/(6*e^3)","A",1
329,1,106,250,0.1127832,"\int e^{c (a+b x)} \sinh ^2(a c+b c x)^{5/2} \, dx","Integrate[E^(c*(a + b*x))*(Sinh[a*c + b*c*x]^2)^(5/2),x]","\frac{\left(\frac{1}{2} e^{-4 c (a+b x)}-5 e^{-2 c (a+b x)}+10 e^{2 c (a+b x)}-\frac{5}{2} e^{4 c (a+b x)}+\frac{1}{3} e^{6 c (a+b x)}-20 b c x\right) \sinh ^2(c (a+b x))^{5/2} \text{csch}^5(c (a+b x))}{64 b c}","\frac{e^{-4 c (a+b x)} \sqrt{\sinh ^2(a c+b c x)} \text{csch}(a c+b c x)}{128 b c}-\frac{5 e^{-2 c (a+b x)} \sqrt{\sinh ^2(a c+b c x)} \text{csch}(a c+b c x)}{64 b c}+\frac{5 e^{2 c (a+b x)} \sqrt{\sinh ^2(a c+b c x)} \text{csch}(a c+b c x)}{32 b c}-\frac{5 e^{4 c (a+b x)} \sqrt{\sinh ^2(a c+b c x)} \text{csch}(a c+b c x)}{128 b c}+\frac{e^{6 c (a+b x)} \sqrt{\sinh ^2(a c+b c x)} \text{csch}(a c+b c x)}{192 b c}-\frac{5}{16} x \sqrt{\sinh ^2(a c+b c x)} \text{csch}(a c+b c x)",1,"((1/(2*E^(4*c*(a + b*x))) - 5/E^(2*c*(a + b*x)) + 10*E^(2*c*(a + b*x)) - (5*E^(4*c*(a + b*x)))/2 + E^(6*c*(a + b*x))/3 - 20*b*c*x)*Csch[c*(a + b*x)]^5*(Sinh[c*(a + b*x)]^2)^(5/2))/(64*b*c)","A",1
330,1,76,162,0.0612614,"\int e^{c (a+b x)} \sinh ^2(a c+b c x)^{3/2} \, dx","Integrate[E^(c*(a + b*x))*(Sinh[a*c + b*c*x]^2)^(3/2),x]","\frac{\left(e^{-2 c (a+b x)}-3 e^{2 c (a+b x)}+\frac{1}{2} e^{4 c (a+b x)}+6 b c x\right) \sinh ^2(c (a+b x))^{3/2} \text{csch}^3(c (a+b x))}{16 b c}","\frac{e^{-2 c (a+b x)} \sqrt{\sinh ^2(a c+b c x)} \text{csch}(a c+b c x)}{16 b c}-\frac{3 e^{2 c (a+b x)} \sqrt{\sinh ^2(a c+b c x)} \text{csch}(a c+b c x)}{16 b c}+\frac{e^{4 c (a+b x)} \sqrt{\sinh ^2(a c+b c x)} \text{csch}(a c+b c x)}{32 b c}+\frac{3}{8} x \sqrt{\sinh ^2(a c+b c x)} \text{csch}(a c+b c x)",1,"((E^(-2*c*(a + b*x)) - 3*E^(2*c*(a + b*x)) + E^(4*c*(a + b*x))/2 + 6*b*c*x)*Csch[c*(a + b*x)]^3*(Sinh[c*(a + b*x)]^2)^(3/2))/(16*b*c)","A",1
331,1,48,74,0.0373609,"\int e^{c (a+b x)} \sqrt{\sinh ^2(a c+b c x)} \, dx","Integrate[E^(c*(a + b*x))*Sqrt[Sinh[a*c + b*c*x]^2],x]","\frac{\left(e^{2 c (a+b x)}-2 b c x\right) \sqrt{\sinh ^2(c (a+b x))} \text{csch}(c (a+b x))}{4 b c}","\frac{e^{2 c (a+b x)} \sqrt{\sinh ^2(a c+b c x)} \text{csch}(a c+b c x)}{4 b c}-\frac{1}{2} x \sqrt{\sinh ^2(a c+b c x)} \text{csch}(a c+b c x)",1,"((E^(2*c*(a + b*x)) - 2*b*c*x)*Csch[c*(a + b*x)]*Sqrt[Sinh[c*(a + b*x)]^2])/(4*b*c)","A",1
332,1,44,46,0.0554468,"\int \frac{e^{c (a+b x)}}{\sqrt{\sinh ^2(a c+b c x)}} \, dx","Integrate[E^(c*(a + b*x))/Sqrt[Sinh[a*c + b*c*x]^2],x]","\frac{\log \left(1-e^{2 c (a+b x)}\right) \sinh (c (a+b x))}{b c \sqrt{\sinh ^2(c (a+b x))}}","\frac{\log \left(1-e^{2 c (a+b x)}\right) \sinh (a c+b c x)}{b c \sqrt{\sinh ^2(a c+b c x)}}",1,"(Log[1 - E^(2*c*(a + b*x))]*Sinh[c*(a + b*x)])/(b*c*Sqrt[Sinh[c*(a + b*x)]^2])","A",1
333,1,46,58,0.0714502,"\int \frac{e^{c (a+b x)}}{\sinh ^2(a c+b c x)^{3/2}} \, dx","Integrate[E^(c*(a + b*x))/(Sinh[a*c + b*c*x]^2)^(3/2),x]","-\frac{4 e^{5 c (a+b x)} \sqrt{\sinh ^2(c (a+b x))}}{b c \left(e^{2 c (a+b x)}-1\right)^3}","-\frac{2 e^{4 c (a+b x)} \sinh (a c+b c x)}{b c \left(1-e^{2 c (a+b x)}\right)^2 \sqrt{\sinh ^2(a c+b c x)}}",1,"(-4*E^(5*c*(a + b*x))*Sqrt[Sinh[c*(a + b*x)]^2])/(b*c*(-1 + E^(2*c*(a + b*x)))^3)","A",1
334,1,72,147,0.0692881,"\int \frac{e^{c (a+b x)}}{\sinh ^2(a c+b c x)^{5/2}} \, dx","Integrate[E^(c*(a + b*x))/(Sinh[a*c + b*c*x]^2)^(5/2),x]","-\frac{4 \left(-4 e^{2 c (a+b x)}+6 e^{4 c (a+b x)}+1\right) \sinh (c (a+b x))}{3 b c \left(e^{2 c (a+b x)}-1\right)^4 \sqrt{\sinh ^2(c (a+b x))}}","-\frac{8 \sinh (a c+b c x)}{b c \left(1-e^{2 c (a+b x)}\right)^2 \sqrt{\sinh ^2(a c+b c x)}}+\frac{32 \sinh (a c+b c x)}{3 b c \left(1-e^{2 c (a+b x)}\right)^3 \sqrt{\sinh ^2(a c+b c x)}}-\frac{4 \sinh (a c+b c x)}{b c \left(1-e^{2 c (a+b x)}\right)^4 \sqrt{\sinh ^2(a c+b c x)}}",1,"(-4*(1 - 4*E^(2*c*(a + b*x)) + 6*E^(4*c*(a + b*x)))*Sinh[c*(a + b*x)])/(3*b*c*(-1 + E^(2*c*(a + b*x)))^4*Sqrt[Sinh[c*(a + b*x)]^2])","A",1
335,1,84,199,0.077166,"\int \frac{e^{c (a+b x)}}{\sinh ^2(a c+b c x)^{7/2}} \, dx","Integrate[E^(c*(a + b*x))/(Sinh[a*c + b*c*x]^2)^(7/2),x]","-\frac{16 \left(6 e^{2 c (a+b x)}-15 e^{4 c (a+b x)}+20 e^{6 c (a+b x)}-1\right) \sinh (c (a+b x))}{15 b c \left(e^{2 c (a+b x)}-1\right)^6 \sqrt{\sinh ^2(c (a+b x))}}","\frac{64 \sinh (a c+b c x)}{3 b c \left(1-e^{2 c (a+b x)}\right)^3 \sqrt{\sinh ^2(a c+b c x)}}-\frac{48 \sinh (a c+b c x)}{b c \left(1-e^{2 c (a+b x)}\right)^4 \sqrt{\sinh ^2(a c+b c x)}}+\frac{192 \sinh (a c+b c x)}{5 b c \left(1-e^{2 c (a+b x)}\right)^5 \sqrt{\sinh ^2(a c+b c x)}}-\frac{32 \sinh (a c+b c x)}{3 b c \left(1-e^{2 c (a+b x)}\right)^6 \sqrt{\sinh ^2(a c+b c x)}}",1,"(-16*(-1 + 6*E^(2*c*(a + b*x)) - 15*E^(4*c*(a + b*x)) + 20*E^(6*c*(a + b*x)))*Sinh[c*(a + b*x)])/(15*b*c*(-1 + E^(2*c*(a + b*x)))^6*Sqrt[Sinh[c*(a + b*x)]^2])","A",1
336,1,28,41,0.0466055,"\int e^x \sinh (a+b x) \, dx","Integrate[E^x*Sinh[a + b*x],x]","\frac{e^x (b \cosh (a+b x)-\sinh (a+b x))}{b^2-1}","\frac{e^x \sinh (a+b x)}{1-b^2}-\frac{b e^x \cosh (a+b x)}{1-b^2}",1,"(E^x*(b*Cosh[a + b*x] - Sinh[a + b*x]))/(-1 + b^2)","A",1
337,1,80,85,0.0929729,"\int e^x \sinh \left(a+c x^2\right) \, dx","Integrate[E^x*Sinh[a + c*x^2],x]","\frac{\sqrt{\pi } e^{\left.-\frac{1}{4}\right/c} \left((\sinh (a)+\cosh (a)) \text{erfi}\left(\frac{2 c x+1}{2 \sqrt{c}}\right)-e^{\left.\frac{1}{2}\right/c} (\cosh (a)-\sinh (a)) \text{erf}\left(\frac{2 c x-1}{2 \sqrt{c}}\right)\right)}{4 \sqrt{c}}","\frac{\sqrt{\pi } e^{\frac{1}{4 c}-a} \text{erf}\left(\frac{1-2 c x}{2 \sqrt{c}}\right)}{4 \sqrt{c}}+\frac{\sqrt{\pi } e^{a-\frac{1}{4 c}} \text{erfi}\left(\frac{2 c x+1}{2 \sqrt{c}}\right)}{4 \sqrt{c}}",1,"(Sqrt[Pi]*(-(E^(1/(2*c))*Erf[(-1 + 2*c*x)/(2*Sqrt[c])]*(Cosh[a] - Sinh[a])) + Erfi[(1 + 2*c*x)/(2*Sqrt[c])]*(Cosh[a] + Sinh[a])))/(4*Sqrt[c]*E^(1/(4*c)))","A",1
338,1,92,101,0.1713322,"\int e^x \sinh \left(a+b x+c x^2\right) \, dx","Integrate[E^x*Sinh[a + b*x + c*x^2],x]","\frac{\sqrt{\pi } e^{-\frac{(b+1)^2}{4 c}} \left((\sinh (a)+\cosh (a)) \text{erfi}\left(\frac{b+2 c x+1}{2 \sqrt{c}}\right)-e^{\frac{b^2+1}{2 c}} (\cosh (a)-\sinh (a)) \text{erf}\left(\frac{b+2 c x-1}{2 \sqrt{c}}\right)\right)}{4 \sqrt{c}}","\frac{\sqrt{\pi } e^{\frac{(1-b)^2}{4 c}-a} \text{erf}\left(\frac{-b-2 c x+1}{2 \sqrt{c}}\right)}{4 \sqrt{c}}+\frac{\sqrt{\pi } e^{a-\frac{(b+1)^2}{4 c}} \text{erfi}\left(\frac{b+2 c x+1}{2 \sqrt{c}}\right)}{4 \sqrt{c}}",1,"(Sqrt[Pi]*(-(E^((1 + b^2)/(2*c))*Erf[(-1 + b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a] - Sinh[a])) + Erfi[(1 + b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a] + Sinh[a])))/(4*Sqrt[c]*E^((1 + b)^2/(4*c)))","A",1
339,1,51,65,0.0667197,"\int e^{x^2} \sinh (a+b x) \, dx","Integrate[E^x^2*Sinh[a + b*x],x]","\frac{1}{4} \sqrt{\pi } e^{-\frac{b^2}{4}} \left((\cosh (a)-\sinh (a)) \text{erfi}\left(\frac{b}{2}-x\right)+(\sinh (a)+\cosh (a)) \text{erfi}\left(\frac{b}{2}+x\right)\right)","\frac{1}{4} \sqrt{\pi } e^{a-\frac{b^2}{4}} \text{erfi}\left(\frac{1}{2} (b+2 x)\right)-\frac{1}{4} \sqrt{\pi } e^{-a-\frac{b^2}{4}} \text{erfi}\left(\frac{1}{2} (2 x-b)\right)",1,"(Sqrt[Pi]*(Erfi[b/2 - x]*(Cosh[a] - Sinh[a]) + Erfi[b/2 + x]*(Cosh[a] + Sinh[a])))/(4*E^(b^2/4))","A",1
340,1,72,65,0.1118565,"\int e^{x^2} \sinh \left(a+c x^2\right) \, dx","Integrate[E^x^2*Sinh[a + c*x^2],x]","\frac{\sqrt{\pi } \left((c-1) \sqrt{c+1} (\sinh (a)+\cosh (a)) \text{erfi}\left(\sqrt{c+1} x\right)-\sqrt{c-1} (c+1) (\cosh (a)-\sinh (a)) \text{erf}\left(\sqrt{c-1} x\right)\right)}{4 \left(c^2-1\right)}","\frac{\sqrt{\pi } e^a \text{erfi}\left(\sqrt{c+1} x\right)}{4 \sqrt{c+1}}-\frac{\sqrt{\pi } e^{-a} \text{erfi}\left(\sqrt{1-c} x\right)}{4 \sqrt{1-c}}",1,"(Sqrt[Pi]*(-(Sqrt[-1 + c]*(1 + c)*Erf[Sqrt[-1 + c]*x]*(Cosh[a] - Sinh[a])) + (-1 + c)*Sqrt[1 + c]*Erfi[Sqrt[1 + c]*x]*(Cosh[a] + Sinh[a])))/(4*(-1 + c^2))","A",1
341,1,123,115,0.3992564,"\int e^{x^2} \sinh \left(a+b x+c x^2\right) \, dx","Integrate[E^x^2*Sinh[a + b*x + c*x^2],x]","\frac{\sqrt{\pi } e^{-\frac{b^2}{4 c+4}} \left((c-1) \sqrt{c+1} (\sinh (a)+\cosh (a)) \text{erfi}\left(\frac{b+2 (c+1) x}{2 \sqrt{c+1}}\right)-\sqrt{c-1} (c+1) e^{\frac{b^2 c}{2 \left(c^2-1\right)}} (\cosh (a)-\sinh (a)) \text{erf}\left(\frac{b+2 (c-1) x}{2 \sqrt{c-1}}\right)\right)}{4 \left(c^2-1\right)}","\frac{\sqrt{\pi } e^{-a-\frac{b^2}{4 (1-c)}} \text{erfi}\left(\frac{b-2 (1-c) x}{2 \sqrt{1-c}}\right)}{4 \sqrt{1-c}}+\frac{\sqrt{\pi } e^{a-\frac{b^2}{4 (c+1)}} \text{erfi}\left(\frac{b+2 (c+1) x}{2 \sqrt{c+1}}\right)}{4 \sqrt{c+1}}",1,"(Sqrt[Pi]*(-(Sqrt[-1 + c]*(1 + c)*E^((b^2*c)/(2*(-1 + c^2)))*Erf[(b + 2*(-1 + c)*x)/(2*Sqrt[-1 + c])]*(Cosh[a] - Sinh[a])) + (-1 + c)*Sqrt[1 + c]*Erfi[(b + 2*(1 + c)*x)/(2*Sqrt[1 + c])]*(Cosh[a] + Sinh[a])))/(4*(-1 + c^2)*E^(b^2/(4 + 4*c)))","A",1
342,1,103,110,0.1406608,"\int f^{a+b x} \sinh \left(d+f x^2\right) \, dx","Integrate[f^(a + b*x)*Sinh[d + f*x^2],x]","\frac{1}{4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{-\frac{b^2 \log ^2(f)}{4 f}} \left((\sinh (d)+\cosh (d)) \text{erfi}\left(\frac{b \log (f)+2 f x}{2 \sqrt{f}}\right)-e^{\frac{b^2 \log ^2(f)}{2 f}} (\cosh (d)-\sinh (d)) \text{erf}\left(\frac{2 f x-b \log (f)}{2 \sqrt{f}}\right)\right)","\frac{1}{4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{d-\frac{b^2 \log ^2(f)}{4 f}} \text{erfi}\left(\frac{b \log (f)+2 f x}{2 \sqrt{f}}\right)-\frac{1}{4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{b^2 \log ^2(f)}{4 f}-d} \text{erf}\left(\frac{2 f x-b \log (f)}{2 \sqrt{f}}\right)",1,"(f^(-1/2 + a)*Sqrt[Pi]*(-(E^((b^2*Log[f]^2)/(2*f))*Erf[(2*f*x - b*Log[f])/(2*Sqrt[f])]*(Cosh[d] - Sinh[d])) + Erfi[(2*f*x + b*Log[f])/(2*Sqrt[f])]*(Cosh[d] + Sinh[d])))/(4*E^((b^2*Log[f]^2)/(4*f)))","A",1
343,1,149,148,0.7650467,"\int f^{a+b x} \sinh ^2\left(d+f x^2\right) \, dx","Integrate[f^(a + b*x)*Sinh[d + f*x^2]^2,x]","\frac{1}{16} f^a \left(\frac{\sqrt{2 \pi } e^{\frac{b^2 \log ^2(f)}{8 f}} (\cosh (2 d)-\sinh (2 d)) \text{erf}\left(\frac{4 f x-b \log (f)}{2 \sqrt{2} \sqrt{f}}\right)}{\sqrt{f}}+\frac{\sqrt{2 \pi } e^{-\frac{b^2 \log ^2(f)}{8 f}} (\sinh (2 d)+\cosh (2 d)) \text{erfi}\left(\frac{b \log (f)+4 f x}{2 \sqrt{2} \sqrt{f}}\right)}{\sqrt{f}}-\frac{8 f^{b x}}{b \log (f)}\right)","\frac{1}{8} \sqrt{\frac{\pi }{2}} f^{a-\frac{1}{2}} e^{\frac{b^2 \log ^2(f)}{8 f}-2 d} \text{erf}\left(\frac{4 f x-b \log (f)}{2 \sqrt{2} \sqrt{f}}\right)+\frac{1}{8} \sqrt{\frac{\pi }{2}} f^{a-\frac{1}{2}} e^{2 d-\frac{b^2 \log ^2(f)}{8 f}} \text{erfi}\left(\frac{b \log (f)+4 f x}{2 \sqrt{2} \sqrt{f}}\right)-\frac{f^{a+b x}}{2 b \log (f)}",1,"(f^a*((-8*f^(b*x))/(b*Log[f]) + (E^((b^2*Log[f]^2)/(8*f))*Sqrt[2*Pi]*Erf[(4*f*x - b*Log[f])/(2*Sqrt[2]*Sqrt[f])]*(Cosh[2*d] - Sinh[2*d]))/Sqrt[f] + (Sqrt[2*Pi]*Erfi[(4*f*x + b*Log[f])/(2*Sqrt[2]*Sqrt[f])]*(Cosh[2*d] + Sinh[2*d]))/(E^((b^2*Log[f]^2)/(8*f))*Sqrt[f])))/16","A",1
344,1,287,239,0.4285143,"\int f^{a+b x} \sinh ^3\left(d+f x^2\right) \, dx","Integrate[f^(a + b*x)*Sinh[d + f*x^2]^3,x]","\frac{1}{16} \sqrt{\frac{\pi }{3}} f^{a-\frac{1}{2}} e^{-\frac{b^2 \log ^2(f)}{4 f}} \left(3 \sqrt{3} e^{\frac{b^2 \log ^2(f)}{2 f}} (\cosh (d)-\sinh (d)) \text{erf}\left(\frac{2 f x-b \log (f)}{2 \sqrt{f}}\right)-e^{\frac{b^2 \log ^2(f)}{3 f}} (\cosh (3 d)-\sinh (3 d)) \text{erf}\left(\frac{6 f x-b \log (f)}{2 \sqrt{3} \sqrt{f}}\right)+\sinh (3 d) e^{\frac{b^2 \log ^2(f)}{6 f}} \text{erfi}\left(\frac{b \log (f)+6 f x}{2 \sqrt{3} \sqrt{f}}\right)+\cosh (3 d) e^{\frac{b^2 \log ^2(f)}{6 f}} \text{erfi}\left(\frac{b \log (f)+6 f x}{2 \sqrt{3} \sqrt{f}}\right)-3 \sqrt{3} \sinh (d) \text{erfi}\left(\frac{b \log (f)+2 f x}{2 \sqrt{f}}\right)-3 \sqrt{3} \cosh (d) \text{erfi}\left(\frac{b \log (f)+2 f x}{2 \sqrt{f}}\right)\right)","\frac{3}{16} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{b^2 \log ^2(f)}{4 f}-d} \text{erf}\left(\frac{2 f x-b \log (f)}{2 \sqrt{f}}\right)-\frac{1}{16} \sqrt{\frac{\pi }{3}} f^{a-\frac{1}{2}} e^{\frac{b^2 \log ^2(f)}{12 f}-3 d} \text{erf}\left(\frac{6 f x-b \log (f)}{2 \sqrt{3} \sqrt{f}}\right)-\frac{3}{16} \sqrt{\pi } f^{a-\frac{1}{2}} e^{d-\frac{b^2 \log ^2(f)}{4 f}} \text{erfi}\left(\frac{b \log (f)+2 f x}{2 \sqrt{f}}\right)+\frac{1}{16} \sqrt{\frac{\pi }{3}} f^{a-\frac{1}{2}} e^{3 d-\frac{b^2 \log ^2(f)}{12 f}} \text{erfi}\left(\frac{b \log (f)+6 f x}{2 \sqrt{3} \sqrt{f}}\right)",1,"(f^(-1/2 + a)*Sqrt[Pi/3]*(-3*Sqrt[3]*Cosh[d]*Erfi[(2*f*x + b*Log[f])/(2*Sqrt[f])] + E^((b^2*Log[f]^2)/(6*f))*Cosh[3*d]*Erfi[(6*f*x + b*Log[f])/(2*Sqrt[3]*Sqrt[f])] + 3*Sqrt[3]*E^((b^2*Log[f]^2)/(2*f))*Erf[(2*f*x - b*Log[f])/(2*Sqrt[f])]*(Cosh[d] - Sinh[d]) - 3*Sqrt[3]*Erfi[(2*f*x + b*Log[f])/(2*Sqrt[f])]*Sinh[d] - E^((b^2*Log[f]^2)/(3*f))*Erf[(6*f*x - b*Log[f])/(2*Sqrt[3]*Sqrt[f])]*(Cosh[3*d] - Sinh[3*d]) + E^((b^2*Log[f]^2)/(6*f))*Erfi[(6*f*x + b*Log[f])/(2*Sqrt[3]*Sqrt[f])]*Sinh[3*d]))/(16*E^((b^2*Log[f]^2)/(4*f)))","A",1
345,1,124,115,0.3134181,"\int f^{a+b x} \sinh \left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x)*Sinh[d + e*x + f*x^2],x]","\frac{1}{4} \sqrt{\pi } f^{a-\frac{b e+f}{2 f}} e^{-\frac{b^2 \log ^2(f)+e^2}{4 f}} \left((\sinh (d)+\cosh (d)) \text{erfi}\left(\frac{b \log (f)+e+2 f x}{2 \sqrt{f}}\right)-(\cosh (d)-\sinh (d)) e^{\frac{b^2 \log ^2(f)+e^2}{2 f}} \text{erf}\left(\frac{-b \log (f)+e+2 f x}{2 \sqrt{f}}\right)\right)","\frac{1}{4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{d-\frac{(b \log (f)+e)^2}{4 f}} \text{erfi}\left(\frac{b \log (f)+e+2 f x}{2 \sqrt{f}}\right)-\frac{1}{4} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{(e-b \log (f))^2}{4 f}-d} \text{erf}\left(\frac{-b \log (f)+e+2 f x}{2 \sqrt{f}}\right)",1,"(f^(a - (b*e + f)/(2*f))*Sqrt[Pi]*(-(E^((e^2 + b^2*Log[f]^2)/(2*f))*Erf[(e + 2*f*x - b*Log[f])/(2*Sqrt[f])]*(Cosh[d] - Sinh[d])) + Erfi[(e + 2*f*x + b*Log[f])/(2*Sqrt[f])]*(Cosh[d] + Sinh[d])))/(4*E^((e^2 + b^2*Log[f]^2)/(4*f)))","A",1
346,1,220,161,0.6429586,"\int f^{a+b x} \sinh ^2\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x)*Sinh[d + e*x + f*x^2]^2,x]","\frac{f^{a-\frac{b e+f}{2 f}} e^{-\frac{b^2 \log ^2(f)+4 e^2}{8 f}} \left(\sqrt{\pi } b \log (f) (\cosh (2 d)-\sinh (2 d)) e^{\frac{b^2 \log ^2(f)+4 e^2}{4 f}} \text{erf}\left(\frac{-b \log (f)+2 e+4 f x}{2 \sqrt{2} \sqrt{f}}\right)-4 \sqrt{2} f^{b \left(\frac{e}{2 f}+x\right)+\frac{1}{2}} e^{\frac{b^2 \log ^2(f)+4 e^2}{8 f}}+\sqrt{\pi } b \log (f) (\sinh (2 d)+\cosh (2 d)) \text{erfi}\left(\frac{b \log (f)+2 e+4 f x}{2 \sqrt{2} \sqrt{f}}\right)\right)}{8 \sqrt{2} b \log (f)}","\frac{1}{8} \sqrt{\frac{\pi }{2}} f^{a-\frac{1}{2}} e^{\frac{(2 e-b \log (f))^2}{8 f}-2 d} \text{erf}\left(\frac{-b \log (f)+2 e+4 f x}{2 \sqrt{2} \sqrt{f}}\right)+\frac{1}{8} \sqrt{\frac{\pi }{2}} f^{a-\frac{1}{2}} e^{2 d-\frac{(b \log (f)+2 e)^2}{8 f}} \text{erfi}\left(\frac{b \log (f)+2 e+4 f x}{2 \sqrt{2} \sqrt{f}}\right)-\frac{f^{a+b x}}{2 b \log (f)}",1,"(f^(a - (b*e + f)/(2*f))*(-4*Sqrt[2]*E^((4*e^2 + b^2*Log[f]^2)/(8*f))*f^(1/2 + b*(e/(2*f) + x)) + b*E^((4*e^2 + b^2*Log[f]^2)/(4*f))*Sqrt[Pi]*Erf[(2*e + 4*f*x - b*Log[f])/(2*Sqrt[2]*Sqrt[f])]*Log[f]*(Cosh[2*d] - Sinh[2*d]) + b*Sqrt[Pi]*Erfi[(2*e + 4*f*x + b*Log[f])/(2*Sqrt[2]*Sqrt[f])]*Log[f]*(Cosh[2*d] + Sinh[2*d])))/(8*Sqrt[2]*b*E^((4*e^2 + b^2*Log[f]^2)/(8*f))*Log[f])","A",1
347,1,354,257,0.7768522,"\int f^{a+b x} \sinh ^3\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x)*Sinh[d + e*x + f*x^2]^3,x]","\frac{1}{16} \sqrt{\frac{\pi }{3}} f^{a-\frac{b e+f}{2 f}} e^{-\frac{b^2 \log ^2(f)+3 e^2}{4 f}} \left(3 \sqrt{3} (\cosh (d)-\sinh (d)) e^{\frac{b^2 \log ^2(f)+2 e^2}{2 f}} \text{erf}\left(\frac{-b \log (f)+e+2 f x}{2 \sqrt{f}}\right)-(\cosh (3 d)-\sinh (3 d)) e^{\frac{2 b^2 \log ^2(f)+9 e^2}{6 f}} \text{erf}\left(\frac{-b \log (f)+3 e+6 f x}{2 \sqrt{3} \sqrt{f}}\right)+\sinh (3 d) e^{\frac{b^2 \log ^2(f)}{6 f}} \text{erfi}\left(\frac{b \log (f)+3 e+6 f x}{2 \sqrt{3} \sqrt{f}}\right)+\cosh (3 d) e^{\frac{b^2 \log ^2(f)}{6 f}} \text{erfi}\left(\frac{b \log (f)+3 e+6 f x}{2 \sqrt{3} \sqrt{f}}\right)-3 \sqrt{3} \sinh (d) e^{\frac{e^2}{2 f}} \text{erfi}\left(\frac{b \log (f)+e+2 f x}{2 \sqrt{f}}\right)-3 \sqrt{3} \cosh (d) e^{\frac{e^2}{2 f}} \text{erfi}\left(\frac{b \log (f)+e+2 f x}{2 \sqrt{f}}\right)\right)","\frac{3}{16} \sqrt{\pi } f^{a-\frac{1}{2}} e^{\frac{(e-b \log (f))^2}{4 f}-d} \text{erf}\left(\frac{-b \log (f)+e+2 f x}{2 \sqrt{f}}\right)-\frac{1}{16} \sqrt{\frac{\pi }{3}} f^{a-\frac{1}{2}} e^{\frac{(3 e-b \log (f))^2}{12 f}-3 d} \text{erf}\left(\frac{-b \log (f)+3 e+6 f x}{2 \sqrt{3} \sqrt{f}}\right)-\frac{3}{16} \sqrt{\pi } f^{a-\frac{1}{2}} e^{d-\frac{(b \log (f)+e)^2}{4 f}} \text{erfi}\left(\frac{b \log (f)+e+2 f x}{2 \sqrt{f}}\right)+\frac{1}{16} \sqrt{\frac{\pi }{3}} f^{a-\frac{1}{2}} e^{3 d-\frac{(b \log (f)+3 e)^2}{12 f}} \text{erfi}\left(\frac{b \log (f)+3 e+6 f x}{2 \sqrt{3} \sqrt{f}}\right)",1,"(f^(a - (b*e + f)/(2*f))*Sqrt[Pi/3]*(-3*Sqrt[3]*E^(e^2/(2*f))*Cosh[d]*Erfi[(e + 2*f*x + b*Log[f])/(2*Sqrt[f])] + E^((b^2*Log[f]^2)/(6*f))*Cosh[3*d]*Erfi[(3*e + 6*f*x + b*Log[f])/(2*Sqrt[3]*Sqrt[f])] + 3*Sqrt[3]*E^((2*e^2 + b^2*Log[f]^2)/(2*f))*Erf[(e + 2*f*x - b*Log[f])/(2*Sqrt[f])]*(Cosh[d] - Sinh[d]) - 3*Sqrt[3]*E^(e^2/(2*f))*Erfi[(e + 2*f*x + b*Log[f])/(2*Sqrt[f])]*Sinh[d] - E^((9*e^2 + 2*b^2*Log[f]^2)/(6*f))*Erf[(3*e + 6*f*x - b*Log[f])/(2*Sqrt[3]*Sqrt[f])]*(Cosh[3*d] - Sinh[3*d]) + E^((b^2*Log[f]^2)/(6*f))*Erfi[(3*e + 6*f*x + b*Log[f])/(2*Sqrt[3]*Sqrt[f])]*Sinh[3*d]))/(16*E^((3*e^2 + b^2*Log[f]^2)/(4*f)))","A",1
348,1,104,133,0.1618662,"\int f^{a+c x^2} \sinh (d+e x) \, dx","Integrate[f^(a + c*x^2)*Sinh[d + e*x],x]","\frac{\sqrt{\pi } f^a e^{-\frac{e^2}{4 c \log (f)}} \left((\sinh (d)-\cosh (d)) \text{erfi}\left(\frac{2 c x \log (f)-e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+(\sinh (d)+\cosh (d)) \text{erfi}\left(\frac{2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)}{4 \sqrt{c} \sqrt{\log (f)}}","\frac{\sqrt{\pi } f^a e^{-\frac{e^2}{4 c \log (f)}-d} \text{erfi}\left(\frac{e-2 c x \log (f)}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{d-\frac{e^2}{4 c \log (f)}} \text{erfi}\left(\frac{2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*(Erfi[(-e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(-Cosh[d] + Sinh[d]) + Erfi[(e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[d] + Sinh[d])))/(4*Sqrt[c]*E^(e^2/(4*c*Log[f]))*Sqrt[Log[f]])","A",1
349,1,131,161,0.2661851,"\int f^{a+c x^2} \sinh ^2(d+e x) \, dx","Integrate[f^(a + c*x^2)*Sinh[d + e*x]^2,x]","\frac{\sqrt{\pi } f^a e^{-\frac{e^2}{c \log (f)}} \left((\cosh (2 d)-\sinh (2 d)) \text{erfi}\left(\frac{c x \log (f)-e}{\sqrt{c} \sqrt{\log (f)}}\right)+(\sinh (2 d)+\cosh (2 d)) \text{erfi}\left(\frac{c x \log (f)+e}{\sqrt{c} \sqrt{\log (f)}}\right)-2 e^{\frac{e^2}{c \log (f)}} \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)\right)}{8 \sqrt{c} \sqrt{\log (f)}}","-\frac{\sqrt{\pi } f^a e^{-\frac{e^2}{c \log (f)}-2 d} \text{erfi}\left(\frac{e-c x \log (f)}{\sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{2 d-\frac{e^2}{c \log (f)}} \text{erfi}\left(\frac{c x \log (f)+e}{\sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*(-2*E^(e^2/(c*Log[f]))*Erfi[Sqrt[c]*x*Sqrt[Log[f]]] + Erfi[(-e + c*x*Log[f])/(Sqrt[c]*Sqrt[Log[f]])]*(Cosh[2*d] - Sinh[2*d]) + Erfi[(e + c*x*Log[f])/(Sqrt[c]*Sqrt[Log[f]])]*(Cosh[2*d] + Sinh[2*d])))/(8*Sqrt[c]*E^(e^2/(c*Log[f]))*Sqrt[Log[f]])","A",1
350,1,214,271,0.4626258,"\int f^{a+c x^2} \sinh ^3(d+e x) \, dx","Integrate[f^(a + c*x^2)*Sinh[d + e*x]^3,x]","\frac{\sqrt{\pi } f^a e^{-\frac{9 e^2}{4 c \log (f)}} \left((\sinh (d)+\cosh (d)) \left(3 (\cosh (2 d)-\sinh (2 d)) e^{\frac{2 e^2}{c \log (f)}} \text{erfi}\left(\frac{2 c x \log (f)-e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+(\sinh (2 d)+\cosh (2 d)) \text{erfi}\left(\frac{2 c x \log (f)+3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)-3 e^{\frac{2 e^2}{c \log (f)}} \text{erfi}\left(\frac{2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)+(\sinh (3 d)-\cosh (3 d)) \text{erfi}\left(\frac{2 c x \log (f)-3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)}{16 \sqrt{c} \sqrt{\log (f)}}","-\frac{3 \sqrt{\pi } f^a e^{-\frac{e^2}{4 c \log (f)}-d} \text{erfi}\left(\frac{e-2 c x \log (f)}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{-\frac{9 e^2}{4 c \log (f)}-3 d} \text{erfi}\left(\frac{3 e-2 c x \log (f)}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}-\frac{3 \sqrt{\pi } f^a e^{d-\frac{e^2}{4 c \log (f)}} \text{erfi}\left(\frac{2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{3 d-\frac{9 e^2}{4 c \log (f)}} \text{erfi}\left(\frac{2 c x \log (f)+3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*((Cosh[d] + Sinh[d])*(-3*E^((2*e^2)/(c*Log[f]))*Erfi[(e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])] + 3*E^((2*e^2)/(c*Log[f]))*Erfi[(-e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[2*d] - Sinh[2*d]) + Erfi[(3*e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[2*d] + Sinh[2*d])) + Erfi[(-3*e + 2*c*x*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(-Cosh[3*d] + Sinh[3*d])))/(16*Sqrt[c]*E^((9*e^2)/(4*c*Log[f]))*Sqrt[Log[f]])","A",1
351,1,76,81,0.3507163,"\int f^{a+c x^2} \sinh \left(d+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Sinh[d + f*x^2],x]","\frac{1}{4} \sqrt{\pi } f^a \left(\frac{(\sinh (d)+\cosh (d)) \text{erfi}\left(x \sqrt{c \log (f)+f}\right)}{\sqrt{c \log (f)+f}}-\frac{(\cosh (d)-\sinh (d)) \text{erf}\left(x \sqrt{f-c \log (f)}\right)}{\sqrt{f-c \log (f)}}\right)","\frac{\sqrt{\pi } e^d f^a \text{erfi}\left(x \sqrt{c \log (f)+f}\right)}{4 \sqrt{c \log (f)+f}}-\frac{\sqrt{\pi } e^{-d} f^a \text{erf}\left(x \sqrt{f-c \log (f)}\right)}{4 \sqrt{f-c \log (f)}}",1,"(f^a*Sqrt[Pi]*(-((Erf[x*Sqrt[f - c*Log[f]]]*(Cosh[d] - Sinh[d]))/Sqrt[f - c*Log[f]]) + (Erfi[x*Sqrt[f + c*Log[f]]]*(Cosh[d] + Sinh[d]))/Sqrt[f + c*Log[f]]))/4","A",1
352,1,179,128,0.5367935,"\int f^{a+c x^2} \sinh ^2\left(d+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Sinh[d + f*x^2]^2,x]","\frac{\sqrt{\pi } f^a \left(\left(8 f^2-2 c^2 \log ^2(f)\right) \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)+\sqrt{c} \sqrt{\log (f)} \left(\sqrt{2 f-c \log (f)} (c \log (f)+2 f) (\sinh (2 d)-\cosh (2 d)) \text{erf}\left(x \sqrt{2 f-c \log (f)}\right)-(2 f-c \log (f)) \sqrt{c \log (f)+2 f} (\sinh (2 d)+\cosh (2 d)) \text{erfi}\left(x \sqrt{c \log (f)+2 f}\right)\right)\right)}{8 \sqrt{c} \sqrt{\log (f)} \left(c^2 \log ^2(f)-4 f^2\right)}","\frac{\sqrt{\pi } e^{-2 d} f^a \text{erf}\left(x \sqrt{2 f-c \log (f)}\right)}{8 \sqrt{2 f-c \log (f)}}+\frac{\sqrt{\pi } e^{2 d} f^a \text{erfi}\left(x \sqrt{c \log (f)+2 f}\right)}{8 \sqrt{c \log (f)+2 f}}-\frac{\sqrt{\pi } f^a \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*(Erfi[Sqrt[c]*x*Sqrt[Log[f]]]*(8*f^2 - 2*c^2*Log[f]^2) + Sqrt[c]*Sqrt[Log[f]]*(Erf[x*Sqrt[2*f - c*Log[f]]]*Sqrt[2*f - c*Log[f]]*(2*f + c*Log[f])*(-Cosh[2*d] + Sinh[2*d]) - Erfi[x*Sqrt[2*f + c*Log[f]]]*(2*f - c*Log[f])*Sqrt[2*f + c*Log[f]]*(Cosh[2*d] + Sinh[2*d]))))/(8*Sqrt[c]*Sqrt[Log[f]]*(-4*f^2 + c^2*Log[f]^2))","A",1
353,1,272,171,1.2261903,"\int f^{a+c x^2} \sinh ^3\left(d+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Sinh[d + f*x^2]^3,x]","\frac{\sqrt{\pi } f^a \left(3 \sqrt{f-c \log (f)} \left(-c^3 \log ^3(f)-c^2 f \log ^2(f)+9 c f^2 \log (f)+9 f^3\right) (\cosh (d)-\sinh (d)) \text{erf}\left(x \sqrt{f-c \log (f)}\right)-(f-c \log (f)) \left(\sqrt{3 f-c \log (f)} \left(c^2 \log ^2(f)+4 c f \log (f)+3 f^2\right) (\cosh (3 d)-\sinh (3 d)) \text{erf}\left(x \sqrt{3 f-c \log (f)}\right)+(3 f-c \log (f)) \left(3 \sqrt{c \log (f)+f} (c \log (f)+3 f) (\sinh (d)+\cosh (d)) \text{erfi}\left(x \sqrt{c \log (f)+f}\right)-(c \log (f)+f) \sqrt{c \log (f)+3 f} (\sinh (3 d)+\cosh (3 d)) \text{erfi}\left(x \sqrt{c \log (f)+3 f}\right)\right)\right)\right)}{16 \left(c^4 \log ^4(f)-10 c^2 f^2 \log ^2(f)+9 f^4\right)}","\frac{3 \sqrt{\pi } e^{-d} f^a \text{erf}\left(x \sqrt{f-c \log (f)}\right)}{16 \sqrt{f-c \log (f)}}-\frac{\sqrt{\pi } e^{-3 d} f^a \text{erf}\left(x \sqrt{3 f-c \log (f)}\right)}{16 \sqrt{3 f-c \log (f)}}-\frac{3 \sqrt{\pi } e^d f^a \text{erfi}\left(x \sqrt{c \log (f)+f}\right)}{16 \sqrt{c \log (f)+f}}+\frac{\sqrt{\pi } e^{3 d} f^a \text{erfi}\left(x \sqrt{c \log (f)+3 f}\right)}{16 \sqrt{c \log (f)+3 f}}",1,"(f^a*Sqrt[Pi]*(3*Erf[x*Sqrt[f - c*Log[f]]]*Sqrt[f - c*Log[f]]*(9*f^3 + 9*c*f^2*Log[f] - c^2*f*Log[f]^2 - c^3*Log[f]^3)*(Cosh[d] - Sinh[d]) - (f - c*Log[f])*(Erf[x*Sqrt[3*f - c*Log[f]]]*Sqrt[3*f - c*Log[f]]*(3*f^2 + 4*c*f*Log[f] + c^2*Log[f]^2)*(Cosh[3*d] - Sinh[3*d]) + (3*f - c*Log[f])*(3*Erfi[x*Sqrt[f + c*Log[f]]]*Sqrt[f + c*Log[f]]*(3*f + c*Log[f])*(Cosh[d] + Sinh[d]) - Erfi[x*Sqrt[3*f + c*Log[f]]]*(f + c*Log[f])*Sqrt[3*f + c*Log[f]]*(Cosh[3*d] + Sinh[3*d])))))/(16*(9*f^4 - 10*c^2*f^2*Log[f]^2 + c^4*Log[f]^4))","A",1
354,1,166,140,0.7419073,"\int f^{a+c x^2} \sinh \left(d+e x+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Sinh[d + e*x + f*x^2],x]","\frac{\sqrt{\pi } f^a e^{-\frac{e^2}{4 (c \log (f)+f)}} \left(\sqrt{f-c \log (f)} (\sinh (d)+\cosh (d)) \text{erfi}\left(\frac{2 c x \log (f)+e+2 f x}{2 \sqrt{c \log (f)+f}}\right)-\sqrt{c \log (f)+f} (\cosh (d)-\sinh (d)) e^{\frac{e^2 f}{2 f^2-2 c^2 \log ^2(f)}} \text{erf}\left(\frac{-2 c x \log (f)+e+2 f x}{2 \sqrt{f-c \log (f)}}\right)\right)}{4 \sqrt{f-c \log (f)} \sqrt{c \log (f)+f}}","\frac{\sqrt{\pi } f^a e^{d-\frac{e^2}{4 (c \log (f)+f)}} \text{erfi}\left(\frac{2 x (c \log (f)+f)+e}{2 \sqrt{c \log (f)+f}}\right)}{4 \sqrt{c \log (f)+f}}-\frac{\sqrt{\pi } f^a e^{\frac{e^2}{4 f-4 c \log (f)}-d} \text{erf}\left(\frac{2 x (f-c \log (f))+e}{2 \sqrt{f-c \log (f)}}\right)}{4 \sqrt{f-c \log (f)}}",1,"(f^a*Sqrt[Pi]*(-(E^((e^2*f)/(2*f^2 - 2*c^2*Log[f]^2))*Erf[(e + 2*f*x - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Sqrt[f + c*Log[f]]*(Cosh[d] - Sinh[d])) + Erfi[(e + 2*f*x + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Sqrt[f - c*Log[f]]*(Cosh[d] + Sinh[d])))/(4*E^(e^2/(4*(f + c*Log[f])))*Sqrt[f - c*Log[f]]*Sqrt[f + c*Log[f]])","A",1
355,1,258,183,1.4644421,"\int f^{a+c x^2} \sinh ^2\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Sinh[d + e*x + f*x^2]^2,x]","\frac{\sqrt{\pi } f^a e^{\frac{e^2}{2 f-c \log (f)}} \left(2 \left(4 f^2-c^2 \log ^2(f)\right) e^{\frac{e^2}{c \log (f)-2 f}} \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)-\sqrt{c} \sqrt{\log (f)} \left((2 f-c \log (f)) \sqrt{c \log (f)+2 f} (\sinh (2 d)+\cosh (2 d)) e^{\frac{4 e^2 f}{c^2 \log ^2(f)-4 f^2}} \text{erfi}\left(\frac{c x \log (f)+e+2 f x}{\sqrt{c \log (f)+2 f}}\right)+\sqrt{2 f-c \log (f)} (c \log (f)+2 f) (\cosh (2 d)-\sinh (2 d)) \text{erf}\left(\frac{-c x \log (f)+e+2 f x}{\sqrt{2 f-c \log (f)}}\right)\right)\right)}{8 \sqrt{c} \sqrt{\log (f)} \left(c^2 \log ^2(f)-4 f^2\right)}","\frac{\sqrt{\pi } f^a e^{\frac{e^2}{2 f-c \log (f)}-2 d} \text{erf}\left(\frac{x (2 f-c \log (f))+e}{\sqrt{2 f-c \log (f)}}\right)}{8 \sqrt{2 f-c \log (f)}}+\frac{\sqrt{\pi } f^a e^{2 d-\frac{e^2}{c \log (f)+2 f}} \text{erfi}\left(\frac{x (c \log (f)+2 f)+e}{\sqrt{c \log (f)+2 f}}\right)}{8 \sqrt{c \log (f)+2 f}}-\frac{\sqrt{\pi } f^a \text{erfi}\left(\sqrt{c} x \sqrt{\log (f)}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(E^(e^2/(2*f - c*Log[f]))*f^a*Sqrt[Pi]*(2*E^(e^2/(-2*f + c*Log[f]))*Erfi[Sqrt[c]*x*Sqrt[Log[f]]]*(4*f^2 - c^2*Log[f]^2) - Sqrt[c]*Sqrt[Log[f]]*(Erf[(e + 2*f*x - c*x*Log[f])/Sqrt[2*f - c*Log[f]]]*Sqrt[2*f - c*Log[f]]*(2*f + c*Log[f])*(Cosh[2*d] - Sinh[2*d]) + E^((4*e^2*f)/(-4*f^2 + c^2*Log[f]^2))*Erfi[(e + 2*f*x + c*x*Log[f])/Sqrt[2*f + c*Log[f]]]*(2*f - c*Log[f])*Sqrt[2*f + c*Log[f]]*(Cosh[2*d] + Sinh[2*d]))))/(8*Sqrt[c]*Sqrt[Log[f]]*(-4*f^2 + c^2*Log[f]^2))","A",1
356,1,480,300,5.9361288,"\int f^{a+c x^2} \sinh ^3\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + c*x^2)*Sinh[d + e*x + f*x^2]^3,x]","\frac{\sqrt{\pi } f^a \exp \left(-\frac{1}{4} e^2 \left(\frac{9}{c \log (f)+3 f}+\frac{1}{c \log (f)+f}\right)\right) \left(3 \sqrt{f-c \log (f)} \left(-c^3 \log ^3(f)-c^2 f \log ^2(f)+9 c f^2 \log (f)+9 f^3\right) (\cosh (d)-\sinh (d)) \exp \left(\frac{1}{4} e^2 \left(\frac{1}{c \log (f)+f}+\frac{9}{c \log (f)+3 f}+\frac{1}{f-c \log (f)}\right)\right) \text{erf}\left(\frac{-2 c x \log (f)+e+2 f x}{2 \sqrt{f-c \log (f)}}\right)-(f-c \log (f)) \left(\sqrt{3 f-c \log (f)} \left(c^2 \log ^2(f)+4 c f \log (f)+3 f^2\right) (\cosh (3 d)-\sinh (3 d)) \exp \left(\frac{1}{4} e^2 \left(\frac{1}{c \log (f)+f}+\frac{9}{c \log (f)+3 f}+\frac{9}{3 f-c \log (f)}\right)\right) \text{erf}\left(\frac{-2 c x \log (f)+3 e+6 f x}{2 \sqrt{3 f-c \log (f)}}\right)+(3 f-c \log (f)) \left(3 \sqrt{c \log (f)+f} (c \log (f)+3 f) (\sinh (d)+\cosh (d)) e^{\frac{9 e^2}{4 (c \log (f)+3 f)}} \text{erfi}\left(\frac{2 c x \log (f)+e+2 f x}{2 \sqrt{c \log (f)+f}}\right)-(c \log (f)+f) \sqrt{c \log (f)+3 f} (\sinh (3 d)+\cosh (3 d)) e^{\frac{e^2}{4 (c \log (f)+f)}} \text{erfi}\left(\frac{2 c x \log (f)+3 e+6 f x}{2 \sqrt{c \log (f)+3 f}}\right)\right)\right)\right)}{16 \left(c^4 \log ^4(f)-10 c^2 f^2 \log ^2(f)+9 f^4\right)}","\frac{3 \sqrt{\pi } f^a e^{\frac{e^2}{4 f-4 c \log (f)}-d} \text{erf}\left(\frac{2 x (f-c \log (f))+e}{2 \sqrt{f-c \log (f)}}\right)}{16 \sqrt{f-c \log (f)}}-\frac{\sqrt{\pi } f^a e^{\frac{9 e^2}{12 f-4 c \log (f)}-3 d} \text{erf}\left(\frac{2 x (3 f-c \log (f))+3 e}{2 \sqrt{3 f-c \log (f)}}\right)}{16 \sqrt{3 f-c \log (f)}}-\frac{3 \sqrt{\pi } f^a e^{d-\frac{e^2}{4 (c \log (f)+f)}} \text{erfi}\left(\frac{2 x (c \log (f)+f)+e}{2 \sqrt{c \log (f)+f}}\right)}{16 \sqrt{c \log (f)+f}}+\frac{\sqrt{\pi } f^a e^{3 d-\frac{9 e^2}{4 (c \log (f)+3 f)}} \text{erfi}\left(\frac{2 x (c \log (f)+3 f)+3 e}{2 \sqrt{c \log (f)+3 f}}\right)}{16 \sqrt{c \log (f)+3 f}}",1,"(f^a*Sqrt[Pi]*(3*E^((e^2*((f - c*Log[f])^(-1) + (f + c*Log[f])^(-1) + 9/(3*f + c*Log[f])))/4)*Erf[(e + 2*f*x - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Sqrt[f - c*Log[f]]*(9*f^3 + 9*c*f^2*Log[f] - c^2*f*Log[f]^2 - c^3*Log[f]^3)*(Cosh[d] - Sinh[d]) - (f - c*Log[f])*(E^((e^2*(9/(3*f - c*Log[f]) + (f + c*Log[f])^(-1) + 9/(3*f + c*Log[f])))/4)*Erf[(3*e + 6*f*x - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Sqrt[3*f - c*Log[f]]*(3*f^2 + 4*c*f*Log[f] + c^2*Log[f]^2)*(Cosh[3*d] - Sinh[3*d]) + (3*f - c*Log[f])*(3*E^((9*e^2)/(4*(3*f + c*Log[f])))*Erfi[(e + 2*f*x + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Sqrt[f + c*Log[f]]*(3*f + c*Log[f])*(Cosh[d] + Sinh[d]) - E^(e^2/(4*(f + c*Log[f])))*Erfi[(3*e + 6*f*x + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*(f + c*Log[f])*Sqrt[3*f + c*Log[f]]*(Cosh[3*d] + Sinh[3*d])))))/(16*E^((e^2*((f + c*Log[f])^(-1) + 9/(3*f + c*Log[f])))/4)*(9*f^4 - 10*c^2*f^2*Log[f]^2 + c^4*Log[f]^4))","A",0
357,1,135,153,0.3391177,"\int f^{a+b x+c x^2} \sinh (d+e x) \, dx","Integrate[f^(a + b*x + c*x^2)*Sinh[d + e*x],x]","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} e^{-\frac{e (2 b \log (f)+e)}{4 c \log (f)}} \left((\sinh (d)+\cosh (d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)-e^{\frac{b e}{c}} (\cosh (d)-\sinh (d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)-e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)}{4 \sqrt{c} \sqrt{\log (f)}}","\frac{\sqrt{\pi } f^a e^{-\frac{(e-b \log (f))^2}{4 c \log (f)}-d} \text{erfi}\left(\frac{-b \log (f)-2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{d-\frac{(b \log (f)+e)^2}{4 c \log (f)}} \text{erfi}\left(\frac{b \log (f)+2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^(a - b^2/(4*c))*Sqrt[Pi]*(-(E^((b*e)/c)*Erfi[(-e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[d] - Sinh[d])) + Erfi[(e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[d] + Sinh[d])))/(4*Sqrt[c]*E^((e*(e + 2*b*Log[f]))/(4*c*Log[f]))*Sqrt[Log[f]])","A",1
358,1,183,219,0.6262067,"\int f^{a+b x+c x^2} \sinh ^2(d+e x) \, dx","Integrate[f^(a + b*x + c*x^2)*Sinh[d + e*x]^2,x]","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} e^{-\frac{e (b \log (f)+e)}{c \log (f)}} \left(e^{\frac{2 b e}{c}} (\cosh (2 d)-\sinh (2 d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)-2 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+(\sinh (2 d)+\cosh (2 d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)+2 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)-2 e^{\frac{e (b \log (f)+e)}{c \log (f)}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)\right)}{8 \sqrt{c} \sqrt{\log (f)}}","-\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } f^a e^{-\frac{(2 e-b \log (f))^2}{4 c \log (f)}-2 d} \text{erfi}\left(\frac{-b \log (f)-2 c x \log (f)+2 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{2 d-\frac{(b \log (f)+2 e)^2}{4 c \log (f)}} \text{erfi}\left(\frac{b \log (f)+2 c x \log (f)+2 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{8 \sqrt{c} \sqrt{\log (f)}}",1,"(f^(a - b^2/(4*c))*Sqrt[Pi]*(-2*E^((e*(e + b*Log[f]))/(c*Log[f]))*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])] + E^((2*b*e)/c)*Erfi[(-2*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[2*d] - Sinh[2*d]) + Erfi[(2*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[2*d] + Sinh[2*d])))/(8*Sqrt[c]*E^((e*(e + b*Log[f]))/(c*Log[f]))*Sqrt[Log[f]])","A",1
359,1,263,315,1.0199567,"\int f^{a+b x+c x^2} \sinh ^3(d+e x) \, dx","Integrate[f^(a + b*x + c*x^2)*Sinh[d + e*x]^3,x]","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} e^{-\frac{3 e (2 b \log (f)+3 e)}{4 c \log (f)}} \left((\sinh (d)+\cosh (d)) \left(3 (\cosh (2 d)-\sinh (2 d)) e^{\frac{2 e (b \log (f)+e)}{c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)-e}{2 \sqrt{c} \sqrt{\log (f)}}\right)+(\sinh (2 d)+\cosh (2 d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)+3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)-3 e^{\frac{e (b \log (f)+2 e)}{c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)-e^{\frac{3 b e}{c}} (\cosh (3 d)-\sinh (3 d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)-3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)\right)}{16 \sqrt{c} \sqrt{\log (f)}}","-\frac{3 \sqrt{\pi } f^a e^{-\frac{(e-b \log (f))^2}{4 c \log (f)}-d} \text{erfi}\left(\frac{-b \log (f)-2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{-\frac{(3 e-b \log (f))^2}{4 c \log (f)}-3 d} \text{erfi}\left(\frac{-b \log (f)-2 c x \log (f)+3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}-\frac{3 \sqrt{\pi } f^a e^{d-\frac{(b \log (f)+e)^2}{4 c \log (f)}} \text{erfi}\left(\frac{b \log (f)+2 c x \log (f)+e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a e^{3 d-\frac{(b \log (f)+3 e)^2}{4 c \log (f)}} \text{erfi}\left(\frac{b \log (f)+2 c x \log (f)+3 e}{2 \sqrt{c} \sqrt{\log (f)}}\right)}{16 \sqrt{c} \sqrt{\log (f)}}",1,"(f^(a - b^2/(4*c))*Sqrt[Pi]*((Cosh[d] + Sinh[d])*(-3*E^((e*(2*e + b*Log[f]))/(c*Log[f]))*Erfi[(e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])] + 3*E^((2*e*(e + b*Log[f]))/(c*Log[f]))*Erfi[(-e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[2*d] - Sinh[2*d]) + Erfi[(3*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[2*d] + Sinh[2*d])) - E^((3*b*e)/c)*Erfi[(-3*e + (b + 2*c*x)*Log[f])/(2*Sqrt[c]*Sqrt[Log[f]])]*(Cosh[3*d] - Sinh[3*d])))/(16*Sqrt[c]*E^((3*e*(3*e + 2*b*Log[f]))/(4*c*Log[f]))*Sqrt[Log[f]])","A",1
360,1,179,154,0.8113271,"\int f^{a+b x+c x^2} \sinh \left(d+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Sinh[d + f*x^2],x]","\frac{\sqrt{\pi } f^a e^{-\frac{b^2 \log ^2(f)}{4 (c \log (f)+f)}} \left(\sqrt{f-c \log (f)} (\sinh (d)+\cosh (d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)+2 f x}{2 \sqrt{c \log (f)+f}}\right)-\sqrt{c \log (f)+f} (\cosh (d)-\sinh (d)) e^{\frac{b^2 f \log ^2(f)}{2 f^2-2 c^2 \log ^2(f)}} \text{erf}\left(\frac{2 f x-\log (f) (b+2 c x)}{2 \sqrt{f-c \log (f)}}\right)\right)}{4 \sqrt{f-c \log (f)} \sqrt{c \log (f)+f}}","\frac{\sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{4 f-4 c \log (f)}-d} \text{erf}\left(\frac{b \log (f)-2 x (f-c \log (f))}{2 \sqrt{f-c \log (f)}}\right)}{4 \sqrt{f-c \log (f)}}+\frac{\sqrt{\pi } f^a e^{d-\frac{b^2 \log ^2(f)}{4 (c \log (f)+f)}} \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+f)}{2 \sqrt{c \log (f)+f}}\right)}{4 \sqrt{c \log (f)+f}}",1,"(f^a*Sqrt[Pi]*(-(E^((b^2*f*Log[f]^2)/(2*f^2 - 2*c^2*Log[f]^2))*Erf[(2*f*x - (b + 2*c*x)*Log[f])/(2*Sqrt[f - c*Log[f]])]*Sqrt[f + c*Log[f]]*(Cosh[d] - Sinh[d])) + Erfi[(2*f*x + (b + 2*c*x)*Log[f])/(2*Sqrt[f + c*Log[f]])]*Sqrt[f - c*Log[f]]*(Cosh[d] + Sinh[d])))/(4*E^((b^2*Log[f]^2)/(4*(f + c*Log[f])))*Sqrt[f - c*Log[f]]*Sqrt[f + c*Log[f]])","A",1
361,1,257,225,2.2748858,"\int f^{a+b x+c x^2} \sinh ^2\left(d+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Sinh[d + f*x^2]^2,x]","\frac{1}{8} \sqrt{\pi } f^a \left(-\frac{e^{-\frac{b^2 \log ^2(f)}{4 c \log (f)+8 f}} \left(\sqrt{2 f-c \log (f)} (c \log (f)+2 f) (\cosh (2 d)-\sinh (2 d)) e^{\frac{b^2 f \log ^2(f)}{4 f^2-c^2 \log ^2(f)}} \text{erf}\left(\frac{4 f x-\log (f) (b+2 c x)}{2 \sqrt{2 f-c \log (f)}}\right)+(2 f-c \log (f)) \sqrt{c \log (f)+2 f} (\sinh (2 d)+\cosh (2 d)) \text{erfi}\left(\frac{\log (f) (b+2 c x)+4 f x}{2 \sqrt{c \log (f)+2 f}}\right)\right)}{c^2 \log ^2(f)-4 f^2}-\frac{2 f^{-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{\sqrt{c} \sqrt{\log (f)}}\right)","-\frac{\sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{8 f-4 c \log (f)}-2 d} \text{erf}\left(\frac{b \log (f)-2 x (2 f-c \log (f))}{2 \sqrt{2 f-c \log (f)}}\right)}{8 \sqrt{2 f-c \log (f)}}+\frac{\sqrt{\pi } f^a e^{2 d-\frac{b^2 \log ^2(f)}{4 c \log (f)+8 f}} \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+2 f)}{2 \sqrt{c \log (f)+2 f}}\right)}{8 \sqrt{c \log (f)+2 f}}-\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*((-2*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(Sqrt[c]*f^(b^2/(4*c))*Sqrt[Log[f]]) - (E^((b^2*f*Log[f]^2)/(4*f^2 - c^2*Log[f]^2))*Erf[(4*f*x - (b + 2*c*x)*Log[f])/(2*Sqrt[2*f - c*Log[f]])]*Sqrt[2*f - c*Log[f]]*(2*f + c*Log[f])*(Cosh[2*d] - Sinh[2*d]) + Erfi[(4*f*x + (b + 2*c*x)*Log[f])/(2*Sqrt[2*f + c*Log[f]])]*(2*f - c*Log[f])*Sqrt[2*f + c*Log[f]]*(Cosh[2*d] + Sinh[2*d]))/(E^((b^2*Log[f]^2)/(8*f + 4*c*Log[f]))*(-4*f^2 + c^2*Log[f]^2))))/8","A",1
362,1,2511,323,6.5165784,"\int f^{a+b x+c x^2} \sinh ^3\left(d+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Sinh[d + f*x^2]^3,x]","\text{Result too large to show}","-\frac{3 \sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{4 f-4 c \log (f)}-d} \text{erf}\left(\frac{b \log (f)-2 x (f-c \log (f))}{2 \sqrt{f-c \log (f)}}\right)}{16 \sqrt{f-c \log (f)}}+\frac{\sqrt{\pi } f^a e^{\frac{b^2 \log ^2(f)}{12 f-4 c \log (f)}-3 d} \text{erf}\left(\frac{b \log (f)-2 x (3 f-c \log (f))}{2 \sqrt{3 f-c \log (f)}}\right)}{16 \sqrt{3 f-c \log (f)}}-\frac{3 \sqrt{\pi } f^a e^{d-\frac{b^2 \log ^2(f)}{4 (c \log (f)+f)}} \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+f)}{2 \sqrt{c \log (f)+f}}\right)}{16 \sqrt{c \log (f)+f}}+\frac{\sqrt{\pi } f^a e^{3 d-\frac{b^2 \log ^2(f)}{4 (c \log (f)+3 f)}} \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+3 f)}{2 \sqrt{c \log (f)+3 f}}\right)}{16 \sqrt{c \log (f)+3 f}}",1,"(f^a*Sqrt[Pi]*(27*E^((b^2*Log[f]^2)/(4*(f - c*Log[f])))*f^3*Cosh[d]*Erf[(2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Sqrt[f - c*Log[f]] + 27*c*E^((b^2*Log[f]^2)/(4*(f - c*Log[f])))*f^2*Cosh[d]*Erf[(2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]*Sqrt[f - c*Log[f]] - 3*c^2*E^((b^2*Log[f]^2)/(4*(f - c*Log[f])))*f*Cosh[d]*Erf[(2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]^2*Sqrt[f - c*Log[f]] - 3*c^3*E^((b^2*Log[f]^2)/(4*(f - c*Log[f])))*Cosh[d]*Erf[(2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]^3*Sqrt[f - c*Log[f]] - 3*E^((b^2*Log[f]^2)/(4*(3*f - c*Log[f])))*f^3*Cosh[3*d]*Erf[(6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Sqrt[3*f - c*Log[f]] - c*E^((b^2*Log[f]^2)/(4*(3*f - c*Log[f])))*f^2*Cosh[3*d]*Erf[(6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]*Sqrt[3*f - c*Log[f]] + 3*c^2*E^((b^2*Log[f]^2)/(4*(3*f - c*Log[f])))*f*Cosh[3*d]*Erf[(6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]^2*Sqrt[3*f - c*Log[f]] + c^3*E^((b^2*Log[f]^2)/(4*(3*f - c*Log[f])))*Cosh[3*d]*Erf[(6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]^3*Sqrt[3*f - c*Log[f]] - (27*f^3*Cosh[d]*Erfi[(2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Sqrt[f + c*Log[f]])/E^((b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (27*c*f^2*Cosh[d]*Erfi[(2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]*Sqrt[f + c*Log[f]])/E^((b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (3*c^2*f*Cosh[d]*Erfi[(2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]^2*Sqrt[f + c*Log[f]])/E^((b^2*Log[f]^2)/(4*(f + c*Log[f]))) - (3*c^3*Cosh[d]*Erfi[(2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]^3*Sqrt[f + c*Log[f]])/E^((b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (3*f^3*Cosh[3*d]*Erfi[(6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Sqrt[3*f + c*Log[f]])/E^((b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (c*f^2*Cosh[3*d]*Erfi[(6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]*Sqrt[3*f + c*Log[f]])/E^((b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (3*c^2*f*Cosh[3*d]*Erfi[(6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]^2*Sqrt[3*f + c*Log[f]])/E^((b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) + (c^3*Cosh[3*d]*Erfi[(6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]^3*Sqrt[3*f + c*Log[f]])/E^((b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - 27*E^((b^2*Log[f]^2)/(4*(f - c*Log[f])))*f^3*Erf[(2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Sqrt[f - c*Log[f]]*Sinh[d] - 27*c*E^((b^2*Log[f]^2)/(4*(f - c*Log[f])))*f^2*Erf[(2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]*Sqrt[f - c*Log[f]]*Sinh[d] + 3*c^2*E^((b^2*Log[f]^2)/(4*(f - c*Log[f])))*f*Erf[(2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]^2*Sqrt[f - c*Log[f]]*Sinh[d] + 3*c^3*E^((b^2*Log[f]^2)/(4*(f - c*Log[f])))*Erf[(2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]^3*Sqrt[f - c*Log[f]]*Sinh[d] - (27*f^3*Erfi[(2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Sqrt[f + c*Log[f]]*Sinh[d])/E^((b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (27*c*f^2*Erfi[(2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]*Sqrt[f + c*Log[f]]*Sinh[d])/E^((b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (3*c^2*f*Erfi[(2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]^2*Sqrt[f + c*Log[f]]*Sinh[d])/E^((b^2*Log[f]^2)/(4*(f + c*Log[f]))) - (3*c^3*Erfi[(2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]^3*Sqrt[f + c*Log[f]]*Sinh[d])/E^((b^2*Log[f]^2)/(4*(f + c*Log[f]))) + 3*E^((b^2*Log[f]^2)/(4*(3*f - c*Log[f])))*f^3*Erf[(6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Sqrt[3*f - c*Log[f]]*Sinh[3*d] + c*E^((b^2*Log[f]^2)/(4*(3*f - c*Log[f])))*f^2*Erf[(6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]*Sqrt[3*f - c*Log[f]]*Sinh[3*d] - 3*c^2*E^((b^2*Log[f]^2)/(4*(3*f - c*Log[f])))*f*Erf[(6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]^2*Sqrt[3*f - c*Log[f]]*Sinh[3*d] - c^3*E^((b^2*Log[f]^2)/(4*(3*f - c*Log[f])))*Erf[(6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]^3*Sqrt[3*f - c*Log[f]]*Sinh[3*d] + (3*f^3*Erfi[(6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Sqrt[3*f + c*Log[f]]*Sinh[3*d])/E^((b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (c*f^2*Erfi[(6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]*Sqrt[3*f + c*Log[f]]*Sinh[3*d])/E^((b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (3*c^2*f*Erfi[(6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]^2*Sqrt[3*f + c*Log[f]]*Sinh[3*d])/E^((b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) + (c^3*Erfi[(6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]^3*Sqrt[3*f + c*Log[f]]*Sinh[3*d])/E^((b^2*Log[f]^2)/(4*(3*f + c*Log[f])))))/(16*(f - c*Log[f])*(3*f - c*Log[f])*(f + c*Log[f])*(3*f + c*Log[f]))","B",1
363,1,252,161,1.5551225,"\int f^{a+b x+c x^2} \sinh \left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Sinh[d + e*x + f*x^2],x]","\frac{\sqrt{\pi } e^{-\frac{b^2 \log ^2(f)+e^2}{4 (c \log (f)+f)}} f^{a+\frac{b e f}{c^2 \log ^2(f)-f^2}} \left((f-c \log (f)) \sqrt{c \log (f)+f} (\sinh (d)+\cosh (d)) f^{\frac{b e}{2 f-2 c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)+e+2 f x}{2 \sqrt{c \log (f)+f}}\right)-\sqrt{f-c \log (f)} (c \log (f)+f) (\cosh (d)-\sinh (d)) f^{\frac{b e}{2 (c \log (f)+f)}} \exp \left(\frac{f \left(b^2 \log ^2(f)+e^2\right)}{2 \left(f^2-c^2 \log ^2(f)\right)}\right) \text{erf}\left(\frac{-\log (f) (b+2 c x)+e+2 f x}{2 \sqrt{f-c \log (f)}}\right)\right)}{4 \left(f^2-c^2 \log ^2(f)\right)}","\frac{\sqrt{\pi } f^a e^{d-\frac{(b \log (f)+e)^2}{4 (c \log (f)+f)}} \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+f)+e}{2 \sqrt{c \log (f)+f}}\right)}{4 \sqrt{c \log (f)+f}}-\frac{\sqrt{\pi } f^a e^{\frac{(e-b \log (f))^2}{4 (f-c \log (f))}-d} \text{erf}\left(\frac{-b \log (f)+2 x (f-c \log (f))+e}{2 \sqrt{f-c \log (f)}}\right)}{4 \sqrt{f-c \log (f)}}",1,"(f^(a + (b*e*f)/(-f^2 + c^2*Log[f]^2))*Sqrt[Pi]*(-(E^((f*(e^2 + b^2*Log[f]^2))/(2*(f^2 - c^2*Log[f]^2)))*f^((b*e)/(2*(f + c*Log[f])))*Erf[(e + 2*f*x - (b + 2*c*x)*Log[f])/(2*Sqrt[f - c*Log[f]])]*Sqrt[f - c*Log[f]]*(f + c*Log[f])*(Cosh[d] - Sinh[d])) + f^((b*e)/(2*f - 2*c*Log[f]))*Erfi[(e + 2*f*x + (b + 2*c*x)*Log[f])/(2*Sqrt[f + c*Log[f]])]*(f - c*Log[f])*Sqrt[f + c*Log[f]]*(Cosh[d] + Sinh[d])))/(4*E^((e^2 + b^2*Log[f]^2)/(4*(f + c*Log[f])))*(f^2 - c^2*Log[f]^2))","A",0
364,1,339,239,6.233658,"\int f^{a+b x+c x^2} \sinh ^2\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Sinh[d + e*x + f*x^2]^2,x]","-\frac{\sqrt{\pi } e^{-\frac{b^2 \log ^2(f)+4 e^2}{4 c \log (f)+8 f}} f^{a+\frac{4 b e f}{c^2 \log ^2(f)-4 f^2}} \left(\sqrt{2 f-c \log (f)} (c \log (f)+2 f) (\cosh (2 d)-\sinh (2 d)) f^{\frac{b e}{c \log (f)+2 f}} \exp \left(\frac{f \left(b^2 \log ^2(f)+4 e^2\right)}{4 f^2-c^2 \log ^2(f)}\right) \text{erf}\left(\frac{2 (e+2 f x)-\log (f) (b+2 c x)}{2 \sqrt{2 f-c \log (f)}}\right)+(2 f-c \log (f)) \sqrt{c \log (f)+2 f} (\sinh (2 d)+\cosh (2 d)) f^{\frac{b e}{2 f-c \log (f)}} \text{erfi}\left(\frac{\log (f) (b+2 c x)+2 (e+2 f x)}{2 \sqrt{c \log (f)+2 f}}\right)\right)}{8 \left(c^2 \log ^2(f)-4 f^2\right)}-\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}","-\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 \sqrt{c} \sqrt{\log (f)}}+\frac{\sqrt{\pi } f^a \exp \left(\frac{(2 e-b \log (f))^2}{8 f-4 c \log (f)}-2 d\right) \text{erf}\left(\frac{-b \log (f)+2 x (2 f-c \log (f))+2 e}{2 \sqrt{2 f-c \log (f)}}\right)}{8 \sqrt{2 f-c \log (f)}}+\frac{\sqrt{\pi } f^a \exp \left(2 d-\frac{(b \log (f)+2 e)^2}{4 c \log (f)+8 f}\right) \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+2 f)+2 e}{2 \sqrt{c \log (f)+2 f}}\right)}{8 \sqrt{c \log (f)+2 f}}",1,"-1/4*(f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(Sqrt[c]*Sqrt[Log[f]]) - (f^(a + (4*b*e*f)/(-4*f^2 + c^2*Log[f]^2))*Sqrt[Pi]*(E^((f*(4*e^2 + b^2*Log[f]^2))/(4*f^2 - c^2*Log[f]^2))*f^((b*e)/(2*f + c*Log[f]))*Erf[(2*(e + 2*f*x) - (b + 2*c*x)*Log[f])/(2*Sqrt[2*f - c*Log[f]])]*Sqrt[2*f - c*Log[f]]*(2*f + c*Log[f])*(Cosh[2*d] - Sinh[2*d]) + f^((b*e)/(2*f - c*Log[f]))*Erfi[(2*(e + 2*f*x) + (b + 2*c*x)*Log[f])/(2*Sqrt[2*f + c*Log[f]])]*(2*f - c*Log[f])*Sqrt[2*f + c*Log[f]]*(Cosh[2*d] + Sinh[2*d])))/(8*E^((4*e^2 + b^2*Log[f]^2)/(8*f + 4*c*Log[f]))*(-4*f^2 + c^2*Log[f]^2))","A",0
365,1,2991,344,6.6521437,"\int f^{a+b x+c x^2} \sinh ^3\left(d+e x+f x^2\right) \, dx","Integrate[f^(a + b*x + c*x^2)*Sinh[d + e*x + f*x^2]^3,x]","\text{Result too large to show}","-\frac{\sqrt{\pi } f^a \exp \left(\frac{(3 e-b \log (f))^2}{12 f-4 c \log (f)}-3 d\right) \text{erf}\left(\frac{-b \log (f)+2 x (3 f-c \log (f))+3 e}{2 \sqrt{3 f-c \log (f)}}\right)}{16 \sqrt{3 f-c \log (f)}}+\frac{3 \sqrt{\pi } f^a e^{\frac{(e-b \log (f))^2}{4 (f-c \log (f))}-d} \text{erf}\left(\frac{-b \log (f)+2 x (f-c \log (f))+e}{2 \sqrt{f-c \log (f)}}\right)}{16 \sqrt{f-c \log (f)}}+\frac{\sqrt{\pi } f^a \exp \left(3 d-\frac{(b \log (f)+3 e)^2}{4 (c \log (f)+3 f)}\right) \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+3 f)+3 e}{2 \sqrt{c \log (f)+3 f}}\right)}{16 \sqrt{c \log (f)+3 f}}-\frac{3 \sqrt{\pi } f^a e^{d-\frac{(b \log (f)+e)^2}{4 (c \log (f)+f)}} \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+f)+e}{2 \sqrt{c \log (f)+f}}\right)}{16 \sqrt{c \log (f)+f}}",1,"(f^a*Sqrt[Pi]*((27*f^3*Cosh[d]*Erf[(e + 2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Sqrt[f - c*Log[f]])/E^((-e^2 + 2*b*e*Log[f] - b^2*Log[f]^2)/(4*(f - c*Log[f]))) + (27*c*f^2*Cosh[d]*Erf[(e + 2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]*Sqrt[f - c*Log[f]])/E^((-e^2 + 2*b*e*Log[f] - b^2*Log[f]^2)/(4*(f - c*Log[f]))) - (3*c^2*f*Cosh[d]*Erf[(e + 2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]^2*Sqrt[f - c*Log[f]])/E^((-e^2 + 2*b*e*Log[f] - b^2*Log[f]^2)/(4*(f - c*Log[f]))) - (3*c^3*Cosh[d]*Erf[(e + 2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]^3*Sqrt[f - c*Log[f]])/E^((-e^2 + 2*b*e*Log[f] - b^2*Log[f]^2)/(4*(f - c*Log[f]))) - (3*f^3*Cosh[3*d]*Erf[(3*e + 6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Sqrt[3*f - c*Log[f]])/E^((-9*e^2 + 6*b*e*Log[f] - b^2*Log[f]^2)/(4*(3*f - c*Log[f]))) - (c*f^2*Cosh[3*d]*Erf[(3*e + 6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]*Sqrt[3*f - c*Log[f]])/E^((-9*e^2 + 6*b*e*Log[f] - b^2*Log[f]^2)/(4*(3*f - c*Log[f]))) + (3*c^2*f*Cosh[3*d]*Erf[(3*e + 6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]^2*Sqrt[3*f - c*Log[f]])/E^((-9*e^2 + 6*b*e*Log[f] - b^2*Log[f]^2)/(4*(3*f - c*Log[f]))) + (c^3*Cosh[3*d]*Erf[(3*e + 6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]^3*Sqrt[3*f - c*Log[f]])/E^((-9*e^2 + 6*b*e*Log[f] - b^2*Log[f]^2)/(4*(3*f - c*Log[f]))) - (27*f^3*Cosh[d]*Erfi[(e + 2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Sqrt[f + c*Log[f]])/E^((e^2 + 2*b*e*Log[f] + b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (27*c*f^2*Cosh[d]*Erfi[(e + 2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]*Sqrt[f + c*Log[f]])/E^((e^2 + 2*b*e*Log[f] + b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (3*c^2*f*Cosh[d]*Erfi[(e + 2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]^2*Sqrt[f + c*Log[f]])/E^((e^2 + 2*b*e*Log[f] + b^2*Log[f]^2)/(4*(f + c*Log[f]))) - (3*c^3*Cosh[d]*Erfi[(e + 2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]^3*Sqrt[f + c*Log[f]])/E^((e^2 + 2*b*e*Log[f] + b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (3*f^3*Cosh[3*d]*Erfi[(3*e + 6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Sqrt[3*f + c*Log[f]])/E^((9*e^2 + 6*b*e*Log[f] + b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (c*f^2*Cosh[3*d]*Erfi[(3*e + 6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]*Sqrt[3*f + c*Log[f]])/E^((9*e^2 + 6*b*e*Log[f] + b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (3*c^2*f*Cosh[3*d]*Erfi[(3*e + 6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]^2*Sqrt[3*f + c*Log[f]])/E^((9*e^2 + 6*b*e*Log[f] + b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) + (c^3*Cosh[3*d]*Erfi[(3*e + 6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]^3*Sqrt[3*f + c*Log[f]])/E^((9*e^2 + 6*b*e*Log[f] + b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (27*f^3*Erf[(e + 2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Sqrt[f - c*Log[f]]*Sinh[d])/E^((-e^2 + 2*b*e*Log[f] - b^2*Log[f]^2)/(4*(f - c*Log[f]))) - (27*c*f^2*Erf[(e + 2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]*Sqrt[f - c*Log[f]]*Sinh[d])/E^((-e^2 + 2*b*e*Log[f] - b^2*Log[f]^2)/(4*(f - c*Log[f]))) + (3*c^2*f*Erf[(e + 2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]^2*Sqrt[f - c*Log[f]]*Sinh[d])/E^((-e^2 + 2*b*e*Log[f] - b^2*Log[f]^2)/(4*(f - c*Log[f]))) + (3*c^3*Erf[(e + 2*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[f - c*Log[f]])]*Log[f]^3*Sqrt[f - c*Log[f]]*Sinh[d])/E^((-e^2 + 2*b*e*Log[f] - b^2*Log[f]^2)/(4*(f - c*Log[f]))) - (27*f^3*Erfi[(e + 2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Sqrt[f + c*Log[f]]*Sinh[d])/E^((e^2 + 2*b*e*Log[f] + b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (27*c*f^2*Erfi[(e + 2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]*Sqrt[f + c*Log[f]]*Sinh[d])/E^((e^2 + 2*b*e*Log[f] + b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (3*c^2*f*Erfi[(e + 2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]^2*Sqrt[f + c*Log[f]]*Sinh[d])/E^((e^2 + 2*b*e*Log[f] + b^2*Log[f]^2)/(4*(f + c*Log[f]))) - (3*c^3*Erfi[(e + 2*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[f + c*Log[f]])]*Log[f]^3*Sqrt[f + c*Log[f]]*Sinh[d])/E^((e^2 + 2*b*e*Log[f] + b^2*Log[f]^2)/(4*(f + c*Log[f]))) + (3*f^3*Erf[(3*e + 6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Sqrt[3*f - c*Log[f]]*Sinh[3*d])/E^((-9*e^2 + 6*b*e*Log[f] - b^2*Log[f]^2)/(4*(3*f - c*Log[f]))) + (c*f^2*Erf[(3*e + 6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]*Sqrt[3*f - c*Log[f]]*Sinh[3*d])/E^((-9*e^2 + 6*b*e*Log[f] - b^2*Log[f]^2)/(4*(3*f - c*Log[f]))) - (3*c^2*f*Erf[(3*e + 6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]^2*Sqrt[3*f - c*Log[f]]*Sinh[3*d])/E^((-9*e^2 + 6*b*e*Log[f] - b^2*Log[f]^2)/(4*(3*f - c*Log[f]))) - (c^3*Erf[(3*e + 6*f*x - b*Log[f] - 2*c*x*Log[f])/(2*Sqrt[3*f - c*Log[f]])]*Log[f]^3*Sqrt[3*f - c*Log[f]]*Sinh[3*d])/E^((-9*e^2 + 6*b*e*Log[f] - b^2*Log[f]^2)/(4*(3*f - c*Log[f]))) + (3*f^3*Erfi[(3*e + 6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Sqrt[3*f + c*Log[f]]*Sinh[3*d])/E^((9*e^2 + 6*b*e*Log[f] + b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (c*f^2*Erfi[(3*e + 6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]*Sqrt[3*f + c*Log[f]]*Sinh[3*d])/E^((9*e^2 + 6*b*e*Log[f] + b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) - (3*c^2*f*Erfi[(3*e + 6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]^2*Sqrt[3*f + c*Log[f]]*Sinh[3*d])/E^((9*e^2 + 6*b*e*Log[f] + b^2*Log[f]^2)/(4*(3*f + c*Log[f]))) + (c^3*Erfi[(3*e + 6*f*x + b*Log[f] + 2*c*x*Log[f])/(2*Sqrt[3*f + c*Log[f]])]*Log[f]^3*Sqrt[3*f + c*Log[f]]*Sinh[3*d])/E^((9*e^2 + 6*b*e*Log[f] + b^2*Log[f]^2)/(4*(3*f + c*Log[f])))))/(16*(f - c*Log[f])*(3*f - c*Log[f])*(f + c*Log[f])*(3*f + c*Log[f]))","B",1
366,1,30,30,0.0571069,"\int (x+\sinh (x))^2 \, dx","Integrate[(x + Sinh[x])^2,x]","\frac{1}{6} x \left(2 x^2-3\right)-2 \sinh (x)+\frac{1}{4} \sinh (2 x)+2 x \cosh (x)","\frac{x^3}{3}-\frac{x}{2}-2 \sinh (x)+2 x \cosh (x)+\frac{1}{2} \sinh (x) \cosh (x)",1,"(x*(-3 + 2*x^2))/6 + 2*x*Cosh[x] - 2*Sinh[x] + Sinh[2*x]/4","A",1
367,1,48,56,0.0867368,"\int (x+\sinh (x))^3 \, dx","Integrate[(x + Sinh[x])^3,x]","\frac{1}{24} \left(6 x \left(x^3-3 x-24 \sinh (x)+3 \sinh (2 x)\right)+18 \left(4 x^2+7\right) \cosh (x)-9 \cosh (2 x)+2 \cosh (3 x)\right)","\frac{x^4}{4}-\frac{3 x^2}{4}+3 x^2 \cosh (x)-\frac{3 \sinh ^2(x)}{4}-6 x \sinh (x)+\frac{\cosh ^3(x)}{3}+5 \cosh (x)+\frac{3}{2} x \sinh (x) \cosh (x)",1,"(18*(7 + 4*x^2)*Cosh[x] - 9*Cosh[2*x] + 2*Cosh[3*x] + 6*x*(-3*x + x^3 - 24*Sinh[x] + 3*Sinh[2*x]))/24","A",1
368,1,180,213,0.3265879,"\int \frac{\sinh (a+b x)}{c+d x^2} \, dx","Integrate[Sinh[a + b*x]/(c + d*x^2),x]","\frac{i \left(\sinh \left(a-\frac{i b \sqrt{c}}{\sqrt{d}}\right) \text{Ci}\left(i b x-\frac{b \sqrt{c}}{\sqrt{d}}\right)-\sinh \left(a+\frac{i b \sqrt{c}}{\sqrt{d}}\right) \text{Ci}\left(i x b+\frac{\sqrt{c} b}{\sqrt{d}}\right)+i \left(\cosh \left(a-\frac{i b \sqrt{c}}{\sqrt{d}}\right) \text{Si}\left(\frac{b \sqrt{c}}{\sqrt{d}}-i b x\right)+\cosh \left(a+\frac{i b \sqrt{c}}{\sqrt{d}}\right) \text{Si}\left(i x b+\frac{\sqrt{c} b}{\sqrt{d}}\right)\right)\right)}{2 \sqrt{c} \sqrt{d}}","-\frac{\sinh \left(a-\frac{b \sqrt{-c}}{\sqrt{d}}\right) \text{Chi}\left(x b+\frac{\sqrt{-c} b}{\sqrt{d}}\right)}{2 \sqrt{-c} \sqrt{d}}+\frac{\sinh \left(a+\frac{b \sqrt{-c}}{\sqrt{d}}\right) \text{Chi}\left(\frac{b \sqrt{-c}}{\sqrt{d}}-b x\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\cosh \left(a+\frac{b \sqrt{-c}}{\sqrt{d}}\right) \text{Shi}\left(\frac{b \sqrt{-c}}{\sqrt{d}}-b x\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{\cosh \left(a-\frac{b \sqrt{-c}}{\sqrt{d}}\right) \text{Shi}\left(x b+\frac{\sqrt{-c} b}{\sqrt{d}}\right)}{2 \sqrt{-c} \sqrt{d}}",1,"((I/2)*(CosIntegral[-((b*Sqrt[c])/Sqrt[d]) + I*b*x]*Sinh[a - (I*b*Sqrt[c])/Sqrt[d]] - CosIntegral[(b*Sqrt[c])/Sqrt[d] + I*b*x]*Sinh[a + (I*b*Sqrt[c])/Sqrt[d]] + I*(Cosh[a - (I*b*Sqrt[c])/Sqrt[d]]*SinIntegral[(b*Sqrt[c])/Sqrt[d] - I*b*x] + Cosh[a + (I*b*Sqrt[c])/Sqrt[d]]*SinIntegral[(b*Sqrt[c])/Sqrt[d] + I*b*x])))/(Sqrt[c]*Sqrt[d])","C",0
369,1,248,271,0.5371621,"\int \frac{\sinh (a+b x)}{c+d x+e x^2} \, dx","Integrate[Sinh[a + b*x]/(c + d*x + e*x^2),x]","\frac{\sinh \left(a+\frac{b \left(\sqrt{d^2-4 c e}-d\right)}{2 e}\right) \text{Ci}\left(\frac{i b \left(d+2 e x-\sqrt{d^2-4 c e}\right)}{2 e}\right)-\sinh \left(a-\frac{b \left(\sqrt{d^2-4 c e}+d\right)}{2 e}\right) \text{Ci}\left(\frac{i b \left(d+2 e x+\sqrt{d^2-4 c e}\right)}{2 e}\right)-\cosh \left(a-\frac{b \left(\sqrt{d^2-4 c e}+d\right)}{2 e}\right) \text{Shi}\left(\frac{b \left(d+2 e x+\sqrt{d^2-4 c e}\right)}{2 e}\right)+i \cosh \left(a+\frac{b \left(\sqrt{d^2-4 c e}-d\right)}{2 e}\right) \text{Si}\left(\frac{i b \left(\sqrt{d^2-4 c e}-d\right)}{2 e}-i b x\right)}{\sqrt{d^2-4 c e}}","\frac{\sinh \left(a-\frac{b \left(d-\sqrt{d^2-4 c e}\right)}{2 e}\right) \text{Chi}\left(\frac{b \left(d-\sqrt{d^2-4 c e}\right)}{2 e}+b x\right)}{\sqrt{d^2-4 c e}}-\frac{\sinh \left(a-\frac{b \left(\sqrt{d^2-4 c e}+d\right)}{2 e}\right) \text{Chi}\left(\frac{b \left(d+\sqrt{d^2-4 c e}\right)}{2 e}+b x\right)}{\sqrt{d^2-4 c e}}+\frac{\cosh \left(a-\frac{b \left(d-\sqrt{d^2-4 c e}\right)}{2 e}\right) \text{Shi}\left(\frac{b \left(d-\sqrt{d^2-4 c e}\right)}{2 e}+b x\right)}{\sqrt{d^2-4 c e}}-\frac{\cosh \left(a-\frac{b \left(\sqrt{d^2-4 c e}+d\right)}{2 e}\right) \text{Shi}\left(\frac{b \left(d+\sqrt{d^2-4 c e}\right)}{2 e}+b x\right)}{\sqrt{d^2-4 c e}}",1,"(CosIntegral[((I/2)*b*(d - Sqrt[d^2 - 4*c*e] + 2*e*x))/e]*Sinh[a + (b*(-d + Sqrt[d^2 - 4*c*e]))/(2*e)] - CosIntegral[((I/2)*b*(d + Sqrt[d^2 - 4*c*e] + 2*e*x))/e]*Sinh[a - (b*(d + Sqrt[d^2 - 4*c*e]))/(2*e)] - Cosh[a - (b*(d + Sqrt[d^2 - 4*c*e]))/(2*e)]*SinhIntegral[(b*(d + Sqrt[d^2 - 4*c*e] + 2*e*x))/(2*e)] + I*Cosh[a + (b*(-d + Sqrt[d^2 - 4*c*e]))/(2*e)]*SinIntegral[((I/2)*b*(-d + Sqrt[d^2 - 4*c*e]))/e - I*b*x])/Sqrt[d^2 - 4*c*e]","C",0