1,1,179,0,0.1251045,"\int (c+d x)^3 \text{sech}(a+b x) \, dx","Int[(c + d*x)^3*Sech[a + b*x],x]","\frac{6 i d^2 (c+d x) \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^3}-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^2}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^2}-\frac{6 i d^3 \text{PolyLog}\left(4,-i e^{a+b x}\right)}{b^4}+\frac{6 i d^3 \text{PolyLog}\left(4,i e^{a+b x}\right)}{b^4}+\frac{2 (c+d x)^3 \tan ^{-1}\left(e^{a+b x}\right)}{b}","\frac{6 i d^2 (c+d x) \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^3}-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^2}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^2}-\frac{6 i d^3 \text{PolyLog}\left(4,-i e^{a+b x}\right)}{b^4}+\frac{6 i d^3 \text{PolyLog}\left(4,i e^{a+b x}\right)}{b^4}+\frac{2 (c+d x)^3 \tan ^{-1}\left(e^{a+b x}\right)}{b}",1,"(2*(c + d*x)^3*ArcTan[E^(a + b*x)])/b - ((3*I)*d*(c + d*x)^2*PolyLog[2, (-I)*E^(a + b*x)])/b^2 + ((3*I)*d*(c + d*x)^2*PolyLog[2, I*E^(a + b*x)])/b^2 + ((6*I)*d^2*(c + d*x)*PolyLog[3, (-I)*E^(a + b*x)])/b^3 - ((6*I)*d^2*(c + d*x)*PolyLog[3, I*E^(a + b*x)])/b^3 - ((6*I)*d^3*PolyLog[4, (-I)*E^(a + b*x)])/b^4 + ((6*I)*d^3*PolyLog[4, I*E^(a + b*x)])/b^4","A",9,5,14,0.3571,1,"{4180, 2531, 6609, 2282, 6589}"
2,1,119,0,0.0820517,"\int (c+d x)^2 \text{sech}(a+b x) \, dx","Int[(c + d*x)^2*Sech[a + b*x],x]","-\frac{2 i d (c+d x) \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^2}+\frac{2 i d (c+d x) \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^2}+\frac{2 i d^2 \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^3}-\frac{2 i d^2 \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^3}+\frac{2 (c+d x)^2 \tan ^{-1}\left(e^{a+b x}\right)}{b}","-\frac{2 i d (c+d x) \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^2}+\frac{2 i d (c+d x) \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^2}+\frac{2 i d^2 \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^3}-\frac{2 i d^2 \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^3}+\frac{2 (c+d x)^2 \tan ^{-1}\left(e^{a+b x}\right)}{b}",1,"(2*(c + d*x)^2*ArcTan[E^(a + b*x)])/b - ((2*I)*d*(c + d*x)*PolyLog[2, (-I)*E^(a + b*x)])/b^2 + ((2*I)*d*(c + d*x)*PolyLog[2, I*E^(a + b*x)])/b^2 + ((2*I)*d^2*PolyLog[3, (-I)*E^(a + b*x)])/b^3 - ((2*I)*d^2*PolyLog[3, I*E^(a + b*x)])/b^3","A",7,4,14,0.2857,1,"{4180, 2531, 2282, 6589}"
3,1,61,0,0.0380289,"\int (c+d x) \text{sech}(a+b x) \, dx","Int[(c + d*x)*Sech[a + b*x],x]","-\frac{i d \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^2}+\frac{i d \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^2}+\frac{2 (c+d x) \tan ^{-1}\left(e^{a+b x}\right)}{b}","-\frac{i d \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^2}+\frac{i d \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^2}+\frac{2 (c+d x) \tan ^{-1}\left(e^{a+b x}\right)}{b}",1,"(2*(c + d*x)*ArcTan[E^(a + b*x)])/b - (I*d*PolyLog[2, (-I)*E^(a + b*x)])/b^2 + (I*d*PolyLog[2, I*E^(a + b*x)])/b^2","A",5,3,12,0.2500,1,"{4180, 2279, 2391}"
4,0,0,0,0.0223575,"\int \frac{\text{sech}(a+b x)}{c+d x} \, dx","Int[Sech[a + b*x]/(c + d*x),x]","\int \frac{\text{sech}(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{sech}(a+b x)}{c+d x},x\right)",0,"Defer[Int][Sech[a + b*x]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
5,1,103,0,0.2164747,"\int (c+d x)^3 \text{sech}^2(a+b x) \, dx","Int[(c + d*x)^3*Sech[a + b*x]^2,x]","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(2,-e^{2 (a+b x)}\right)}{b^3}+\frac{3 d^3 \text{PolyLog}\left(3,-e^{2 (a+b x)}\right)}{2 b^4}-\frac{3 d (c+d x)^2 \log \left(e^{2 (a+b x)}+1\right)}{b^2}+\frac{(c+d x)^3 \tanh (a+b x)}{b}+\frac{(c+d x)^3}{b}","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(2,-e^{2 (a+b x)}\right)}{b^3}+\frac{3 d^3 \text{PolyLog}\left(3,-e^{2 (a+b x)}\right)}{2 b^4}-\frac{3 d (c+d x)^2 \log \left(e^{2 (a+b x)}+1\right)}{b^2}+\frac{(c+d x)^3 \tanh (a+b x)}{b}+\frac{(c+d x)^3}{b}",1,"(c + d*x)^3/b - (3*d*(c + d*x)^2*Log[1 + E^(2*(a + b*x))])/b^2 - (3*d^2*(c + d*x)*PolyLog[2, -E^(2*(a + b*x))])/b^3 + (3*d^3*PolyLog[3, -E^(2*(a + b*x))])/(2*b^4) + ((c + d*x)^3*Tanh[a + b*x])/b","A",6,6,16,0.3750,1,"{4184, 3718, 2190, 2531, 2282, 6589}"
6,1,73,0,0.1382483,"\int (c+d x)^2 \text{sech}^2(a+b x) \, dx","Int[(c + d*x)^2*Sech[a + b*x]^2,x]","-\frac{d^2 \text{PolyLog}\left(2,-e^{2 (a+b x)}\right)}{b^3}-\frac{2 d (c+d x) \log \left(e^{2 (a+b x)}+1\right)}{b^2}+\frac{(c+d x)^2 \tanh (a+b x)}{b}+\frac{(c+d x)^2}{b}","-\frac{d^2 \text{PolyLog}\left(2,-e^{2 (a+b x)}\right)}{b^3}-\frac{2 d (c+d x) \log \left(e^{2 (a+b x)}+1\right)}{b^2}+\frac{(c+d x)^2 \tanh (a+b x)}{b}+\frac{(c+d x)^2}{b}",1,"(c + d*x)^2/b - (2*d*(c + d*x)*Log[1 + E^(2*(a + b*x))])/b^2 - (d^2*PolyLog[2, -E^(2*(a + b*x))])/b^3 + ((c + d*x)^2*Tanh[a + b*x])/b","A",5,5,16,0.3125,1,"{4184, 3718, 2190, 2279, 2391}"
7,1,29,0,0.0303165,"\int (c+d x) \text{sech}^2(a+b x) \, dx","Int[(c + d*x)*Sech[a + b*x]^2,x]","\frac{(c+d x) \tanh (a+b x)}{b}-\frac{d \log (\cosh (a+b x))}{b^2}","\frac{(c+d x) \tanh (a+b x)}{b}-\frac{d \log (\cosh (a+b x))}{b^2}",1,"-((d*Log[Cosh[a + b*x]])/b^2) + ((c + d*x)*Tanh[a + b*x])/b","A",2,2,14,0.1429,1,"{4184, 3475}"
8,0,0,0,0.0394697,"\int \frac{\text{sech}^2(a+b x)}{c+d x} \, dx","Int[Sech[a + b*x]^2/(c + d*x),x]","\int \frac{\text{sech}^2(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{sech}^2(a+b x)}{c+d x},x\right)",0,"Defer[Int][Sech[a + b*x]^2/(c + d*x), x]","A",0,0,0,0,-1,"{}"
9,1,296,0,0.216175,"\int (c+d x)^3 \text{sech}^3(a+b x) \, dx","Int[(c + d*x)^3*Sech[a + b*x]^3,x]","\frac{3 i d^2 (c+d x) \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^3}-\frac{3 i d^2 (c+d x) \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-i e^{a+b x}\right)}{2 b^2}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,i e^{a+b x}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(4,-i e^{a+b x}\right)}{b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,i e^{a+b x}\right)}{b^4}-\frac{6 d^2 (c+d x) \tan ^{-1}\left(e^{a+b x}\right)}{b^3}+\frac{3 d (c+d x)^2 \text{sech}(a+b x)}{2 b^2}+\frac{(c+d x)^3 \tan ^{-1}\left(e^{a+b x}\right)}{b}+\frac{(c+d x)^3 \tanh (a+b x) \text{sech}(a+b x)}{2 b}","\frac{3 i d^2 (c+d x) \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^3}-\frac{3 i d^2 (c+d x) \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-i e^{a+b x}\right)}{2 b^2}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,i e^{a+b x}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(4,-i e^{a+b x}\right)}{b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,i e^{a+b x}\right)}{b^4}-\frac{6 d^2 (c+d x) \tan ^{-1}\left(e^{a+b x}\right)}{b^3}+\frac{3 d (c+d x)^2 \text{sech}(a+b x)}{2 b^2}+\frac{(c+d x)^3 \tan ^{-1}\left(e^{a+b x}\right)}{b}+\frac{(c+d x)^3 \tanh (a+b x) \text{sech}(a+b x)}{2 b}",1,"(-6*d^2*(c + d*x)*ArcTan[E^(a + b*x)])/b^3 + ((c + d*x)^3*ArcTan[E^(a + b*x)])/b + ((3*I)*d^3*PolyLog[2, (-I)*E^(a + b*x)])/b^4 - (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, (-I)*E^(a + b*x)])/b^2 - ((3*I)*d^3*PolyLog[2, I*E^(a + b*x)])/b^4 + (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, I*E^(a + b*x)])/b^2 + ((3*I)*d^2*(c + d*x)*PolyLog[3, (-I)*E^(a + b*x)])/b^3 - ((3*I)*d^2*(c + d*x)*PolyLog[3, I*E^(a + b*x)])/b^3 - ((3*I)*d^3*PolyLog[4, (-I)*E^(a + b*x)])/b^4 + ((3*I)*d^3*PolyLog[4, I*E^(a + b*x)])/b^4 + (3*d*(c + d*x)^2*Sech[a + b*x])/(2*b^2) + ((c + d*x)^3*Sech[a + b*x]*Tanh[a + b*x])/(2*b)","A",15,8,16,0.5000,1,"{4186, 4180, 2279, 2391, 2531, 6609, 2282, 6589}"
10,1,175,0,0.1309425,"\int (c+d x)^2 \text{sech}^3(a+b x) \, dx","Int[(c + d*x)^2*Sech[a + b*x]^3,x]","-\frac{i d (c+d x) \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^2}+\frac{i d (c+d x) \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^2}+\frac{i d^2 \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^3}-\frac{i d^2 \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^3}+\frac{d (c+d x) \text{sech}(a+b x)}{b^2}-\frac{d^2 \tan ^{-1}(\sinh (a+b x))}{b^3}+\frac{(c+d x)^2 \tan ^{-1}\left(e^{a+b x}\right)}{b}+\frac{(c+d x)^2 \tanh (a+b x) \text{sech}(a+b x)}{2 b}","-\frac{i d (c+d x) \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^2}+\frac{i d (c+d x) \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^2}+\frac{i d^2 \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^3}-\frac{i d^2 \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^3}+\frac{d (c+d x) \text{sech}(a+b x)}{b^2}-\frac{d^2 \tan ^{-1}(\sinh (a+b x))}{b^3}+\frac{(c+d x)^2 \tan ^{-1}\left(e^{a+b x}\right)}{b}+\frac{(c+d x)^2 \tanh (a+b x) \text{sech}(a+b x)}{2 b}",1,"((c + d*x)^2*ArcTan[E^(a + b*x)])/b - (d^2*ArcTan[Sinh[a + b*x]])/b^3 - (I*d*(c + d*x)*PolyLog[2, (-I)*E^(a + b*x)])/b^2 + (I*d*(c + d*x)*PolyLog[2, I*E^(a + b*x)])/b^2 + (I*d^2*PolyLog[3, (-I)*E^(a + b*x)])/b^3 - (I*d^2*PolyLog[3, I*E^(a + b*x)])/b^3 + (d*(c + d*x)*Sech[a + b*x])/b^2 + ((c + d*x)^2*Sech[a + b*x]*Tanh[a + b*x])/(2*b)","A",9,6,16,0.3750,1,"{4186, 3770, 4180, 2531, 2282, 6589}"
11,1,102,0,0.0640534,"\int (c+d x) \text{sech}^3(a+b x) \, dx","Int[(c + d*x)*Sech[a + b*x]^3,x]","-\frac{i d \text{PolyLog}\left(2,-i e^{a+b x}\right)}{2 b^2}+\frac{i d \text{PolyLog}\left(2,i e^{a+b x}\right)}{2 b^2}+\frac{d \text{sech}(a+b x)}{2 b^2}+\frac{(c+d x) \tan ^{-1}\left(e^{a+b x}\right)}{b}+\frac{(c+d x) \tanh (a+b x) \text{sech}(a+b x)}{2 b}","-\frac{i d \text{PolyLog}\left(2,-i e^{a+b x}\right)}{2 b^2}+\frac{i d \text{PolyLog}\left(2,i e^{a+b x}\right)}{2 b^2}+\frac{d \text{sech}(a+b x)}{2 b^2}+\frac{(c+d x) \tan ^{-1}\left(e^{a+b x}\right)}{b}+\frac{(c+d x) \tanh (a+b x) \text{sech}(a+b x)}{2 b}",1,"((c + d*x)*ArcTan[E^(a + b*x)])/b - ((I/2)*d*PolyLog[2, (-I)*E^(a + b*x)])/b^2 + ((I/2)*d*PolyLog[2, I*E^(a + b*x)])/b^2 + (d*Sech[a + b*x])/(2*b^2) + ((c + d*x)*Sech[a + b*x]*Tanh[a + b*x])/(2*b)","A",6,4,14,0.2857,1,"{4185, 4180, 2279, 2391}"
12,0,0,0,0.0384049,"\int \frac{\text{sech}^3(a+b x)}{c+d x} \, dx","Int[Sech[a + b*x]^3/(c + d*x),x]","\int \frac{\text{sech}^3(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{sech}^3(a+b x)}{c+d x},x\right)",0,"Defer[Int][Sech[a + b*x]^3/(c + d*x), x]","A",0,0,0,0,-1,"{}"
13,1,24,0,0.0868486,"\int \left(\frac{x}{\text{sech}^{\frac{3}{2}}(x)}-\frac{1}{3} x \sqrt{\text{sech}(x)}\right) \, dx","Int[x/Sech[x]^(3/2) - (x*Sqrt[Sech[x]])/3,x]","\frac{2 x \sinh (x)}{3 \sqrt{\text{sech}(x)}}-\frac{4}{9 \text{sech}^{\frac{3}{2}}(x)}","\frac{2 x \sinh (x)}{3 \sqrt{\text{sech}(x)}}-\frac{4}{9 \text{sech}^{\frac{3}{2}}(x)}",1,"-4/(9*Sech[x]^(3/2)) + (2*x*Sinh[x])/(3*Sqrt[Sech[x]])","A",4,2,20,0.1000,1,"{4187, 4189}"
14,1,24,0,0.0820009,"\int \left(\frac{x}{\text{sech}^{\frac{5}{2}}(x)}-\frac{3 x}{5 \sqrt{\text{sech}(x)}}\right) \, dx","Int[x/Sech[x]^(5/2) - (3*x)/(5*Sqrt[Sech[x]]),x]","\frac{2 x \sinh (x)}{5 \text{sech}^{\frac{3}{2}}(x)}-\frac{4}{25 \text{sech}^{\frac{5}{2}}(x)}","\frac{2 x \sinh (x)}{5 \text{sech}^{\frac{3}{2}}(x)}-\frac{4}{25 \text{sech}^{\frac{5}{2}}(x)}",1,"-4/(25*Sech[x]^(5/2)) + (2*x*Sinh[x])/(5*Sech[x]^(3/2))","A",4,2,20,0.1000,1,"{4187, 4189}"
15,1,47,0,0.0980385,"\int \left(\frac{x}{\text{sech}^{\frac{7}{2}}(x)}-\frac{5}{21} x \sqrt{\text{sech}(x)}\right) \, dx","Int[x/Sech[x]^(7/2) - (5*x*Sqrt[Sech[x]])/21,x]","-\frac{20}{63 \text{sech}^{\frac{3}{2}}(x)}-\frac{4}{49 \text{sech}^{\frac{7}{2}}(x)}+\frac{2 x \sinh (x)}{7 \text{sech}^{\frac{5}{2}}(x)}+\frac{10 x \sinh (x)}{21 \sqrt{\text{sech}(x)}}","-\frac{20}{63 \text{sech}^{\frac{3}{2}}(x)}-\frac{4}{49 \text{sech}^{\frac{7}{2}}(x)}+\frac{2 x \sinh (x)}{7 \text{sech}^{\frac{5}{2}}(x)}+\frac{10 x \sinh (x)}{21 \sqrt{\text{sech}(x)}}",1,"-4/(49*Sech[x]^(7/2)) - 20/(63*Sech[x]^(3/2)) + (2*x*Sinh[x])/(7*Sech[x]^(5/2)) + (10*x*Sinh[x])/(21*Sqrt[Sech[x]])","A",5,2,20,0.1000,1,"{4187, 4189}"
16,1,66,0,0.1578823,"\int \left(\frac{x^2}{\text{sech}^{\frac{3}{2}}(x)}-\frac{1}{3} x^2 \sqrt{\text{sech}(x)}\right) \, dx","Int[x^2/Sech[x]^(3/2) - (x^2*Sqrt[Sech[x]])/3,x]","\frac{2 x^2 \sinh (x)}{3 \sqrt{\text{sech}(x)}}-\frac{8 x}{9 \text{sech}^{\frac{3}{2}}(x)}+\frac{16 \sinh (x)}{27 \sqrt{\text{sech}(x)}}-\frac{16}{27} i \sqrt{\cosh (x)} \sqrt{\text{sech}(x)} F\left(\left.\frac{i x}{2}\right|2\right)","\frac{2 x^2 \sinh (x)}{3 \sqrt{\text{sech}(x)}}-\frac{8 x}{9 \text{sech}^{\frac{3}{2}}(x)}+\frac{16 \sinh (x)}{27 \sqrt{\text{sech}(x)}}-\frac{16}{27} i \sqrt{\cosh (x)} \sqrt{\text{sech}(x)} F\left(\left.\frac{i x}{2}\right|2\right)",1,"(-8*x)/(9*Sech[x]^(3/2)) - ((16*I)/27)*Sqrt[Cosh[x]]*EllipticF[(I/2)*x, 2]*Sqrt[Sech[x]] + (16*Sinh[x])/(27*Sqrt[Sech[x]]) + (2*x^2*Sinh[x])/(3*Sqrt[Sech[x]])","A",7,5,24,0.2083,1,"{4188, 4189, 3769, 3771, 2641}"