Table of Integrals - Forms Involving `sech ax`

The integrals below involve `sech ax`.

1) `int  sech ax  dx = 2/a tan^-1 e^(ax)`

2) `int  sech^2 ax  dx = (tanh ax)/a`

3) `int  sech^3 ax  dx = (sech ax*tanh ax)/(2a)+1/(2a) tan^-1 sinh ax`

4) `int  sech^n ax*tanh ax  dx = -(sech^n ax)/(na)`

5) `int  1/(sech ax)  dx = (sinh ax)/a`

6) `int  x sech ax  dx = 1/a^2{(ax)^2/2-(ax)^4/8+(5(ax)^6)/144+...((-1)^nE_n(ax)^(2n+2))/((2n+2)(2n)!)+...}`

7) `int  x sech^2 ax  dx = (x tanh ax)/a-1/a^2 ln cosh ax`

8) `int  (sech ax)/x  dx = ln x-(ax)^2/4+(5(ax)^4)/96-(61(ax)^6)/4320+...((-1)^nE_n(ax)^(2n))/(2n(2n)!)+...`

9) `int  1/(q+p sech ax)  dx = x/q-p/q int 1/(p+q cosh ax)  dx`

                    **[See integral #20 in the table involving `cosh ax`]

10) `int  sech^n ax  dx = (sech^(n-2) ax tanh ax)/(a(n-1))+(n-2)/(n-1) int sech^(n-2) ax  dx`