Table of Integrals - Forms Involving `sec ax`

The integrals below involve `sec ax`.

1) `int  sec ax  dx = 1/a ln(sec ax+tan ax)=1/a ln tan ((ax)/2+pi/4)`

2) `int  sec^2 ax  dx = (tan ax)/a`

3) `int  sec^3 ax  dx = (sec ax*tan ax)/(2a)+1/(2a)ln(secax+tan ax)`

4) `int  sec^n ax*tan ax  dx = (sec^n ax)/(na)`

5) `int  1/(sec ax)  dx = (sin ax)/a`

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

7) `int  (sec ax)/x  dx = ln x+(ax)^2/4+(5(ax)^4)/96+(61(ax)^6)/4320+...+(E_n(ax)^(2n))/(2n(2n)!)+...`

8) `int  x*sec^2ax  dx = x/a tan ax+1/a^2 ln cos ax`

9) `int  1/(q+p sec ax)  dx = x/q-p/qint  1/(p+q cos ax)  dx`

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