Table of Integrals - Forms Involving `tanh ax`

The integrals below involve `tanh ax`.

1) `int  tanh ax  dx = 1/a ln cosh ax`

2) `int  tanh^2 ax  dx = x-(tanh ax)/a`

3) `int  tanh^3 ax  dx = 1/a ln cosh ax-(tanh^2 ax)/(2a)`

4) `int  tanh^n ax\ text{sech}\^2 ax  dx = (tanh^(n+1)ax)/((n+1)a)`

5) `int  (\text{sech}\^2 ax)/(tanh ax)  dx = 1/a ln tanh ax`

6) `int  1/(tanh ax)  dx = 1/a ln sinh ax`

7) `int  x tanh ax  dx = 1/a^2{(ax)^3/3-(ax)^5/15+(2(ax)^7)/105-...((-1)^(n-1)2^(2n)(2^(2n)-1)B_n(ax)^(2n+1))/((2n+1)!)+...}`

8) `int  x*tanh^2 ax  dx = x^2/2-(x tanh ax)/a+1/a^2 ln cosh ax`

9) `int  (tanh ax)/x  dx = ax-(ax)^3/9+(2(ax)^5)/75-...((-1)^(n-1)2^(2n)(2^(2n)-1)B_n(ax)^(2n-1))/((2n-1)(2n)!)+...`

10) `int  1/(p+q tanh ax)  dx = (px)/(p^2-q^2)-q/(a(p^2-q^2)) ln (q sinh ax+p cosh ax)`

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