Table of Integrals - Forms Involving `coth ax`

The integrals below involve `coth ax`.

1) `int   coth ax  dx = 1/a ln sinh ax`

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

3) `int  coth^3 ax  dx = 1/a ln sinh ax-(coth^2 ax)/(2a)`

4) `int  coth^n ax*\text{csch}\^2 ax  dx = -(coth^(n+1) ax)/((n+1)a)`

5) `int  (\text{csch}\^2 ax)/(coth ax)  dx = -1/a ln coth ax`

6) `int  1/(coth ax)  dx = 1/a ln cosh ax`

7) `int  x coth ax  dx = 1/a^2{ax+(ax)^3/9-(ax)^5/225+...((-1)^(n-1)2^(2n)B_n(ax)^(2n+1))/((2n+1)!)+...}`

8) `int  x coth^2 ax  dx = x^2/2-(x coth ax)/a+1/a^2 ln sinh ax`

9) `int  (coth ax)/x  dx = -1/(ax)+(ax)/3-(ax)^3/135+...((-1)^n2^(2n)B_n(ax)^(2n-1))/((2n-1)(2n)!)+...`

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

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