Table of Integrals, Series, and Products, 8th Edition

$\begin{array}{ccc}{\displaystyle \int \frac{x}{{\text{cosh}}^{2n-1}x}\text{d}x}\hfill & =\hfill & {\displaystyle \sum _{k=1}^{n-1}\frac{(2n-3)(2n-5)...(2n-2k+1)}{(2n-2)(2n-4)...(2n-2k)}}\hfill \\ \times \left[\frac{x\text{sinh}x}{{\cosh }^{2n-2k}x}+\frac{1}{(2n-2k-1){\text{ cosh}}^{2n-2k-1}x}\right]\hfill & +\frac{(2n-3)!!}{(2n-2)!!}{\displaystyle \int \frac{x\text{d}x}{\text{cosh}x}}\hfill \end{array}$

(see 2.477 16)GU (353)(10e)

15. 

${\displaystyle \int \frac{xdx}{\text{sinh}x}={\displaystyle \sum _{k=0}^{\infty }\frac{2-2^{2k}}{(2k+1)\left(2k\right)!}}}{B}_{2k}{x}^{2k}+1[|x|<\pi ]$

GU (353)(8b)a

16. 

${\displaystyle \int \frac{x\text{d}x}{\text{cosh}x}={\displaystyle \sum _{k=0}^{\infty }\frac{E_{2k}{x}^{2k+2}}{(2k+\text{ 2})\left(2k\right)!}}}[|x|<\frac{\pi }{2}]$

GU (353)(10b)a

17. 

${\displaystyle \int \frac{x\text{d}x}{{\text{sinh}}^{2}x}}=-x\text{coth}x+\text{ln sinh }x$

MZ 257

18. 

${\displaystyle \int \frac{x\text{d}x}{{\text{cosh}}^{2}x}}=$