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

Powers of hyperbolic functions and hyperbolic functions of linear functions of the argument

2.425

1. 

$\begin{array}{ccc}{\displaystyle \int \text{sinh}(ax+b)\text{sinh}(cx+d)\text{d}x}\hfill & =\hfill & \frac{1}{2(a+c)}\text{sinh}\left[(a+c)x+b+d\right]\hfill \\ -\frac{1}{2(a-c)}\text{sinh}\left[(a-c)x+b-d\right]\hfill \\ [a^2\ne c^2]\hfill \end{array}$

  GU (352)(2a)

2. 

$\begin{array}{ccc}{\displaystyle \int \text{sinh}(ax+b}\left)\text{cosh}\right(cx+d)\text{d}x\hfill & =\hfill & \frac{1}{2(a+c)}\text{cosh}\left[(a+c)x+b+d\right]\hfill \\ +\frac{1}{2(a-c)}\text{cosh}\left[(a-c)x+b-d\right]\hfill \\ [a^2\ne c^2]\hfill \end{array}$

  GU (352)(2c)

3. 

$\begin{array}{ccc}{\displaystyle \int \text{cosh}(ax+b)\text{cosh}(cx+d)\text{d}x}\hfill & =\hfill & \frac{1}{2(a+c)}\text{sinh}\left[(a+c)x+b+d\right]\hfill \\ +\frac{1}{2(a-c)}\text{sinh}\left[(a-c)x+b-d\right]\hfill \\ \hfill \end{array}$