INTEGRALS CONTAINING Sinh(ax) and Cosh(ax)(

1.
$\displaystyle\int\sinh ax\cosh ax dx=\displaystyle \frac{\sinh^2 ax}{2a}$

2.
$\displaystyle\int\sinh px\cosh qx dx=\displaystyle \frac{\cosh(p+q)x}{2(p+q)}+\displaystyle \frac{\cosh(p-q)x}{2(p-q)}$

3.
$\displaystyle\int\sinh^n ax\cosh ax dx=\displaystyle \frac{\sinh^{n+1}ax}{(n+1)a}$

4.
$\displaystyle\int\cosh^n ax\sinh ax dx=\displaystyle \frac{\cosh^{n+1}ax}{(n+1)a}$

5.
$\displaystyle\int\sinh^2 ax \cosh^2 ax dx=\displaystyle \frac{\sinh 4ax}{32a}-\displaystyle \frac{x}{8}$

6.
$\displaystyle\int\displaystyle \frac{dx}{\sinh ax\cosh ax}=\displaystyle \frac{1}{a}\ln\tanh ax$

7.
$\displaystyle\int\displaystyle \frac{dx}{\sinh^2 ax\cosh ax}=-\displaystyle \frac{1}{a}\tan^{-1}\sinh ax-\displaystyle \frac{1}{a\sinh ax}$

8.
$\displaystyle\int\displaystyle \frac{dx}{\sinh ax\cosh^2 ax}=\displaystyle \frac{1}{a\cosh ax}+\displaystyle \frac{1}{a}\ln\tan\displaystyle \frac{ax}{2}$

9.
$\displaystyle\int\displaystyle \frac{dx}{\sinh^2 ax \cosh^2 ax}=-\displaystyle \frac{2 \coth 2ax}{a}$

10.
$\displaystyle\int\displaystyle \frac{\sinh^2 ax}{\cosh ax}dx=\displaystyle \frac{\sinh ax}{a}-\displaystyle \frac{1}{a}\tan^{-1}\sinh ax$

11.
$\displaystyle\int\displaystyle \frac{\cosh^2 ax}{\sinh ax}dx=\displaystyle \frac{\cosh ax}{a}+\displaystyle \frac{1}{a}\ln\tan\displaystyle \frac{ax}{2}$

12.
$\displaystyle\int\displaystyle \frac{dx}{\cosh ax(1+\sinh ax)}=\displaystyle \f...
...yle \frac{1+\sinh ax}{\cosh ax}\right)+\displaystyle \frac{1}{a}\tan^{-1}e^{ax}$

13.
$\displaystyle\int\displaystyle \frac{dx}{\sinh ax(\cosh ax+1)}=\displaystyle \f...
...1}{2a}\ln\tanh\displaystyle \frac{ax}{2}+\displaystyle \frac{1}{2a(\cosh ax+1)}$

14.
$\displaystyle\int\displaystyle \frac{dx}{\sinh ax(\cosh ax-1)}=-\displaystyle \...
...1}{2a}\ln\tanh\displaystyle \frac{ax}{2}-\displaystyle \frac{1}{2a(\cosh ax-1)}$

[Tables]

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