Hello,

Do we have any formula for

Integral of $\displaystyle \int{e^(ax)\cosh(x)dx}$

and also $\displaystyle \int{e^(ax)\sinh(x)dx}$

- Mar 7th 2011, 06:03 AMHamedA formula for the integral of exponentials and hyperbolic trig functions
Hello,

Do we have any formula for

Integral of $\displaystyle \int{e^(ax)\cosh(x)dx}$

and also $\displaystyle \int{e^(ax)\sinh(x)dx}$ - Mar 7th 2011, 06:13 AMPlato
- Mar 7th 2011, 06:15 AMProve It
Assuming that you meant $\displaystyle \displaystyle \int{e^{ax}\cosh{bx}\,dx}$ and $\displaystyle \displaystyle \int{e^{ax}\sinh{bx}\,dx}$, for each you need to use Integration by Parts twice.

- Mar 7th 2011, 06:17 AMPlato
- Mar 7th 2011, 06:26 AMProve It
- Mar 7th 2011, 06:27 AMHallsofIvy
Yes, but as you said before, that is very simple. Assuming it is in fact, $\displaystyle e^{ax}sinh(bx)$, perhaps the simplest thing to do is to write it as

$\displaystyle e^{ax}\left(\frac{e^{bx}- e^{-bx}}{2}\right)= \frac{e^{(a+b)x}- e^{(a- b)x}}{2}$

and integrate that. - Mar 7th 2011, 06:41 AMHamed
x not t

for e^(ax)cos(bx)dx= [(e^(ax))/(a^2+b^2)]*(acosbx+bsinbx)

Can we have sth for e^(ax)cosh(bx)dx?

and e^(ax)sinh(bx)dx

How can I use TEX? - Mar 7th 2011, 06:44 AMAckbeet
See here for a LaTeX tutorial.

- Mar 7th 2011, 06:45 AMPlato
In that case use post #6. It is the best way to do it.

There is a LaTeX tutorial here. - Mar 7th 2011, 06:51 AMHamed
- Mar 7th 2011, 07:04 AMPlato
You should be able to do this for yourself.

$\displaystyle \displaystyle\int {\frac{1}

{2}\left( {e^{\left( {a + b} \right)x} - e^{\left( {a - b} \right)x} } \right)dx} = \frac{1}

{2}\left( {\frac{{e^{\left( {a + b} \right)x} }}

{{a + b}} - \frac{{e^{\left( {a - b} \right)x} }}

{{a - b}}} \right) + C$ - Mar 7th 2011, 08:59 AMProve It
I don't know what you mean by "sth', but if you need to write your indefinite integral in terms of sines and cosines, use integration by parts twice.

Otherwise, if you want a quick way to perform the integration, first convert the hyperbolic functions to their exponential forms.