Hello,
Do we have any formula for
Integral of $\displaystyle \int{e^(ax)\cosh(x)dx}$
and also $\displaystyle \int{e^(ax)\sinh(x)dx}$
Hello,
Do we have any formula for
Integral of $\displaystyle \int{e^(ax)\cosh(x)dx}$
and also $\displaystyle \int{e^(ax)\sinh(x)dx}$
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.
In that case use post #6. It is the best way to do it.
There is a LaTeX tutorial here.
You should be able to do this for yourself.
$\displaystyle \displaystyle\int {\frac{1}
{2}\left( {e^{\left( {a + b} \right)x} - e^{\left( {a - b} \right)x} } \right)dx} = \frac{1}
{2}\left( {\frac{{e^{\left( {a + b} \right)x} }}
{{a + b}} - \frac{{e^{\left( {a - b} \right)x} }}
{{a - b}}} \right) + C$
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.