If you know about complex numbers, you can use the identities:

sinh(ix) = isin(x)
cosh(ix) = cos(x)

to derive sinh, cosh identities from sin, cos identities. Essentially everything is the same except a product of sinhs has a minus sign where a product of sins would have a plus sign.

One way is to expand out the exponentials. Another way is to use the identity

cosh² x = ½(cosh 2x + 1)

Either way the integration is straight forward.

Kerwin

Thanks Kerwin.

You can find more hyperbolic identities in our on-line maths dictionary, www.thesaurus.maths.org .