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ò Cosh2x dx and hyperbolic identities
By Anonymous on Thursday, March 8, 2001 - 10:16 pm:

How do you integrate ò Cosh2x dx?
What are the various identities you can use when integrating hyperbolics?

By Anonymous on Thursday, March 8, 2001 - 10:34 pm:

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.

By Kerwin Hui (Kwkh2) on Thursday, March 8, 2001 - 11:34 pm:

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

cosh2 x º ½(cosh 2x + 1)

Either way the integration is straight forward.

Kerwin

By Anonymous on Friday, March 9, 2001 - 12:25 pm:

Thanks Kerwin.

By The Editor:

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