Question: Some Integration Problems

1) Consider the followin Integral:

int(cosh(a*x)*cos(b*x),x)

How can I tell maple to give the results in terms of hyperbolic and harmonic funtions?
The maple returns the answer in term of exponentials with imaginary powers.
Also, I could not use the "simplify" command to turn the answer returned by maple into an answer in terms of what I want! Please see the code below.


2) Is there a way that I can update the maple integration database manaully?

 

Example.mw

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