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Question: A problem with integration

Question:A problem with integration

vfleurov 5 Maple 2019
integration
January 03 2020
1

I do a calculation o a simple integral

 

      int(cosh(cos(2*t)), t = 0 .. 2*Pi)

 

and get the answer 0 (zero), which I know is incorrect. The cosh function of a real argument is always positive.

 

If I represent the cosh function as a sum of two exponentials

(1/2)*(int(cosh(cos(2*t)), t = 0 .. 2*Pi) + int(cosh(-cos(2*t)), t = 0 .. 2*Pi))

 

I get    

2*Pi*BesselI(0, 1)

which looks much better.

 

What's the matter? Why Maple yields two different results? Victor.

 

 
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