How do you integrate $int (cosx)(coshx)$ using integration by parts?

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Answer 1 · 2018-04-11T21:40:53

below

$I = int \ cosx \ coshx \ dx$

$= int \ cosx \ d(sinh x)$

$= cosx sinh x - int \ d( cosx) \ sinh x$

$= cosx sinh x + int sin x \ sinh x \ dx$

$= cosx sinh x + int sin x \ d(cosh x)$

$= cosx sinh x + (sin x cosh x - int \ d(sin x )\ cosh x)$

$= cosx sinh x + sin x cosh x - I$

$implies I = 1/2 ( cosx sinh x + sin x cosh x) + C$

How do you integrate int (cosx)(coshx)int (cosx)(coshx) using integration by parts?