Evaluate an integral of the form \(\displaystyle\int{\cos{{\left(\omega{t}\right)}}}{\ln{{\cos{{\left(\omega{t}\right)}}}}}{\left.{d}{t}\right.}\)

alparcero97oy

alparcero97oy

Answered question

2022-04-03

Evaluate an integral of the form
cos(ωt)lncos(ωt)dt

Answer & Explanation

Ben Castillo

Ben Castillo

Beginner2022-04-04Added 13 answers

Integrate by parts:
dxcosxlog(cosx)=sinxlog(cosx)+dxsin2xcosx
=sinxlog(cosx)sinx+dxsecx
=sinxlog(cosx)sinx+log(secx+tanx)+C

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