Answered: integrate e^(ax)*cos(bx) dx

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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integrate e^(ax)*cos(bx) dx

Expert Solution

Step 1: Given problem

$We space have space to space evaluate space the space integral space colon space integral straight e to the power of ax cos open parentheses bx close parentheses space dx space F o r m u l a space t o space b e space u s e d colon space I n t e g r a l space b y space p a r t s colon space integral u v space d x equals u integral v d x minus integral open square brackets fraction numerator d u over denominator d x end fraction integral v d x close square brackets d x integral cos b x space d x equals fraction numerator sin open parentheses b x close parentheses over denominator b end fraction plus C space semicolon space integral sin b x space d x equals negative fraction numerator cos open parentheses b x close parentheses over denominator b end fraction plus C$