University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 8 - Section 8.5 - Integral Tables and Computer Algebra Systems - Exercises - Page 451: 15

Answer

$$\int e^{2t}\cos3tdt=\frac{e^{2t}}{13}(2\cos3t+3\sin3t)+C$$

Work Step by Step

$$A=\int e^{2t}\cos3tdt$$ Use Formula 115, which states that $$\int e^{ax}\cos bxdx=\frac{e^{ax}}{a^2+b^2}(a\cos bx+b\sin bx)+C$$ for $a=2$ and $b=3$ here: $$A=\frac{e^{2t}}{2^2+3^2}(2\cos3t+3\sin3t)+C$$ $$A=\frac{e^{2t}}{13}(2\cos3t+3\sin3t)+C$$
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