Answer
$$\frac{2^xe^{4x}}{4+\ln 2}+c.$$
Work Step by Step
Since $2^x=e^{x\ln 2}$, then we have
$$\int 2^xe^{4x}dx =\int e^{(4+\ln 2)x}dx=\frac{e^{(4+\ln 2)x}}{4+\ln 2}+c\\
=\frac{2^xe^{4x}}{4+\ln 2}+c.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 7 - Exponential Functions - 7.8 Inverse Trigonometric Functions - Exercises - Page 375: 82
Update this answer!
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
