Answer
$\frac{1}{4}e^{4x}+x+c $
Work Step by Step
Recall that $(e^x)'=e^x$
We have
$$
\int (e^{4x} +1 )dx=\frac{1}{4} \int 4(e^{4x}+1) dx +c=\frac{1}{4}e^{4x}+x+c
.
$$
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 - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 328: 75
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