Answer
$$\frac{1}{2}\ln10.$$
Work Step by Step
We have
$$\int^7_2\frac{xdx}{x^2+1}=\frac{1}{2}\int^7_2\frac{2xdx}{x^2+1}=\frac{1}{2}\ln(x^2+1)|^7_2\\
=\frac{1}{2}\ln50 -\frac{1}{2}\ln5=\frac{1}{2}\ln\frac{50}{5}=\frac{1}{2}\ln10.$$
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: 54
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