Answer
See explanations.
Work Step by Step
Letting $u=\frac{t}{x}$, we have $du=\frac{dt}{x}dt$ and $t=x\to u=1, t=xy\to u=y$.
Evaluate the integral
$LHS=\int_x^{xy}\frac{1}{t}dt=\int_1^y(\frac{1}{xu})(xdu)=\int_1^y(\frac{1}{u})du=RHS$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 5: Integrals - Section 5.5 - Indefinite Integrals and the Substitution Method - Exercises 5.5 - Page 305: 88
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