Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 8: Techniques of Integration - Practice Exercises - Page 517: 9


$\ln |x-1|+2 \ln |x-2| +c$

Work Step by Step

The integration by parts formula suggests that $\int a'(x) b(x)=a(x) b(x)-\int a(x) b'(x)dx$ Now, we have $I=\int \dfrac{x}{x^2-3x+2}=\int \dfrac{x}{(x-1)(x-2)}$ Now, need to write the integral into partial fractions. So, $I=\int \dfrac{x}{(x-1)(x-2)}=\int \dfrac{1}{(x-1)} dx +\int \dfrac{2}{(x-2)} dx$ Thus, $I=\int \dfrac{x}{(x-1)(x-2)}=\ln |x-1|+2 \ln |x-2| +c$
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