Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.1 Exercises: 46

Answer

$\frac 1 {\sqrt 5}arctan\frac {x-2}{\sqrt 5}+C$

Work Step by Step

$\int \frac 1 {x^2-4x+4+5}dx$ $\int \frac 1 {(x-2)^2+5}dx$ $a=\sqrt 5, u=x-2, du=dx$ $\int \frac {du}{a^2+u^2}$ $\frac 1 a arctan \frac u a +C$ $\frac 1 {\sqrt 5}arctan\frac {x-2}{\sqrt 5}+C$
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