Answer
$6arcsin(\frac {x-5}5)+C$
Work Step by Step
$10x-x^2=25-(5-x)^2$
$\int \frac 6 {\sqrt {10x-x^2}}dx$
$6\int \frac 1 {\sqrt {25-(5-x)^2}}$
$-6\int \frac {-1} {\sqrt {5^2-(5-x)^2}}$
$-6arcsin(\frac {5-x}5)+C$
$6arcsin(\frac {x-5}5)+C$
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
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 - Page 512: 43
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