Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 275: 29


$$2\sqrt{t+12 }+C$$

Work Step by Step

Given $$ \int \frac{d t}{\sqrt{t+12}}$$ Let $$ u^2= t+12\ \ \ \Rightarrow\ \ du= dt$$ Then \begin{align*} \int \frac{d t}{\sqrt{t+12}}&= \int \frac{2ud u}{u} \\ &=2u+c\\ &= 2\sqrt{t+12 }+C \end{align*}
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