Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - Chapter Review Exercises - Page 460: 27


$$\frac{2 \tan ^{\frac{3}{2}} x}{3}+C$$

Work Step by Step

Given $$ \int \sqrt{\tan x} \sec ^{2} x d x$$ Let $ u=\tan x\to du=\sec^2 xdx$ \begin{aligned} \int \sqrt{\tan x} \sec ^{2} x d x &=\int \sqrt{u} d u \\ &=\frac{u^{\frac{3}{2}}}{\frac{3}{2}}+C \\ &=\frac{2 \tan ^{\frac{3}{2}} x}{3}+C \end{aligned}
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