## Thomas' Calculus 13th Edition

Published by Pearson

# Chapter 5: Integrals - Section 5.5 - Indefinite Integrals and the Substitution Method - Exercises 5.5 - Page 295: 26

#### Answer

$\frac{1}{4}tan^8(\frac{x}{2})+C$

#### Work Step by Step

Let u=$tan(\frac{x}{2})=>du=\frac{1}{2}sec^2(\frac{x}{2})dx=>2du=sec^2(\frac{x}{2})dx$ =$\int tan^7(\frac{x}{2})sec^(\frac{x}{2})dx$ =$\int u^7(2du)=2(\frac{1}{8}u^8)+C$ =$\frac{1}{4}tan^8(\frac{x}{2})+C$

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