## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 276: 53

#### Answer

$$3 \tan ^{4} x-2 \tan ^{3} x+C$$

#### Work Step by Step

Given $$\int \sec ^{2}(x) \cdot\left(12 \tan ^{3} x-6 \tan ^{2} x\right) d x$$ Let $$u=\tan x \ \ \ \ \Rightarrow \ \ \ du = \sec^2 x dx$$ Then \begin{aligned} \int \sec ^{2}(x) \cdot\left(12 \tan ^{3} x-6 \tan ^{2} x\right) d x &=\int\left(12 u^{3}-6 u^{2}\right) d u \\ &=3 u^{4}-2 u^{3}+C \\ &=3 \tan ^{4} x-2 \tan ^{3} x+C \end{aligned}

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.