Chapter 4 - Integration - 4.3 Integration By Substitution - Exercises Set 4.3 - Page 286: 15

$\frac{1}{4}\sec 4x+C$

Use the substitution $u=4xdx$. Then $du=4dx$, so $dx=\frac{1}{4}du$. $\int\sec 4x \tan 4x dx$ $=\int\sec u\tan u *\frac{1}{4}du$ $=\int\frac{1}{4}\sec u\tan u du$ $=\frac{1}{4}\sec u+C$ $=\frac{1}{4}\sec 4x+C$