Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 276: 56

$$ \frac{1}{5} \tan^{5}x+C$$

Given $$ \int \sec ^{2} x \tan ^{4} x d x $$ Let $$u=\tan x \ \ \ \ \Rightarrow \ \ \ du =\sec ^{2} x dx $$ \begin{aligned} \int \sec ^{2} x \tan ^{4} x d x &=\int u^{4} d u \\ &=\frac{1}{5} u^{5}+C\\ &= \frac{1}{5} \tan^{5}x+C \end{aligned}