∫ sec 3 ( x ) tan ( x ) u = sec ( x ) d u = sec ( x ) tan ( x ) d x ∫ sec 3 ( x ) tan ( x ) = ∫ u 2 d u = {\displaystyle {\begin{aligned}&\int \sec ^{3}(x)\tan(x)\,&u=\sec(x)&du=\sec(x)\tan(x)\,dx&\int \sec ^{3}(x)\tan(x)\,&&=\int u^{2}\,du&&=\end{aligned}}}
