5.5 The Substitution Rule/39

$\int \sec ^{3}(x)\tan(x)\,$

$u=\sec(x)$

$du=\sec(x)\tan(x)\,dx$

$\int \sec ^{3}(x)\tan(x)\,=\int u^{2}\,du$

$={\frac {1}{3}}u^{3}\,+\,c$

<math>\frac{1}{3}\sec^{3}(x)\,+\,c