5.5 The Substitution Rule/39: Difference between revisions

Latest revision as of 19:57, 1 September 2022

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

$u=\sec(x)$

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

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

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

$={\frac {1}{3}}\sec ^{3}(x)\,+\,c$

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	<math>=\frac{1}{3}u^{3}\,+\,c</math>		<math>=\frac{1}{3}u^{3}\,+\,c</math>

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