5.5 The Substitution Rule/39: Difference between revisions

Revision as of 19:56, 1 September 2022

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

$u=\sec(x)$

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

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

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

@@ Line 2: / Line 2: @@
-u=\sec(x)</math>
+<math>u=\sec(x)</math>
 <math>du=\sec(x)\tan(x)\,dx</math>
-<math>\int\sec^{3}(x)\tan(x)\,</math>
+<math>\int\sec^{3}(x)\tan(x)\,=\int u^{2}\,du</math>
-<math>=\int u^{2}\,du</math>
 <math>=\frac{1}{3}u^{3}\,+\,c</math>