5.5 The Substitution Rule/39: Difference between revisions

Latest revision as of 19:57, 1 September 2022

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

$u=\sec(x)$

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

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

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

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

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