5.5 The Substitution Rule/30 - Revision history

Dvaezazizi@laalliance.org: Protected "5.5 The Substitution Rule/30" ([Edit=Allow only administrators] (indefinite) [Move=Allow only administrators] (indefinite))

2022-08-26T19:10:55Z

Protected "5.5 The Substitution Rule/30" ([Edit=Allow only administrators] (indefinite) [Move=Allow only administrators] (indefinite))

← Older revision	Revision as of 19:10, 26 August 2022
(No difference)

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← Older revision		Revision as of 19:06, 26 August 2022
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	\int \frac{\sin{(\ln{(x))}}}{x}dx &= \int\frac{1}{x}\sin(\ln{(x)})dx = \int\left(\frac{1}{x}dx\right)\sin{(\ln{(x)})} \\[2ex]		\int \frac{\sin{(\ln{(x))}}}{x}dx &= \int\frac{1}{x}\sin(\ln{(x)})dx = \int\left(\frac{1}{x}dx\right)\sin{(\ln{(x)})} \\[2ex]

	&= \int (du)\sin{(u)} = \int \sin{(u)}du		&= \int (du)\sin{(u)} = \int \sin{(u)}du \\[2ex]

	&= -\cos{(u)} + C		&= -\cos{(u)} + C

2022-08-26T19:06:45Z

← Older revision		Revision as of 19:06, 26 August 2022
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	\begin{align}		\begin{align}

	\int \frac{\sin{(\ln{(x))}}}{x}dx &= \int\frac{1}{x}\sin(\ln{(x)})dx = \int\left(\frac{1}{x}dx\right)\sin{(\ln{(x)})}		\int \frac{\sin{(\ln{(x))}}}{x}dx &= \int\frac{1}{x}\sin(\ln{(x)})dx = \int\left(\frac{1}{x}dx\right)\sin{(\ln{(x)})} \\[2ex]

			&= \int (du)\sin{(u)} = \int \sin{(u)}du

			&= -\cos{(u)} + C

	\end{align}		\end{align}
	</math>		</math>

2022-08-26T19:05:32Z

← Older revision		Revision as of 19:05, 26 August 2022
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	\begin{align}		\begin{align}

	\int \frac{\sin{(\ln{(x))}}}{x}dx &= \int\frac{1}{x}\sin(\ln{(x)})dx = \int\left(\frac{1}{x}dx\right)\sin{(\ln{(x)}}		\int \frac{\sin{(\ln{(x))}}}{x}dx &= \int\frac{1}{x}\sin(\ln{(x)})dx = \int\left(\frac{1}{x}dx\right)\sin{(\ln{(x)})}

	\end{align}		\end{align}
	</math>		</math>

2022-08-26T19:05:18Z

← Older revision		Revision as of 19:05, 26 August 2022
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	\begin{align}		\begin{align}

	\int \frac{\sin{(\ln{(x))}}}{x}dx = \int\frac{1}{x}\sin(\ln{(x)})dx		\int \frac{\sin{(\ln{(x))}}}{x}dx &= \int\frac{1}{x}\sin(\ln{(x)})dx = \int\left(\frac{1}{x}dx\right)\sin{(\ln{(x)}}

	\end{align}		\end{align}
	</math>		</math>

2022-08-26T19:04:25Z

← Older revision		Revision as of 19:04, 26 August 2022
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	<math>		<math>
	\begin{align}		\begin{align}
	~~\int x^3(2+x^4)^5dx &= \int (x^3dx)(2+x^4) = \int \left(\frac{1}{4}du\right)(u) = \frac{1}{4}\int u\,du \\[2ex]~~

	&= \frac{1}{~~4} \left[~~\~~frac~~{~~u^{1+1~~}}{~~1+1~~}\~~right] + C =~~ \frac{~~u^2~~}{8} ~~+ C~~ \\~~[2ex]~~		\int \frac{\sin{(\ln{(x))}}}{x}dx = \int\frac{1}{x}\sin(\ln{(x)})dx

	~~&= \frac~~{(2+x^4)^2}~~{8} + C~~

	\end{align}		\end{align}
	</math>		</math>

2022-08-26T19:03:40Z