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| \begin{align} | | \begin{align} |
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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_{0}^{7} \sqrt{4+3x}\,dx \\[2ex] |
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| &= \int (du)\sin{(u)} = \int \sin{(u)}du \\[2ex] | | &= \int (du)\sin{(u)} = \int \sin{(u)}du \\[2ex] |
Revision as of 19:16, 26 August 2022
![{\displaystyle {\begin{aligned}u&=4+3x\\[2ex]du&=3\,dx\\[2ex]{\frac {1}{3}}du&=dx\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/75fbdf9385d28dbfa67df6bec234667b6be64498)
![{\displaystyle {\begin{aligned}\int _{0}^{7}{\sqrt {4+3x}}\,dx\\[2ex]&=\int (du)\sin {(u)}=\int \sin {(u)}du\\[2ex]&=-\cos {(u)}+C\\[2ex]&=-\cos {(\ln {(x)})}+C\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/34027ef0163245c2a4bec4ddea0b613bfed3f7bc)