5.5 The Substitution Rule/7: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
<math> | <math> | ||
\int\xsin | \int\xsin{x^{2}}dx | ||
</math> | </math> | ||
| Line 7: | Line 7: | ||
u &=x^{2} \\[2ex] | u &=x^{2} \\[2ex] | ||
du &=2xdx \\[2ex] | du &=2xdx \\[2ex] | ||
\frac{1}{2}du=dx | \frac{1}{2}du &=dx \\[2ex] | ||
\end{align} | \end{align} | ||
| Line 15: | Line 15: | ||
\begin{align} | \begin{align} | ||
\int\xsin | \int\xsin{x^{2}}dx &=\frac{1}{2}\int\sin{u}du \\[2ex] | ||
&= -\frac{1}{2}cos{u}+C | |||
&= -\frac{1}{2}cos{x^{2}}+C | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 16:51, 7 September 2022
Failed to parse (unknown function "\xsin"): {\displaystyle \int\xsin{x^{2}}dx }
![{\displaystyle {\begin{aligned}u&=x^{2}\\[2ex]du&=2xdx\\[2ex]{\frac {1}{2}}du&=dx\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/d3662e4ad2b3d50be2a69669e39b54ac46042ca4)
Failed to parse (unknown function "\xsin"): {\displaystyle \begin{align} \int\xsin{x^{2}}dx &=\frac{1}{2}\int\sin{u}du \\[2ex] &= -\frac{1}{2}cos{u}+C &= -\frac{1}{2}cos{x^{2}}+C \end{align} }