5.5 The Substitution Rule/7: Difference between revisions
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\int\{xsin{(x^{2})}dx &=\frac{1}{2}\int\sin{u}du \\[2ex] | \int\{xsin{(x^{2})}dx &=\frac{1}{2}\int\sin{u}du \\[2ex] | ||
&= -\frac{1}{2}cos{u}+C | &= -\frac{1}{2}cos{u}+C &= -\frac{1}{2}cos{x^{2}}+C | ||
&= -\frac{1}{2}cos{x^{2}}+C | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 16:54, 7 September 2022
![{\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)
![{\displaystyle {\begin{aligned}\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{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/ba672db32537e9fd248ff268d2c8a2ad0217d92b)