5.5 The Substitution Rule/7: Difference between revisions
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<math> | |||
\int x\sin{(x^{2})}dx | |||
</math> | |||
<math> | <math> | ||
\begin{align} | \begin{align} | ||
u &=x^{2} \\[2ex] | |||
du &=2xdx \\[2ex] | |||
\frac{1}{2}du &=dx \\[2ex] | |||
\end{align} | |||
</math> | |||
<math> | |||
\begin{align} | |||
\int x\sin{(x^{2})}dx &=\frac{1}{2}\int\sin{(u)}du \\[2ex] | |||
&= -\frac{1}{2}\cos{(u)}+C \\[2ex] | |||
&= -\frac{1}{2}\cos{(x^{2})}+C | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Latest revision as of 20:02, 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 x\sin {(x^{2})}dx&={\frac {1}{2}}\int \sin {(u)}du\\[2ex]&=-{\frac {1}{2}}\cos {(u)}+C\\[2ex]&=-{\frac {1}{2}}\cos {(x^{2})}+C\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/ee0244989664f2dd175ffcbffed3ada5167b3cf6)