5.5 The Substitution Rule/41: Difference between revisions
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\int \frac{1}{\sqrt{1-x^{2}}} = \int \frac{1}{u} du = \ln |u| +c = \ln |\arcsin {x}| + c | \int \frac{1}{\sqrt{1-x^{2}}} = \int \frac{1}{u} du = \ln |u| +c = \ln |\arcsin {x}| + c | ||
</math> | |||
<math> | |||
\begin{align} | |||
u &= \sqrt{u} | |||
\\[2ex] | |||
du &= \frac{1}{2}\ \frac{1}{\sqrt{t}} dx \\[2ex] | |||
2du &= \frac{1}{\sqrt{t}} dx | |||
\end{align} | |||
</math> | </math> | ||
Revision as of 09:06, 7 September 2022
![{\displaystyle {\begin{aligned}u&={\sqrt {u}}\\[2ex]du&={\frac {1}{2}}\ {\frac {1}{\sqrt {t}}}dx\\[2ex]2du&={\frac {1}{\sqrt {t}}}dx\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/3a37f2379e73449da9a402a6551cdea68c52b387)