5.5 The Substitution Rule/41: Difference between revisions
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<math> | <math> | ||
\begin{align} | \begin{align} | ||
\int \frac{1}{\sqrt{1-x^{2}} \arcsin {x}} = \int \frac{1}{u} du | \int \frac{1}{\sqrt{1-x^{2}} \arcsin {x}} | ||
&= \int \frac{1}{u} du \\[2ex] | |||
&= \ln |u| +c \\[2ex] | &= \ln |u| +c \\[2ex] | ||
&= \ln |\arcsin {x}| + c \\[2ex] | &= \ln |\arcsin {x}| + c \\[2ex] | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 15:51, 7 September 2022
![{\displaystyle {\begin{aligned}u&=\arcsin {x}\\[2ex]du&={\frac {1}{\sqrt {1-x^{2}}}}dx\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/e5c3841c50e1902bc439001180991f85316c3ab8)
![{\displaystyle {\begin{aligned}\int {\frac {1}{{\sqrt {1-x^{2}}}\arcsin {x}}}&=\int {\frac {1}{u}}du\\[2ex]&=\ln |u|+c\\[2ex]&=\ln |\arcsin {x}|+c\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/24fdbd28edf3e2f6c5eecf149fcb48d9438444b2)