Mathematics

# $\displaystyle \int \frac{1}{\sin ^{-1}x\sqrt{\left ( 1-x^{2} \right )}}dx.$

##### ANSWER

$\displaystyle\log \sin^{-1}x.$

##### SOLUTION
Let $\displaystyle I= \int \frac { 1 }{ \sin ^{ -1 } x\sqrt { \left( 1-x^{ 2 } \right) } } dx$
Put $\displaystyle \sin ^{ -1 } x=t\Rightarrow \frac { 1 }{ \sqrt { \left( 1-x^{ 2 } \right) } } dx=dt$
$\displaystyle I=\int { \frac { dt }{ t } } =\log { t } +c=\log { \sin ^{ -1 } x } +c$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
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