Mathematics

# Evaluate the following integral$\int { \cfrac { 1 }{ \sqrt { 1-{ x }^{ 2 } } \left( 2+3\sin ^{ -1 }{ x } \right) } } dx\quad$

##### SOLUTION
Let
$t=2+3{\sin}^{-1}{x}$

$\Rightarrow\,dt=\dfrac{3}{\sqrt{1-{x}^{2}}}dx$

$\Rightarrow\,dt={3}\dfrac{dx}{\sqrt{1-{x}^{2}}}$

$\displaystyle\int{\dfrac{dx}{\sqrt{1-{x}^{2}}\left(2+3{\sin}^{-1}{x}\right)}}$

$=\dfrac{1}{3}\displaystyle\int{\dfrac{dt}{t}}$

$=\dfrac{1}{3}\log{\left|t\right|}+c$

$=\dfrac{1}{3}\log{\left|2+3{\sin}^{-1}{x}\right|}+c$ where $t=2+3{\sin}^{-1}{x}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

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