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NCERT Class XII Mathematics Chapter - - Solutions

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Exercise - 7.2
Integrate the functions in Exercises 23 to 59.
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Question : 45 of 271
Marks: +1, -0
sin⁡−1x1−x2\frac{\sin^{-1}x}{\sqrt{1-x^2}}
Solution:  
Let I=∫sin⁡−1x1−x2 dxI=\int \frac{\sin^{-1}x}{\sqrt{1-x^2}}\,dx
Put sin⁡−1x=t⇒11−x2 dx=dt\sin^{-1}x = t \Rightarrow \frac{1}{\sqrt{1-x^2}}\,dx = dt
⇒I=∫t dt=12t2+C\Rightarrow I = \int t\,dt = \frac{1}{2}t^2 + C =12(sin⁡−1x)2+C= \frac{1}{2}(\sin^{-1}x)^2 + C
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