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int(sin^(- 1)x)/((1-x^2)^(3/2))dx...

`int(sin^(- 1)x)/((1-x^2)^(3/2))dx`

A

`(sin^(-1)x)/(sqrt(1-x^(2)))-(1)/(2)log|1-x^(2)|+C`

B

`xsin^(-1)x+(1)/(2)log|1-x^(2)|+C`

C

`(xsin^(-1)x)/(sqrt(1-x^(2)))+(1)/(2)log|1-x^(2)|+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Put `x=sint" so that "dx=costdtandt=sin^(-1)x`.
`:." "I=int(tcost)/((1-sin^(2)t)^((3)/(2)))dt=int(tcost)/(cos^(3)t)dt=int(tcost)/(cos^(3)t)dt=intunderset(I)(t)underset(II)(sec^(2))tdt`.
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