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intsin^(-1)((2x)/(1+x^(2)))dx=?...

`intsin^(-1)((2x)/(1+x^(2)))dx=?`

A

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

B

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

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Put `x=tant anddx=sec^(2)tdt`.
`:." "I=intsin^(-1)((2tant)/(1+tan^(2)t))sec^(2)tdt=sin^(-1)(sin2t)sec^(2)tdt`
`=2intunderset(I)(t)underset(II)(sec^(2))tdt`.
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