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

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

A

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

B

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

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Put `x=tant anddx=sec^(2)tdt`.
Then, `I=intcos^(-1)((1-tan^(2)t)/(1+tan^(2)t))sec^(2)tdt=intcos^(-1)(cos2t)sec^(2)tdt`
`=2intunderset(I)(t)underset(II)(sec^(2))tdt`.
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