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intcos{2tan^(-1)sqrt((1-x)/(1+x))}dx is ...

`intcos{2tan^(-1)sqrt((1-x)/(1+x))}dx` is equal to

A

`(1)/(8)(x^(2)-1)+C`

B

`(x^(2))/(4)+C`

C

`(x)/(2)+C`

D

`(x^(2))/(2)+C`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `l=intcos{2tan^(-1)sqrt((1-x)/(1+x))}dx`
Put`" "x= cos theta,` then
`l=int cos {2tan^(-1)sqrt((1-cos theta)/(1+cos theta))}dx`
`=int cos{2tan^(-1)(tan.(theta)/(2))}dx`
`=intcos theta dx=int xdx=(x^(2))/(2)+C`
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